Clearing the dusty shelves of old unanswered things. One such is the Lowder-Barnes critique of my application of Bayesian reasoning to reverse the fine tuning argument into a case against God, rather than an argument for God. Actually this is not my argument. It is the argument of three prominent mathematicians in two independent studies. My popularization of it (in conjunction with more data from other physical scientists I cited) appeared in my chapter “Neither Life Nor the Universe Appear Intelligently Designed” in The End of Christianity (ed. John Loftus 2011).
The original versions of the argument appeared as cited therein: Michael Ikeda and Bill Jefferys, “The Anthropic Principle Does Not Support Supernaturalism” (an earlier version of which appeared in Michael Martin and Ricki Monnier, eds., The Improbability of God in 2006) and Elliott Sober, “The Design Argument” (an earlier version of which appeared in W. Mann, ed., The Blackwell Guide to the Philosophy of Religion in 2004; which corrects my footnote in TEC).
Cosmologist Luke Barnes critiqued this in a series of posts, and Jeff Lowder concurred somewhat in The Carrier-Barnes Exchange on Fine-Tuning (which also rounds up all the links in the debate, including my contributions). My principal point then was that Barnes wasn’t even responding to my actual argument (and thus neither to any of the mathematicians, one of whom also an astrophysicist, who originated it). He still hasn’t. Barnes had also tried the same tactics against Victor Stenger on much the same point. In my comments debate with Barnes it became increasingly clear he was a kook who simply never understood or addressed what I actually said in my chapter, and continued to refuse to after repeated requests that he do so. A debate with such a person is impossible. One would make more progress arguing with a wall. So I have nothing further to say to him. My chapter as actually written already refutes him. Since he has never responded to its actual content.
But Jeff Lowder is not a kook. He is a responsible philosopher who listens, takes considerable caution, and will strive to get an opponent’s arguments correct. So I am writing this entry today in response to his take on our debate (a take which wisely avoided even discussing most of Barnes’s weird and irrelevant arguments).
Falling for the Kook’s Framing
Lowder agrees with Barnes on a few things, but only by trusting that Barnes actually correctly described my argument. He didn’t. Lowder would do well to revisit my actual chapter, notes and all, without the distorting lens of Barnes’s approach. Lowder’s overall conclusion was (my numbering for convenience):
In particular, I agree with the following points by Dr. Barnes.
- [1] “Bayes’ theorem, as the name suggests, is a theorem, not an argument, and certainly not a definition.”
- [2] “Also, Carrier seems to be saying that P(h|b), P(~h|b), P(e|h.b), and P(e|~h.b) are the premises from which one formally proves Bayes’ theorem. This fails to understand the difference between the derivation of a theorem and the terms in an equation.”
- [3] “Crucial to this approach is the idea of a reference class – exactly what things should we group together as A-like? This is the Achilles heel of finite frequentism.”
- [4] “It gets even worse if our reference class is too narrow.”
- [5] “This is related to the ‘problem of the single case’. The restriction to known, actual events creates an obvious problem for the study of unique events.”
- [6] “Carrier completely abandons finite frequentism when he comes to discuss the multiverse.”
- [7] “Whatever interpretation of probability that Carrier is applying to the multiverse, it isn’t the same one that he applies to fine-tuning.”
- [8] “If we are using Bayes’ theorem, the likelihood of each hypothesis is extremely relevant.”
None of these are valid points (the last depending on whether he is using the term “likelihood” correctly).
As to [1]: ever since the Principia Mathematica it has been an established fact that nearly all mathematics reduces to formal logic (the exceptions, captured by Gödel’s Theorem, are obscure and not relevant to the present case, since the relevant probability theory can be deduced from Willard Arithmetic which is immune to Gödel’s theorem). Thus in the class of theorems we are discussing, all mathematical theorems are tautologically identical to syllogisms. Which are arguments. I outline how one can reproduce Bayes’ Theorem as a syllogism in Chapter 4 of Proving History, pp. 106-14.
I didn’t carry out the reduction, but anyone familiar with both Bayes’ Theorem (hereafter BT) and conditional logic (i.e. syllogisms constructed of if/then propositions) can see from what I show there that BT indeed is reducible to a syllogism in conditional logic, where the statements of each probability-variable within the formula is a premise in formal logic, and the conclusion of the equation becomes the conclusion of the syllogism. In the simplest terms, “if P(h|b) is w and P(e|h.b) is x and P(e|~h.b) is y, then P(h|e.b) is z,” which is a logically necessary truth, becomes the concluding major premise, and “P(h|b) is w and P(e|h.b) is x and P(e|~h.b) is y” are the minor premises. And one can prove the major premise true by building syllogisms all the way down to the formal proof of BT, again by symbolic logic (which one can again replace with old-fashioned propositional logic if one were so inclined).
So, yes, Bayes’ Theorem is an argument. More specifically it is a form of argument, that is, a logical formula that describes a particular kind of argument. The form of this argument is logically valid. That is, its conclusion is necessarily true when its premises are true. Which means, if the three variables in BT are true (each representing a proposition about a probability, hence a premise in an argument), the epistemic probability that results is then a logically necessary truth—not in the sense that it can’t be false, but in the sense that you cannot deny the conclusion without either rejecting logic or denying that one of the premises (the assigned probabilities) is true. Now, one can indeed challenge a valid argument’s conclusion by challenging its premises. But it is absurd to claim that it is therefore not an argument. This is the kind of kookery Barnes is promulgating and I’m a bit perplexed to see Lowder fall for it.
As to [2]: The quotation is literally nonsensical. I cannot understand why Lowder even thinks the statements here are intelligible. The derivation of the theorem is this. The variables are not “the derivation,” they are propositional statements, in symbolic notation. For example, “P(h|b)” is symbolic notation for the proposition “the probability that a designated hypothesis is true given all available background knowledge but not the evidence to be examined is x,” where x is an assigned probability in the argument.
Barnes could have said that Bayes’ Theorem is not itself an argument but the form of an argument—as I just now said myself—but that would expose the kookery of his point, since I am not using “the form” of the argument stripped of input, I am stating inputs. He’s trying to challenge the inputs, not the logical formula from which I derive a conclusion from those inputs. (At least I hope! If Barnes actually thinks BT is logically invalid, he has gone beyond the status of kook into the camp of the outright insane.) But that’s not what he argued. What he argued literally makes no sense. So I cannot fathom what Lowder thinks he is agreeing with.
As to [3]: The reference class is indeed a question at issue. One I addressed in my chapter. What I said about it, Barnes never interacts with. So again I have no idea what Lowder is agreeing with. On the general problem of deriving frequencies from reference classes, Bayesians have written extensively (philosophers and mathematicians, many of considerable note). Barnes can go argue with them if he wants. On the particular problem relating to this case, I will get to that later. But note that the argument that Barnes is attacking does not even use a prior probability. Our argument is that the evidence entails that fine tuning reduces the probability of God to the prior probability of God. What one then says that prior probability is, is a wholly different question.
Barnes never addresses anything I said about what that prior likely was or how I derived my estimate of it (which estimate was, incidentally, the grossly generous value of 25%). Instead Barnes attacked what I addressed in the chapter as the “threshold” probability discussed in note 31 (p. 411). Yet despite my repeatedly asking him to address what I actually said about that, he never did, and consistently ignored that note and its content (and then incorrectly described what I said in the following note 33 instead!). Why Lowder thinks that is good form in a debate escapes me. If an opponent refuses to address what you said, they simply aren’t debating with you anymore.
As to [4] and [5]: These are the same argument, that the universe is a single case, thus not amendable to frequency analysis by reference class. This is false. In fact, it should be so obviously false to a cosmologist I cannot fathom how a cosmologist could make this argument. In general, unique cases are amendable to frequency analysis by reference class. Because every event in the universe is unique. What it shares with other events is what constructs a reference class (see my example of the “murder of William II” in Proving History, pp. 273ff.). Thus uniqueness is a red herring. There are always abstract features anything shares with many other things, from which an epistemic probability arises. Barnes, however, repeatedly confused epistemic with “true” probabilities, demonstrating he doesn’t know how Bayesian epistemology works, certainly not well enough to be a competent critic of it (on the distinction, see PH, Index, “epistemic probability”). He doesn’t even know about the role of hypothetical reference classes in epistemology (see PH, pp. 257ff.). And notably, he never once interacted with my actual argument for the prior, and thus never rebutted it (in TEC, pp. 280-84, notably many pages before I got to the fine tuning case). Nor did he interact with any of my actual arguments for the unknown coincidence threshold (that note 31 I just mentioned he kept ignoring despite my continually asking him to respond to it).
This last is the more bizarre gaffe of his, because calculating the range of possible universes is a routine practice in cosmological science (as we’ll see Barnes himself later insists!). Any cosmologist will tell you that, so far as we know (remember, we are talking about epistemic probabilities!) our universe is not the only logically possible one to have arisen. That in fact it is not sitting in a reference class of one, but a reference class of an infinite number of configurations of laws and constants. One can indeed say that the frequency of life-bearing universes in that possibility space is unknown. That is indeed one of the things I say myself in the chapter Barnes pretends to be answering (remember, Barnes never interacts with my actual arguments). But it is absurd to say that there is only one universe in that possibility space. The more so as that’s not the reference class we need use anyway. There are indeed non-hypothetical elements to count up in reference instead (all the things that happen without need of gods vs. all the things we have never found god causing: TEC, pp. 282-84; in other words, the prior probability of naturalism).
Barnes would notice that if he didn’t also repeatedly confuse my estimating of the prior (at 25% “God created the universe”) with the threshold probability of coincidences (a distinction I illustrated with the “miraculous machinegun” argument I discuss, a discussion Barnes never actually interacted with, in TEC, pp. 296-98). I tried explaining the difference to him. But that all fell on deaf ears. It’s not clear to me that Lowder even understands the difference. But the difference is crucial, because the fact that the threshold for coincidence is unknown in this case renders all arguments from that threshold invalid. Leaving only the prior probability we started with (that 25% I grossly over-estimated at the start of the chapter).
Here is why (this is a complete reproduction of the note 31 that Barnes and Lowder both ignore and never respond to, despite my repeatedly asking Barnes to do so):
At this point one might try to argue that the prior probability (for the universe case) should be based this time on a narrower reference class of “super improbable” events, such as the set of all things William Dembski quantifies with his probability threshold of 1 in 10^150 (see notes 6 and 13 above), based on the assumption that the ratio of designed-to-chance causes within that set should strongly favor design. But even if this could get us to any actual ratio of NID to ~NID (see discussion of prior probability earlier on why, for lack of data, it probably can’t), it is still inapplicable to the universe’s origin because that threshold was based on the size and age of the universe itself.
We are talking about an event beyond that limiting sphere, and thus must calculate a threshold relative to a larger total set of opportunities, which is precisely what we don’t know anything about. For instance, if the universe in some form will continue to exist for 10^1,000,000 years, then it could easily contain an event as improbable, and that event would as likely be its origin as anything else. In fact, since quantum mechanics entails that a big bang of any size and initial entropy always has some (albeit absurdly small) probability of spontaneously occurring at any time, and since on any long enough timeline any nonzero probability approaches 100 percent no matter how singularly improbable, it could easily be that this has been going on for untold ages, our big bang merely being just one late in the chain. We could be at year 10^1,000,000 right now, and as this conclusion follows from established facts and there is no known fact to contradict it, it’s no more unlikely than the existence of a god (and arguably a great deal more likely).
Since we therefore don’t know what the applicable probability threshold is, we can’t use one (other than by circular logic). To infer design we simply need the result to have features more expected on design than chance, and features that are necessary for observers even to exist will never be such (because those features will appear in both outcomes 100 percent of the time). Dembski’s threshold may pertain to events now in the universe, however, precisely because those outcomes are not necessary. For example, if the total probability of terrestrial biogenesis were 1 in 10^1,000,000 every fourteen billion years, then we would expect to find ourselves much later in the history of the universe—it would not necessarily be the case that we would observe ourselves only fourteen billion years after the big bang; whereas it would necessarily be the case that the universe came to exist with the right properties for us to be observing it at all. Hence the two problems are not commensurate.
This argument Barnes never rebutted. In short, since the only universes that can ever be observed (if there is no God) are universes capable of producing life, if only fine tuned universes are capable of producing life, then if God does not exist, only fine tuned universes can ever be observed. This counter-intuitively entails that fine-tuning is 100% expected on atheism. But a lot of things in probability theory are counter-intuitive—as the Monty Hall Problem illustrates (which also numerous mathematics professors made fools of themselves denying the facts of). So its hurting our brains is not an argument against it. It remains true all the same.
Now, there are two points Barnes tried to attack about this, one was the result itself—that P(fine tuning|atheism) = 1, based on his attempt to reimagine a prior probability of observers—which I’ll get to later; for now, the other was something to do with this threshold probability, i.e. the (faulty) intuition that such an amazing coincidence has to be designed. What I showed is that the threshold probability is a non-starter. You can’t avoid the conclusion by insisting that “at some degree of improbability” it “has” to be design. For some things you can. But not for the universe itself. That is what I demonstrated in the argument quoted above. The argument Barnes repeatedly ignored.
We are simply always left with the prior probability that gods exist and design universes and things. That’s all we have to go on. It literally does not matter how improbable our universe is (as I explain in detail in TEC, pp. 292-98, also ignored by Barnes). That is indeed counter-intuitive. But it is simply the fact of the matter.
As to [6] and [7]: Not only did I never argue my chapter’s conclusion from a multiverse, I explicitly said I was rejecting the existence of a multiverse for the sake of a fortiori argument. That Barnes ignored me, even though I kept telling him this, and he instead kept trying to attack some argument from multiverses I not only never used but explicitly said I wasn’t using, is just more evidence of his kookery. Why Lowder thinks it’s a valid point astonishes me to no end. I did outline an argument from multiverses in note 20 (TEC, pp. 408-09, which I only expanded on elsewhere—and note that objections based on transfinite sets are addressed extensively in the comments there). But I immediately ended that note with “But we don’t need this hypothesis, so I will proceed without it.” Without it. Case closed. Which is why this is so weird. Because this is where Barnes flips his lid about “finite” frequentism (in case you were wondering what that was in reference to). Note I at no point rely on transfinite frequentism in the argument of my chapter, because even where I touch on it here in note 20, I explicitly set aside the result and did not employ it anywhere in my chapter’s argument. I told this to Barnes repeatedly. He never listened to me. And yet everything he said about multiverses and finite frequencies is completely irrelevant to my chapter’s argument.
As to [8]: This statement simply repeats what I myself argue in my chapter in TEC. Illustrating how much Barnes is simply not even interacting with that chapter’s actual argument. Notice that even my note 31 repeats this statement: “To infer design we simply need the result to have features more expected on design than chance.” But fine tuning can never be such a feature, because “features that are necessary for observers even to exist will never” exist “more frequently” in God-made universes than non-God-made universes. In fact it’s the other way around: only God-made universes can contain life without being fine tuned (via application of his miraculous powers). Meanwhile, all universes not made by God that contain observing life will be fine tuned. If there is no God, you will never observe yourself to be in a non-finely-tuned universe. That is literally logically impossible. Unless, of course, fine tuning isn’t necessary for life. In which case, it can’t be evidence for life either.
On every point so far, it appears Lowder bought Barnes’s bizarre kook-worthy framing of the debate, hook-line-and-sinker, and didn’t notice that in not one case is he making a correct statement about the argument of my chapter.
A Brief Red Herring
After stating those mysterious agreements with Barnes, Lowder implies that a frequency interpretation is not necessary to this case, based on the common belief that there are non-frequency interpretations of probability, when in fact I have demonstrated there aren’t. Even “degrees of belief” are a frequency measure (they are simply statements about the frequency of beliefs based on comparable scales of evidence being true), which end up reducing to propositions about ordinary frequencies (as estimations of the true frequency, which conclusion we can prove by observing that they are always adjusted toward the true frequency as information about the latter is acquired). I demonstrate this in Proving History, pp. 265ff. One can debate that (though I’m quite confident you will lose; and in any case, you need to read those pages first, and it’s a separate debate from what we are talking about now). But that’s moot for the present, since Lowder doesn’t produce any argument from this statement of his against my chapter’s argument.
Part Deux
What Lowder then argues is that Barnes goes wrong in misrepresenting my argument. Lowder is correct. Actually, Barnes gets my argument wrong at pretty much every single point. But Lowder points to one example of his own interest, where Barnes mistakenly thinks that when I say it “follows that if we exist and the universe is entirely a product of random chance…then the probability that we would observe the kind of universe we do is 100 percent expected,” I was referring to its exact structure, when I make very clear in the chapter that that is not what I am talking about. I explicitly outline that I am only referring to the generic features necessary for life (e.g. that there be fine tuning, not that it be this specific selection of it). So instead of this being, as Barnes foolishly said, a fallacy of “affirming the consequent,” I was in fact stating a literal tautology. If fine tuning is necessary for life, and there is no God, then necessarily life will only ever exist in correlation with fine-tuning. This is because all universes without fine tuning will thus by definition not contain life. Therefore life will never observe itself being in any other kind of universe than one that’s fine tuned. Even if God did not cause it! Whereas, a God-made universe alone could contain life without fine tuning—because a god can work miracles. This is the actual argument of my chapter (on the matter of cosmology). Barnes to this day has never responded to it.
But Lowder then wonders if I am correct to have said, “Would any of those conscious observers,” in a randomly generated universe, “be right in concluding that their universe was intelligently designed to produce them? No. Not even one of them would be.” Lowder queries:
It would be most helpful if Carrier would explicitly defend this statement: “No. Not even one of them would be.” Unless I’ve misunderstood his argument, I think this is false. If we include in our background knowledge the fact that Carrier’s hypothetical conscious observers exist in a universe we know is the result of a random simulation, then we already know their universe is the result of a random simulation. Facts about the relative frequency aren’t even needed: we know the universe is the result of a random simulation. If, however, we exclude that from our background knowledge, so that we are in the same epistemic situation as the hypothetical observers, then things are not so easy. Again, it would be helpful if Carrier could spell out his reasoning here.
This statement tells me Lowder did not read my chapter, or at least not with sufficient care. He is still buying into Barnes’s bonkers framing of the debate, instead of actually going to the source and reading what I actually argued. The argument they are excerpting starts by explaining that we are (as outsiders) judging the judgment of people inside a simulation in which all the universes are randomly generated (by us). That’s the context. Here then is the very next sentence after the one Barnes and Lowder quoted from my chapter:
Would any of those conscious observers be right in concluding that their universe was intelligently designed to produce them? No. Not even one of them would be. If every single one of them would be wrong to conclude that, then it necessarily follows that we would be wrong to conclude that, too (because we’re looking at exactly the same evidence they would be, yet we could be in a randomly generated universe just like them).
Note that what is being said here is that they would not be right to conclude that. That is, if anyone said “we see fine tuning, therefore intelligent design,” they would be full wrong. We, the outsiders observing them, would be the ones who realize they are wrong, and why. And what does this teach us? That we might be them. Consequently we also cannot claim “we see fine tuning, therefore intelligent design.” Because the example proves to us that fine tuning never entails that. To the contrary, every randomly generated universe that has life in it will be finely tuned. That is what the example illustrates.
Therefore, in cosmology, there is no meaningful correlation between fine tuning and intelligent design. It’s equally likely either way. Or worse, because, unlike godless physics, God can make life-bearing universes without fine-tuning, therefore it is actually slightly less likely we’d be in a God-designed universe if we observe fine tuning. Because there is a nonzero probability God would make an un-tuned a universe to contain us, whereas there is a zero probability godless physics ever will (note that “God” here does include “techno-gods,” i.e. non-supernatural designers, when we include simulated universes in the range of possibilities, but that doesn’t change the overall argument, since fine tuning also does not provide evidence of techno-gods, for the exact same reason: see my address of the techno-god scenario earlier in the chapter, TEC, p. 281). By contrast, the correlation between observers in godless universes and fine tuning is fully 100%. Every time there is the one, there will always be the other.
Yes, this does mean that we could still be in a God-tuned universe (and so could the people in the simulation example conclude is possible for them as well), but that simply reduces to the prior probability. The fine tuning makes no difference to the probability. So if it starts 50/50, it remains 50/50. And so we’d (and they’d) still be wrong to conclude they were in an intelligently designed universe, merely from observing fine tuning. This should, of course, be the obvious point of my chapter. Since I say it over and over again with multiple examples (not just this one).
Part Trois
Barnes claims to have hundreds of science papers that refute what I say about the possibility space of universe construction, and Lowder thinks this is devastating, but Barnes does not cite a single paper that answers my point, or that answers the scientists I cited (like Stenger and Krauss): that none of these attempts to calculate the possibility space for universes actually determines the frequency of possible universes that would contain life. And since I wrote this article, numerous leading cosmological physicists went on record siding with me on this, so Barnes is pretty well cooked here. I’m voicing the expert consensus. He’s ignoring it. He is thus simply wrong. Because we don’t know how many variables there are. We don’t know all the outcomes of varying them against each other. And, ironically for Barnes, we don’t have the transfinite mathematics to solve the problem. I am not aware of any paper in cosmology that addresses these issues, and actually concludes a non-speculative number for how many universes will contain observers. The consensus is: we don’t know. We have neither the data nor the tools to know.
This is another example of where Lowder sadly is misled by Barnes’s misrepresentation of my argument. In this case, it’s not even an argument in my chapter in TEC, and thus actually has nothing to do with my use of Bayes’ Theorem. It’s unclear if Lowder even realizes this…Barnes has skipped to quoting and arguing against a completely unrelated blog post of mine. And then he fakes what I said in it by separating one line from its very next sentence. My argument in the article was, “We actually do not know that there is only a narrow life-permitting range of possible configurations of the universe.” Barnes can cite no paper refuting that statement. I give two reasons why. Barnes pretends I only gave one. And then when he gets to the second, he forgets the relevance of my second argument to the first.
Only one of my two arguments for that general thesis (that we don’t know) is that some studies get a wide range not a narrow one (these are cited by various experts including Stenger and Krauss; it is impossible that Barnes is unaware of the papers that argue this, if he has indeed surveyed them all; I know they exist, because I’ve read more than one; e.g. Fred Adams, “Stars in Other Universes: Stellar Structure with Different Fundamental Constants,” Journal of Cosmology and Astroparticle Physics 8 [August 2008]…note this is not the “monkey god” thing Barnes spitefully loathes; which suggests to me he is not being honest in what he claims to know about the literature). So we have inconsistent results. That is one reason to conclude we don’t really know. [Though Barnes has subsequently convinced me that there there could be good rebuttals to all of these, so I won’t depend on them further.] Then I go on to give the second reason, which is that even those papers are useless.
Notice Barnes does not tell his readers this. Notice that Lowder didn’t even notice that I said that. Lowder appears to have been duped by Barnes into thinking I said it was a fact now that “the number of configurations that are life permitting actually ends up respectably high (between 1 in 8 and 1 in 4…).” Nope. Because my very next sentence, the sentence Barnes hides until later, and pretends isn’t a continuation of the same argument, says: “And even those models are artificially limiting the constants that vary to the constants in our universe, when in fact there can be any number of other constants and variables, which renders it completely impossible for any mortal to calculate the probability of a life-bearing universe from any randomly produced universe. As any honest cosmologist will tell you.” Barnes is not an honest cosmologist. Again, not one of the papers he compiles a list of addresses this problem—or the mathematical problem, which I even explicitly cited the latest paper on, and yet which notably Barnes erases from his quotations of me, evidently preferring to pretend it didn’t exist than attempt to answer it.
How Lowder thinks this is even honest debate, much less “devastating,” is again bewildering to me. This is creationist tactics: misrepresent what someone says by clever quote mining, make false claims about the literature, hide the contrary literature (even when your opponent cites it), and never address what your opponent actually said, while blathering with bombast at how stupid he is for making such a stupid argument that in fact he never made. Lowder should not be falling for this routine.
It’s just worse when Lowder’s red flag detector didn’t go off when Barnes argues that there “can’t” be other constants (i.e. other forces, dimensions, and particles than the ones in our universe) because, “For a given possible universe, we specify the physics. So we know that there are no other constants and variables. A universe with other constants would be a different universe.” This is an absolute howler of an argument. It should have puzzled Lowder, not evoked an “I think I agree with this.” Walk through the thinking here. We know there cannot (!) be or ever have been or ever will be a different universe with different forces, dimensions, and particles than our universe has, because “we specify the physics” (Uh, no, sorry, nature specifies the physics; we just try to guess at what nature does and/or can do) and because “A universe with other constants would be a different universe.” WTF? Um, that’s what we are talking about…different universes!
I literally cannot make any sense of Barnes’s argument here. I cannot even imagine what Lowder thinks that argument was. Obviously, among all the possible universes that could result from random chance, infinitely many will indeed be different from ours, and will indeed have different forces, dimensions, and particles than ours. It is appalling that any self-respecting cosmologist would attempt to deny this, or try to fool people into thinking they were denying it. If Barnes has some fabulous logical proof that universes with different forces, dimensions, and particles than ours are logically impossible, I definitely want to see that proof, because it would be a great asset against creationism! I won’t hold my breath.
It’s unclear why Barnes’s subsequent points are even relevant to anything I said, or what relevance Lowder sees in them warranting a mention. But as Lowder says nothing substantive at this point, there is nothing more to respond to. Otherwise, this digression only relates to how “fine” the fine tuning needs to be. It could be “not very.” But I would still count that as fine tuning for my argument in TEC, since even at best it’s still well enough below even odds, which is what is supposed to carry an argument for design.
Part Quatre: The Real Heart of the Matter
Finally, Barnes switches back to my chapter in TEC. Why he interluded on that unrelated blog article, I don’t know (he says someone pointed him to it, so I guess it was a squirrel that distracted him). But he goes back now because of our debate in comments on my blog, which annoyed him to no end, so now he tries to rebuild his argument against my Bayesian argument about fine tuning in the TEC chapter. But all he does is again completely ignore everything in my chapter.
Once again Barnes tries to argue a point without addressing my responses already to it in TEC. This is the wall I’m arguing with. Why Lowder thinks a wall is a good debate opponent is another mystery. Others then finally pointed Lowder to another endnote in my TEC chapter that reveals what Barnes is ignoring (actually, just one of a dozen things in that chapter that he is ignoring), and Lowder seems to agree with it. At least he says he does. Which would mean Lowder disagrees with Barnes, and in fact concurs that Barnes has failed to address my actual argument, and has never rebutted it, despite abundant handwaving. And indeed, Barnes has never correctly described my argument. And thus in fact has never rebutted it.
Lowder, being the most charitable fellow on the planet, decides (in practice, not in word) to give up on Barnes and instead try to make Barnes’s argument for him, since Barnes evidently can’t. So now we have something solely from Lowder, an argument Barnes could never intelligibly articulate. And this pertains to what I mentioned before: Barnes’s constantly blundered and failed attempts to argue I’m wrong to conclude that P(fine tuning|atheism) = 1. Note that this is actually not “my” conclusion. It is the conclusion of three mathematicians (including one astrophysicist) in two different studies converging on the same result independently of each other. I merely marshal a lot of analogies and arguments to explain and back it up. All of which Barnes ignores. (Barnes also ignores the original papers I’m summarizing.)
Barnes wants to get a different result by insisting the prior probability of observers is low—which means, because prior probabilities are always relative probabilities, that that probability is low without God, i.e. that it is on prior considerations far more likely that observers would exist if God exists than if He doesn’t. It’s unclear to me that Barnes actually realizes this…he does not appear as facile with Bayes’ Theorem as his love of equations suggests…but this is what he has to argue. Because the only way the prior probability of observers can be low, is if the prior probability of observers is high on some alternative hypothesis. It can only be low with respect to an alternative. I never get any clear impression that Barnes understands this. So he is really, in fact, arguing for the existence of God. He is basically saying, “we are so amazingly unlikely, therefore God must exist.” He might not realize that’s what he’s arguing. But it is. And this is the reasoning refuted by Sober, Ikeda, and Jefferys. Whose arguments Barnes never rebuts. [My wording in this and the next paragraph is atrocious. I was trying to refer to using as the prior probability of the competing hypotheses, the posterior probability of a previous run of the equation on the sole evidence of there being observers before adding the observation of fine tuning. I clarify here.]
This is of course moot, anyway, because, in line with Sober, Ikeda, and Jefferys, I show in my chapter that no such conclusion about the priors is at all possible. Barnes never interacts with my arguments on this point. The fact of the matter is we do not know that the prior probability of there being observers at all (within a universe) is higher on the God hypothesis than on the contrary. It does not logically follow from “God exists” that God would produce other observers at all, much less do so by making a finely tuned physical universe that produces said life by non-miraculous physics (much less such a life-hostile universe, a point with which Lowder agrees; see my articulation of this point in TEC, pp. 294-95). Whereas that we would observe ourselves in a finely tuned physical universe that produces life by non-miraculous physics if there happens to be no God is 100% certain. Because there is no other logically possible universe we could observe ourselves in (if of course we include techno-Gods in the category of “God,” as I already noted).
This remains the case even if the odds of a life-bearing universe forming without God are 10^1,000,000 to 1 against. Or any odds whatever. Because no matter what those odds are, the existence of observers is still just as likely on God or not-God, and thus simply remains the prior probability that such a God exists at all. Which, remember, I set at an over-generous 25% at the start of the chapter. Which entails a 75% chance observers exist and God doesn’t. We might then be the product of an amazing coincidence. But so would the existence of a God be an amazing coincidence. The balance is a wash. (The incalculable luckiness of God I’ve discussed elsewhere.) As I explained in note 31 (fully quoted above) we do not know anything whatever that can change this balance of odds. We simply do not know that our existence is any more remarkable on either hypothesis. And since all godless universes that will ever be observed will be fine tuned, fine tuning can never be evidence for God.
This is explicitly the argument of my chapter in TEC, as I here quote from the main text on page 294:
This conclusion cannot rationally be denied: if only finely tuned universes can produce life, then if intelligent observers exist (and we can see they do), then the probability that their universe will be finely tuned will be 100 percent. Always. Regardless of whether a “finely tuned universe” is a product of chance, and regardless of how improbable a chance it is.[n. 23] Because “intelligent observers exist” entails we could never observe anything else. The only way the odds could ever be anything less than 100 percent is if you can have intelligent observers without a finely tuned universe (as then, and only then, it would at least be logically possible for there not to be a finely tuned universe if there are intelligent observers). But as it happens, you can only have that (a non-finely tuned universe with intelligent observers) in an intelligently designed universe. Ironic, yes. But true.
That’s the fact of it. And Barnes has never produced a valid argument to the contrary. This is where note 23 in my chapter comes in (which number’s placement in the text was shown above):
This is undeniable: if only a finely tuned universe can produce life, then by definition P(FINELY TUNED UNIVERSE|INTELLIGENT OBSERVERS EXIST) = 1, because of (a) the logical fact that “if and only if A, then B” entails “if B, then A” (hence “if and only if a finely tuned universe, then intelligent observers” entails “if intelligent observers, then a finely tuned universe,” which is strict entailment, hence true regardless of how that fine-tuning came about; by analogy with “if and only if colors exist, then orange is a color” entails “if orange is a color, then colors exist”; note that this is not the fallacy of affirming the consequent because it properly derives from a biconditional)…
Notice how I explicitly refute the charge of “affirming the consequent,” even mentioning the fallacy by name, yet Barnes leveled that charge at me anyway, without ever once even mentioning that I already directly addressed it, and without ever interacting with my actual argument against that charge, or even describing my actual argument against that charge. That’s the kind of character we are dealing with here. Lowder needs to stop being charitable with this guy.
Note 23 directly continues:
…and because of (b) the fact in conditional probability that P(INTELLIGENT OBSERVERS EXIST) = 1 (the probability that we are mistaken about intelligent observers existing is zero, à la Descartes, therefore the probability that they exist is 100 percent) and P(A and B) = P(A|B) × P(B), and 1 × 1 = 1. [Christian apologist Robin] Collins concedes that if we include in b “everything we know about the world, including our existence,” then P(L|~God&A LIFE-BEARING UNIVERSE IS OBSERVED) = 100 percent (Collins, “The Teleological Argument,” 207).
[Collins] thus desperately needs to somehow “not count” such known facts. That’s irrational, and he ought to know it’s irrational. He tries anyway (e.g., 241–44), by putting “a life-bearing universe is observed” (his LPU) in e instead of b. But then b still contains “observers exist,” which still entails “a life-bearing universe exists,” and anything entailed by a 100 percent probability has itself a probability of 100 percent (as proven above). In other words, since the probability of observing ~LPU if ~LPU is zero (since if ~LPU, observers won’t exist), it can never be the case that P(LPU|~God.b) < 100 percent as Collins claims (on 207), because if the probability of ~LPU is zero the probability of LPU is 1 (being the converse), and b contains “observers exist,” which entails the probability of ~LPU is zero.
If (in even greater desperation) Collins tried putting “observers exist” in e, b would then contain the Cartesian fact “I think, therefore I am,” which then entails e. So we’re back at 100 percent again. If (in even greater desperation) Collins tried putting “I think, therefore I am” in e, his conclusion would only be true for people who aren’t observers (since b then contains no observers), and since the probability of there being people who aren’t observers is zero, his calculation would be irrelevant (it would be true only for people who don’t exist, i.e., any conclusion that is conditional on “there are no observers” is of no interest to observers).
This is pretty devastating. Barnes never mentions this argument and never responds to this argument. In fact he never rebuts any of my actual arguments. And this is no exception. Lowder has to concur. But tries to help Barnes out as best he can:
I agree with his analysis, but — you knew there was a “but” coming — I think this misses the point, which seems to be a restatement of the anthropic principle dressed up in the formalism of probability notation. Yes, if we include “(embodied) intelligent observers exist” in our background knowledge (B), then it follows that a life-permitting universe (LPU) exists. But that isn’t very interesting. In one sense, this move simply pushes the problem back a step.
Note that Lowder is now ignoring my argument. Because I already showed what happens when you push it back a step. You end up with Cartesian existence in b. Which entails observers exist. We are back at 100%. And then I showed what happens when you push it back even another step, and remove even our knowledge of ourselves existing from b. You end up making statements about universes without observers in them. Which can never be observed.
There is no escaping this. Either you are making statements about universes that have a ZERO% chance of being observed (and therefore cannot be true of our universe), or you are making statements that are 100% guaranteed to be observed. There is no third option. And this entails the conclusion. Because if a condition has a ZERO% chance of being observed, then it can never pertain to us. Because we observe we exist. So what “would be observed” if we didn’t exist has no relevance to explaining our existence. Because nothing can ever be observed if we (observers) don’t exist. And the converse of 0% is 100%. You always end up with the same 100%: we can never observe any other universe. Period.
Again, I mean not this exact precise universe, but a universe with the generic features alleged to indicate design, such as fine tuning. Because if no one will ever exist in a non-finely tuned universe so as to observe it—and they won’t—then we will only ever observe finely tuned universes. Therefore, fine tuning is always 100% expected for all observers. Period.
There simply is no escape. Except on the God hypothesis—but admitting that God (and indeed God alone) allows us to observe non-finely tuned universes, crushes the hopes of creationists further, because that entails that fine tuning is less likely to be observed if God exists…which makes fine tuning evidence against God! So they can’t go that route. And there is no other route to go.
The bottom line is, fine tuning can never be evidence for God. Never. Not ever. Not in any logically possible universe. Because all logically possible universes with observers in them but without gods in them will be fine tuned. All of them. Every last one.
This is what Barnes doesn’t get. And what Lowder is struggling to understand as well. It grates against his intuition. I know. But intuition sucks at things like this. Trust the logic. Your intuition was built for savanna apes. Not for existential probability calculus.
That Lowder doesn’t understand the point yet is revealed by his closing statement. In response to my conclusion that there are statements that are “true only for people who don’t exist” and therefore of no interest to us, Lowder says “Dr. Carrier doesn’t speak for all observers. I’m an observer and find the question of interest.” This is an odd thing to say. Because I was not saying it isn’t interesting to think about. What I was saying is that it can never be relevant to us. Things that are true about universes that lack observers are not things of any relevance to us because we don’t live in one of those universes. We never can. And never would. So, yes, it might be amusing “to think about,” but it still won’t be relevant. Because we will never observe ourselves in one of those universes. More importantly, we never can. And never would. So that they might exist is moot. The probability of observing them is still ZERO%. Therefore the probability of observing a finely tuned universe instead is still 100%. And that’s why fine tuning can never be evidence for God.
Remember those people in the simulated universes that were randomly generated? They will never observe themselves in a non-finely-tuned universe. Because they logically never could. That is why fine tuning can never be evidence for intelligent design. It produces no likelihood ratio favoring it. And it never could. Not ever. That might be hard to comprehend. But don’t shoot the messenger. I’m just telling you how it is.
- Update: The debate continues.
On atheism fine tuning is expected because only universes that can sustain life will have life capable of observing it. On theism however, god could create life in a universe that had laws that were not capable of sustaining life, and keep that life alive through a perpetual miracle. If we had discovered that the laws and parameters of the universe we observe were inhospitable for sustaining life, and yet life somehow existed in a way that was completely inexplicable by natural means, then that would actually be evidence of design, since atheism or naturalism could never account for that. The existence of life would literally be a miracle in the traditional sense of violating the laws of physics in a way science could never explain.
That would indeed be one way to reach that conclusion eventually.
And that it is possible means the probability that God would instead use completely mechanical physics is less than 100%. Even if it were 90% (I’d like to see by what argument someone would claim it’s that high), it remains 100% on atheism (because there are no other ways on atheism for life to exist), producing a likelihood ratio of 9/10 against theism on the observation that fine tuning exists.
Hi,
I am trying to work though your post and I am having some difficulties understanding your argument. Since your argument relies upon Bayesian reasoning, it would perhaps be a good idea if you could just state the computation you have in mind? The way I understand the argument we are working with variables:
G/A : God exists or does not exist
O: I (or you) are here to observe the universe
FT: The universe (appears) to be finely tuned for life
It is possible to have a long discussion about the meaning of fine tuning or the proper way to treat indexical information (I am here to observe the universe) however I think in order to spell out the argument we can treat these untuitively. If this is missing something important do point it out when it becomes relevant.
(1) I take it we both agree that O and FT are true (the later for the sake of argument) and we assume we live in a single universe (no multiverse, again for the sake of argument). Also lets assume p(G) = p(A) for simplicity.
(2) I assume we are interested in computing p(A|O, FT) and p(G|O, FT) (the probability of Gods existence or non-existence given the evidence. Is this true?
I am not sure how p(G|O, FT) is computed in your argument. It would seem natural from a Bayesian perspective to compute it as the ratio (you can include p(A) or p(G) if you like; I have allowed them to cancel out for simplicity):
P(A| O, FT) / P(G| O, FT) = p(O, FT | A) / p(O, FT | G) = p(O| FT, A) p(FT|A) / [p(O| FT,G) p(FT|G)]
However I am not sure how the argument proceeds from here. Which of these quantities are equal to 1 and why? In your post you argue that p(FT | O, A) = 1. I agree with that, but plugging this in gives (for instance):
P(A| O, FT) / P(G| O, FT) = p(O|A) / [p(FT| O,G) p(O|G)]
Even in this case we are still left with various probabilities and it is not apparent why this fraction has to go either way. I think many theists would argue that if God exists, he would have good reasons to create humans (p(O | G) high as I think you grant for the sake of argument) whereas it may be the case if God does not exist the universe could be such as to not produce life (p(O | A) could be low). It is an interesting point that p(FT|O, G) could be low – we could live in a non-nonsensical universe– but a theist might argue life in a non-life permitting universe is not elegant and God would not opt for sustaining life by continuous miracles because that would be religiously inelegant or somesuch.
Anyway, I hope you can clarify what computation you have in mind.
Cheers,
Tim
Ps. I cannot help noticing the remark:
After stating those mysterious agreements with Barnes, Lowder implies that a frequency interpretation is not necessary to this case, based on the common belief that there are non-frequency interpretations of probability, when in fact I have demonstrated there aren’t. Even “degrees of belief” are a frequency measure (they are simply statements about the frequency of beliefs based on comparable scales of evidence being true), which end up reducing to propositions about ordinary frequencies
We have argued this point before in relationship to my review:
http://www.scribd.com/doc/271358647/Richard-Carrier-Proving-History-Review
in the thread:
http://www.richardcarrier.info/archives/8192
and I am quite surprised you directly rule out the existence of non-frequency interpretations of probability as, even if your interpretation is logically consistent which I am not convinced of yet, this is by far the most popular interpretation in my experience. Do you imply these cannot exist because they are logically contradictory or simply that your interpretation should superseede them because you feel it is more fundamental? How about a Kolmogorov measure-theoretical approach to probabilities which is fundamental to for instance modern Bayesian non-parametrics?
Speaking of your proposed interpretation, did you resolve the question on how to interpret a probability such as 1/sqrt(2) or pi/4 as a ”frequency measure” (I am not sure I understand what that is) according to your view?
You know, you could just read the papers I’m talking about. My chapter in TEC is detailed and has extensive notes with mathematical notations interpreting the text. The papers by Sober and Ikeda & Jefferys do the same, from different angles but getting the same result.
You are already repeating much of that material (evidently unawares) and any questions you have about it are already answered in those sources. That’s why we wrote them.
For example, “whereas it may be the case if God does not exist the universe could be such as to not produce life (p(O | A) could be low” is an unfinished thought. Low with respect to what? That probability can’t just be “low.” It can only be low relative to the alternative. The probability is a relative probability, not an absolute probability. That’s why, if you are rich, the probability of your having gotten rich by winning the lottery is not the probability of winning the lottery but the ratio of rich people who got rich by winning the lottery to all other rich people. So the question isn’t about the threshold probability of a coincidence on A. The question is the relative probability of O between A and T. Which is simply the prior probability that T.
-:-
On the side question:
I’m willing to be amazed by someone finding an example of probability actually being used in a way that doesn’t reduce to just one more measure of frequency. I just haven’t seen any; and this is a pretty well-trodden field, so I should have by now.
Non-parametric statistics is simply frequency statistics without the assumption of bell curve distributions. So are you actually trying to claim this is not a frequency measure?? Kolmogorov himself explains why it very much is a frequency measure (in his case, in the abstract: of ratios of elements in classified sets; his axioms make this explicit). So I don’t understand your question.
I never use such frequency measures. So why do I need to interpret them? If someone thinks they are meaningful or useful, let them defend their application.
Hi Richard,
I am simply trying to understand the logical structure of the argument which I do not believe is stated anywhere in TEC or your past posts (that is, how the argument stated in words is supposed to translate into equations). At any rate, the crux of my point is that if we accept the ratio of the posterior probability of Atheism / Gods existence is (under your assumptions):
P(A| O, FT) / P(G| O, FT) = p(O|A) / [p(FT| O,G) p(O|G)]
Then I think it is fairly clear many theists would argue that God would be likely to create a universe with observers whereas on atheism the universe may be one without observers — P(O| A) has to be much lower than p(FT | A) after all– and I believe you assumed in TEC (for the sake of argument) the probability a universe was fine tuned on atheism could be assumed to be quite low (1 to 101000000 in TEC) for the sake of argument. As you stated in PH, under ideal circumstances discussion about probabilistic reasoning should be about both parties proposing an appropriate Bayesian computation and stating why they believe the probabilities are the way they are; this is all I am asking for.
Re. the side note, I should have been more specific and said I worked with Baysian non-parametric statistics, that is with random functions and measures (i.e. priors on infinite dimensional objects). It is correct Kolmogorov himself subscribed to a variant of frequentism (though he was not very clear about the issue in his writings), however his axioms are interpretation free and surely require handling general probabilities such as pi/4.
I am puzzled by your last comment:
Tim: Speaking of your proposed interpretation, did you resolve the question on how to interpret a probability such as 1/sqrt(2) or pi/4 as a ”frequency measure” (I am not sure I understand what that is) according to your view?
Carrier: I never use such frequency measures. So why do I need to interpret them? If someone thinks they are meaningful or useful, let them defend their application.
Your statement was about *all* probabilities. Since p(X) = pi/4 is clearly a well-defined statement about the probability of X a statement about all probability must either deny this is a probability (in which case surely we must agree we do not end up with modern probability theory!) or at least admit it is at best an interpretation of a subset of all probabilities, namely rational probabilities.
The equations are all in the TEC article. And likewise even more so in the Sober and Ikeda & Jefferys articles I am summarizing and explaining. With full and detailed explanations.
Feel free to respond to what we’ve actually written. There is no point in asking what we’ve written, when you can go and read it, and respond to that.
Based on what? Assumptions they input. Which reduces the prior. It’s as big a coincidence to have a God who needs to create people (much less like this) as to have a godless universe do it.
But what Sober and Ikeda & Jefferys showed is that even that doesn’t matter. Because FT is fully 1:1 correlative with godless observers. So it literally doesn’t matter how unlikely it is. Hence my machinegun analogy (which I adapted from the firing squad analogy used in the other papers). Fine tuning thus never alters the posterior probability. Because it can never be the case that fine tuning is “more common” in Godly observed universes than Godless observed universes.
So we are reduced back to the prior probability of God. That’s the only thing that remains.
Again, this is all explained in our articles. Read them.
First, Kolmogorov could not have been clearer. His axioms explicitly define all probabilities as frequency measures between elements in sets. I linked you to his work on this. How you can think he “was not very clear” is astonishing to me. It makes me think you have not actually read him.
Second, Kolmogorov never said anything about pi/4 even being a legitimate probability measure. I suspect in fact that his axioms would rule it out, but I haven’t verified that (I could be wrong, see below); in any case, anyone who would claim that that’s an actual probability measure bears the burden of proving that it is. At first glance to me, a (pi/4)% chance of winning at poker is as unintelligible as a 110% chance of winning at poker.
If you think otherwise, the burden is on you to prove otherwise. It’s not on me. Prima facie, (pi/4)% is unintelligible. Maybe you should explain what you are trying to say with a statement like “a (pi/4)% chance of winning at poker” (or darts—to offer you a geometric model rather than a simple permutation model). What would such a statement even mean? And how would you ever arrive at it? Once you answer that, then we can see if it’s measuring a frequency.
(The only examples of generating irrational probabilities I can find are all derivatives of frequency measures, e.g. as discussed here. Likewise in Quantum Mechanics, where probability is a division of geometric space, measuring, yet again, a frequency of occurrence. It would be the same for infinitesimal probabilities as well, insofar as we can operate in a transfinite probability domain.)
Dr. Carrier, no need to open this comment, just heads up on an apologist article that argues against your conclusion re: Quirinius.
http://www.psephizo.com/biblical-studies/was-luke-in-error-about-the-date-of-jesus-birth/
Are you sure my Dating article doesn’t already rebut the arguments there? Because every time someone says this, I waste an hour reading a long boring article only to find that I already rebutted their argument in my original.
So it would be very helpful if you could check (here is a summary of my article and all the arguments it rebuts already) and let me know (by quotation) exactly what, if anything, is being newly argued in the linked piece. You’d be doing me a big favor with that (and my readers will benefit).
P.S. This comment is certainly worth posting here. I like collecting these in any case; and an article about responding to an online piece is a suitable place for mentioning others, even on different topics, now that I am running a looser relevance standard in my comments policy. I mention this just FYI for the benefit of all my readers.
http://www.psephizo.com/biblical-studies/was-luke-in-error-about-the-date-of-jesus-birth/
Same old, same old.
Update: Added some sentences at the end of section “Trois” to explain the connection between that digression and the rest of the article. The new material, now closing the section, reads:
The formulation of fine-tuning implies that the emergence of observers is inevitable. If observers do not emerge, then the level of fine-tuning was not sufficient for observers to emerge.
It’s possible someone could try to exploit a gap between the definition of life and of observers.
It may eventually become possible to observe universes which are not capable of supporting life like ours using non-miraculous means which could eventually lead to the evolution of life in universes which are not intrinsically capable of evolving life. In fact this could be argued for our own universe.
Ancient Indian philosophies such as Buddhism, Samkhya, Advaita Vedanta, Jainism, Vaisesika etc. use better logical arguments against a Creator than western atheism.
Let’s see the colour of your money then.
Pardon if I’m coming in too uninformed here, but isn’t it necessary for the theistic fine-tuning argument that the reference class of possible universes not be limited to our own? If the various laws of physics and parameters thereof could not have possibly been other than they are, then the putative creator has nothing to tune!
Yes. Barnes is not making sense.
He may just be a really crappy writer. What I assumed he meant, which is also just as false, is that the only things that could vary are our forces and constants (e.g. the four or five forces and the Standard Model which isn’t even complete). Thus, he does mean there can be variant universes, he just wants to deny that there could be universes with different forces than these, or different particles than these, etc., therefore we can “know” all the possible universes, just by running the numbers on the known data (never mind that we don’t know all the forces even in our own universe—we still don’t know what dark energy is or what is causing it’s effects—or all of our own particles—we hypothesized the graviton but haven’t empirically confirmed it, and most cosmological theories posit yet other particles at higher energies). But in fact, all cosmologists I know admit there can be in other possible worlds other forces and particles (and other physics) unknown to our world.
Just as an example, string theory posits a vast landscape of possible universes, almost all of which are mathematically inaccessible to us (i.e. they are too complex for us to even map out what they’d be like, much less whether they might contain some kind of observational life). But string theory is hypothetical. We don’t know that it is true. And alternatives to it entail different landscapes. All of the papers Barnes is referring to all discuss only an arbitrary subset of possible universes, by arbitrarily constraining the variables in some way (and the best of them explicitly note this as a limitation of their study).
So to claim we can “know” how many possible worlds will contain life is simply lying. It’s lying not only on the physics (per above), but also on the mathematics (per my linked article).
The latter is especially hilarious because not only does Barnes contradict himself by seeming to simultaneously insist on and deny variant universes (which I think, charitably reading him per above, is not so much a contradiction), but he even more ardently contradicts himself by denying transfinite probability calculations are possible, and not realizing that the fine tuning argument requires completing transfinite probability calculations!
The latter at least could be avoided if we can prove string theory true and assume no other universes are possible but through string theoretic configurations (at least absent a god). But then a wholly different mathematical problem arises: the extreme complexity of 10^100 or even 10^500 versions of hyperdimensional physics.
There is future hope. Since symmetry functions can be shown to be logically necessary given a certain geometry of spacetime, and more and more laws and constants are being shown to derive from symmetries (and thus actually are not variable), it is theoretically possible that a completed physics will show all our forces, particles, physical laws and constants are logically necessary consequences of symmetry functions. All that could then vary would be the geometry. In a sense, that is precisely the argument of string theory. That leaves us with a vast quantity of possible geometries to choose from, so variant universes remain, but it’s further theoretically possible that most of those geometries necessarily include spaces like ours, or eventually produce spaces like ours.
But we are a long way from knowing this. I think it’s a promising prospect. But that doesn’t carry weight as an argument.
Dearest Richard,
It is obvious that you are blinded by your own narcissism. Everyone except your most devoted sycophants can see that you had your ass handed to you in that exchange with Dr. Barnes. I’m really glad that you brought attention to this, but can’t believe that you actually did so intentionally.
The four part series of blog posts from Dr. Barnes is just so awesome. He completely eviscerated you and exposes you as nothing but an incompetent poser. All of those thousands of unnecessary words in your blog posts are nothing but a thick veneer of BS-a sad attempt to hide the fact that you have no clue about what you are writing about.
My suggestion to you is to actually read some of the books about Bayesian statistics that Dr. Barnes recommended to you. Since you won’t do that, just keep the laughs coming. You really should challenge more cosmologists and mathematicians to debate you. Embrace your role as the intellectual court jester of atheism.
This is an amusing chuckle. I’m quite content the non-delusional can compare the two and come to quite a different conclusion. I hardly need argue further.
Note to my audience: this troll is this guy. A documented liar. So you have strong warrant to check his claims for yourself rather than trust his purported judgment.
Hi Richard,
The articles you cite contains many different equations. I was simply asking you to clarify what exact equation you have in mind, however if you are not interested or able to do this then that is up to you.
My point I wanted to get to is this: Suppose we have two theories T1 and T2 and for the sake of argument you can consider these to be some generic cosmological theories (ýou don’t have to assume they are exchaustive). They only differ in that according to T1 we expect to find a universe with our laws and constants with probability p(FT | T1) = 1/10 and according to T2 we expect to find a universe with our laws and constants with probability p(FT | T2) = 1/10’000. Then assuming they are a-priori equally probable: p(T1) = p(T2) then according to the argument above we obtain:
P(T1 | FT, O) / P(T2 | FT, O) = P(O| FT, T1) p(FT|T1) / [P(O| FT, T2) p(FT|T2)]
= 1’000 * p(O | FT, T1)/ p(O | FT, T2)
So if we assume observers such as us are equally likely (or unlikely) on the two theories *given* the cosmos is fine tunded for life (which seems quite innocent – after all both theories predict the same laws of nature!) this favors theory T1 over theory T2. So this seems quite straight-forward and I belive you would agree with this calculation. I have two points:
My first point is that it does indeed seem we are able to use (apparent) fine-tuning to select between different theories (T1 and T2) in the above example. So of course a theist might claim that T1 = G and T2 = A and, if we grant for the sake of argument the chance of the universe being fine tuned for life is very low on atheism (which is the case I believe your book chapter discusses) and conversely that the chance the universe would be rigged to produce us is very high and God is perhaps somewhat more likely at least to place us in a life-permitting universe than a non-life permitting universe I do not see why we should not conclude
P(G | FT, O) / P(A | FT, O) >> 1
In this case. I agree we can tweak priors and all sorts of things so this equation can come out whatever way we wish, however I think my argument above is in line with the assumptions made in TEC and at any rate please do consider clarifying what equation you are using to compute P(A | FT, O) / P(G | FT, O) (which is the quantity we are interested in!), I simply cannot find it in TEC or your blog post or any of the two articles you reference.
My second point relates to the claim:
“Barnes’s constantly blundered and failed attempts to argue I’m wrong to conclude that P(fine tuning|atheism) = 1.”
I simply do not see why this should be the case at all. After all, A (atheism) encompas many different theories some according to some a fine-tuned universe is very unlikely. Suppose A encompas theories T1, T2, T3, … which are mutually excluding (A = T1 or T2 or ..) we can then compute
P(FT | A) = p(T1 or T2 or … | FT)P(FT)/(p(T1) + p(T2) + .. )
= (p(T1 | FT) + p(T2 | FT) + …) P(FT)/(p(T1) + p(T2) + .. )
= (p(FT| T1)p(T1) + p(FT | T2)p(T2) + …) /(p(T1) + p(T2) + .. )
So if just for *some* theory p(FT | T) < 1 then p(FT | A) < 1(!), and surely we can imagine theories upon which fine-tuning is unlikely. However the equation might of course be a typo and you intended to have the observer on the right-hand side, i.e. P(fine tuning|atheism, O) = 1, which I agree with. This is why I asked if you could clarify what you were computing.
Cheers,
Tim
The way this works is, you pick one to discuss.
Otherwise, I won’t know which one you are talking about. Or what you want to say about it.
Tim Hendrix: Suppose we have two theories T1 and T2 and for the sake of argument you can consider these to be some generic cosmological theories (ýou don’t have to assume they are exchaustive). They only differ in that according to T1 we expect to find a universe with our laws and constants with probability p(FT | T1) = 1/10 and according to T2 we expect to find a universe with our laws and constants with probability p(FT | T2) = 1/10’000.
This would be of interest in determining the most likely cause of the observation FT within A. But P(FT observed|atheism) remains 1. Regardless of whether we can know T2 is more likely than T1.
I have no idea how one would get this result, given the arguments in TEC. So it seems like you just aren’t even interacting with the arguments in TEC.
What I am (and they are) arguing is that when A and O are found together, that conjunction is 100% correlated with FT, i.e. if FT is necessary for life, then it is logically impossible for O and A to be true, and FT to be false. Thus since P(FT | A, O) = 1, P(A | FT, O) can’t vary according to P(FT) alone. It has to vary according to something else. (Hence my looking for other things to determine the relative priors for G and A.)
One can try two things: (1) argue that the “coicidence threshold” for God is higher than for a Godless FT, but no data allows that conclusion (both appear amazing coincidences of incalculable degree; Godless FT in particular as we cannot even find a coincidence threshold for it; but as I now note one could add the same problem exists for God, as God having maximal specified complexity in several attributes, e.g. an infinitely complex mind, entails incalculable improbabilities as well; whereas conversely the threshold on naturalism could well be incalculably high). So that’s out (hence my note 31). The other alternative is appealing to background evidence for supernatural agents vs. natural causes (the method I use earlier in the chapter, to get an absurdly generous P(G|b) of 0.25).
But FT gives us nothing. If atheism is true, FT is the only thing we can ever observe (because we can’t ever observe the alternative, i.e. A will never correlate with O, i.e. P(O |A, ~FT) = 0, which contradicts observation (we are 100% certain P(O) is not 0%, so on any probability dependent on A and O, P(FT) is always 1. Thus, we are left back with the prior probability that G or A. FT has no effect.
Observing FT therefore cannot increase the probability of God. One has to appeal to something else. Even at the level of dependent probability, the probability that O on A may be umteen zillion to one, but the probability that O on G may also be umteen zillion to one, because the probability that G may be umteen zillion to one (and the probability commutes). If both are umteen zillion to one, then the prior probability of each is 50% with respect to the other.
And we don’t know these probabilities. We don’t know that God is a more likely coincidence than Nature. So there is no argument to advance here.
So, you seem confused by either or both of two things: you aren’t getting that people in A can only ever observe FT, therefore observing FT can produce no likelihood ratio favoring G; or you aren’t getting the point of note 31 that trying to argue from “greater coincidence” is impossible for want of data.
At this point it’s not clear to me which you are saying “do not see.”
Re. Probabilities,
“Second, Kolmogorov never said anything about pi/4 even being a legitimate probability measure. I suspect in fact that his axioms would rule it out, but I haven’t verified that (I could be wrong, see below); in any case, anyone who would claim that that’s an actual probability measure bears the burden of proving that it is. At first glance to me, a (pi/4)% chance of winning at poker is as unintelligible as a 110% chance of winning at poker.”
Turning to the crux of the matter: “Second, Kolmogorov never said anything about pi/4 even being a legitimate probability measure”. We are not talking about whether pi/4 is a legitimate measure (a probability measure is, well, a measure and not a number) but if it is the probability of an event. If you simply look at wikipedia under the kolmogorov axioms and see the first axiom: “The probability of an event is a non-negative real number:”. So this include pi/4. As to the second part of your point, *we need probabilities such as pi/4*. The reason is we want the probabilities to have the topological properties of the reals such as being a compact set in order to express convergence theorems. If you insist probabilities are rational numbers you are simply throwing out a huge chunk of probability theory for no apparent reason.
Now regarding the poker hand, yes, we do not see pi/4 when playing poker, however this is no more an argument than saying that since we don’t see pi when counting fingers pi does not exist. For instance:
1) If you fire a pellet gun at random at a circle drawn within the unit square the chance it will hit within the circle given it hits within the unit square is pi/4.
2) In classical physics, in units where kB = 1 and assuming T=1, if a system can be in two states with energy 0 and 1 the ground-state probability according to the Boltzman distribution is 1 / (1+ 1/e)
3) The answer to the Buffons needle paradox: “Suppose we have a floor made of parallel strips of wood, each the same width, and we drop a needle onto the floor. What is theprobability that the needle will lie across a line between two strips?” involve pi.
“The only examples of generating irrational probabilities I can find are all derivatives of frequency measures”
The article you cite provides a way to construct an algorithm (which, by the way, depends on random numbers) for representing an irrational probability, *notice the authors agree that probabilities can indeed be irrational*. You simply can’t make the move that a mathematical object only exist if we can find a way to generate or represent it in practice, that would after all rule out pi itself and most abstract mathematics.
Suppose I said: There do not exist non-frequency interpretation of numbers. All numbers are measures of frequency. Any mathematician would then say: But what about pi? or e? or sqrt(2)?. I could then claim that since I had only seen these as derived as frequencies (for instance a series expansion) these examples did not count; surely this would convince no one as a finite series expansion is different than the real numbers and we do have good ways to construct the reals using e.g. Dedekind cuts or whatever however these involve general (infinite) convergent series. The only way to fix this sort of definition is to say:
“My interpretation of a probability of 1/sqrt(2) is that i imagine an infinite sequence of events happening at probability 1/sqrt(2) and take the limit frequence of this series”
or somesuch but this is entirely circular.
His other axioms involve building elements in sets, though. Whether that can produce irrational ratios is not obvious, but I think now it should be doable if that procedure maps to geometry, where spaces can have irrationally fractious areas, and relative frequency is an area measure. Hence my remark about Quantum Mechanics and the dartboard. And your analysis further convinces me.
So, it’s a frequency measure.
@Tim Hendrix
It’s fruitless to “suppose” that you said: “There do not exist non-frequency interpretation of numbers”, do you seriously think all truth statements about “numbers” should be true about “probabilities”? The two are different concepts. (maybe it could be said that all numbers are quantities or somesuch)
(So that thought experiment won’t get you anywhere, it will only result in exploring the difference between numbers and probabilities, not really whether or not probabilities are frequencies)
Pay attention to where you were asked what you think “probability”, specifically (not numbers, not unicycles), means other than something about frequency.
Also I can’t believe you just supplied two examples (a dartboard and a computer algorithm) without realizing that you had just confirmed that you yourself can’t think of any situation where it is meaningful to label a number a “probability” that didn’t involve a frequency.
Just to be fair, Brian: You and I have mistook him for arguing ///all truth statements about “numbers” should be true about “probabilities”?///
I don’t think that was Tim’s actual point.
But you are correct in your closing observation:
I actually used the dartboard analogy first. But Tim endorsed it. The observation is correct: even with irrational probabilities, so far even he can’t think of non-frequency interpretations of them. One could at best try to argue that an irrational area of a dartboard cannot be struck at every point within it by a dart, but I now don’t think that’s what Tim would argue (I only mistakenly thought it was). And arguing that would amount to arguing that irrational probabilities are fictional artifacts of arithmetic systems and not actual probabilities (but instead approximations to them). But I’m satisfied such an argument can’t proceed anyway: a dart can hit every point in an irrational fraction of a dartboard. So it’s still a frequency—just a ratio of areas rather than cardinals, and therefore the frequency with which a dart will hit the designated area.
Eh, maybe I should have toned down my rant a bit…
Maybe a bit. 🙂
Update: For convenience I’ve added:
Hi Richard,
Okay then I will let’s see if we can make some progress like this. In the example I gave above where we have two generic theories T1 and T2 for how the universe came about which are a-priori equally probable: p(T1) = p(T2) and where we assume fine tuning FT is much more likely on one than another: p(FT | T2) = 1/10’000 and p(FT | T1) can we then agree that:
P(T1 | FT, O) / P(T2 | FT, O) = P(O| FT, T1) p(FT|T1) / [P(O| FT, T2) p(FT|T2)]
= 1’000 * p(O | FT, T1)/ p(O | FT, T2)
and so if we assume O is about equally probable given FT (the universe is the way it is) and the two theories then this would indeed favor T1 over T2?
Can we then perhaps further agree that if a religious person claims (for religious reasons) that on his theory (T1) fine-tuning is very likely p(FT| T1) ~ 1 for some religious reason and we still hold the two theories to be equally likely this would be an instance where fine-tuning could reasonably be said to favor a religious explanation?
Now a further point is that I remain very curious what computation leads to the conclusion p(FT | A) = 1. Is that supposed to be true for any theory compatible with atheism? (notice the right-hand side does not contain an observer O).
No. Because on the “religious” FT theory, FT is not 100% expected. In fact, when O, P(FT) is only not 1 on G. It’s always 1 on A. So the likelihood ratio actually trends in favor of A (because FT is more common if A and O than if G and O).
Which, as I explain in TEC and here, is only true for universes without observers in them. We aren’t in such a universe. So it isn’t true for us. (Remember, this is epistemic probability.)
It is simply not possible to condition the probability of an observation on the absence of observations. That’s always zero. For everything, from doorknobs to doughnuts.
His other axioms involve building elements in sets, though. Whether that can produce irrational ratios is not obvious,
His other axioms do relate to sets namely a sigma-algebra (the elements of the sigma-algebra corresponds to events btw). It is *trivial* to produce a probability measure which corresponds to an irrational number (just to nitpick, not irrational ratios but just irrational numbers). Just take the uniform probability measure on the unit square with the standard (borel) sigma algebra. The upper-quadrant of the unit disc
A = { (x,y) in R^2 | x^2 + y^2 = 0, y >= 0}
is clearly contained in this sigma algebra and p(A) = pi/4. I mean, that’s a trivial constructive example of an event with probability which is not a rational number. And so we arrive at the problem: if we define probabilities as ‘measures of frequencies’ (whatever that is!), how exactly should that definition make sense of irrational probabilities?
Hence my remark about Quantum Mechanics and the dartboard. And your analysis further convinces me.
I mean no offence but if you are in doubt about whether one can construct irrational probabilities in a (Kolmogorov) measure-theoretical approach to probabilities I suggest you read any basic text on the matter or simply the wikipedia articles before forming a fixed opinion and stating that the definition you propose must supersede all other definitions. I mean, suppose you argued against someone who stated that Jesus existed and everything else was not rational, and at some point it became clear he didn’t know what language the most early manuscripts of the gospels were written in, I am sure you would suggest he tried to do some more reading before making up his mind.
Cheers,
Tim
I concur. Frequencies can indeed be expressed as ratios of areas of contact (I’ve done that myself before, so I should have remembered that). Those are still frequencies. So, we’ve gone the other way: you yourself have now established that irrational probabilities are frequencies. Thanks! You saved me the trouble.
Update: Whops deleted some of the definition of the set it should of course be:
A = { (x,y) in R^2 | x^2 + y^2 = 0, y >= 0}
I think that’s exactly what you wrote. Am I missing something? (It’s not crucial. Since I agree with your conclusion. But I’d like to make sure your comment contains the exact material you want.)
Brian Pansky: I mean no offense but just take the standard Borel sigma algebra on the unit interval and the (standard) unit-rate measure (the uniform probability distribution if you will). For any real number x in the unit interval
Ex = [0, x]
is an event according to the Kolmogorov axioms with probability p(Ex) = x (yes, x can be irrational). Can we agree on this basic point?. You don’t have to trust me, this is standard textbook stuff, just look at the wikipedia page for probability measures and the wikipedia page for Borel algebra. To say probabilities can’t be irrational is, well, irrational :-).
(Just FYI, yes, we do all agree on that now. Brian wasn’t really asking about that anyway. Though they were indeed heavy handed. The issue is that it’s still a frequency, so it looked like a red herring to have even brought it up. Hence our overreaction.)
Hi Richard,
I wish I knew how to make proper quotes :-). When you wrote no, what was that in relation to?
Is it fair to say that your argument that p(FT | A) = 1 is essentially that if FT was false and God did not exist we would not be here to make the statement and so we can conclude FT is true? If so, suppose T1 is *any* theory compatible (i.e. contained in A). Can we then also conclude that p(FT | T1) = 1? (in this case my argument clearly fails). If no, how would you address my argument above where I divide A into many non-overlapping theories?
Not just make the statement. Make the observation. In every logically possible universe in which both atheism is true and observers exist, all will correlate with the observation of FT. So if we see observers (and the probability that we do is full 100%), and there is no God (the hypothesis being conditioned on), it is necessarily the case that FT will be observed.
I think you are getting off track a bit by talking about FT being “true” or false,” not for reasons you intend; but FT could be false in two different ways: as I note in the article, it could be the case that FT is not required for life at all, in which case it still can’t be evidence for design (because FT would not be an indicator of an intention to produce life); or FT could be false because life is actually impossible in this universe and therefore we exist only by miraculous act of God (in which case we’d be concluding God exists; per the comment upthread by Thinker).
Accordingly, P(FT|A)=1 does not tell us what
P(~FT|A) isP(~FT) is. And P(FT|A)=1 is operating within the frame of assumptions of the FT Argument, i.e. it is assuming the proposition “without a God, FT is necessary for life” is true.Of course not. Just because P(I will die|atheism) = 1 does not mean we can’t show that some causes of death are more likely than others. Likewise just because P(FT|atheism) = 1 does not mean we can’t show some causes of that observation are more likely than others. I mentioned this already upthread. I think you didn’t catch that (“This would be of interest in determining the most likely cause of the observation FT within A. But P(FT observed|atheism) remains 1. Regardless of whether we can know T2 is more likely than T1.”).
Surely you could yourself see that even when the sum of all P(T{n}|A) = 1, it does not follow that we must conclude every T is equally likely.
Hi Richard,
I think what happened was that I got the equation right both times but your html parser thought some of it was a html tag and deleted it. I hope this comes out clear enough:
A = { (x,y) in R^2 | x^2 + y^2 leq. 1, x geq 0, y geq 0}
where leq: less than or equal and geq : greater than or equal.
Oh good point. The comment box software can do that (to try and prevent malicious code being entered).
Noted. Thanks.
There is no reason that you should have to debate those two fools any further. Your chapter in The End of Christianity is the final, definitive, and authoritative refutation of all design and fine tuning arguments. Any attempt Barnes or Lowder to contest this tour de force is just evidence that they are irrational, delusional, or liars. You said it best when you described it thusly:
“another deliberate tour de force refuting the Design argument in every major form, including the Fine Tuning Argument, the Argument from Improbable Biogenesis, and the Argument to Irreducible Complexity, as well as arguments from mind, beauty, and intelligibility. I strove to make this chapter so tight and decisive as to be required reading on the subject, and what you should always refer Christians to when debating any design argument. In my opinion, that argument is now done for. RIP.”
Christians, haters, and trolls like some of the commenters above (“the yeti”, “Tim Hendrix” ) need to heed those words.
Design and fine tuning arguments are done for. RIP. The silly kooks and trolls who continue to criticize your superb work only discredit themselves as delusional fools.
(Another troll.)
Frequentism and Bayesianism have been mentioned repeatedly in this exchange, but it seems to me that the technical differences between the two different approaches have never been explained adequately. I don’t think that the “Bayesianism as Epistemic Frequentism” section in Proving History (pages 265-80) is adequate either.
I would like to recommend a few resources that attempt to clarify the technical differences. They’re all authored by a fellow named Jake VanderPlas.
They can be found at:
https://speakerdeck.com/jakevdp/frequentism-and-bayesianism-whats-the-big-deal-scipy-2014
http://jakevdp.github.io/blog/2014/03/11/frequentism-and-bayesianism-a-practical-intro/
None of those address anything I say in Proving History. To the contrary, PH agrees with all of that.
You seem to be confusing statistical methods with interpretations of probability. The “Bayesianism as Epistemic Frequentism” section is about the latter, not the former. Note “Epistemic Frequentism.” That should have clued you in. If the actual explicit explanations that followed didn’t. What differs between the two as interpretations of probability is that they are both measuring the frequency of different things. Though the one (Bayesianism) is an epistemic approximation to the other, which other (frequentism) attempts to be objective (it isn’t really, as recent severe critiques in the literature have shown, but it is at least an idealization of one set of objective probabilities, in the same way Newton’s laws are an idealization of certain physical dynamics, yet apples still never fall at exactly the same rate every time in every place).
What I show in that section is that it is simply not true that Bayesians aren’t using a frequency interpretation of probability. They are. They are just talking at a higher level of abstraction than the frequentists, who are measuring the frequency of events, while Bayesians are measuring the frequency of conclusions being correct under given conditions. The frequentists, meanwhile, suffer from not taking into account all possible causes of observations (e.g. fraud) nor all information pertaining to probability (e.g. hypothetically extended data sets), as discussed in earlier sections of PH.
I’m not nearly as math savy as many of the previous commenters, but i believe i understand the basic gist of your bayesian case against fine tuning. I know that you said you weren’t dealing the multiverse in the post above but i wanted to mention something related to that. I recently attended a Veritas forum panel discussion here at Indiana University on “Naturalism, Faith and Meaning”. There was a group of four professors of different fields discussing the issues. At one point the philosphy professor (Tim O’Connor I think) mentioned that he was a theist and found FT compelling support for his position. When another panelist objected to FT on the basis of the possibility of a multiverse, O’Connor said that he had an argument for the multiverse being evidence for “a higher order fine tuning”. He didn’t explicate his case but it struck me as odd on its face. It seems to me that he was pushing the same problem back to a presumed deity that creates the multiverse and somehow organizes it in such a way that some will have life bearing constants. To my mind this assumes that a nontheistically arising multiverse would be less likely to generate one with FT that has observors than one that was theistically caused. But i thought a multiverse, by its very nature, sprouts an infinite array of possible combinations of constants. If this is so I cannot understand how the “higher order FT” can gain any ground since both the theistic and atheistic versions would generate observor-generating universes. Im not up on the math or physics, but i was wondering if you had heard of this higher order multiverse version of FT or had any comments on this approach. Thanks
Right. I’m familiar with that argument (it’s been floated several times by major apologists, e.g. W.L. Craig). They can’t actually have such an argument, of course, because we don’t actually have a completed physics of multiverse generation. So we don’t actually know fine tuning is needed for it. But we actually don’t know fine tuning is needed for life, either (as even the McGrews, Christian apologists, have proved in the article I cited and Barnes repeatedly ignored). That’s simply a conceit of the FT argument, based on physicists making careless or naive statements about what they mistakenly think they can know.
Hence my article in TEC, as also Sober et al., simply assumes we know as the FT Argument claims, so as to show that that assumption actually destroys the argument from its own premises; but as I note in this article here, I’m willing to take even coarse tuning as fine tuning, as long as it requires any probability significantly below 50/50, which without a multiverse theory I think is well enough likely. (I turn the McGrew argument on its head epistemically: though they show that we do not know there aren’t domains within the infinite set of possibilities that are packed with life-friendly options, we still have only found domains that are hugely imbalanced against that, so, so far as we know, we should assume FT is a lower than even odds probability, even if we can’t say precisely how low.)
But back to the multiverse tuning argument: the gist of it is that there have to be a lucky coincidence of physical laws to cause any multiverse system, and therefore even if we proved we were in a multiverse system, someone still has to have set up that system, otherwise there wouldn’t have been a multiverse to create us. It’s basically just the FT Argument all over again, using the parameters of the “meta-universe” as what has to be tuned rather than the parameters of this universe. Which on that argument they can concede are 100% expected because the multiverse ensures them—and so they then argue that’s why God created a multiverse!
There are two problems with this. First, it becomes increasingly ridiculous to argue that God needed to create a multiverse to create this universe just to create life. It’s already ridiculous that God needs a finely tuned universe at all. That actually is extremely unlikely—hence further evidence against the existence of God; just like the human brain: complex and vulnerable brains are the only way thought can exist if God doesn’t, whereas invulnerable souls can exist if God does, so it makes no sense that God would realize our minds with complex and vulnerable brains, whereas that is exactly 100% what we expect to see if there is no God (this is one of many similar arguments I deploy in the TEC chapter, only one section of which is about FT).
So already FT looks exactly like a godless universe, not a goddy one. If you want to know what a goddy universe looks like, just read Genesis 1 literally…which, after all, is why the Hebrews wrote that: that’s just the sort of thing they, because it’s just the sort of thing anyone, would think a God would do, and it requires no fine tuning of anything. To add on top of that that God not only couldn’t make the universe in Genesis 1, but was somehow “forced” to make an FT universe instead, which looks exactly like the only kind of universe we could find ourselves in if there wasn’t a God, and that God was so enfeebled that he couldn’t even make an FT universe, but had to make a multiverse first, just so as to get the FT universe, is to make theology look like the profoundest of jokes.
Ultimately, that ends up making the existence of God even less likely. As Captain Kirk said, “What need does God have with a starship?” one has to ask the same, “What need does God have of a multiverse?” And already the same goes for monoverse FT…”What need does God have of quarks and electromagnetic constants and stellar nucleosis and a universe 14 billion years old, 93 billion lightyears across, filled with trillions of dead planets, etc.?”
So, really, his “argument” from multiverse fine tuning will become self-refuting on complete analysis.
Secondly, it is necessarily the case that any multiverse system will need be vastly less fine tuned than this universe, so the question arises why one would assume it needs to be finely tuned at all? Usually these guys don’t know that most physical laws and constants follow necessarily from symmetry principles and a given spacetime geometry; and probably, all physical laws and constants do (this is the case on string theory, for example). So they are logically necessary. They don’t need even tuning, much less fine tuning. What makes for different universes (i.e. ones that can and ones that can’t produce observant life) would then be variances in the geometry, i.e. the particular shape and structure of space-time (how many open dimensions; how many closed-loop dimensions; and how many time/asymmetric dimensions).
They would try to respond then by saying “Who picked the right geometry?” But that’s missing the point. If a completely random chaos of spacetimes churned up, i.e. you pick randomly from all possible geometries (i.e. no one chose at all), the probability you will pick a vast multiverse approaches 1. Christian apologists can’t wrap their head around the fact that a singular geometry is the least likely thing to arise if we are picking at random. Just try to pick a random number of universes (in this case = geometrically variant regions of spacetime) between 1 and infinity. What are the odds that you will pick 1? Infinity to one against, really. Even if one tried to object to that on the grounds that we don’t have a fully normalized transfinite probability calculus, you can still get to the conclusion by the method of exhaustion (a la Archimedes), and show the trend point of the curve is towards ZERO% as the number of possible options approaches infinity (and there is no argument by which one can reverse that trend “at” infinity). Whereas, how many universes are you likely to have, if the number of them you pick is randomly chosen between 1 and infinity? Whatever it is, it is near 100% certain to be an incomprehensibly vast number. Again, this can be shown by method of exhaustion (showing that for any arbitrary number of universes, the probability of selecting it or higher approaches 100% as the number of possibilities to choose from approaches infinity, and again with no argument by which one can reverse that trend “at” infinity).
So no fine tuning is required for multiverse theory. A totally random selection of a shape (from among all possible shapes) is all one needs. Most shapes are going to be extremely complex (i.e. have all kinds of regions and pockets different from each other), so random chance will almost certainly generate that, and not a monoverse (of one single consistent shape) of any sort. This is of course already well known from statistical mechanics, which shows that the Laws of Thermodynamics are necessarily true in all universes with the same underlying features (pretty much any set of colliding particles in a spacetime region), due simply to the fact that random chance sooner selects highly complex arrangements (the chaos of a gas in a spherical tank) than highly simplified ones (all the molecules of that gas arranged into the shape of a cube in the center of the otherwise empty tank). Likewise, highly complex multiverses are vastly more probable on purely random selection than singular monoverses.
Richard,
I wanted to be the one who left the least important, yet relevant comment here, since I have no formal training in logic. As someone who grew up watching him every day, it’s Monty Hall, not Haul.
Do I win?
Good catch. Thanks!
It just shows desperation and dishonesty that Christians are just as likely to reach for a multiverse theory as they are to reach for the extreme opposite nearly to the point of solipsism, where the universe is still under ten thousand years old, reducing the universe to a few thousand light years at most, if that, since the stars could still be just holes in the bowl of sky just over our heads. In this scenario it’s even more likely that this tiny bubble we live in is also a bubble of special physical laws. Why does a billion light years of universe need special laws when God only created life here and send His Son here? The notion of fine tuning sounds perfect to people who believe they are special.
It’s particularly amusing that some of the argumentation on the other side depends on assuming that if God decided to create a universe, He would, of course, create a universe with intelligent observers. Talk about pretending to know God’s mind!
I’m reminded of Dr. Manhattan in Watchmen – “Just look around you. Mars gets along perfectly well without so much as a microorganism. Here, it’s a constantly changing topographical map … flowing and shifting around the pole in ripples 10,000 years wide. So tell me … how would all of this be greatly improved by an oil pipeline? By a shopping mall?”
(Not that I agree with the implicit anti-capitalist/anti-consumerist dyspepsia all that much, but you get the point 🙂 )
Indeed.
It’s an old argument actually. If God was perfect, it is logically impossible that he would create anything. Creating entails God was incomplete, that he needed to do something, that something wasn’t perfect…but if only he existed, then that means he wasn’t perfect. Creation reveals that God was imperfect. Which contradicts the theology that he must be perfect.
Apologists have answers to that, but they don’t really address the deeper problem: if God had been perfect in that sense (in the sense of not needing any other thing or person, being content to remain as he was), he would not have created anything. And it’s hard to escape the realization that there is no argument that assures us that that isn’t the God we would have.
Lots of conceivable gods have no motivation to create anything. And even those few that are oddly specific as to conveniently have such motives, would not be motivated to create this kind of world, when they could just make a perfect angel-filled heaven and be done with it. So to get all the way to a God who would make this world, a world that in a dozen ways looks exactly like the world we would have if there is no god, and which is imperfect and messed up in countless ways besides, and then hide…that requires an extraordinarily specific and remarkably convenient set of assumptions, indeed bizarre assumptions, about how that God would have to think, in order to get this universe as a predicted outcome.
Hi Richard,
Okay I think I am making headway to understand where we differ. I think the crucial bit is we are very careful with our variables. Recall I define
O: We are here on this earth to observe the universe (you can alternatively use: life exists or (as I would prefer) an observer with my exact memories exist)
FT: The universes constants are suitable for life
A,G: Atheism (universe came across by natural means and not design) or God (~A = G; In this definition G=NID)
So with these definitions I have a few comments
A) Let me try to make my comment about theories compatible with naturalism more clear. It relates to this quote from your piece:
And this pertains to what I mentioned before: Barnes’s constantly blundered and failed attempts to argue I’m wrong to conclude that P(fine tuning|atheism) = 1.
You wrote in support of this statement:
“Not just make the statement [that life is fine-tuned]. Make the observation. In every logically possible universe in which both atheism is true and observers exist, all will correlate with the observation of FT. So if we see observers (and the probability that we do is full 100%), and there is no God (the hypothesis being conditioned on), it is necessarily the case that FT will be observed.”
But this is just saying that if we are here to observe anything and there is no God then FT is true, P(FT | O, A) = 1. But this is not p(FT|A) = 1 (if atheism is true fine tuning is true) which I still don’t see you have demonstrated anywhere. How do you go from the above argument to p(FT|A) = 1?
The problem is as follows: Suppose S is the event our solar system formed and A is just Atheism (natural universe, big bang, etc.) then why can’t I argue in line with what you wrote that p(S | A) = 1 since if the solar system did not form, we would not be here to make ‘the observation’, and then p(S|A) = 1? Now I think this argument is really p(S|A.O) = 1 (which I of course accepts!) but this leaves it wide open why we should accept p(FT|A) = 1.
B) My second point is that p(FT|A) = 1 has nasty consequences and I don’t think it is compatible with other things stated in TEC. This is why I still hope you will clarify your argument as you stated should we should all do in PH and provide the computation you have in mind using the symbols you have introduced.
Anyway, notice that for ANY events F, A, X where p(AX) > 0 (X is compatible with A) it holds that
IF p(F|A) = 1 THEN p(F|A.X) = 1
(try to draw a Venn diagram to see this is the case)
So my point is then that if we assume p(F|A) = 1 as you claim, then for any other naturalistic theory for how the universe came about such as
“T: There is a single universe and the laws of our universe are randomly selected from all (say) 10^500 string theories without supernatural intervention”
we have that p(F | A.T) = 1. That is, I simply do not see how we can say anymore that laws are “fine-tuned” in any sense on any theory. Is this really all that reasonably an assumption? If not, where exactly does I go wrong (the “argument” above is just basic probability theory).
C) My third point relates to footnote 29 of TEC which I think spells out the crux of the argument. You assume p(FT|A.O) = 1 and grant (to simplify things) that P(FT|G.O) = 1. Then you introduce
L = “a kind of life-bearing universe exists whose odds of existence without a God are 1 in 101’000’000”.
My first question is what that statement translates into symbolically? The only sensible thing I see is:
p(FT|A) = 1/101’000’000
because that seems quite literally to be what it says but that is in contradiction to what has been previously written. Do you see why it would be helpful to have the argument spelled out?
Moving to footnote 29 there is the argument (the argument uses NID=’non-terrestial design’ instead of G but elsewhere in TEC these are considered interchangeable and my point holds either way)
p(G | FT.b) = p(G |b) p(FT| G.b) / [p(G |b) p(FT| G.b) + p(A|b) p(FT|A.b)] = 0.25 * 1 / (0.25 * 1 + 0.75 * 1) = 0.25
The problem here is how O is treated. I can only assume O is considered part of b, so lets suppose b = O.b’ where b’ is the background evidence not relating to intelligent life existing in the universe. Then the above argument assumes that
p(A | O.b’) = 0.75
(if intelligent observers exist then atheism is true with probability 0.75) but that is not the prior probability of atheism, p(A|b’), but a POSTERIOR probability as it is conditional on O, intelligent observers, which is part of the evidence we have at hand.
Thus the whole argument in TEC consists of first assuming atheism is 3 times more likely than theism given intelligent life exists and then figuring out a pre-requisite for intelligent life, laws compatible with intelligent life, does not alter the already-assumed conclusion.
Is this correctly understood and if not how does O figure into the equation in footnote 29?
A more fair computation:
p(A | O.b’) = p(O|A.b’) p(A|b’)/[ p(O|A.b’) p(A|b’)+ p(O|G.b’) p(G|b’)]
Which clearly depend on how likely we believe life is given atheism vs. if God exists and (as theists claim) intend to create life. Depending on how one answers these questions, in particular if one believes intelligent life O is less likely on atheism than on theism, then the fine-tuning argument would in this case bear evidence towards the existence of God.
Finally why is p(A|O.b’) = 0.75? this is just declared in the beginning of the chapter of TEC but without an argument, at least an argument conditional on O.
Just to be clear, remember godless supernaturalism is also possible. We both do assume that’s an unlikely alternative. I deem it to have a vanishingly small prior (as I actually do God; my 0.25 is an absurd generosity). But it can rear it’s head again when discussing the math. I shall assume it won’t significantly. But just FYI.
O is b. All probabilities in BT are conditioned on b. And you can’t remove O from b. Because that can only be done in a universe without O. Which we aren’t in.
There is no such variable P(FT|A) in BT. There is only P(FT|A.b). I assume you are aware of that.
Hence my discussion in TEC, quoted in the article here, of Collins attempting to get around this problem.
If S were necessary for us to exist, then that is indeed what would follow. It just happens to be the case that there isn’t any sense in which S is necessary for us to exist. Not only can we exist in other solar systems, we could find ourselves in places other than solar systems.
This is the point of my note 31’s closing lines: it is not necessary that we exist so early in this universe, so if that were improbable, that improbability would get into the math (although it would be hard to explain how that supports G since G doesn’t explain the wait; but if science confirmed the universe along with earth and its solar system were 6,000 years old, then we’d have a strong case for G). But anything that is necessary for us to exist, will always be observed, regardless of G or A. It therefore cannot support G over A. Only something that will be observed more often on G than on A can be evidence for G. But something that always is observed on A cannot ever be observed “more often” on G. Because there is no “more often” than always.
That’s only if F entails X. Draw a Venn diagram to see this is the case.
It’s possible to have X without F. It’s possible to have X without A. It’s therefore possible to have X without A and F.
So I’m not getting your point.
Seriously?
Did you not read my point about P(I will die|atheism)?
It’s rude not to pay attention, and to ignore my rebuttals and repeat the same argument I just rebutted.
Please don’t do that.
You are clearly wrong. And I’m astonished that you think what you just said made sense.
Let’s imagine we have string theory (S), quantum loop gravity theory (Q), and Newtonian Mechanics (N) as competing explanations of the universe, each “explaining” how FT came about (the latter by statistical mechanics). For simplicity assume this exhausts all possibilities (it won’t matter; you can add infinite alternatives, it won’t effect the following point, it will just require an introduction of a summation function).
If P(FT|A) = 1, then P(S|A) + P(Q|A) + P(N|A) = 1.
How, then, can it entail P(S|A) = 1?
Please. Think this through.
So, when I ask you what the probability is that I got rich by winning the lottery, P(I got rich by winning the lottery | I am rich), you would answer with the probability of winning the lottery?
Oh dear.
No.
The probability that I got rich by winning the lottery, P(I got rich by winning the lottery | I am rich), is the frequency of rich people who got rich by winning the lottery. Which could be 0.01, if 1% of all rich people got rich by lotteries, while the probability of winning a lottery could be 0.00001. The probability of winning the lottery is irrelevant to the question.
Now suppose the only way to get rich is by winning the lottery. And there are only two lotteries. And one (Lottery A) has a chance of winning of 1 in 1,000,000 and the other (Lottery B) of 1 in 500,000. And assume everyone plays both lotteries. What then is the probability that someone who is rich got rich by winning the lottery? It is 100%. Not 1 in 1,000,000 or 1 in 500,000 or even the converse of the probability of failing to win both. It’s simply always 100%. Because the people who aren’t rich, of course, aren’t being asked about; we aren’t among them; in this world, where lottery is the only way to get rich, if we observe we are rich, we know we won the lottery, so the probability of having done so is irrelevant—to the question P(I got rich by winning the lottery | I am rich), as that is always going to be 1.
However, we can still say something about this: if I am rich, which lottery did I win? You will not answer that with “there is a 1 in 1,000,000 it was Lottery A” (as you just did). Because that’s incorrect. The probability that we won lottery A is actually 1 in 3.
I’ll let you figure out why that is.
Now, what happens when we don’t know how unlikely winning either lottery is? And there is no accessible data to find out (e.g. no population polls, etc.). Principle of indifference then entails each is just as likely. 50/50. In that case, if the probability of winning Lottery A is 1 in 1,000,000, then the probability of winning Lottery B is (so far as we know) also 1 in 1,000,000. And since those are the only two ways of getting rich, the odds of having gotten rich by Lottery A are 1 in 2. Likewise for Lottery B. It’s simply 50/50. It is not (as you just said), “1 in 1,000,000.” It’s actually even odds. 50/50. So we can’t argue we are more likely to have won the one lottery than the other. For lack of any pertinent data.
That’s the argument of my note 31.
You don’t have to assume this. In my note on Collins I explicitly say it. And explicitly deal with attempts to deny it. Like you just attempted. Again.
Do you see why it is frustrating that you won’t read the material you are critiquing?
You almost get it.
By your reasoning just now, prior probabilities don’t exist. All probabilities are posterior probabilities. That’s sort of true. But not relevantly here.
Because we can substitute O for b (as in fact I did in that note). Indeed we can say (as I do in my note on Collins) that O is the sole content of b (that and the truths of logic and math etc., of course). But does that allow you to say that the prior is the posterior? No.
A is not in b. A is h (i.e. h{a} against h{g}). P(FT|A,O) is simply P(FT|h,b). Which is the likelihood. Then P(H|b) must be P(A|O). So the prior is P(A|O). Which contains no mention of FT. FT is in e, not b. I conclude P(A|O) is at least 0.75. In no way does the existence of FT relate to that calculation. You’ll notice it’s nowhere in there. It’s neither in A (i.e. h). Nor in O (i.e. b).
If you take O out, you have no observation (you are defining the condition as lacking any observations, and conditioning all probabilities on nothing ever being observed)…i.e. the probability of any observation is literally exactly zero. Not close to zero. Not vanishingly small. Zero. Full on. Zero.
But we do observe stuff. So any equation conditioning on nothing being observed is false. For us, anyway; it could be true for non-existent observers in observerless universes which will never contain observers, but we aren’t them—we know this with 100% certainty; indeed, unlike G or A, this is the one thing of which we are absolutely 100% certain…not close to 100%; full on actually 100%.
That’s why you can’t take O out of b. As I explained in the note on Collins. Just as you can’t take “logic” and “mathematics” out of b, and then use BT to argue up is down and black is white.
If you want to make statements about the universe we are in, you have to have O in b. O may be the only thing in b. But it can’t be gotten out. Because taking it out converts the equation into a statement about universes we aren’t in. Which is not a relevant statement to explaining the universe we are in.
Hence your subsequent equation is simply not applicable.
WTF? How do you imagine three whole pages of argument (pp. 282-84) as being “without an argument”?
And why do you think it isn’t conditional on O? When in fact it’s explicitly conditioned not just on O, but a described array of background observations, which entail O?
(Note it is Collins who forces us to reduce b to only O. I did not do that myself. I actually use all past science and observations as b, everything not directly on the question of design examined in e, as in fact one should. That you don’t know this? A big tell that you did not read the TEC chapter.)
Re. probabilities
It seems after our previous discussion we are in agreement that
A) the probability of an event can be an irrational numbers
and that
B) an irrational number cannot be a frequency (a fraction of two integers)
so a definition of probabilities as a ‘measure of frequencies’ seems difficult to make precise. From PH:
They [Bayesian] are talking about the frequency with which beliefs of a given type are true, where
of a given type means backed by the kind of evidence and data
that produces those kinds of prior and consequent probabilities. For
example, if I say I am 95% certain h is true, I am saying that of all
the things I believe that I believe on the same strength and type of
evidence as I have for h, 1 in 20 of those beliefs will nevertheless still
be false
So just continuing the above definition which should work on all probabilities:
For example, if I say I am 1/pi certain h is true, I am saying that of all
the things I believe that I believe on the same strength and type of
evidence as I have for h, ? in ? of those beliefs will nevertheless still
be false
Do you see why I am worried?
I agree you can find a way to define 1/pi in terms of events we imagine. Say for instance that:
For example, if I say I am 1/pi certain h is true, I am saying that I can imagine a sequence of events happening independently with probability 1/pi and if i imagine the limit of the frequency of the true events to the total number of events in that infinite sequence this will converge to 1/pi with probability 1.
But this definition is obviously both different than that in PH and it seems quite circular (either randomness or probability or both is used). Furthermore it is difficult to say it really *defines* what a probability is in any normative sense or that it is different than good old standard frequentism re-dressed as a thought-experiment. Recall
Frequentist probability or frequentism is a standard interpretation of probability; it defines an event’s probability as the limit of its relative frequency in a large number of trials. [https://en.wikipedia.org/wiki/Frequentist_probability]
Have you read Jaynes “Probability Theory”?
Cheers,
Tim
No. We just showed frequencies include a ratio of two areas. So your definition of frequency is incorrect. Not the other way around.
This is indeed how Quantum Mechanics measures frequency (e.g. of where a photon will strike a plate after passing through a deflector). Likewise frequentist statistics (which measures frequencies by placing areas under a curve in ratio to each other). So you can’t possibly claim these aren’t frequencies. When even the most fanatical form of frequentism says otherwise!
I likewise talk about dividing up “probability space,” which just means “frequency space.” The frequency with which one conclusion will turn out to be true will equal the frequency with which a photon will strike a corresponding area of a plate, for example. It’s still a frequency. And even if it weren’t, then it’s an approximation to a frequency (and the quantization state at fine resolution reveals the real frequency by permutation theory).
This is unintelligible. I can’t even tell what you are trying to argue.
Dartboards again. Let’s go real, and use the photons hitting a plate after passing a slot, and the quantum mechanics that explains the frequency with which photons will hit within a particular area of that plate. We can define an area of that plate equal to 1/pi (if we can’t, then 1/pi becomes meaningless again; I’m assuming you agree we can, and thus we can put two finite areas in ratio to each other equal to 1/pi). So, we would say the frequency with which photons will strike in that designated area is 1/pi. That’s a frequency. And indeed, the number of photons hitting that area vs. the remaining area will indeed converge on 1/pi as we approach infinity. Welcome to the weird world of infinities.
Now, you can go William Lane Craig on us, and insist that whenever infinities give us weird results, we should reject the results. In that case, 1/pi is an approximation to a frequency, whatever actual frequency will add up at infinity for the photons hitting the plate. And there is something to that, in that spacetime is quantized (not continuous), so actually, there probability will be a quantized (integer) frequency in the end, and the 1/pi was just an approximation to it. Either way, it’s a frequency.
So, with the probability that a belief will be true when given a certain scale of evidence: such beliefs will turn out to be true (hit that area of the plate rather than the rest of the plate) as often as 1/pi (albeit at infinite runs), or else they will turn out to be true (hit that area of the plate rather than the rest of the plate) as often as whatever integer frequency 1/pi approximates to as a geometric function on a quantized space (if the plate has a smallest area and can’t be infinitely divided—in which case, 1/pi only happens when we can infinitely divide the plate—hence that magic of infinity again—but if that should be impossible, then so is 1/pi as a true frequency impossible—it can then only be an estimate of the true frequency using the inapplicable conceit of an infinite division of the probability space, which will be close enough for our purposes and thus usable but fictional).
I am with “The Thinker”. Why does an omnipotent god need to fine tune the universe? “God” is already credited with not needing to obey the laws of physics so he/she/it could have made people in any form he pleased in any damned universe he pleased. We could be intelligent electrons in a soup of photons if he/she/it chose. Moreover, if god created everything then he has to be outside the universe and of a substance outside of physics; he can’t be made of photons, electrons, quarks, or whatever since he made these things. If we are created “in his image” why are we made of natural stuff rather than the unnatural stuff of god? Anyway, the whole god concept is to absurd to even think about.
Hi Richard,
Thanks to your last post I think I finally understands your argument, however I think at the hearth of it is a basic misunderstanding:
Tim Hendrix: But this is just saying that if we are here to observe anything and there is no God then FT is true, P(FT | O, A) = 1. But this is not p(FT|A) = 1 (if atheism is true fine tuning is true) which I still don’t see you have demonstrated anywhere.
Richard: O is b. All probabilities in BT are conditioned on b. And you can’t remove O from b. Because that can only be done in a universe without O. Which we aren’t in. There is no such variable P(FT|A) in BT. There is only P(FT|A.b). I assume you are aware of that.
Just to be clear, I was only following your convention of writing p(FT|A). I understand you now to say all probabilities should be conditioned on b (our background information) and importantly this include O (observers exist) and that this (the inclusion of O in b) is a fundamental principle:
RC: So any equation conditioning on nothing being observed is false. … That’s why you can’t take O out of b. As I explained in the note on Collins. … If you want to make statements about the universe we are in, you have to have O in b. O may be the only thing in b. But it can’t be gotten out.
So the way I now understand your piece and TEC is that you have adopted the stance we should condition all probabilities on b (which include O, observers exist) during our calculations. I think this is flat-out wrong: Yes, O is important data (the existence of intelligent life) in any discussion about fine-tuning, but we should treat it like other data using Bayes theorem. Before I address why I think this is the case I want to touch upon some consequences of adopting your stance which relates to our past discussion.
Misunderstanding 1:
The first misunderstanding I hope to clear up relates to basic probability theory:
Tim Hendrix: My second point is that p(FT|A) = 1 has nasty consequences and I don’t think it is compatible with other things stated in TEC. … notice that for ANY events F, A, X where p(AX) > 0 (X is compatible with A) it holds that
IF p(F|A) = 1 THEN p(F|A.X) = 1
(try to draw a Venn diagram to see this is the case)
RC: That’s only if F entails X. Draw a Venn diagram to see this is the case.
It’s possible to have X without F. It’s possible to have X without A. It’s therefore possible to have X without A and F.
So I’m not getting your point.
What I wrote, if IF p(F|A) = 1 THEN p(F|A.X) = 1 for any X compatible with A: p(AX) > 0, is a not a philosophical point or anything but just a matter of basic probability theory. A proof:
Suppose p(F|A) = 1 then p(~F|A) = 0. It follows p(~F.A) = 0 and so p(~F.A.X) = 0 for any event X. In this case: p(A.X) = p(F.A.X) + p(~F.A.X) = p(F.A.X)
It follows that if p(A.X)>0 then p(F|A.X) = 1.
So I hope we can now agree on this point going forward. If you for one reason or another do not trust the above proof then Jaynes discussed the exact same point in Chapter 2 equation 30 (http://bayes.wustl.edu/etj/prob/book.pdf).
The reason why this is important is that it reveals some difficulties with your assumption which I tried to point out:
Nasty consequence 1:
Tim Hendrix: So my point is then that if we assume p(F|A) = 1 as you claim, then for any other naturalistic theory for how the universe came about such as “T: There is a single universe and the laws of our universe are randomly selected from all (say) 10^500 string theories without supernatural intervention” we have that p(F | A.T) = 1.
Your response:
Richard: Seriously?
Did you not read my point about P(I will die|atheism)?
It’s rude not to pay attention, and to ignore my rebuttals and repeat the same argument I just rebutted.
Please don’t do that.
Well, yes seriously :-). Its right there in the math, if you just replace X with T you get p(F|A.T) = 1 as a matter of simple algebra. That is, under the assumptions you are working under, if atheism is true then for *ANY* particular theory for the fine-tuning of the universe no matter how incidental fine-tuning appears to be in that theory (for instance our laws of nature are selected randomly from 10^500 theories) then the probability of fine-tuning is 1. p(FT|A.T) = 1.
So my point is that under your assumptions, that we must always condition on O or simply just the statement p(F|A) = 1, we cannot state that fine-tuning is unlikely at all. All papers written on fine tuning which allows some chance of fine-tuning or says life-permitting universe are somewhat unlikely are disproven with one swoop– can you see why this is worrying?
As to your example, I simply don’t see why it is relevant which is why I didn’t mention it. In the example “I will die” appears on the left-hand side of the probability and not on the right-hand side as T does.
Nasty consequence 2:
If we adopt the view we should necessarily condition all probabilities on b which include O, what is then the probability that intelligent observers exist based on any world-view or theory T which is consistent with intelligent life arising at all? Well obviously:
p(O|T.b) = p(O|T.O.b’) = 1.
So on any theory, the chance of there being intelligent life in the universe is 1. But this is absurd! Intelligent life evolving is a chance event, both because evolution is based on chance and because life can go extinct due to disasters. So there is a chance –even if it is just very very very small— of no intelligent life coming about in the life-time of our universe. But the view you take, that we should condition everything on b (and that b must include O) is in contradiction to this.
Nasty consequence 3
As to your lottery discussion, my point is how on your view we should quantify the information you yourself introduced in TEC:
L = “a kind of life-bearing universe exists whose odds of existence without a God are 1 in 101’000’000”
I would normally write this as
P(LP | A) = 1/101’000’000
Or to be more exact:
P(LP | A.b’) = 1/101’000’000
However now that you have adopted the principle we should condition everything on b (which include that there is life) then it would appear there is no longer a way to quantify this piece of information since all we have to work with is p(LP|A.b) which is clearly equal to 1 per my previous discussion (if we assume observers exist then the universe must be life permitting). Yes I think your lottery example is correct, but it is not answering my point: How do we express L as a statement about probabilities if we *must* condition on O as you state?
Addressing the argument
Regarding the argument why we should condition everything on b (which must include O):
If you take O out [of b], you have no observation (you are defining the condition as lacking any observations, and conditioning all probabilities on nothing ever being observed)…i.e. the probability of any observation is literally exactly zero. Not close to zero. Not vanishingly small. Zero. Full on. Zero.
But we do observe stuff. So any equation conditioning on nothing being observed is false. For us, anyway; it could be true for non-existent observers in observerless universes which will never contain observers, but we aren’t them—we know this with 100% certainty; indeed, unlike G or A, this is the one thing of which we are absolutely 100% certain…not close to 100%; full on actually 100%.
That’s why you can’t take O out of b. As I explained in the note on Collins. Just as you can’t take “logic” and “mathematics” out of b, and then use BT to argue up is down and black is white.
Come on, it is fundamental in Bayes to condition on counterfactuals. Obviously for any hypothesis H yes we SHOULD condition on b which include O to begin with however we can always perform the decomposition:
p(H|b) = p(H|b’.O) = p(H.O|b’) /p(O|b’) = p(O|H.b’)p(H|b’)/p(O|b’)
In which case p(H|b’) is not conditional on O – denying this is just denying the basic rules of probability theory. Regarding the reasoning behind this:
“RC: If you take O out [of b], you have no observation (you are defining the condition as lacking any observations, and conditioning all probabilities on nothing ever being observed)”
This is fallacious. When I do not condition an expression on O (for instance p(H|b’), it is not the case that I am conditioning all probabilities on nothing ever being observed. I am simply not conditioning ON there being any observers, not asserting the universe is devoid OF observers. You see the difference?
RC: If you want to make statements about the universe we are in, you have to have O in b. O may be the only thing in b. But it can’t be gotten out. Because taking it out converts the equation into a statement about universes we aren’t in.
I remain beyond puzzled by these statements. For instance if I compute the probability of the rings around saturn forming, I can very well do this without conditioning on there being observers in the universe, or I can condition it on knowing there is no intelligent life in the universe – the probabilities would come out all the same since humans were not involved in making the rings.
Tim Hendrix: Finally why is p(A|O.b’) = 0.75? this is just declared in the beginningg of the chapter of TEC but without an argument, at least an argument conditional on O.
RC: WTF? How do you imagine three whole pages of argument (pp. 282-84) as being “without an argument”?
And why do you think it isn’t conditional on O? When in fact it’s explicitly conditioned not just on O, but a described array of background observations, which entail O?
If starting a discussion about whether the existence of fine tuning and intelligent life gives evidence for God by asserting: Given the universe contains intelligent life, the non-existence of God is three-times as plausible as his existence is not a wafer-thin distance away from the fallacy of affirming the consequent then I don’t see what is. Regarding the argument in TEC, it is in the main the observation we do not see Gods design a whole lot but humans do. Now I agree this is an important observation and the prior probability of Gods existence is likely not high, but the prior in this context is p(G|b’), NOT conditional on O (the existence of intelligent life) which is the very thing fine-tuning arguments uses as data.
Cheers,
Tim
Adopted the stance?
That’s not a stance. That’s a mathematical requirement of Bayes’ Theorem. You just said you agreed it was. So why are you now calling it a “stance” one can choose to “adopt”?
And some data must go in b. You can’t have an empty b. For example, logic and mathematics have to be in b. Or else the theorem is invalidated. Likewise, all knowledge that cannot be false must go in b. Like that we exist.
Otherwise, you are describing a statement about a universe we aren’t in. That’s called a counterfactual. Counterfactuals are not true of factual states of affairs. If you condition all probabilities on our not existing, you are describing a state of affairs that doesn’t exist. Its conclusion therefore will not apply to us.
Again, you need to start responding to what I’ve already said in TEC. Stop ignoring the article you claim to be answering.
In this case, for instance, in note 33 (p. 412), which concludes:
In other words, you can make statements from a non-existent POV, as if you were God, looking at a bunch of universes, and talking about how many are empty, and concluding that’s how many are empty if God does not exist (forgetting for the moment that you have to be God and therefore God has to exist to be making this observation…). But you are not God, you cannot sit in some seat somewhere (that isn’t itself a universe) and look at empty universes, none of which need have people in them for you to be sitting in that seat looking. This is a POV that is wholly counterfactual. This is not the situation we are in. The situation we are in is that we are prevented from ever seeing empty universes (even if in some future time we can with technology, we will only be able to do so from within a non-empty universe or because of one). It is logically impossible to be in that seat. Therefore, any equation that assumes we are in that seat is not logically valid (i.e. you can’t condition probabilities on logical impossibilities).
So the number of empty universes is irrelevant. We will never observe ourselves in them. And we cannot condition the probabilities in BT on things that have never and will never happen. This is fundamental to Bayes’ Theorem.
Reductio ad absurdum:
Suppose p(I will die|A) = 1 then p(I will not die|A) = 0. It follows p(I will not die.A) = 0 and so p(I will not die + A + I will die of cancer) = 0 for any event X = I will die of cancer. In this case: p(A + I will die of cancer) = p(I will die + A + I will die of cancer) + p(I will not die + A + I will die of cancer) = p(I will die + A + I will die of cancer)
It follows that if p(A + I will die of cancer)>0 then p(I will die|A + I will die of cancer) = 1.
The last statement is not a conclusion that P(X) = 1. It is in fact the wholly uninteresting statement that if I die of cancer I will die. That is not a “nasty consequence.” It’s an obvious fact.
Hence my point: I have no idea what your point is.
But I think I mistook you for saying something else. So this helps…
If you mean:
p(Fine Tuning|Atheism + A Theory that Causes Fine Tuning is True) = 1, then yes.
This is like someone being rich in a world where the only way to get rich is winning a lottery.
You can observe that there is a nonzero probability no one will win and thus no one will be rich in that universe. But you know that’s out. Because you are rich. So you already know a lottery has been won. So the probability no one is rich is a counter-factual. It’s no longer relevant. Observation has already ruled it out.
So what one must do is calculate the prior probability that we are wrong that “the only way to get rich is winning a lottery.”
Hence, that’s what I do for NID.
And that’s it.
No. You can say winning a lottery is unlikely, and that it is 100% certain you won the lottery.
Those are not incompatible statements. Particularly when it is literally logically impossible to observe something (“I am rich”) without the event occurring (“I won the lottery”). Hence the note 33 point about the empty universes: how many they are is irrelevant. Likewise so is the probability of winning a lottery. If “the only way to be rich is to win the lottery” and the probability of anyone having won a lottery is 1 in 1,000,000, it is not the case that there is only a 1 in 1,000,000 chance “I am rich,” when I observe I am rich. That probability is no longer relevant to the probability that my observation is correct (that, in fact, I am rich).
No. Not “on any theory.” On any theory that allows FT when we observe we exist. You have to combine both facts. Yes, there is a probability no one would ever have existed. But that’s irrelevant when someone exists.
Just like if there were three ways (and only three ways) to get rich, and the probability of any of them happening (i.e any one or more of the three) was 1 in 1,000,000. When we observe we exist, we know we got rich by one of those three ways. So it is not the case that there is a 999,999 to 1 chance we are wrong to say we are rich when we observe that we are, simply because it’s so unlikely we’d be rich. We observe we are rich. So the unlikelihood of that is now irrelevant.
Note that we can now insert one of those three ways of getting rich to be “God made us rich.” Notice nothing changes to the conclusion.
This is the argument of TEC (and of Sober et al.).
Not my principle. It’s a fundamental requirement of BT. You cannot opt not to adopt it.
Yeah. Precisely the point of note 31. We have no relevant data to quantify the relative probability of getting a lucky universe or a lucky God. End of story. And note 31 explains why this is true for the lucky universe side. And my article here has added what I thought was obvious, that the same point holds for the God side.
So we are back to looking for some other way to determine that ratio. Some data we actually have. Hence my prior.
We don’t. L is 100%. For all the reasons explained in the TEC article, e.g. the machinegun argument (which you still don’t address).
Just as if we can’t be rich unless we won a lottery. If we observe we are rich, then the probability we got rich by winning the lottery is not the probability of winning the lottery. It is, instead, 100%.
Anything else is counterfactual and thus irrelevant to us. If we want to explain how we got rich, we cannot say “there is a 1 in 1,000,000 chance we got rich by winning the lottery, because that’s the probability of winning the lottery.” That’s false. If we observe we are rich, and you can only get rich by winning the lottery, it cannot be the case that there is a 999,999 to 1 chance you got rich some other way.
You seem not to grasp this point. All your intuitions about probability go out the window when you add the condition that an observation is impossible but for b. Once that observation is impossible but for b, when the observation is made, you are stuck with b. All probabilities must then be conditioned on that b.
You can still say “it was a 1 in 1,000,000 chance that you would be rich,” but you can’t say “there is only a 1 in 1,000,000 chance you are rich.” Because when you are observing you are rich, the probability of being right about that is not the probability of having gotten rich.
You are confusing the two. It can be true that there is a 1 in 1,000,000 chance I’d be rich and at the same time true that there is a 100% chance I am rich. You need to stop confusing those two statements as if they were the same statement. And you need to stop confusing the chance of being rich with the chance of having gotten rich because of some cause.
I’m not going to keep replying to anything else you say until you grasp this.
Because I’m tired of repeating myself over and over and over and over again.
Hi again,
Time Hendrix: B) an irrational number cannot be a frequency (a fraction of two integers)
RC: No. We just showed frequencies include a ratio of two areas. So your definition of frequency is incorrect. Not the other way around.
Only if you re-define what a frequency is: In statistics the frequency (or absolute frequency) of an event i is the number n_i of times the event occurred in an experiment or study https://en.wikipedia.org/wiki/Frequency_(statistics). I encourage you to verify this definition for yourself with any textbook on statistics
RC: Likewise frequentist statistics (which measures frequencies by placing areas under a curve in ratio to each other). So you can’t possibly claim these aren’t frequencies. When even the most fanatical form of frequentism says otherwise!
I likewise talk about dividing up “probability space,” which just means “frequency space.” The frequency with which one conclusion will turn out to be true will equal the frequency with which a photon will strike a corresponding area of a plate, for example. It’s still a frequency. And even if it weren’t, then it’s an approximation to a frequency (and the quantization state at fine resolution reveals the real frequency by permutation theory).
Integrals of curves (I assume the curve you have in mind is the probability density function of some distribution?) is a tool to assign probabilities to events (the area integrated), this is true in Bayesian and frequentist statistics. These are not frequencies as frequencies are defined as integer counts (see the Wikipedia definition or look in any textbook for instance Jaynes). Please, I think it is rather silly to keep having this discussion where I use words in statistics with their common meaning and you use them with a different meaning.
RC: I likewise talk about dividing up “probability space,” which just means “frequency space.” Just to nitpick there is no such thing as a frequency space and I think you mean ”perturbation theory” and not ”permutation theory”. At any rate, yes, we can imagine this thought experiment, but this just mean we are defining probabilities in terms of a random process. Defining probability in terms of the limit behaviour of a thought-experiment involving randomization is not adding anything new and it runs the risk of being circular.
RC: Let’s go real, and use the photons hitting a plate after passing a slot, and the quantum mechanics that explains the frequency with which photons will hit within a particular area of that plate. We can define an area of that plate equal to 1/pi (if we can’t, then 1/pi becomes meaningless again; I’m assuming you agree we can, and thus we can put two finite areas in ratio to each other equal to 1/pi). So, we would say the frequency with which photons will strike in that designated area is 1/pi. That’s a frequency. And indeed, the number of photons hitting that area vs. the remaining area will indeed converge on 1/pi as we approach infinity. Welcome to the weird world of infinities
No it’s not a frequency, it’s a limit statement about a frequency (see above). How does this definition work if we consider events which are not defined as the unit disc, but as the 20-dimensional unit ball? Quantum tabletop experiment in 21 dimensions?
RC: So, with the probability that a belief will be true when given a certain scale of evidence: such beliefs will turn out to be true (hit that area of the plate rather than the rest of the plate) as often as 1/pi (albeit at infinite runs), or else they will turn out to be true (hit that area of the plate rather than the rest of the plate) as often as whatever integer frequency 1/pi approximates to as a geometric function on a quantized space (if the plate has a smallest area and can’t be infinitely divided
There is a basic confusion about what is considered an interpretation of probability theory. Yes, you can set up the quantum experiment to converge to a number (say 1/pi), however why not use any other experiment?. What is wrong of saying: My interpretation of probabilities is that when someone says the probability of A is x: p(A)=x, that probability means that you take a cake, cut it into two pieces such that the ratio of one piece to the whole cake is x. Sure it’s not very fancy, but why is it not just as good?
The definition you consider is simply the frequentist definition of probabilities, but instead of considering the limit frequency of the actual system in question (say the probability of a die coming up heads is the limit behaviour of rolls of the die), you rather considers the limit behaviour of a fictive system (a fictive quantum tabletop experiment rigged to produce the same probability). It’s the frequentist definition of probabilities with additional difficulties, namely why this obtains normative power and how you define the fictive experiment without using probabilistic terms (randomness, etc.).
Jaynes discussed these issues extensively. Have you read Jaynes book?
Cheers,
Tim
I fail to see the relevance of your last remarks. If “these are not frequencies as frequencies are defined as integer counts” then you (you—yes, you) must then conclude 1/pi is an approximation of a frequency. It is thus a fictional frequency, but still references a frequency (it aims at indicating some integer frequency near it). Likewise with “a limit statement about a frequency.” It’s still just approximating a frequency. Which is still a frequency. It is a statement trying to get near an actual frequency, and thus stands in for that effort, and thus for that frequency. I see no point in continuing to dispute this. It’s obvious it’s frequencies all the way down. Either the frequencies themselves, or attempts to approximate them. You yourself have verified nothing else is the case.
Hi Richard,
Thank you for your response. I feel more and more we are talking past each other. The aspects of my last post I was the most interested in hearing your view upon are things you did not have time to address and I believe you feel the same for me.
As I wrote in my last post, I think our disagreements can be boiled down to one single thing and so, in the interest of getting something constructive out of this conversation, perhaps we can highlight this single thing and both commit to our respective views? If you too have limited time, please just consider what I write in this post and skip my response to the other items of your post below:
So to tend to this one single thing once and for all: I will let
b’ : background information not relating to the existence of intelligent life in the universe or fine tuning (this may be very little. Mathematics and logic perhaps)
O : That we (intelligent, observing life) exists in the universe
H: Any hypothesis.
b= b’.O (what you call background-knowledge in TEC, the combination of b’ and O).
So my main point is this: Must we condition all probabilities in our discussion on b = O.b’? Just to illustrate how we disagree:
Tim Hendrix: So the way I now understand your piece and TEC is that you have adopted the stance we should condition all probabilities on b (which include O, observers exist) during our calculations.
RC: Adopted the stance?
That’s not a stance. That’s a mathematical requirement of Bayes’ Theorem. You just said you agreed it was. So why are you now calling it a “stance” one can choose to “adopt”?
Just to make it very clear where we are in agreement: When we wish to compute the (posterior) probability of a hypothesis H, we must take all relevant background knowledge into account, and this includes O (we exists). Where I think we disagree is if we should condition ALL other probabilities on O which I believe is clearly not the case. To repeat what I think is the most central aspect of my previous post:
Tim: Obviously for any hypothesis H yes we SHOULD condition on b which include O to begin with however we can always perform the decomposition:
(eq.1:) p(H|b) = p(H|b’.O) = p(H.O|b’) /p(O|b’) = p(O|H.b’)p(H|b’)/p(O|b’)
So notice that on the left-hand side (the posterior of H) we DO condition on O (as I 100% agree with you we should) however on the left-hand side for instance p(H|b’) does NOT include O.
This brings me to my main question:
Main Question1: Do you accept that the above decomposition eq.1 –i.e. expressing p(H|b) in terms of p(H|b’), a probability which is not conditioned on O—is valid? I.e. is that something we are in fact “allowed” to do when considering the probability of p(H|b)?
I take most of what you write in your post to be an argument for saying that no, you can’t condition on just b’ (for instance have a term like p(H|b’)) and will proceed from this assumption when addressing the various arguments you lay out in your piece in support of it. Assuming this is the case I have one additional question:
Main Question 2: Do you agree eq.1 follows from the rules of probability theory? That is, if we are not allowed to use p(H|b’), this must necessarily be because of a philosophical (if you will) reason?
I will write Y1 for my view, that one answers yes to the above question (i.e. yes, we can perform the above decomposition eq. 1 and have probabilities like p(H|b’) without O) and N1 for the alternative view, no, you can’t do that in practice and from now on subscribe the view N1 to you.
If I am mistaken in subscribing N1 to you then the rest of my post is based on a false assumptions. I hope in this case you will just take the time for the benefit of me and other readers who may be confused to clarify your view on eq.1 and perhaps turn to a single additional question near the end which is then relevant (my version of the fine-tuning argument).
So turning to the rest of the post (you can skip this if you like)
First my argument for why Y1 is true: It follows from the basic rules of probability theory, hence we can always do it since we believe these rules are true. Mind we don’t have to do it (like we don’t have to perform any given calculation) but there’s no problem in doing it.
Secondly, when we address fine-tuning arguments, we should treat O (the existence of intelligent life) as important data since this is what the fine-tuning argument directly addresses. Hence p(G|b’) is the proper prior for (for instance) Gods existence: The probability God exists without committing to the existence of intelligent life or not. Keep in mind I 100% agree with you that p(G|b’.O.D) is the relevant quantity to compute – if God exists given intelligent life exists and other data D—but this is just saying there is a difference between a prior and a posterior and a prior should not take all data into account.
Addressing your arguments:
RC: You can’t have an empty b. For example, logic and mathematics have to be in b. Or else the theorem is invalidated. Likewise, all knowledge that cannot be false must go in b. Like that we exist.
Otherwise, you are describing a statement about a universe we aren’t in. That’s called a counterfactual. Counterfactuals are not true of factual states of affairs. If you condition all probabilities on our not existing, you are describing a state of affairs that doesn’t exist. Its conclusion therefore will not apply to us.
This is a combination of two misunderstandings:
1) I never said we should condition on life NOT existing (~O). I said we should not condition on O. This is the difference between p(H|b’) and p(H|b’.~O) which are very different things.
2) I never said anything about ALL probabilities. Clearly the posterior should be condition on O (and all other data at hand).
3) No, we should not condition the posterior on a counterfactual, however counterfactuals arise in Bayesian computations all the time.
Regarding your excerpt from TEC and the subsequent argument:
RC: (…)you are not God, you cannot sit in some seat somewhere (that isn’t itself a universe) and look at empty universes, none of which need have people in them for you to be sitting in that seat looking. This is a POV that is wholly counterfactual. This is not the situation we are in. The situation we are in is that we are prevented from ever seeing empty universes (even if in some future time we can with technology, we will only be able to do so from within a non-empty universe or because of one). It is logically impossible to be in that seat. Therefore, any equation that assumes we are in that seat is not logically valid (i.e. you can’t condition probabilities on logical impossibilities).
It is true we should not condition on something which is logically impossible, however a description of a universe without an observer is not logically impossible. Scientists do it all the time! I just did it!. It’s counterfactual, true, but I can also imagine the probability there would have been a nuclear war if Hitler had lost the second world war: p(WW3 | Hitler Lost). This too is entirely counterfactual, but not impossible at all.
Just to point it out again, notice conditioning on a universe without an observer is p(H|b’.~O) and not p(H|b’) which is the prior I am discussing.
Relating to my discussion of the statement p(FT|A) = 1 implying p(FT|A.T) = 1 (for any theory T), I take it that when you accept N1 you really mean by p(FT|A) = 1 that p(FT|A.b’.O) = 1 –as I have stated many times I agree with this conclusion. My point is that in order to express fine tuning being unlikely on atheism, we must talk about the probability:
P(FT|A.b’) = 0.001 (say)
Notice this statement does not condition on O and if we did we would immediately conclude p(FT|A.b’.O) = 1. I pointed out that if you believe all probabilities are conditional on O (N1), then we can’t express this probability anymore. So what are we to make of it? You wrote:
RC: No. You can say winning a lottery is unlikely, and that it is 100% certain you won the lottery. Those are not incompatible statements. Particularly when it is literally logically impossible to observe something (“I am rich”) without the event occurring (“I won the lottery”). Hence the note 33 point about the empty universes: how many they are is irrelevant. Likewise so is the probability of winning a lottery. If “the only way to be rich is to win the lottery” and the probability of anyone having won a lottery is 1 in 1,000,000, it is not the case that there is only a 1 in 1,000,000 chance “I am rich,” when I observe I am rich. That probability is no longer relevant to the probability that my observation is correct (that, in fact, I am rich).
I agree that the two statements are not incompatible and I have never disagreed with that point. They are the statements:
P(I won the lottery | I am rich . b’)
And
P(I won the lottery|b’)
My point remains however that if we insist we should condition on O (I am rich in the above analogy), you can no longer express p(“I won the lottery”|b’) since this does not condition on “I am rich”. Likewise I agree there is no contradiction in saying p(FT|A.O.b’) = 1 and p(FT|A.b’) = 0.00001; but if we accept N1 we can’t have the last equation and so we can’t express fine tuning. Did that clarify my point? Otherwise please shut me up once and for all by simply state symbolically how you would express that fine-tuning is unlikely assuming N1:
p(PLEASE FILL OUT THIS) = 0.0001
My next example was illustrating the same point and if you answer the last question in the above you will shut me up for once about this example too.
Regarding N1:
Tim Hendrix: However now that you have adopted the principle we should condition everything on b …
RC: Not my principle. It’s a fundamental requirement of BT. You cannot opt not to adopt it.
Please see eq.1 where it is evident you can have p(H|b’) (no conditioning on O) even if we insist we should always condition the posterior of H on O. I do not see why it can be called a fundamental requirement as I have never seen it expressed anywhere and it contradicts basic probability theory.
Regarding N1:
Tim Hendrix: …then it would appear there is no longer a way to quantify this piece of information…
RC: Yeah. Precisely the point of note 31. We have no relevant data to quantify the relative probability of getting a lucky universe or a lucky God. End of story. And note 31 explains why this is true for the lucky universe side. And my article here has added what I thought was obvious, that the same point holds for the God side.
So we are back to looking for some other way to determine that ratio. Some data we actually have. Hence my prior.
Wait a second – are you now abandoning N1 and saying we should only adopt it on pragmatic grounds? If we don’t have any information regarding a proposition, we should just assign a probability of 0.5 of it being true. Hence p(A|b’) = p(G|b’) = 0.5. I even believe this is stated in PH.
Tim Hendrix: Yes I think your lottery example is correct, but it is not answering my point: How do we express L [L = “a kind of life-bearing universe exists whose odds of existence without a God are 1 in 101’000’000”] as a statement about probabilities if we *must* condition on O as you state?
RC: We don’t. L is 100%.
For all the reasons explained in the TEC article, e.g. the machinegun argument (which you still don’t address).
Just as if we can’t be rich unless we won a lottery. If we observe we are rich, then the probability we got rich by winning the lottery is not the probability of winning the lottery. It is, instead, 100%.
Anything else is counterfactual and thus irrelevant to us. If we want to explain how we got rich, we cannot say “there is a 1 in 1,000,000 chance we got rich by winning the lottery, because that’s the probability of winning the lottery.” That’s false. If we observe we are rich, and you can only get rich by winning the lottery, it cannot be the case that there is a 999,999 to 1 chance you got rich some other way.
You seem not to grasp this point. All your intuitions about probability go out the window when you add the condition that an observation is impossible but for b. Once that observation is impossible but for b, when the observation is made, you are stuck with b. All probabilities must then be conditioned on that b.
(…)
I’m not going to keep replying to anything else you say until you grasp this.
Because I’m tired of repeating myself over and over and over and over again.
But if we can’t express L using probabilities (I agree 100% we can’t if we accept N1), then the statement in TEC about probabilities is impossible to utter right? I mean this goes back to my previous point that if we adopt N1, then we can’t express fine-tuning being improbable on atheism (p(FT|A.b’) = 0.0001).
As to the machine-gun analogy, Luke Barnes and I are in 100% agreement. You simply assign values to a posterior and this does not accurately reflect the knowledge you would normally have if you go in a room, the machine gun fires at random, and you survive because all shots miss you. I will be happy to write this up but it is essentially just a restatement of what Luke wrote.
I sense your frustration of going over the same point again and again and please believe me I do get what you are saying (i.e. that if we adopt N1 all statements about fine tuning are with probability 1 since we must assume they are conditional on life existing, p(FT|A.b’.O) = 1), but this is in turn not my point. So let’s agree to leave this matter side and focus on the central matter N1?
Cheers,
Tim
Ps.
My “last question” if you contrary to my assumption do not agree with N1. My point is simply what I have stated previously, we can compute the probability on Gods existence or non-existence given fine-tuning and that we exist as:
P(A| O.FT.b’) / P(G| O.FT.b’) = p(O| FT.A.b’) p(FT|A.b’) / [p(O| FT.G. b’) p(FT|G..b’)]
(so the question is if we can do this) Where it is assumed Gods existence or non-existence is equally probable (p(G|b’) = p(A|b’)) a-priori. So if we assume fine-tuning is a-prior quite unlikely on atheism (p(FT|A.b’)=low) whereas God is quite likely to fine-tune for life since his intention is to bring forth life or whatever (p(FT|G.b’) =high) and the universe proceeds after natural laws after big bang/creation:
p(O| FT.A.b’) = p(G| FT.A.b’) (approximately)
Then the above would provide an argument in favor of Gods existence. Now I don’t agree with the conclusion of this argument on various grounds, but it shows we can’t conclude FT and our existence is evidence against a God or necessarily neutral as the argument in TEC assumes.
Then you are the one talking past my article.
I am talking about what my article says. If you aren’t talking about that, you are wasting everyone’s time here.
There are three points you keep failing to get. And until you get them, conversation is pointless on this.
POINT ONE: You cannot get rid of O. Because you have to condition statements on what is true, not on what is false. To wit:
No. O is not “in combination” with b. O is in b. Just like logic and mathematics.
Because you cannot condition a probability on there being no observations.
Because we are observing.
Thus, to make statements about us you have to condition all probabilities on our existing.
Period.
Just as, again, if we are rich, and the only way to get rich is winning a lottery, we then have to condition all probabilities on our already having won the lottery.
Period.
You can talk about the differing probabilities of winning different lotteries. But that we won one is 100% certain. No probability conditioned on “we didn’t win any lottery” can be true for us when we observe we are rich—unless there is some way to get rich other than winning a lottery. Which is the prior. But that has to be calculated some other way. And you can avoid even that by simply allowing that all possible ways are “lotteries” in their own right (of different kinds, e.g. the lottery for getting a God, the lottery for succeeding at business, etc.). So you can talk about the relative probabilities of winning one of them, but you can’t talk about our not having won one. Because it is then logically necessary that we did. Otherwise we wouldn’t be rich.
And that’s why, if one lottery (“getting the right Big Bang lottery”) is 1 in x chance of making us rich / making observers and another lottery (“getting the right God lottery”) is also 1 in x chance of making us rich / making observers, then the prior probability we got rich / became observers by “getting the right Big Bang lottery” is 0.50, not 1 in x.
If you don’t understand this, you don’t understand probability.
-:-
POINT TWO: When something is logically necessary, the probability of it being false is 0. To wit:
Not when logical necessity is at hand, when probabilities are 0 and 1.
Because P(O or ~O) = P(O) + P(~O), thus where FT = “Fine tuning is observed,” P(FT|O+A or ~O+A) = P(FT|O+A) + P(FT|~O+A). P(FT|O+A) = 1 (because if O and A, you can never observe ~FT). So already we know P(FT|~O) has to be 0 (unless you don’t know how probability works). But in case you don’t know how math works, we can also know P(FT|~O+A) has to be 0 because if there are no observations, then “Fine tuning is observed” is always false (because nothing can be observed if there are no observations, not even FT).
-:-
POINT THREE: The unlikelihood of a thing happening is not the probability that it happened once it is observed. Once it is observed, you have to explain (A) how it happened, not (B) what would be true if it didn’t.
It does not matter that there could have been worlds without observers or how many such worlds there could have been. Just as it does not matter that there could have been a world with no rich people in it or how many such worlds there could have been. If the only way to get rich is x, then when you observe you are rich, the probability of having gotten rich by x is always 1. No matter how unlikely x is—in other words, no matter how many possible worlds lack x. You simply aren’t in that world. So statements about that world are irrelevant to you.
-:-
I’m again not answering any more of your wall of words until you grasp these three points.
RC: I fail to see the relevance of your last remarks. If “these are not frequencies as frequencies are defined as integer counts” then you (you—yes, you) must then conclude 1/pi is an approximation of a frequency. It is thus a fictional frequency, but still references a frequency (it aims at indicating some integer frequency near it). Likewise with “a limit statement about a frequency.” It’s still just approximating a frequency. Which is still a frequency. It is a statement trying to get near an actual frequency, and thus stands in for that effort, and thus for that frequency. I see no point in continuing to dispute this. It’s obvious it’s frequencies all the way down. Either the frequencies themselves, or attempts to approximate them. You yourself have verified nothing else is the case.
1/pi is not an approximation to a frequency, it is a real (irrational) number. I ofcourse agree we can approximate it arbitrarily well with fractions, but it is still an irrational number.
Now to my main point, the definition of probaiblity in PH is:
They [Bayesian] are talking about the frequency with which beliefs of a given type are true, where
of a given type means backed by the kind of evidence and data
that produces those kinds of prior and consequent probabilities. For
example, if I say I am 95% certain h is true, I am saying that of all
the things I believe that I believe on the same strength and type of
evidence as I have for h, 1 in 20 of those beliefs will nevertheless still
be false
this definition rests upon a finite frequency of something concrete (the things I actually believe on a given strength of evidence). If we make a move towards a limit statement about a quantum apparatus which approximates 1/pi in some manner by shooting particles against a disc then this definition is quite different than what you have above. It is as I see it just a way to write up the number 1/pi in a complicated way and not a definition of what a probability is. Imagine for instance what the above definition would look like if we did not consider a 2D disc but a 20-dimensional ball (this is trivial to write up in with the Kolmogorov axioms so these events too exists).
As I see it the view you take then becomes more or less:
1) Reason as we are Bayesians, i.e. assign probability to one-of events like the existence of Jesus
2) When talking about probabilities of e.g. it raining tomorrow, use the definition of PH
3) Adopt a frequentist-inspired thought experiment when we talk about general probabilities (when you think about a probability of 1/e, 1/pi, 1/sqrt(2) or whatever, imagine the following quantum apparatus that if run for an infinite time would compute the number 1/e, 1/pi, 1/sqrt(2), ….
This is not in my view an interpretation of probabilities, it is not even a clearly specified attempt at a definition. You can feel free to disagree, once again I very strongly recommend you to read Jaynes or Hayek or some other proper treatment of Bayesian epistemology. At the very least I utterly fail to see how it can be claimed all interpretations of probabilities should be superseded with the above sketch.
But when you have an infinite number of them, all bets are off. This is exactly like darts hitting a dartboard. Or photons hitting a plate. Beliefs hitting the truth. It’s all based on a ratio of areas where they can hit or miss.
So you have a choice. You can admit that a dart/photon/belief can hit 1/pi places on a target area, and thus admit 1/pi is a frequency. Or you have to concede that a dart/photon/belief cannot hit 1/pi places on a target area, because it must hit an integer amount, in which case you are conceding 1/pi is an approximation to the actual number of places the dart/photon/belief can hit. In which case you are agreeing 1/pi is a frequency approximator.
Those are your only two options.
Either one is a frequency or frequency estimate.
So you have a choice. You can admit that a dart/photon/belief can hit 1/pi places on a target area, and thus admit 1/pi is a frequency. Or you have to concede that a dart/photon/belief cannot hit 1/pi places on a target area, because it must hit an integer amount, in which case you are conceding 1/pi is an approximation to the actual number of places the dart/photon/belief can hit. In which case you are agreeing 1/pi is a frequency approximator.
Those are your only two options.
It is not true to say there are 1/pi “places” on the plate since “place” indicate an integer amount. Anyway, third option:
Bayesianism: I can say I have a degree-of-belief of 1/pi that the photon will hit the plate. Full stop. No photon cannons required, no limits, no quantum mechanics, no thought-experiments, no nothing like that.
It’s that simply. What is the matter with this perspective? Just read the first two chapters of Jaynes (or Cox original piece) to see why this definition has normative consequences for how probabilities transform (i.e. the rules of probability theory, I am sure you are going to like it.
I can try to explain this if you are interested, but I think it would be much more helpful to read Jaynes (the first chapters are freely available online, i linked them previously) as his explanation is bound to be superior to mine.
That’s precisely the question: in geometry where there are infinite places to hit (which is how we get results like 1/pi, by exhaustion of infinite sums), we can get results like 1/pi places to hit. Or else we can’t. So either we can (frequency) or we can’t (frequency approximator). No other option.
Tim Hendrix: I can say I have a degree-of-belief of 1/pi that the photon will hit the plate. Full stop.
No. Because that’s meaningless. What does it mean to say your degree of belief is x rather than y?
It can only mean one thing (as I prove in PH): that you will be right x amount of the time rather than y amount of the time (and indeed time can be geometrically divided, just like a plate, and thus you can have a 1/pi amount of time). Think it through. You’ll realize this is necessarily the case. You can also prove it by showing how you change your “degree of belief” when you get more information about the actual frequency of the thing you are talking about…notice where the delta trends.
But more directly to the actual scam you just tried to run:
When discussing explanations on an area of a plate, you can’t avoid the only two options by inventing something that doesn’t even correspond to an area of a plate. That tells me you don’t even know how logic works.
P.S. Maybe you don’t realize “I can say I have a degree-of-belief of 1/pi that the photon will hit the plate” is not a valid statement in our discussion. We were talking about the probability that the photon will hit one part of the plate rather than another. Not whether the photon will hit the plate at all. That is what QM calculates: the probability that a photon will hit area A of the plate rather than area B. And it can get a result like 1/pi, as the size of area A (and 1 – 1/pi is the size of area B). So the probability that the photon will hit area A is 1/pi. And it is so only because the area is being divided. Not because you have a hunch. You can only have a degree of belief that the photon will hit area A, that somehow magically exactly corresponds to the geometric ratio of areas A/B, if you are admitting area ratios are frequencies and your degree of belief is anchored to the resulting calculated frequency of where a photon will hit a plate.
Richard: Don’t get me wrong, I am sympathetic to your view probabilities should refer to frequencies, it is very intuitively appealing but it has a lot of downsides and inconsistencies that people discovered in the second half of the second century. It is tempting to try to fix these by ad-hoc measures and thought-experiments, but try to read e.g. Jaynes to see how much simpler these are treated under a Bayesian framework.
See my last P.S. about Quantum Mechanics. Jaynes is irrelevent. You are the one who isn’t paying attention here.
Everything Jaynes said is translatable to what I am saying. That is in fact exactly what I show in PH. You won’t grasp that until you grasp what I just said about Quantum Mechanics and area ratios and frequencies of photons hitting designated areas.
Barnes certainly dealt with your claim that you can’t take “observers exist” out of the background information. He showed quite clearly why that claim is wrong in his fourth post.
First, terms in Bayes’ theorem ignore things we know for sure all the time. I mean “all the time,” literally, as in literally every time we use it. When updating the posterior probability after learning some proposition e is true we use the term p(e|h.b) which is not conditioned on e (of course) despite the fact that we have learned it is true. Since o (observers exist) is just a specific case of evidence your claim looks dubious already. I’m sure you’ve encountered people making this very mistake with e that you are making with o. They think that once e has been observed that p(e|h.b) becomes equal to 1.
Your view of the propositions in our model as some kind of infinite whack-a-mole game, where every time we try to partition o into the evidence bucket it reappears in the background bucket, has no basis in the mathematics of probability. In fact, as Barnes points out our “buckets” are just arbitrary labels. We can partition the propositions however we like to, hopefully, get terms we can estimate. There is nothing special about the background bucket to induce this whack-a-mole game.
Which brings us to another point Barnes’ makes which is that p(~NID|b) can always be factored into two terms such that, even though the final result does depend on observers existing, the intermediate terms do not. And, again, there is nothing wrong with that (just as there is nothing wrong with p(e|h.b) not conditioning on e). So you are wrong that you can just make the low probability of o obtaining in the first place disappear.
Now above, you make the point that we would have to know how likely it is for God to make life so we have something to compare the small number to. That is a sound point but it is a different point as well. You have been pretty adamant that no matter how unlikely life is under naturalism it doesn’t matter… at all… EVER.. as a matter of principle. This is false. It could matter if someone produces a convincing argument that God would want to create life (and as I’m sure you are aware several philosophers/theologians have tried to do just that).
For a more intuitive way to understand Barnes’ point just imagine taking fine tuning to its limits. Let’s say we have concluded (like you did, correctly) that if life exists in a naturalistic universe then the laws of physics will be life friendly (by definition). But lets say we also discovered, somehow, that life was impossible through merely naturalistic means. Life exists. What would be the probability naturalism is true now?
Obviously it would be zero. Something exists that is incompatible with it. But, according to your principle, we can never take account of the fact that p(o|n)=0. Somehow the fact that if naturalism is true then life friendly physics is guaranteed has blocked us from considering it . At least that’s what you’ve said when p(o|n)>0 and there is nothing special about zero so… ??
If Bayes’ theorem requires your principle about o and can’t come to the correct conclusion here then, well, R.I.P. Bayes’ Theorem . As you know Bayes’ Theorem is supposed to reduce to propositional logic.
If naturalism then no observers are possible,
observers exist,
therefore naturalism is not true
That is clearly a correct conclusion. Adding “if naturalism is true then physics will be life friendly” does not change that conclusion. Your usage of Bayes’ Theorem ought to be able to handle that or you’ve gone wrong somewhere.
Einniv:
I’ve already addressed all this. Even to Barnes. But now again here.
Go back up the comments thread and read my replies to Hendrix. In fact, I highly recommend you start with one of the last ones here.
From there up, you’ll find I’ve already answered all these claims. Indeed I already did in my TEC article. Barnes just ignored everything I said. But here again I’ve made everything even clearer.
And Barnes has developed no intelligible reply. Nor yet have you.
(And I’ll remind you, we are talking about the work of several expert mathematicians, who arrived at these conclusions twice independently of each other. I’m just the messenger. You seem to think I’m making this up on my own.)
Richard: I look forward to responding to your post later.
However the two main questions in my previous post, main question 1 and 2, I would be very interested in your answer. Where do you stand on them?
May last three-point comment is my response.
The window is about to close (my comments lock after six days). So if you still think those three points can be refuted (you need to refute them with the lottery example first; if you can’t, then you can’t in the the design case, because the God lottery and the Big Bang lottery are just two lotteries), you will need to continue privately by email. But my patience is running thin. No more stalling with long winded digressions. Prove the lottery argument wrong on the three points. Otherwise, concede.
Update: The debate continues.
Dear Richard,
I generally admire your sound reasoning, but I think the article by Michael Ikeda and Bill Jefferys you cite here, “The Anthropic Principle Does Not Support Supernaturalism” is seriously flawed. The authors immediately go one step further than what the title suggests by claiming that the fine-tuning argument even counts against a supernatural origin of the universe. This must be false.
The argument rests on a definition of “life friendly” that is misleading and ambiguous. According to the authors “life friendly” is defined as: “the conditions in our universe (such as physical laws, etc.) permit or are compatible with life existing naturalistically.” I would propose that a fair definition of life friendly omits the last word (“naturalistically”) and includes supernatural laws: the conditions in our universe (namely physical, naturalistic laws as well as supernatural laws) permit or are compatible with life existing. Sound reasoning about naturalism and supernaturalism implies that nothing can be derived about mere life friendliness from naturalistic life friendliness and fine-tunedness alone. A universe that is fine-tuned and naturalistically life friendly but supernaturalistically life unfriendly, is not merely life friendly. For example, a supernatural law might destroy life at its origin. On the other hand, a universe that is not naturalistically life friendly, but supernaturalistically life friendly might very well be life friendly, as believed by many creationists and intelligent design proponents. It is very well possible that intelligent life in our universe requires a combination of naturalistic fine-tuning, and supernatural interventions to overcome certain unlikely steps in a Darwinistic evolution.
If the authors really wish to equate “life friendly” to “naturalistically life friendly”, then they should be very careful to stick to that definition. However, they fail to do so. I cite: “the observation that our universe is “life-friendly” (can never be evidence against the hypothesis that the universe is governed solely by naturalistic law.)”, and also: “(the probability that naturalism is true,) given the observed fact that the universe is “life friendly””. In what sense do we observe that the universe is naturalistically life friendly? This seems an impossible type of observation. Given that abiogenesis is not yet understood, let alone probabilistically computed, no scientist can rule out the possibility that some supernatural help was required for us to exist. So in these cited statements, the authors are suddenly using my proposed definition of life friendliness. I conclude that the whole argument rests on an ambiguity.
Nevertheless, I wish to thank you for nicely gathering the evidence against theism and supernaturality.
Best regards,
Ward Blondé
No, they’re right. Supernaturally caused universes don’t need to be finely tuned. Naturally caused universes do. The inevitable logical consequence of that fact is that fine tuning is always evidence against supernaturalism. They’re right.
You are confusing “can’t rule out” with “argues for”; but also, you are confusing the fine tuning argument with the abiogenesis argument. We actually have fairly good calculations on the lower bound probability of natural biogenesis. It’s well within parameters for this universe (I’ve even published a peer reviewed article on that, in the journal Biology and Philosophy; natural biogenesis on present evidence must have a probability greater than 1 in 10^42; the statistical threshold for our universe at size and scale, is 1 in 10^150; some sort of natural biogenesis within it is therefore guaranteed). The fine tuning argument is not an argument from abiogenesis, but from the physical parameters necessary to make biogenesis likely without intelligent intervention. That our universe is so tuned is already an accepted fact. Hence abiogenesis is a long dead argument. And apologists, who know what they’re talking about, thus have moved to fine tuning. But that then runs into the problem Ikeda and Jeffreys found (also independently discovered by Sober).
In short, biogenesis is not a problem for naturalism. Once we are given the present universe (and its observed age, size, and constants), the probability of at least one natural biogenesis event in it by now is as near to 100% as makes all odds. And there is no evidence otherwise. So the fine tuning question remains. Enter Ikeda & Jeffreys and Sober.
They are only addressing fine tuning. If you were to argue that science is wrong that natural biogenesis is likely on present tuning, then you are arguing fine tuning doesn’t exist, which is a completely different argument. One they were not tasked with addressing.
Dear Richard,
I think you are accusing me of the error that your camp is making when you say that I confuse “can’t rule out” with “argues for”. I haven’t even expressed my own opinion about whether finetuning rules out, argues for or leaves supernaturalism as it is. You and the authors of the article are making this ternary option into a binary option: if it doesn’t argues for, it must be ruling out. I only expressed that this reasoning is false. My personal opinion is that finetuning has no impact at all on the question whether there are supernatural laws. But it certainly doesn’t rule it out.
But since you do not admit the error and give an explanation about abiogenesis, you should be able to answer the following question:
using the definition of life friendly in Michael Ikeda and Bill Jefferys’ paper, can we observe that the big bang universe is life friendly, without using any knowledge about abiogenesis?
This question has two different answers, depending on the ambiguity of their usage of life friendly.
Best regards,
Ward
No, they are all arguing for probability, not “ruling out.” Their argument is Bayesian, not deductive.
As to the facts, I don’t know what you mean by “without using any knowledge.” Of course we should use all the knowledge we have. No correct probability can arise, if we exclude facts from the givens that generate that probability. And that self-replicating strings of amino acids exist that are simple enough to have a known probability of spontaneous assembly of better than 1 in 10^42, and we know the number of spontaneous events in the known universe cannot be less than 1 in 10^150, the probability of spontaneous life arising naturally in the universe is as near to 100% as makes all odds. That’s what fine tuning is then invoked to explain. You can either deny that fine tuning exists (in which case you are no longer responding to Ikeda et al. because they are working from the given premise that it does), or accept that it does (in which case there is no argument from biogenesis for supernaturalism; there can only be left over an argument from fine tuning for supernaturalism, which Ikeda et al. prove fails because the probability goes the other way). And even if you straddle A and B, you still are not answering them, because you are neither operating from the same premise their paper is predicated on, nor addressing what conclusion they reach from that premise.
Hi, Dr. Carrier. Just wanted to make a suggestion.
Years ago, you said
IMO, this needs to be pushed more when refuting the fine-tuning argument. You kinda touch on this point in The End of Christianity when you said “Think of getting an amazing hand at poker: whether the hand was rigged or if you just got lucky, the evidence is identical. So the mere fact that an amazing hand at poker is extremely improbable is not evidence of cheating. Thus “it’s improbable” is simply not a valid argument for design”, but I really think this is the main issue that people are interested in with this argument. The WAP (Weak Anthropic Principle, not the Cardi B and Meg song) explains why conscious observers in all natural universes will observe fine-tuning, as you often point out, but not why there are conscious observers at all. That first quote is the heart of the problem with the argument, and should be emphasised more.
Not to tell you how to do your job tho, just to be clear. Just recommending it so that when we discuss these things with believers, we can get at the real issue.