Christian historian Dr. Wallace Marshall and I are debating whether or not enough evidence points to the existence of a god. For background and format, and Dr. Wallace’s opening statement, see entry one. For subsequent entries, see index.
This time we are still focusing on the Kalam Cosmological Argument: in response to Dr. Marshall’s latest response, due to limitations of space I will here summarize only the essential points I think need to be acknowledged.
That the Evidence Points to Atheism (IV)
by Richard Carrier, Ph.D.
I hope Dr. Marshall will acknowledge the following.
Noting a Logical Impossibility Is Not Begging the Question
In the absence of anything to realize any physical laws (and it does not matter whether physical things need exist or not to do that), no physical laws will exist. Including causal laws. So the first cause cannot be governed by such a law. Because it is a logical contradiction to claim causal laws exist before causal laws exist.
Similarly, it’s a logical impossibility to exist nowhere and still exist, or to never exist and still exist. These are directly contradictory claims. Mathematical objects, for example, insofar as they even exist, certainly cannot exist “before” time any more than they could exist north of the North Pole.
Actual Infinities Are Not Impossible
Marshall has cited no living mathematician, expert in transfinite mathematics, who says actually infinite quantities can’t exist in reality. I have cited nearly a dozen who concede they can. Including all of Marshall’s own cited sources.
As I noted (in my last and previous replies), Marshall’s “position is refuted in the very introduction to the collection of essays Dr. Marshall cites.” I also explained how Marshall is misunderstanding a quote lifted from Herb Silverman; as I confirmed with Silverman himself. I even double checked; Silverman concurs, “the concept of infinity could have been created by human beings, but that doesn’t mean there can’t be actual infinities,” but rather that “there [is] no real number ‘infinity’ that can be treated as other real numbers.”[1] Just as all my other cited sources confirm.
Infinity only produces paradoxes when we incorrectly assume it conforms to the axioms of finite arithmetic. Zeno made the same mistake when he used paradoxes to argue movement is impossible. He was wrong. Marshall is likewise wrong.
All living experts agree it’s not valid to argue that because infinite quantities behave differently than finite ones, therefore they cannot exist. All Marshall keeps saying is that they behave differently. He has never provided a deductively valid syllogism getting from “they behave differently” to “they don’t exist.”[2]
Even Marshall’s insistence that you have to “add up” an infinity to have one is false. If there’s no beginning, there’s no need for anyone to have started adding. If there are infinitely many places to be (as past eternality entails), it’s invalid to insist there are no places we can be. Indeed Marshall’s quotation of Oppy is disingenuous here; Oppy’s saying these absurdities are only alleged is not conceding Marshall’s argument. To the contrary, Oppy extensively refutes it.[3]
When will Marshall acknowledge this?
We Don’t Know What Precedes a Quantum Threshold
Marshall does not understand why many cosmologists disagree with the conclusions of the BGV theorem (I’ve cited several). It’s not merely that it relies on undemonstrated assumptions. It’s that one of those assumptions is known to be false: that reality can be described without quantum mechanics.
As Vilenkin explained in the very letter to William Lane Craig that Marshall previously cited:
The question of whether or not the universe had a beginning assumes a classical spacetime … [but] quantum fluctuations in the structure of spacetime could be so large that these classical concepts become totally inapplicable. … This is what I mean when I say that we do not even know what the right questions are.
Hence in Vilenkin’s response to the Carroll-Chen model, all Vilenkin actually says is that the BGV theorem proves time must still go back to a quantum instability; he does not say what may or cannot have preceded that instability.[4] He defines a beginning not as Marshall does (as the beginning of everything that ever existed) but as the timeline we are now on being “past-geodesically incomplete,” meaning, it stops at some point in the past at some kind of “quantum collapse,” beyond which we cannot know what exists or existed.[5] Because we have no theory of quantum gravity. So at that point of collapse, “we do not even know what the right questions are.” Much less what the answers are.
That’s why, for example, Sean Carroll says the BGV does not address what might precede the quantum event described in the Carroll-Chen model. All it does is establish that there was one. But quantum indeterminism entails all bets are off at that point. The BGV says nothing about that. It nowhere states that quantum instability prevents there being something else beyond that horizon. Only that this horizon must exist.
This is not addressed by Aguirre and Kehayias, whom Marshall quotes concluding “it is very difficult to devise a system … that does nothing ‘forever’, then evolves.” No one here is talking about a quantum system that “does nothing forever,” but an endless series of quantum instabilities that resolve in endlessly repeated Big Bang events, exactly as Aguirre and Kehayias demonstrate,[6] particularly in conjunction with Carroll and Chen.
Simultaneous Causation Eliminates Any Need of Transcendent Causes
Nevertheless, for convenience, even though it’s unknown, I’ll heretofore assume spacetime had a beginning in accord with the BGV theorem, which I noted Susskind demonstrated (and the BGV authors agree) entails a vast multiverse prior to and causing our local Big Bang.
As I’ve noted, the only logically possible location of the first cause is simultaneous with its effect, as Marshall concedes it may be. But that eliminates the final step of the KCM. If a first cause can exist, uncaused, simultaneous with its effect, then it is no longer the case that a seed of spacetime cannot be that cause.
Marshall is proposing the first uncaused cause is a bizarre, extremely complex entity never evidenced anywhere in science. But I, and science, propose the first uncaused cause is a singular empty point or quantum of spacetime. One or the other (god or quantum) “just exists” for no reason. But we can show that on far fewer assumptions than God requires, and on known science, a primordial point of spacetime as first cause can explain all current observation.
Quantum examples simpler and better supported exist in science.[7] I’ve elsewhere demonstrated even a completely lawless first state will produce the observed universe.[8] God is certainly not simpler than an empty state devoid of all contents and extension; yet such a state inevitably produces a random multiverse owing to its very instability: because it’s logically necessarily the case that an empty state governed by no laws inevitably spawns a random outcome among all possibilities, which are infinite in number, ergo the probability of a single state—like remaining nothing—is infinity to one against.[9]
So there is just no way to get to God here.
-:-
Such is my latest response.
Continue on to Dr. Marshall’s response here.
-:-
Endnotes
[1] Email from Herb Silverman to Richard Carrier, “Re: Marshall’s Reply” (14 May 219). Note, for reference, that in mathematical notation, infinities are categorized as the set of hyperreals, not the set of real numbers that Silverman references, because infinite quantities do not have a location on a number line.
[2] This is well explained by Louis J. Swingrover in his position paper “Difficulties With William Lane Craig’s Arguments for Finitism.” See also Wes Morriston, “Craig on the Actual Infinite,” Religious Studies 38.2 (2002): 147-66; Landon Hedrick, “Heartbreak at Hilbert’s Hotel,” Religious Studies 50.1 (2014): 27-46; Graham Oppy, “Inverse Operations with Transfinite Numbers and the Kalam Cosmological Argument,” International Philosophical Quarterly 35.2 (1995): 219-21.
[3] Oppy, “Inverse Operations,” op. cit. Even in the very book Marshall quotes, Oppy goes on to challenge that these are absurdities, not agree they are: Philosophical Perspectives on Infinity (2009), pp. 48-275.
[4] Audrey Mithani and Alexander Vilenkin, “Did the Universe Have a Beginning?” (20 April 2012).
[5] See Leonardo Gualtieri and Valeria Ferrari, “Black Holes in General Relativity” (2011), p. 7, noting that a past-incomplete geodesic means ending at an actual or coordinate singularity. That actual singularities are impossible on quantum mechanics, and thus we do not actually know what happens at (much less before) a “coordinate singularity,” see my discussion in “The Big Debate: Comments on the Barker-Carrier vs. Corey-Rajabali Team Debate” (2004).
[6] Anthony Aguirre and John Kehayias, “Quantum Instability of the Emergent Universe” (2013), p. 5.
[7] For example, as I’ve already mentioned, Lawrence Krauss, A Universe from Nothing (2012); Dongshan He, Dongfeng Gao, and Qing-yu Cai, “Spontaneous Creation of the Universe from Nothing” (4 April 2014); even, essentially, Marshall’s own cited source, Aguirre and Kehayias, op. cit., and Sean Carroll and Jennifer Chen, “Spontaneous Inflation and the Origin of the Arrow of Time” (27 October 2004).
[8] Richard Carrier, “The Problem with Nothing: Why The Indefensibility of Ex Nihilo Nihil Goes Wrong for Theists” (29 August 2018).
[9] As is fully explained and demonstrated with ten numbered propositions in “The Problem with Nothing,” op. cit., which I’ve cited in every entry in this debate.
There is no way to prove whether there is a god or not either way. Evidence is moot. One says this is evidence, another says this is evidence there is no deity. It’s an argument that will always end in a stalemate. But it sure is fun….
I disagree. Read my opening statement.
Richard, the following is my attempt to refute the claim that there is no truth to the matter of god’s existence. This has been a model of mine for a while. I would love for you to vet it and let me know how correct it is, and how it can be improved. If this is not the appropriate place then don’t post this here, but respond by email as you see fit.
Consider the purpose of knowledge. Curiosity evolved for the same reason as everything else – survival and reproduction. However, we need not speak of survival and reproduction. We can simply talk about ultimate desires (desires that are not the result of other deeper desires), knowing that they evolved for the purpose of survival and reproduction. Thus, curiosity evolved to help us fulfill our ultimate desires.
How does it accomplish this? At every moment we face a number of action options. Each option has a set of probable consequences. We use this set of consequences (and their probabilities) to assign a value to the consequence set according to how well it matches our ultimate desires. Then we compare the value of each action option and choose the option with the highest value.
The key step for this argument is our ability to move from action to consequence set. This requires an understanding of cause-effect relationships in the world around us. This is the purpose of knowledge – we use it to make predictions about the effects of our actions so that we can get the effects that we desire.
A statement such as “there exists a god who behaves exactly as though he does not exist” does not make testable predictions. There is no way to believe this statement. For to believe an idea is to use it to choose action options that maximize the value of consequences. Since this statement has no consequences, it cannot be used in this way. That is, it cannot actually be believed. Thus, it has no truth status. It is neither true nor false.
Thus, either the existence of a particular god makes predictions about observable phenomena or not. If it makes predictions then we can observe the relevant phenomenon to verify or falsify god’s existence. If it does not then the question is meaningless.
Most god ideas are falsifiable. Certainly Yahweh is this type of god. His existence has a great many implications for observable phenomena – answered prayer is but one. And this, the only meaningful type of god, is the type of god about which Carrier and Marshal are debating.
That’s all true too.
But epistemologically there is a more direct reason a rational person must disbelieve in entities like “a god who behaves exactly as though he does not exist.” Such an entity is just a sub-category of Cartesian Demon; and we must disbelieve all Cartesian Demons (absent specific evidence they really exist; meaning, not evidence they possibly exist, but probably do).
I outline why here. But in short, such entities require that a huge set of bizarre conditions be true (specific and highly unusual powers and motives), which are inherently improbable (even in their quantity, but even more so in their extreme unusuality), and no evidence they are true exists so their inherent improbability remains.
Thus, such entities start with very small prior probabilities. And when no evidence exists to raise that probability (as you note), the prior remains the posterior, i.e. the prior probability such an entity exists is simply the probability it exists. Which, being very low, means we ought not believe any such entity exists.
Has your lawlessness creates a multiverse idea been put in a peer reviewed journal? Not to use as an argument against you, just curious to read more about it.
I haven’t had time to develop it in that venue yet. But as it is a logically deductive argument, you can vet it yourself. All you need understand is basic logic. So go check it out. Find the logical flaw in it. And if you can’t, please explain why you can’t.
I guess I don’t understand how a “state” of nothing could exist. Because it seems that your argument would entail that from a “state” of nothing then came everything.
But since there is no such thing as time or space in such a state, there would be no such state. You cannot go before the beginning of time because time is logically necessary to be the beginning.
I’ve been a long time reader, and this argument is one of the most interesting things I have ever read. But it is incredibly abstract and hard to think about.
Follow the links to where I discuss these arguments. They explain what you are overlooking. You’ll find your own reasoning is close to hitting on the relevant point.
For there to have been a nothing-state, there must have been somewhere for it to be—otherwise it by definition never existed and so something has always existed. Those are the only two logically possible options.
Thus a nothing-state, if one existed, must have had a location. Therefore at least a quantum or dimensionless point of spacetime must have existed—because it is then a logically necessary being. It is also a logically necessary being in the other case, e.g. past eternality. Thus spacetime is a logically necessary being in all possible conditions. It therefore requires no explanation for its existence (at least no more than anything else, like a god, would).
And this is indeed for some of the reasons you suggest, e.g. no state or being can have preceded time; it’s logically impossible. Therefore if time was not past eternal, it is necessarily itself the first being. One need then only debate what properties it had; and if you take away all properties and contents that one can take away without creating a logical contradiction, what you have is the most nothing nothing-state that could ever have been. Since no other nothing-states can ever have been, we need not concern ourselves with them; because they are logically impossible.
Once you’ve gotten to that point, it can be shown that the resulting model entails a near infinite multiverse will arise. Which then will produce a universe like ours to near 100% certainty. All as a result of logically necessary truths.
“Similarly, it’s a logical impossibility to exist nowhere and still exist, or to never exist and still exist. ”
only in the universe.
So per Dr Carrier, unless god ixists in a place
and unless god ixists in a time zone – the ixistuns uv god is impossibl.
But if god ixistid in a place and in a time – he’d be a part uv the universe ie creation…which means he’s creatid which means he ain’t god.
I don’t no xtians but sunne muslim agree that god cannot ixist anywher or anywhen. as where / when r creatid.
ie God nesasrily ixists without place without time without size without direction etc.
All u’v dun is assurtid that god isn’t in the house- so t so speak. which no wun sed he was firstof.
fruitless strawman / aunt sally argumuntasn.
No. Not “only in the universe.” “That doesn’t exist anywhere” is synonymous with “That doesn’t exist.” Anywhere. Much less outside the universe. Likewise “that has never existed” means, literally synonymously, “that does not exist.” There is no more way to exist before time existed than to exist north of the North Pole. It’s a logical impossibility. And anyone who believes otherwise, is simply committing to its irrationality.
Well by ‘universe’ I ment, of course, any universe- ‘everything that physically/materially exists, including the entirety of space and time, all forms of matter, energy and momentum, and the physical laws and constants that govern them’
“There is no more way to exist before time existed than to exist north of the North Pole.”
This is certainly true for items in the univurs.
Now ‘North pole’ is a spatial construct.
the wurd ‘never’ – not at any time’ is a tempural construct
The theist wud definitly agree with this
since ‘north of the north pole’ connotes ‘space’; similarly the wurd ‘nevr’ implies ‘time’. ‘space’ and ‘time’ are creatid and therefore part of the universe.
‘He’s nevr seen’ and ‘He’s not seen’
arn’t nesasrily synonymus.
‘He’s never ixistid’ – and ‘He dusn’t ixist’ arn’t synonymus eithr. For difrunt reasuns I suppose.
God is beyond space and time. He dusn’t ixist in time/space. That’s classical theism 101.
‘…committing to its irrationality.’
Ar u saying Dr Carrier that theists by definition are being irrational when believing in God’s ixistuns?
No. This is analytical not synthetic. It is impossible to exist north of the north pole owing to the definition of terms. It is not logically possible by any means. Whatever. Ditto “before time.” Those words are contradictory. Anyone who doesn’t acknowledge this is being irrational, or doesn’t understand what we are talking about.
“No. This is analytical not synthetic. It is impossible to exist north of the north pole owing to the definition of terms.”
Yes it’s impossibl t ixist north of the north pole.
Analytically or synthetically –
because these our true by definition or experience in our universe becus we’r still tawking about a ‘north’
or ‘before’ time.
The Theist redily and very happily grants you all of this.
But with God such things ar inapplicabl: there is no befor/after/during/north /south/east/west/up/down/size/shape/where/when/how/inside/outside etc
A dialog:
Theist: I believ in God whu is by definition timeless.
Non Theist: Timeless? Logically impossibl therefor irrational as things are by definition timeful etc
Theist: No, God is not creation….
&c.
Very unsatisfying.
__
I’ll end this here – I’v made my point severally I think.
Saying “god can be logically impossible” is simply lunacy. It concedes the fact that god is logically impossible; and yet continues to believe him not only possible, but actual. Madness.
That is the opposite of rational. And I need not heed any irrational assertion.
Please don’t misundrstand Dr Carrier:
“Saying “god can be logically impossible” is simply lunacy. It concedes the fact that god is logically impossible”
That’s the qestiun begging claim’v the theist viz:
unless god ixists in a universe, he cannot lojikly ixist.
Theist makes no such cuncessiun.
God is lojikal. He ixists sans time or place.
It wud be illojikal for Him t ixist within his own creation.
God ixistid and there naught else.
He creatid time and place, and He is as he was with no change etc.
Calling theists ‘mad’ cuz they believ in a spaceless/timeless god isn’t very helpful, I sujest.
I don’t say god must exist in the universe. He simply must exist somewhere. There has to be a time at which he exists. There has to be a place where he exists. Elsewise he simply does not exist. Because that is what it means to say something doesn’t exist.
Any gainsaying of this is just irrational. And committing to being irrational is crazy.
Dr Carrier, I think I see the problem. It’s in the understanding of the “somewhere” in which God supposedly exists. It seems logically incoherent to say the “somewhere” has to exist “before He can exist there”.
I would suggest the other somewhere/other dimension (or other omnitemporal plane) must exist from eternity “because” God must exist from eternity. The atheist (and some theists) try to squeeze/reduce the concept of Creator/God into the limited dimensions of our spacetime universe (or just another similar to ours). The person that asks “where is God, show me God or why doesn’t God make Himself visible to me” doesn’t realize the limitations of his inquiry.
On a side note Dr Carrier, Acts 1:3, Jn 10:38 & 20:30-31 among other places shows the Christian faith IS rooted in evidence. Which vs. in Heb 11 insists (or do you find that) the Christian faith “must not” be based in evidence?
Finally, to the other readers. I misunderstood Dr Carrier’s training in Greek because of his conclusion of the Ελληνική κοίνε, των Εβραίων 11 (Greek koine, of Hebrews 11). I apologized for upsetting him and I apologize for the mix-up. It was never my intention to lie. It was my mistake. I wrote a simple message to him in Greek which he should easily understand and to show him I have “actual” experience in Greek (lived there) and that I, too, am not lying and so he would not quickly dismiss my comments on the NT.
If any space and time exist without god, our space and time can exist without god. We therefore then have no need of god. As that famous Laplace quote to Napoleon goes.
This is why the KCA can’t get off the ground. It trades on a logical impossibility: that something must exist when there is nowhere anything exists and everything never exists. Once we allow that places to be and times to be don’t require a god to exist, there is no KCA.
On Hebrews 11, the entire argument there is to believe without evidence just like every other person it cites as an example did (every example of which likewise being a fiction invented precisely to sell that very argument). See my discussion of this in Not the Impossible Faith (the back pages have an extended TOC, the mention of Hebrews is in there somewhere as a subheading).
And I hope you know modern Greek is a very different language from ancient Greek. Not only are the valences of words different, but the grammar and syntax has changed considerably.
“the concept of infinity could have been created by human beings, but that doesn’t mean there can’t be actual infinities,”
I’m a bit confused by the above statement. Has there ever been a known concept (in the history of concepts) that wasn’t created by a human being?
As perplexing and confusing as it might be we know that the “concept” (idea) of infinity exists. Isn’t it a given that the concept itself (along with all other “concepts”) were created by human beings?
By saying that the concept of infinity “could have been” created by human beings suggests the possibility that something other than humans can come up with such concepts. Or it could mean that we’re not sure if human beings have come up with such a concept. But we know the latter can’t be true because here we are discussing that very concept.
Please clarify.
I’m sure he meant the subjunctive not the indicative. He is allowing for, e.g., Platonic realism, not because he is a Platonic realist, but simply to account for alternative views to his own. So, he means, “even if the concept was invented, it is still the case that…”
People have a hard time grasping the distinction between “numbers are invented, but quantities are real.” See my section discussing this distinction in How Can Morals Be Both Invented and True.
How life was or is constantly created is the unanswered question that might lead to a god existence…
[Duplicated material deleted–ed.]
Do not send duplicate comments to multiple threads. Particularly when they have already been answered the first time.
For those who want to read the original comment and my reply, please go to the other thread. No further discussion will occur here.
The first link in endnote [2] is broken. I think that is important.
I know someone who claims God exists in a different dimension. What does that mean, what is its truth value, and why?
Thank you. Fixed.
Do keep reporting broken links. I might not catch them otherwise. But for those who want to find a document before I have time to repair a broken link to it, remember you can search the indicated author and title on Google to find it.
On the question asked:
It’s at least logically coherent to admit God has to exist somewhere, so there has to be somewhere for him to exist before he can exist there, whether another dimension or whatever. But it creates the problem that he therefore can’t have caused that place to exist. Ergo we are stuck with another unexplained, uncaused thing (the “dimension” he’s in). But why do we need God then? If places can exist uncaused by him, we can explain all of existence by simply positing that one place to be existed, containing far simpler and more plausible first things than a god (or indeed, even nothing, which is certainly simpler than “God”).
“But it creates the problem that he therefore can’t have caused that place to exist. ”
Indeed – this is the very argumunt used by sunnes t confute the corporealists (wahhabes/salafes/she’es/mu’tazilist rationalists/likeners
etc) in ordr t affirm that Allah ixists without place/space/location/dimensiun/body etc
The human mind is ankr’d in this univurs/space/time – and is simply incapabl’v grasping/comprihending the ineffability’v Allah.
‘Ther is not a thing like Him’ quran 42.11
U might as well ask an ameba to exegese Philosophiæ Naturalis Principia Mathematica.
Not tho’ the soljr nu sumwun had blundr’d:
Theirs not t’ make reply, Theirs not t’ reason why, Theirs but t’ du and die: Int’ the valley of Deth Rode the six hundrid.
Defending gibberish by repeatedly insisting people repeated that gibberish does not make it not gibberish.
If it’s true the human mind was unable to grasp the ineffability of God as you claim, then every human explanation of the existence of God is necessarily false. Game over.
I hadn’t considered it until a few days ago, but from a deist point of view, there was exactly one supernatural event (God’s creation) and everything else in the last 13.8 billion years has been a series of natural occurrences. That seems to be Marshall’s argument as well. What are the odds? Slim I’d think. Why would there be one and only one supernatural event?
Dr. Carrier wrote:
“Similarly, it’s a logical impossibility to exist nowhere and still exist, or to never exist and still exist. These are directly contradictory claims.”
Response: This would certainly seem to be true if we assume that somewhere always has a specific location and takes up some amount of space (which sounds like a logical assumption). But we would also have to assume that the object in question takes up some material space and therefore needs a material space to exist. And if so that material space would presumably be equal to or greater than the amount of space that the object in question needs to occupy.
Is it possible that unlike other objects in this Universe there could be an object (such as God) that exists but takes up no material space to exist and therefore does not require a specific somewhere to exist (be located)? Or are we saying that nothing (God or otherwise) could’ve existed before space and time because it is presumed to have occupied some space and required some space to exist? In other words if we are going to allow the possibility that something could’ve existed before space and time and (and therefore not consist of or require space and time) then do we have reason to entirely exclude God as a possibility?
Furthermore is it possible that the object in question and the place it exists are one in the same? Could a Theist argue that God is both the object and place that existed before space and time? And just as you argued that you can’t treat infinity like finite numbers (it doesn’t apply) might it be fair to argue that if such a God exists you can’t apply the same locale requirements that you would of other objects in our known space and time universe?
It doesn’t have to be space. It just has to be somewhere. Because that’s what it means to be. To be nowhere, is to not be.
It doesn’t require volume. It only requires location.
It is as logically impossible to exist “before” time as it is to exist “north” of the North Pole. It’s simply a logical impossibility, like a positive integer existing before zero on an ordered line of real numbers.
But yes: a god could exist simultaneously with a spacetime. Then he’d have a location, and thus it would be logically possible to say he existed.
So that’s the only option available. But that means spacetime must exist independently of god, and more necessarily than god, and therefore requires no explanation for its existence (at least no more than god would). God cannot “pre-exist” time so as to create it. That is literally a logical impossibility.
You could also say spacetime is god, like you suggest. That’s called pantheism. It would be heresy for a Christian to propose that. But it’s at least an available option. The challenge then is to prove spacetime is conscious (and not just spacetime). All evidence shows it’s not. This is really what we are debating: whether spacetime is (or even needs to be) conscious or not.
The cosmological argument cannot help here. All it gets us to is spacetime. Not consciousness.
Just trying to wrap my mind around the idea of an actual infinite quantity of things. Thought it might be helpful to throw out a specific example and get some feedback as to how such a thing might be possible. So lets consider the example of an infinite number of universes existing before our own. moreover lets hypothetically suppose that for whatever reason our universe is the last one that could ever exists. Now lets ask the question how many universes have ever existed? Well the first thing the strikes me as being undeniable is that were dealing with a fixed quantity here. Because the group of members under consideration is neither increasing or declining. Or in other words it can be said we have “this many and no more”. Now if we really have a fixed number, then it also must be that if we subtract one member from the group then the total number remaining has been reduced by one. In fact if we really have a fixed total then the number remaining will always be reduced in direct proportion to the number subtracted. Thus in princible the total number in the group can be reduced to zero. Which of course could not possibly happen if the number of universes were actually infinite. For me the key issue here is whether a group of things which is neither increasing or decreasing in number can yield any thing other than a fixed unchanging total number of members. Also if the total is fixed then how could there not be a corresponding number for each member in the group? Could we say we “ran out” of natural numbers?? And if there’s a corresponding number then those numbers can be arranged in a sequence from highest to lowest and thus we can only have a finite total . Ok so were have I gone wrong here ? Would this not be a fixed total or would one argue that a fixed total can still be infinite
Note your mind is finite. So you will only be able to grasp transfinite set theory with conceptual difficulty. You should expect that, not be surprised by it.
As to the first question, what do you mean by “a fixed quantity”? If you just mean a finite quantity, you’ve already dropped off the map of your own example; the scenario is of a transfinite quantity, so operating from an assumption it’s finite is an error. There is no “highest number” yet there are infinitely many numbers. We never “run out” of numbers. There is no sense in which we can say some number doesn’t exist because it’s too large or whatever. They all exist, insofar as any do. This does not make numbers impossible. So neither would it make infinite universes impossible. (Indeed, if God is omniscient, he knows all numbers, and therefore an actual infinity exists in God’s mind. And if it can exist there, it can exist anywhere.)
Once you acknowledge we are only talking about transfinite quantities, and therefore the rules only provably true for finite quantities do not apply, you do not get the same results with adding and subtracting. Once you are in the field of the transfinite, you are off the number line.
Consequently any adding and subtracting does not get you a number on the number line. It remains transfinite. This is the difference between finite and transfinite quantities. Finite, adding or subtracting moves you on the number line. Transfinite, there is no number line, and consequently nowhere to move. You can have more and still be infinite. You can have less and still be infinite. This is what “infinity” means.
Only if you subtract an infinite quantity do you have a chance of getting to a finite quantity, and even that depends on how the subtraction operates. Not all subtraction is the same anymore once we are in transfinite sets. Because the axioms of finite arithmetic do not apply. This is what happens when you get infinite stuff. It behaves like infinite stuff. Not finite stuff. It would be illogical to expect it to act like a thing it is not. That would be like expecting a square to have the properties of a circle.
In the given case you describe, it would take infinite subtractions to get to “zero universes.” If you are doing it in sequence, one at a time, it will take you infinite time. You’ll thus never complete the task. As one should expect. If you get to do it “all at once” then you get to delete all existence. Just the same as if the number of universes were finite. Again as one should expect.
So I don’t see anything contrary to expectation here.
Everything else looks like you want infinite quantities to act like finite ones. But that’s itself illogical. If “fixed” only means “exists,” then you can subtract forever and still have universes left over; unless you are allowed somehow to actually get to the end of forever, then you can get rid of them all. There is no “finite” subtraction that gets you there. Only infinite subtractions can. Because it’s an infinite number. But if “fixed” means “on a number line,” then you just aren’t talking about transfinite quantities at all.
“So lets consider the example of an infinite number of universes existing before our own.”
“in other words it can be said we have “this many and no more”.”
These are contradictory statements…
That’s one way to put it. Once you are off the number line, you no longer are talking about numbers that are “this many and no more”; you are talking about numbers that are by definition beyond that, quantities that can be added to or subtracted from and still have more than any finite number possible. That’s what an infinity is.
“quantities that can be added to or subtracted from and still have more than any finite number possible. ”
So if I’m understanding correctly, with respect to infinities, it is possible to add to and subtract from but (unlike with finite numbers) doing so has no impact on the total (because there is no “total”).
That is some mind blowing sh*t man
It’s not that there is “no total” but that there are infinitely many “totals” that we call “infinity.” We have no tools with which to distinguish them; and they all have the same properties peculiar to all infinities, so there isn’t even any meaningful difference between them in the sense there is for finite numbers.
And that’s just for aleph-1, the basic infinity. There are actually infinities that are larger than other infinities, but only because they have infinitely more things added, rather than finitely more things added; and only in particular ways.
And indeed, this is all well beyond our regular experience-base and thus mind blowing.
Regarding the “Quantum Instability of the Emergent Universe”
Aguirre is talking about George Ellis model where “the inflationary universe emerges from a small static state that has within it the seeds for the development of the macroscopic universe. The universe has a finite initial size, with a finite amount of inflation occurring over an infinite time in the past, and with inflation then coming to an end via reheating in the standard way.”
The initial static state can be thought of as a small “cosmic egg” of spacetime that exists forever until it spontaneously breaks open to produce an expanding universe.”
Source: “The Emergent Universe: inflationary cosmology with no singularity”
This does not apply to other models, like the “He-Gao-Cai model” because their model do not claim any classical space-time; only a quantum state. Which is different from the Emergent Scenario, because it predicts small Einstein Classical space-time existed forever.
In addition to that, the paper by Aguirre is not an absolute fact. If you search in the Google Scholar, “Instability of emergent universe” you will find a lot of more than just Aguirre’s opinion. And if you google “Stability of emergent universe” you will also find a lot of proposals solving the said instability. One example is this “Stability of the Einstein static universe in f(R, T) gravity”
Where the author cited the work made by Aguirre and wrote:
“Though the main component for constructing emergent scenarios is the ES solution, the original model does not appear to be successful in solving the singularity problem, since there is no stable ES solution in classical GR. In other words, owing to the existence of perturbations, such as quantum fluctuations [70], it is too difficult for the universe to settle down for a long time in such an initial static state [4, 5, 6, 7, 8]. However, it is a general belief that in its earliest stages, the universe is presumably under extreme physical conditions, so that new effects, such as those coming from quantization of gravity, modifications of GR theory or even other new physics, may become significant. As a matter of fact, dealing with the cosmological equations of modified gravity theories may leave us with many new static solutions, whose stability properties would crucially depend on the details of the theory.”
In the the abstract they wrote: “We also investigate homogeneous scalar perturbations for the mentioned models. The stability regions of the solutions are parametrized by a linear equation of state (EoS) parameter and other free parameters that will be introduced for the models. Our results suggest that modifications in f(R, T) gravity would lead to stable solutions which are unstable in f(R) gravity model.”
So, it’s clear the new Emergent Scenario is a viable model.
U’r, dautless, awer’v the aristotelian arab-iranian polymath Ibn Sēna whu also disussis simultaneity
https://plato.stanford.edu/entries/ibn-sina-metaphysics/
but elswher attemptid t pruv god
https://en.wikipedia.org/wiki/Proof_of_the_Truthful
whum “Historian of philosophy Peter Adamson called the argument one of the most influential medieval arguments for God’s existence”
whu also sez
“Unthinkable: The Islamic thinker who ‘proved’ God exists Medieval philosophers don’t get much attention these days but Avicenna deserves it, says Prof Peter Adamson”
https://www.irishtimes.com/culture/unthinkable-the-islamic-thinker-who-proved-god-exists-1.2931754
as Avicenna states in the Kitāb al-Išārāt (Dunyā, III vol., 95), creation is not conceivable in terms of time because a time before the creative act of God would end up being an intermediate between the First Principle and the world:
The action of the First Cause must therefore be conceived as exempt from any mediation. Nothing (neither a matter, nor an act of will, nor even time) can be inserted between the Principle and Its effect (see also Ḥudūd: 42–43). An image often occurs in Avicenna’s writings: the causality of the First Principle is similar to that of the hand that moves the key in the lock of a door: the movement of the hand and that of the key—respectively the cause and the effect—are simultaneous, and yet one is prior to the other. Priority is essential, not temporal (Ilāhiyyāt, IV, 1, 165).
Richard, I think your point about simultaneity is very good. Vilenkin seems to agree with you on this point.
Vilenkin argued that the “tunneling from nothing” universe happens spontaneously and simultaneously with the beginning of time. In his book Many Worlds in One (pp.181, 186), he explains his proposal:
Indeed. And I appreciate your doing the work to add that quotation and citation here. That’s helpful to everyone reading this thread!