One question atheists tend to be bad at answering, because they rarely give it much competent thought, is the ontology of logic: what, physically, does it mean to say that logically impossible things can’t ever happen or exist? Or as a theist might pose the question: if physicalism is true, and only physical things exist (and in our observed case, that means “nothing but” arrangements of matter-energy in space-time), how is it that anything obeys the “Laws of Logic”? Those aren’t, supposedly, laws of physics, right? And in any event, laws of physics are contingent—they could have been different. What keeps Laws of Logic from having been different? Why are they special? And how is it that anything in a purely physical universe obeys them?

Of course a lot of silly apologetics then spins off of the typical “you can’t answer that” God-of-the-Gaps approach here. We need God, you see, to make sure things obey logic, or for logic to even exist as a compelling force over reality. Because, you know, logic is “mental,” or something, yet it governs everywhere, so there has to be some supreme mind manifesting it, which would be God. Yadayada. You get Presuppositionalism out of this; as well as variants of its less loony cousin, the Argument from Reason. As usual, the approach is bogus. Because it simply isn’t true that “you can’t answer that.” One actually can show why logic will be an inalienable governing property of anything that could ever exist. No gods—or minds—needed.

The Mathematical Version

To understand this it helps to explore a related argument: the claim that we can’t explain why everything is mathematical, “therefore, God.” This I have already summarized well enough, in All Godless Universes Are Mathematical, with a little more in a sub-section of my related answer to the question How Can Morals Be Both Invented and True? The overall point being that the theist here is trading on a confusion, as commonly they do. They conflate “mathematics” as a technology (a system of human-made symbols and rules) with the things mathematics is about (quantities, patterns, and relations).

This is more obvious when we compare two specific terms within the subject of mathematics: numbers and quantities. Quantities are physically real (potentially and actually; no minds needed); but numbers are made-up. They are just words humans invented to represent quantities in “bypass computations.” By which I mean, our brains were not physically built to run complex numerical computations (they evolved some so-so heuristics of middling reliability instead), but were built to use language, and thus construct and analyze—a.k.a. “compute”—sentences. And it just so happens that we can piggyback on that talent to run complex mathematical computations, by simply substituting a mathematical language we invented for the natural languages we ordinarily use. We can even do this at depths and scales our brains are incapable of themselves, by running the computations on paper (or chalkboard or what have you), simply following step-by-step procedures with the same talent for that as we evolved to make spearheads, huts, and axes (and now, of course, we’ve leveraged that craft skill all the way up to writing and running code on actual digital computers, building machines to do the work for us—as we’ve done for nearly all else).

So mathematics is made up. Numbers, symbols, equations, rules, procedures. All invented—and by humans, not gods. What is factually true, what we didn’t invent, are facts about quantities, patterns, and relations between. Mathematics is an invented tool for computing what those facts are, from available data. With certain inputs, and a certain algorithm (procedure) for processing (computing) that information, we get certain outputs. Hence there are, for example, at least two different systems of trigonometry (the Greek system of chords and the Indian system of sines and cosines; we now use the Indian, because medieval Christians forgot the Greek one). Both are “true” in the sense that they correctly calculate the properties of angled space; but both were invented by humans to do that (hence why we could find two different ways of doing it; there are no doubt more).

Language is likewise invented, to achieve the goal of communication. The brain architecture that makes language easy to invent and use is an evolved skill of the human brain (which is why almost no other animals can do it), but languages themselves are made-up. And once you pick the goal (whatever it is you want to accomplish with a language), it is then an objective fact of the world which languages are going to be better than others for any given purpose. Many will turn out to be equally good; some will turn out to be better or worse. But even as we are therefore discovering better ways to encode concepts in a language (whatever the metric we are using at the time: whether making it more efficient, more versatile, more precise, more emotionally impactful, etc.), we are still inventing the tool (the specific language) that achieves that goal. Hence why there are many languages; including many mathematical languages (and likewise many logics, and logical symbolisms).

And hence we get numbers as invented words that signify quantities. Quantities exist to be discovered. But numbers are invented to talk about them and run computations concerning them. One is an objective fact of the world independent of human invention. The other is a human invention. One does not require minds to exist. The other does. But even the one that does require minds—the names we invented for quantities and operations, and the procedures we invented to extract information from them—demonstrably was developed by those minds. No God came down and taught us any logics, mathematics, or methodologies. We invented all those things on our own; which is why it took hundreds of thousands of years for us to test and experiment and perfect them into the powerful technologies they are today (and why you don’t find any of them in Scripture). Meanwhile the things that existed outside our minds, to be discovered—quantities and patterns, and their relations—require no mind to exist.

Hence numbers are always made up; but the quantities they signify are not. And yet some made-up systems of numbers work better at signifying quantities and their relations; but only because we are trying to figure out the clearest or most efficient way to run computations on them, by inventing computational codes and procedures for it, and observing how they perform—just as we are trying to figure out the best way to govern our lives and societies, through inventing behavioral codes and procedures for it. Or like agriculture and medicine—just like mathematics and logic—even if there are no gods, there will always be a better (and ultimately a “best”) way to live and govern—as also to run computations to extract information from a field of data. What information exists in a field of data is fixed by reality, waiting to be discovered; as is what techniques and procedures can or can’t extract it. But the precise techniques and procedures (logic and math) that we settle on to extract that information are inventions. Like the wheel: we invented that, but only because the physics of the world makes it so that circles work better than squares for the needed function; logic and math, same.

The number nine, for example, can be represented by infinitely many symbols and syllables. But the fact that the corresponding quantity can be divided into three sets of three is a physical, discoverable fact about that quantity. And yet all the symbolic computational ways by which we can prove or discover that fact are as infinite as all the ways there can be to represent any one fact in that relation (the quantities, the ratios; like, “the number nine” and “the number three”). The procedure is both invented (we creatively come up with one of the infinitely many ways there are to do what we want, and arbitrarily assign symbols and sounds to represent each component and step) and discovered (there are only some procedures that will actually work for what we want, and many more that won’t).

In the case of mathematics, it is more apparent why that is: to say that there are nine eggs in a basket literally is to say that there are three sets of three eggs in that basket. A perfect mind would simply immediately see this, and thus never have to compute the fact; consequently, it would have no need of what we call “mathematics.” Just as you can look and instantly apprehend the presence of three eggs, without ever having to do any arithmetic, a perfect mind would instantly apprehend the presence of nine eggs and its identicality to three sets of three eggs. Whereas we, with very computationally limited minds, have to invent and install and follow a procedure that allows us to work this out. We just happen to call that procedure “mathematics.” But all it’s doing is bypassing the limits of the innate computational abilities of our brains with a procedure (essentially running software on our hardware) that is itself capable of computing what is already factually, objectively, physically true about those nine eggs. It’s a mechanism for extracting information.

“But we can do it without the eggs; how can we discover things about physical facts that don’t even exist yet and aren’t ever being observed?” This gets to what human cognition is doing, and that’s something I’ll get into in my following article on The Agument from Reason. For now, just consider that the way humans (and even many digital computers now) “reason” about things is to generate a virtual model of them and then “explore the model” to learn things about it. Of course, what is learned will be there only because we built the model that way. As any expert in logic will tell you, the conclusions of logical formulae are not new information, but information that already existed in the premises. All the logic did was extract that information from those premises so we could apprehend it. Virtual models do the same thing: any system that has the same components, will thereby have the same contents to be discovered. Any quantity of nine things, will by its very own description, contain three sets of three things. The only way it could be different is if you change the model in some way—which is equivalent to changing the premises in a logical argument.

This was illustrated when Leibniz and Newton both independently discovered calculus, when they both tried solving the same problem. Both their systems of calculus were different. Yet both described the same general real-world system, by describing the components of that system and looking around in that model for ways to learn things about it. Using this technique they each “discovered” what is essentially a different analog computer program for solving a computation problem about summing infinitesimals—one that uses human hands, brains, and language as the processor. The objective fact of the world—and it is indeed a physical fact about our world—is that such an algorithm works. But the algorithm itself was still invented. That’s why we could come up with two of them. The calculus of Leibniz, was not the same as the calculus of Newton; but it did achieve the same ends, which was to extract the needed information (in their case, accelerations) from the available data (in their case, velocities and their continuous changes).

But really, even simultaneous invention would not be unexpected. For some things, there is only one good way to do them. So two independent inventors looking for how to accomplish the same thing, can of course discover the same way of doing it. Especially when there is no other. Hence the wheel, fire, agriculture were probably discovered independently multiple times. Because the same goal always physically requires the same basic tasks. So anyone looking to invent a way to achieve any given goal in the world, will end up discovering the same way to do it, or certainly ways relevantly similar. But what we end up with was still invented. It wasn’t born into us. It wasn’t evolved into us. God didn’t decree it. It wasn’t written anywhere. We made it up. But we made it up in our effort to discover and thus exploit what was already there (wheels roll better than blocks).

So one might ask whether, because we are making it all up, we can just make anything up. For example, can you invent a rule that true things are false? Yes. Of course. But would that rule work in navigating physical reality? Well, no. That’s all there is to it. That’s why you can’t just make up blocks that roll as well as wheels. Likewise, can you invent a mathematical system whereby nine things are ten things and thus not identical to “three sets of three” but “three sets of three and one left over”? Certainly. But the moment you do that, you are simply redefining the phoneme “nine” to mean a quantity of ten. If you try to insist that a quantity of nine things can also at the same time be ten things, you would simply not be describing physical reality. Once the quantity is nine, no matter what you call it, it simply is nine, not ten. So the question then becomes: can there be a world—maybe not our world but just a possible world; could our world have been changed in some way—where “once the quantity is nine, it simply is nine, not ten” is false?

Which gets right down, really, to only one question: can logically contradictory states of affairs ever physically (as in, really) exist, in any possible world?

The Laws of Logic

So the question is: could there be a world where the laws of logic weren’t true? That would mean those laws would not describe the fundamental structure or behavior of that world. Which means all we really have to ask to answer that question is: what would we have to physically change about this world, to get a world not governed by one or more of those laws of logic? Which in turn means asking what it is that each law of logic is physically describing about any world—and then getting rid of that thing, whatever it is, and then seeing what would remain. Would it be anything? Or would it be nothing—or indeed even less than nothing? For if we cannot even describe a state of nothing without the laws of logic, then we have found what it is those laws capture about all existential states of being, and thus why no possible state can ever obtain that isn’t described by those laws.

So…what are the “Laws of Logic”? There are many axiomatic mathematical and logical systems, which can be described as defined by many different sets of “laws,” which here means rules of computation that we decide shall always apply when the given system of computation is used. Like a game: we invent the rules, and then apply them to see what happens. But that’s always an arbitrary invention; those rules are set by fiat, a matter of human choice. What we want to know is: what laws undergird all logics, such that no logic would successfully compute anything, unless it conformed to (and hence follows) those specific core rules? Aristotle worked this out over two thousand years ago; and to understand that see Wikipedia’s handy summary in Laws of Thought; as well as of attempts to get around his discovery with Paraconsistent Logics.

There are three rules of computation that are always true of all functional logics (ironically, even paraconsistent logics, which always end up just trying to redefine terms and distinctions in ways still subject to Aristotle’s Laws): the Law of Identity (in one symbolic system stated as p iff p), the Law of Excluded Middle (ibid. p or ¬p), and the Law of Non-Contradiction (ibid. ¬ (p ∧ ¬p)). But these laws have been shown to all just be different formulations of the same thing. The Law of Identity (e.g. “A is A”) is simply a different way of stating the Law of Non-Contradiction (e.g. “A cannot also be ¬A”); and the Law of Excluded Middle (e.g. “A and ¬A exhaust all possibilities”) is simply a consequence of asserting either of the others (e.g. violating this rule leads to violating either of the other two rules). So all three Laws of Logic are just different ways of saying the same thing; but our brains don’t readily comprehend what that is, so we have to compute why each formulation amounts to asserting the same thing as the others. But assert the same thing they do.

Of these, the Law of Non-Contradiction is the easiest to settle on as defining them all. It is, ultimately, the one particular thing we are referring to when declaring something to be “logically possible” or “logically impossible,” or even, the converse declaration to that, “logically necessary.” And it is the one thing we need to explain when explaining why all possible existent states obey this principle. For the Law of Identity, one can simply set that aside as an obvious principle of semantics: you aren’t saying anything, if you aren’t fixing any one particular thing to be what you mean. If the meaning of every word can change arbitrarily at a whim at any moment, nothing is being said. And ultimately, the only reason “A is A” is because “A is not ¬A,” i.e. if you allow sometimes for A to be something else even in the same line of computation, then you are declaring A is sometimes ¬A, thereby violating the Law of Non-Contradiction. Likewise, what we mean by ¬A simply is The Law of Excluded Middle: all things that are not A. The only way to maintain the Law of Non-Contradiction is therefore to maintain the Law of Identity; and the Law of Excluded Middle derives from this as well, albeit by a more convoluted route of computation.

These laws of course only hold when strictly held. For example, the Law of Excluded Middle is sometimes said to mean every assertion is either true or false, but that isn’t strictly what it says. It says, first, that if A and ¬A assert anything at all, then (for example) A must be either true or false; so we aren’t applying this law to unintelligible or meaningless assertions, or assertions that have no truth value. This is only a law governing assertions about what is or is not true. And second, this is only an ontological description, not an epistemic one. Just because A has to be either true or false does not mean we will therefore know whether A is true or false. When, for example, we are in a state of concluding A is as likely to be true as false (i.e. we know nothing whatever that makes A more likely or less likely), it is still the case that, in reality, A is either true or false; and we are simply assigning a probability to either. This still must obey the Laws; for example, we cannot assign to A a probability of 50% and to ¬A a probability of 40%, as that leaves 10% left over, and that simply isn’t what we mean by ¬A. Hence the Law of Excluded Middle entails that if P(A) is 50% then P(¬A) is as well.

Finally, Quantum Mechanics does not violate the Laws of Logic either. An entangled state (for example, Schrödinger’s cat—as physically impossible as that might be—when it is in a superposed state of neither alive nor dead) is simply a third conditional state. For example, if A is “cat is alive,” then ¬A cannot be “cat is dead,” because the Law of Excluded Middle entails there is a third possibility to include in the rejection set. So, by Aristotle’s Laws of Logic, if A is “cat is alive,” then ¬A is “cat is either dead or in superposition.” One can define “superposition” as a type of death and thus restore the binary condition (“cat is either alive or dead”), but that doesn’t really make superposition identical to what we commonly mean by death, any more than “cat is dead” would be physically indistinguishable from “cat is frozen in a cryo-chamber and therefore in de-animated stasis,” which obviously is not the case: that we would recognize as meaningfully different from “cat is dead.” We might sooner there define “cat is frozen in a cryo-chamber and therefore in de-animated stasis” as a form of being “alive,” but that doesn’t escape the Laws of Logic either. However you label the conditional possibilities, you still have to obey the Law of Excluded Middle.

In other words, you can’t change what things are by changing what you call them. And even if you could (if, for example, we lived in a magical world where our simply renaming things physically transformed them accordingly), that process would still obey the same Laws of Logic. For example, it would remain the case that whatever you transmutated this way will have been at some existential point a different thing; it will not physically be the case that it was never transmutated from one thing into another. And yes, this does mean that time travel simpliciter is logically impossible. If something ever was something else, it must have been something else in some meaningful—distinguishing—sense. A must remain A. It cannot simultaneously be ¬A.

Hence any system of time travel that actually could exist, won’t work like it usually does in the movies. For example, going back in time and preventing the Holocaust leaves the Holocaust still having happened in some distant meta-time, i.e. there was still “a time” during which someone had not yet gone back in time to prevent it, and therefore all the suffering experienced in it was, and will always have been, experienced in some sense. So really, there is no way to erase that having happened; the best one could do is create a different world in which it won’t (like in a manner well illustrated in the film Source Code). Meanwhile, the only method of time travel that does exist, doesn’t even work like it does in the one movie that tried to make it work that way. In all other respects, “time travel” as you encounter it in the movies entails simultaneously moving forward in time (or remaining stationary in time) and moving backward in time, which is a self-contradiction and therefore logically impossible. A time traveler who coherently went backwards in time would devolve into a fetus and die.

At any rate, this gets us down to just one basic Law of Logic: the Law of Non-Contradiction (or LNC). Which states that contradictory states of affairs simply cannot occur. Not in any possible world. Thus, once you define A and ¬A, you are simply defining the LNC (as well as the other two laws). Which means there is no change you could make to our world, not even in concept, that would get it to violate that Law. And this is, quite simply, a physical law. It is not some mystical law of thought dependent on a mind. It is simply a description of any physical reality. In essence, this is the most fundamental law of physics there is.

But if the LNC is really just a fundamental physical law, could it have been different? Most physical laws we think could have been different than they are. Why couldn’t this one have been? Couldn’t there be worlds not governed by this law? And wouldn’t a state of absolutely nothing surely fail to be governed by it—being governed, presumably, by nothing?

Why the Law of Non-Contradiction Will Always Be True

In All Godless Universes Are Mathematical I demonstrated a fairly unavoidable point: it is not possible to have any universe that wouldn’t be describable mathematically. There is therefore no mystery to why ours is. And the way to get to this revelation is to simply try to think of what you could change about our universe to get it to not be describable with mathematics. Since math simply is any linguistic-computational system for describing quantities, patterns, and relations, the only way to get a universe not describable with mathematics would be to eliminate all quantities and patterns and relations. But the absence of all quantities, patterns, and relations is…well, the absence of a universe. So you literally can’t have “a universe” and it not be describable mathematically.

Maybe, you might then say, we can at least conclude that a state of absolutely nothing is therefore not describable with mathematics. But even that is not true. As “nothing” means a whole bunch of zero quantities of things. And zero is a measurable quantity. It is therefore describable mathematically. And that even has computable mathematical consequences (see The Problem with Nothing and Koons Cosmology vs. The Problem with Nothing). The empty set is a set. And as such, it is a state of affairs that has consequences that follow from its distinct content. Quite simply, nothing is a particular state of being, one distinguishable from all other states of being. It is therefore mathematically describable. So you can’t even get nothing to be non-mathematical.

This of course all follows from presuming that even the Law of Non-Contradiction—and therefore also the Laws of Identity and Excluded Middle—still applies to an absolute nothing-state. One might try to question that. Of course, not everyone wants to—especially when they realize what that would mean. For example, to say that a nothing-state won’t even obey logic actually eliminates anything else you could possibly say about it. Like, say, that it won’t spontaneously generate an entire biophilic universe—you can’t argue to that conclusion from logic. Because you just said logic does not confine what a nothing-state will do. If a nothing does not obey even logic, then it necessarily could do anything, even illogical things. So you couldn’t even say “it’s improbable” that nothing would produce an entire biophilic universe, as that requires assuming some sort of logic constrains what’s probable in that condition—and you just said it doesn’t. So this is not really a viable move for God apologists. Down that road, they’re screwed.

So they usually try something else. Victor Reppert, for example, tries to avoid this move when he approvingly cites Aristotle, Metaphysics 4.4 (= 1005b-1006d), against the plausibility of any form of logical antirealism in his book C. S. Lewis’s Dangerous Idea (p. 81). But when making this move, Reppert didn’t do what he ought to have done: present Aristotle’s actual explanation of logical laws. Because that happened to be entirely physicalist. And Reppert was trying to insist the Laws of Logic need a divine mind to exist and govern anything. But Aristotle proved they don’t.

Here is what Aristotle had to say about his Laws of Logic:

The starting-point for all such discussions is not the claim that one should state that something is or is not so (because this might be supposed to be a begging of the question), but that he should say something significant both to himself and to another (this is essential if any argument is to follow; for otherwise such a person cannot reason either with himself or with another); and if this is granted, demonstration will be possible, for there will be something already defined.

Aristotle, Metaphysics 1006a

Aristotle goes on to explain that words have definite meanings because they are assigned them by human convention, and for that very reason words cannot also mean what they by definition deny (ibid. 1006a-1007a). Hence, for Aristotle, logical laws derive necessarily and automatically from the existence of communication (defining terms and reasoning with others) and computation (reasoning with oneself). The moment you have those, in any possible universe, you will always have logical laws. It can never be any other way, simply because it is not any other way. Once you describe the thing, the laws of logic are inherent in what you have just described; to get those laws to go away, you have to change that description, but any doing so that gets rid of those laws also gets rid of literally everything else. Logic is thus physically inherent in all possible states of being. To say that something does or does not exist is identical to saying it conforms to the Laws of Logic. Logic is simply a description of what it means to exist—even, indeed, for “nothing” to exist.

Extending this point to physical reality, Aristotle argued:

Again, if all contradictory predications of the same subject at the same time are true, clearly all things will be one. For if it is equally possible either to affirm or deny anything of anything, the same thing will be a trireme and a wall and a man, which is what necessarily follows for those who hold the theory of Protagoras. For if anyone thinks that a man is not a trireme, he is clearly not a trireme, but he also is a trireme if the contradictory statement is true. So the result is the dictum of Anaxagoras, “all things are mixed together,” so that nothing truly exists.

Aristotle, Metaphysics 1007b

You might not immediately follow what he is saying here, but it is actually quite profound. As Aristotle explains, any posit we make asserts that something exists, while a negation asserts that it does not; so to assert both is to declare, literally, nothing (Ibid. 1007b-1008a). That is, a self-contradiction communicates nothing, and represents nothing even in the mind of one who wishes to declare it. Thus, it could not correspond to anything real; even if you tried to say that it corresponds to the null set you’d be wrong, because the null set by its own description lacks anything at all (no men or triremes), and therefore is still making a distinction that a contradiction is denying. This of course follows as a consequence of language: language simply doesn’t communicate anything otherwise; and thus can never compute anything otherwise. But Aristotle is now observing what is even more fundamental than that: that this also follows physically.

For if everything is true, then there is only one thing—in other words, there is no difference between one object and another. In fact, there would then be no objects (exactly as Protagoras concluded). For to be an object requires distinction from something else; and distinction literally is what we mean by a non-contradiction. A distinction is the literal, physical, descriptive opposite of a contradiction. It therefore follows that in any universe where distinct objects and properties exist—where distinctions exist, of any kind—no self-contradictory propositions will be true of that universe (Ibid. 1008b). So what it means to say that no contradictions obtain is simply that distinctions obtain. Every world, and every state of being, in which distinctions exist, is thereby already being described as a world or state conforming to the Law of Non-Contradiction. Because that law is simply saying “distinctions exist.” It therefore is the description of all distinction-states.

Therefore, there can be no world or state of being that doesn’t obey the Law of Non-Contradiction, unless you can get there to be no distinctions in that world or state of being. But the absence of all distinctions describes nothing at all—in fact, even a state of nothing contains distinctions (to say there is nothing, is to assert a distinction between that and something); so even nothing can’t be divested of distinctions. That’s why even a state of absolutely nothing is going to be described by, and thus conform to, the Law of Non-Contradiction. When we thus conclude that only “a state of being with no distinctions” will not be described by the LNC, what we are saying is only states of being that can never exist will not be described by the LNC. A state of there being nothing, by contrast, can exist—and as it is thereby manifesting distinctions, it will be described by the LNC.

You can work through every possibility, explore the entire information space; you will never be able to describe, or ever find yourself in, any state of being that lacks distinctions. And that is why—physically why—you will never be able to describe, or find yourself in, any state of being that doesn’t conform to the Law of Non-Contradiction (and therefore also the Laws of Identity and Excluded Middle). Indeed, this is true even apart from the fact that “you” existing (so as to find yourself in any state) is itself a distinction (in fact a whole slew of them, as you are definitely quite a complex entity), and thus automatically are described by—and thereby conform to—the Laws of Logic. Because you don’t even need that detail; as any distinction at all has that consequence. And there is nothing—not even nothing itself—that lacks distinctions.

This is also the case (for essentially the same reason) for the observation that in any universe where spacial dimensions exist without curvature, no parallel lines will ever meet. The axiom (in this case the Euclidean parallel postulate) describes a physical fact of any universe that was as described (“where three spacial dimensions exist without curvature”). That postulate is not some Platonic form or some mystical “law” beyond space and time. It is simply a physical property of any such universe, such that there is no universe you could ever meaningfully describe where the axiom of parallels will not to be true except universes that are physically different in the way required (e.g. you have to add curvature, to get that axiom to no longer be true). Thus the axiom is simply part of the physical description of that universe. No mysterious logical relation is needed for this to be true: just the physical facts themselves. To say “three spacial dimensions exist without curvature” simply itself contains the information “no parallel lines will ever meet,” and one need merely run a computation to discover that—unless you have a perfect mind, then it will be immediately obvious to you that those are the same world, that those two statements simply mean the same thing (or to be more precise, the first statement contains the second in its very meaning).

And this is exactly what is going on as well for the Law of Non-Contradiction (and thus all three of Aristotle’s Laws of Logic). The LNC is therefore just like any other physical law: it defines and thus describes any universe that contains distinctions, which is every universe describable (and thus realizable)—including even an absolute nothing-state—since we cannot conceive of (as in compute or even theoretically build) any universe or state of being, at all, without positing at least one distinction. We can indeed search the entire information space, and we’ll ever find any universe or state of being without a distinction being made; and we can quickly perceive why. Making any state of existence real simply is the act of establishing a distinction—most likely more than one. This, again, is not because of some mysterious logical superlaw, but because the physical facts of any universe we care to construct are just so, simply as described. This is why we can’t “get” a universe that doesn’t obey the LNC: we can’t get a universe, or any existing thing at all, without making distinctions.

In short, the Laws of Logic literally are the (potential or actual) physical properties of every (potential or actual) universe that they describe. This does mean that if there is any universe that the Laws of Logic do not physically describe, then, obviously, logic would not apply to it. So far, humanity has not been able to imagine, construct, model, describe, or simulate any such universe or state of being; and we can observe why: there is no way to “imagine, construct, model, describe, or simulate” anything without making distinctions, and making distinctions simply is an assertion of the LNC. They are one and the same thing.

True, this could be because of some strange limitation inherent in all computation (a la Gödel). Maybe there is a state of things that can both exist and contain no distinctions, within itself or from anything else, and we just “can’t apprehend that.” But that’s highly unlikely; indeed, it would require a highly improbable Cartesian Demon for us to be deceived about that. It would also be irrelevant really, since we obviously don’t live in such a universe; and the discovery of such a possibility would be no more devastating to logic than the discovery of non-Euclidean geometry was to geometry. After all, in our physical universe, parallel lines can meet. Yet geometry is not overthrown.

But this is still why we can’t adopt “just any” conventions for logic—we must discover which conventions that best get at the truth, just as we must discover the best ways to grow corn or hit targets with guns. By the same token, the aim of language is communication. And though any language is possible, all languages must follow the same basic rules for communication to be functional—and that is simply a physical fact of the universe; in fact of any universe. It’s simply a defining property of language itself (see Sense and Goodness without God, pp. 42-43, 188-91). And since “reasoning” is nothing more than communicating with oneself, the same conclusion applies to all logics and maths.

Nothing else need be the case for that to be so. As soon as distinctions exist (and they certainly will in any universe where people can exist), what then exists will always be consistently describable with Aristotle’s Laws of Logic. Those are therefore fairly sure to be useful rules to follow in any truth-finding engine or procedure.

How Physical Fact Connects with Human Thought

The fact that there are distinctions is always a physical or at least objective fact of some kind. And all physical facts are, by definition, distinctions—between each other, and from alternatives. The LNC is therefore a law of physics, fundamental to all physical worlds and all physical systems. It is an inalienable property of simply existing. Consequently, physicalism has no difficulty accounting for why the LNC (as every other fundamental Law of Logic) always describes every possible thing, and can never be violated by any actual thing; and this in turn fully explains why we would find it useful in building any reliable truth-finding process, and how even natural selection could strike upon notions of it as it builds ever-more-reliable truth-finding machines.

In human application, logical “laws” are simply rules of computation. Like the laws of physics, which simply describe how the physical universe actually, physically behaves, the laws of logic do nothing more than describe certain kinds of truth-finding computational procedure. These “laws” are also no different than, for example, the “laws” of agriculture—the rules of conduct that dictate successful vs. unsuccessful cultivation of crops. In both cases, the “laws” are “discovered” by experimentation and test as being the best way to take advantage of the way the universe works. Hence all you need for those laws to exist, is a universe that works a certain way. And yet it will automatically follow from the existence of any such universe that there will be a best way to describe and manipulate it, and that “best way” will always be something humans can search for and discover, and then describe and use. We then call these procedures “rules” or “laws.”

Logical laws are, really, the laws of linguistic communication—whether communicating with oneself (for purposes of computation) or communicating with others (for purposes of transmitting data or conclusions to other “computers”). The moment any language exists, logic exists; for logic is the procedure required for language to succeed. Since it is a procedure, it requires no special supernatural “entities.” The laws, when written down, merely describe the behavior of natural entities that successfully communicate (with themselves or others). They describe and prescribe certain behaviors that are useful, just as agribusiness describes and prescribes certain behaviors that are useful. Therefore, any universe in which computation and communication exist will also automatically contain discoverable laws of logic. It is physically impossible for it to be otherwise. Every possible universe in which communication or computation can exist, will have some such logic.

If we go one step further and ask why these rules make computing conclusions about the world so successful—why did they turn out to be the best ones, rather than other ones we might have come up with or tried—then we get to Aristotle’s fundamental insight: to exist or even not exist simply is to manifest a distinction in the world; and the Law of Non-Contradiction simply describes all states and worlds that consist of distinctions; therefore anything that ever exists will be described by the LNC. And all other laws of logic follow, in one way or another, from the LNC. And that is why you just can’t get a world, or any state of being, that doesn’t obey the LNC. Take any world, any circumstance, and there is nothing you can change or take away or add that will get the LNC to stop describing it, and thus stop applying to it. It is simply a fundamental physical fact of all states of being that will ever exist.

And it’s no surprise we figured this out. Human brains evolved the computational ability to discover better ways of doing things, including better ways to think and communicate, but also better ways to grow cabbage or traverse distances or kill, and so on—it’s all the same ability: to explore, experiment, compute, and invent better procedures to achieve any goal. Once you have that ability, you automatically have the ability to discover logical laws, just as one can discover agricultural laws, or laws of medicine, or architecture, or anything else. It is just a matter of time and circumstance.

And since one of our most potent evolutionary advantages was language, and the procedure entailed by any successful use of language literally is logic, the eventual discovery of the laws of logic was all but inevitable for human beings. We thus “apprehend” the procedures required by language and computation the same way we “apprehend” the procedures for cultivating cabbage or manufacturing a spear. It is the same act of perception engaged when we observe that a pattern of marks is a face, or a pattern of sound is a song. If we can perceive these things, then we can perceive any other kind of pattern, including patterns called “procedures.” So if perception exists on godless naturalism—and it does—then we can perceive “logical laws” on naturalism.

And there’s no getting around this.

Since “logical laws,” like “agricultural laws” or “physical laws,” are descriptions of things that happen (or that we can make happen, if we follow the procedure involved), and these descriptions are visible as patterns in data, and brains as computers can perceive patterns in data—including patterns that describe things that happen (or that we can make happen, if we follow the procedure involved)—it follows that human brains can perceive logical laws. Just as this perception in the case of agriculture or physics results eventually in our having confidence that following the discovered procedure will improve our cultivation or manipulation of nature—and this is a physical, causal effect (our brains physically compute the perception, the output of which physically affects all future computations that draw on this output as input)—so also this perception in the case of logic results eventually in our having confidence that following the perceived procedure will improve our ability to think and communicate. Obviously this is a physical, causal effect in both cases. Since physical causation is all that is needed, and is easily accounted for here, naturalism can account for not only the existence of logical laws, but also how we could come to discover them, and use them in our reasoning.

So it simply isn’t true, as Victor Reppert once insisted, that if physicalism is true, “then logical laws do not exist or are irrelevant to the formation of beliefs” (p. 82). What he means by “logical laws” are simply rules that describe truth-finding procedures, which can thus be formulated in any language, and thus physically used in any human thought process. And our choosing to use procedures that are more truth-finding to form beliefs certainly does not make logical laws irrelevant—or our knowledge and use of them nonphysical, for that matter. Truth-finding procedures are obviously to be preferred to others, and this can easily be learned by observation. And clearly these procedures must be carried through physically by some computer or other, whether a human brain or not.

I’ll have much more to say on this point in my next article when I summarize why the Argument from Reason fails to pose any challenge to godless naturalism. But for the present point, just as “rules of farming corn” exist, in the sense that there are procedures inherent in the physics of the universe and its contents that result in successful corn farming, and those procedures can be discovered and described by any exploring, procedure-finding species like us, so also “rules of reason” exist, in the same sense: there are procedures that result in successful reasoning—reasoning that leads to true conclusions more often than alternative patterns of reasoning do—and those procedures can in turn be discovered and described. What else needs to be explained? Well, nothing.

There is no intelligible sense in which there can’t be truth-finding procedures in a purely physical universe. Obviously there always will be, in any universe, some procedures better at that than others. Likewise, there is no reason to believe brains of a sufficient complexity can’t discover those procedures (memetically, by learning; or genetically, by natural selection). But we’ve already gone beyond that: not only must these things be true, we have amply confirmed they are true. We can directly see why logical procedures will be the best ones to use for this purpose (in our purely physical universe as much as any), and we have empirically confirmed that we only mechanically (physically) learned this over a long, arduous, eons-long process of trial and error, exploration and experimentation. Exactly as we’d expect if no God existed; not the other way around.

As to how we can come to discover the laws of logic, that is no different than how we came to discover the laws of aerodynamics, or the laws of ballistics. There is no mystery at all in any of these cases. Consider the latter: our brains naturally evolved an intuitive albeit imperfect understanding of the laws of ballistics. When we throw or catch a ball or a spear, our brains compute its trajectory with amazing accuracy. Our brains can also improve this computational ability through experience, by trial and error. But even before we do that, we are already born with a ballistics computer in our head (as are many other animals). It isn’t a superb computer—but that’s because it developed blindly by natural selection, and not by intelligent design. It needs perfecting, and each individual can perfect it through experience. And all this goes on without any conscious awareness of what the computer is doing. But it’s still all just a physical computation in the chemically electrified meat of a brain.

Then, eons later, we came to discover how to precisely describe the operation of such a computer when we discovered the laws of ballistics themselves (by observing and hypothesizing and testing), and defined them (using languages, like mathematics, that we built for that very purpose). And then, with this knowledge in hand, we were able to build nearly flawless ballistics computers superior to our own. But even without that technology we could use our own general-purpose computer—the human cerebral cortex—to run a nearly flawless ballistics computation by running a program we invented and installed called “mathematics.” Our cerebral cortex wasn’t “built” for that, so it is very inefficient when used that way—it takes a lot of time and can make a lot of mistakes—but it can still be used that way, because the computational architecture required is exactly the same as that which our brains developed to communicate in any language and to follow any invented procedure to accomplish any goal. And then, when we wanted to do this even more quickly and reliably, we built a purely physical machine (at one time analog, now digital) to do it for us.

At no point was anything “nonphysical, nonspatial and nontemporal” required, either for Laws of Logic to correctly describe existable things, or for human brains or modern computers to learn and use them to reach conclusions from premises, or for this to be discoverable by either natural selection or intelligent exploration.

Trying to Avoid the Conclusion

One can’t object to any of this by just “insisting” that logical laws are “not like” physical laws and “therefore” can’t be. Yes, physical laws describe the way the universe works, and logical laws describe the way reason works—or, to avoid begging the question, logical laws describe the way a truth-finding machine works, in the very same way the laws of aerodynamics describe the way a flying machine works, or the laws of ballistics describe the way guns shoot their targets. But here the only difference between logical laws and physical laws one might try to press is that physical laws describe physics and logical laws describe logic. But that is a distinction without a difference. Logic is as much a physical procedure as growing crops, hitting targets, or keeping planes in the sky. It’s physics, all the way down.

It also can’t be objected that logical laws are unlike physical laws in that only the former “pertain across possible worlds, including worlds with no physical objects whatsoever” (Reppert, p. 81; cf. p. 94). First, because “physics” does not have to limit itself to “physical objects.” If there were disembodied souls and magic spells in this world, they’d be described by—because they’d consistently follow—their own physical laws. To exist is in always some sense to physically exist. This is not to be confused with the specific philosophical position of physicalism which hypothesizes that only patterns of matter-energy in space-time exist. But physics the science is not constrained by that hypothesis. It only conforms to it because, it just so happens, that’s all so far that it has found to be the case.

Second, many physical laws will pertain across possible worlds: because all worlds with the same features will exhibit the same physics. So, if there is a physical law that describes, and therefore governs, all existent things, then that law will pertain across all existent things, which thereby encompasses everything that could ever exist. Just as if Newton’s Laws of Motion or the Economic Law of Demand described systems that, for some reason, were always present across all possible worlds, then they, too, would pertain across all possible worlds. The only reason they don’t apply across all worlds is that the physical properties they describe don’t exist in all worlds; you can construct worlds without those features. Hence the only reason the LNC does apply across all possible worlds is not because it is in some way mysteriously special, but because it is the only law that describes a physical feature (the existence of distinctions) that does exist in all possible worlds; because you can’t construct possible worlds without making distinctions.

It’s thus not true that, as Reppert insists, “if one accepts the laws of logic, as one must if one claims to have rationally inferred one belief from another, then one must accept some nonphysical, nonspatial and nontemporal reality” (p. 81). Here Reppert is close to discovering why he is wrong, but just when you think he has it, he puts the cart before the horse, then observes that the whole caboose won’t go, and from that concludes it can’t go, without some wizard to cast a spell to levitate the cart so it can drag the horse along. If you think that is a silly way to respond to an inverted horse-and-cart, then you will agree Reppert’s approach to logical laws is silly, too. The only reason one must accept the laws of logic to rationally infer anything is the very same reason one must accept the laws of aerodynamics to fly. Surely Reppert would not conclude that we need some sort of supernatural powers and beings to explain why we need to follow the laws of aerodynamics to fly. The reason we need them is that it is physically impossible to fly any other way, and the only way flight is physically possible is exactly the way described by those laws. All you need for that to be true is a physical universe that is a certain way.

Of course you could “insist” that the laws of aerodynamics are “nonphysical, nonspatial and nontemporal.” You just wouldn’t be saying anything that’s true. Ditto for the laws of reliable computation: reasoning procedures that get reliable results are no more “nonphysical, nonspatial and nontemporal” than procedures that keep planes in the sky. They can be understood conceptually, but only ever replicated in practice in a physical machine. Even in a world where disembodied souls exist, you still have a machine—the soul—that is processing that deterministic procedure of reasoning. This is exactly like the laws of aerodynamics, which do not exist but for the physical objects and relations that physically interact as those laws describe. Hence there is no sense in which this behavior of physical objects, or their existence, or their interaction or relation, is “nonphysical, nonspatial and nontemporal.” Since logic is just a description of any system possessed of distinctions, any system possessed of distinctions will be describable with logic. No “nonphysical, nonspatial and nontemporal” thing need be added for that to be the case. It’s physically the case.

But, you might say, we can use the laws of aerodynamics to describe possible flying machines that never have and never will exist. Indeed. Because the laws of aerodynamics apply to (they describe) all physical worlds that are relevantly similar, including worlds that have flying machines in them that do not exist in this (the actual) world. Hence we can virtually model those worlds and machines (in our minds or, nowadays, a digital computer) and thus explore what is possible even when it does not exist. The same is true of logic. The only difference is that even fewer physical attributes are necessary for those laws to hold true in other worlds—because the mere physical fact of the existence of distinctions is alone sufficient to establish the LNC. And there simply is no such thing as any state of existence that is not a distinction. Which is really all it means to say a world logically cannot exist: there is no way to build one, because that would require making no distinctions, yet making distinctions is the only way to have a world exist rather than not. Making distinctions simply is what it means to say that something can or does exist.

Maybe it is possible, one might say, for computation itself to exist without space, time, and physical objects—I doubt it, but I don’t trouble myself with trying to answer such a question, because it is of no relevance to me, who literally am a physical computer in space-time. Even if computers can exist in other nonphysical worlds, that does not entail that computers can’t exist in purely physical worlds. And the question at issue is solely whether computation can exist in a purely physical world. Thus, when I say computation only exists in this world as a consequence of complex physical machines functioning in space-time, I am not saying this is the only way it can be done (though it might be), but simply that this is all we need to have rational thought exist, and all we observe is actually the case; and since a physicalist world provides all that, a physicalist world is sufficient to explain why rational thought exists.

Another failed attempt to escape this conclusion is Victor Reppert’s observation that “If naturalism is true, then there is no single metaphysically unified entity that accepts the premises, perceives the logical connection between them and draws the conclusion” (p. 84). But since there doesn’t need to be, this is a point of no consequence. Computers run logical inferences on disparate circuits all the time—in fact, can only do so. In future this might in some sense cease to be true only in quantum computing; but the human brain is definitely operating in analog, not quantum fashion, so hypothetical kinds of computers don’t matter to the present point. In current computers there is no need of their circuits (physical or virtual) achieving some sort of ontological oneness. They are separate parts, causally interacting, producing the output from the input, step-by-separate-step (indeed, bit-by-separate-bit even); yet they can execute every rational inference there is. The human brain, likewise.

That the human brain generates a feeling of all this being a unified process has nothing to do with how the process is actually produced, which we well know is by a large number of different circuits, just like digital computers. The feeling that it’s a unified consciousness just magically doing everything without any underlying mechanical computation is just a convenient illusion, a shorthand for logging what has happened, and relating it to a coherent entity and purpose. As digital computers prove, logical inference does not require feeling like a single unified mind doing the thinking; feeling like a single unified mind doing the thinking is simply one way of recording and tracking the logical inferences that are being made.

Indeed, the process of computing this feeling takes measurable time; as Libet-style experiments prove, the brain has made all its choices and done all its thinking about a fifth of a second before it “becomes aware” of having done so in a unified conscious experience. Likewise, all the components of every thought have long been proved to be generated and analyzed in different parts of the brain, and are stitched together through yet other interconnected areas of the brain, disproving any notion of a unified experience being responsible, rather than simply the output. We likewise have used stimulation of neurons, or even the numbing or destruction or loss of them, and fMRI imaging, and many other convergent approaches, to prove reasoning’s components are scattered across the brain. There is no “unified entity” but for the computed feeling of being one—a feeling computed by a giant complex kluge of meat-circuits.

This failure to distinguish the peculiar ways human brains generate a report of what they have computed from the actual computation being run seems to be a fundamental cause of confusion in Christian thinkers like Victor Reppert. For example, “How can it be true,” he asks, “that one thought causes another thought not by actually being its ground, but by being seen to be the ground for it?” (pp. 94-95). Reppert does not appear here to understand what it means to have a logical “ground.” He evidently thinks it’s some kind of extra property, some “third entity,” for example, that exists apart from P and Q, when P “entails” Q. But that’s hocus pocus, rather like thinking there must be invisible angels that are pushing the planets in their orbits, or that a car’s engine would not go but for a magical car-demon jerking its pistons.

When P entails Q this means that the “set” or pattern P contains the set or pattern Q. Thus, all that is needed for “P entails Q” to be true is that Q be contained within the meaning (the mental content; which is a virtual model of the actual or potential physical content) of P. No “third” entity mysteriously called a “ground” needs to exist here. The “ground” is simply nothing other than the fact that P includes Q in its content—which requires nothing but P and Q. Likewise, no mysterious power is needed to detect the fact that Q is contained within P: all you have to do is look at P, and search around to see if Q is in there (and whether Q is wholly in there or extends outside P, and so on; but in every case, it is just a question of detecting different patterns, which any suitably arranged mechanical process can do). Digital computers run sims to do this; and so, essentially, does the human brain. We can see that “there is a live cat in my house” entails “there is blood in my house” because when we run a virtual model of what it means to have a live cat, that model includes blood—inside the cat. There is no great mystery as to how we can construct and search virtual spaces to discover facts like this—in our minds, or in digital computers.

Likewise, Reppert just as senselessly asks, “How could there possibly be states of something that not only do not exist in any particular place or time, but are true in all possible worlds?” (p. 95), referring to the mere “state” of “P entailing Q.” But the state of “P entailing Q” does exist somewhere: of course it exists in our brain (as a physical representation of the logical relation, just as in a solid-state computer running the same computation); and of course (when referring to an actual fact outside the brain) it also exists in the physical world, wherever there is a P and a Q. But more importantly, it also exists as a fact of the universe as a whole (and in fact all universes), just as the law of gravity exists as a fact of the universe as a whole (and would exist in all universes, if they possessed the same physical features that we describe as gravity).

There is no particular “place” or “time” where the law of gravity “is.” It “is” in every place and time where the physical conditions that manifest gravity exist; and would exist even in non-existent places that may or may not ever come to exist, if those places also then possess those same physical features. That is simply true by definition: to say that a universe contains the physical features manifesting gravity simply is to say that gravity exists in that universe. They are not separate assertions. They are exactly the same assertion. Thus we can confirm things about non-existent universes by simply computing what contents that universe would have given its description.

By the same token, the same physical conditions (attributes of the universe) that permit P to entail Q exist in every place and time the relevant laws of logic also describe. For example, the Law of Non-Contradiction “exists,” i.e. applies, wherever distinctions physically exist; because it simply is that fact: the existence of distinctions. Just like gravity, only unlike gravity, “wherever distinctions exist” is always going to be everywhere that exists—because you can take the conditions producing gravity away and still have a place to be, but you can’t take away the existence of distinctions and still have anything left over.

So not only is Reppert’s question “How could there possibly be states of something” that “do not exist in any particular place or time?” based on false assumptions about the physicalist ontology of logic, but his subsequent question, “How could” such states be “true in all possible worlds?” has the whole thing turned completely backwards. The fact is not that logical relations “are” true in all possible worlds, as if they just “happen” to be like some sort of mysterious add-on, but the other way around: the set of “all possible worlds” simply “is” the set of all worlds that can be constructed from (i.e. are described by and thus consistent with) the Laws of Logic. To say “all possible worlds” simply is to say “all worlds governed by logic.” Which, again, simply is to say “all worlds in which distinctions exist,” which we know is all worlds that could ever exist because that is what it means to exist. To exist, is to manifest distinctions. The absence of distinctions simply is the absence of existence. And that is why there are impossible worlds and impossible states of being.

Reppert similarly insists there is still a mystery in the fact that the recognition of logical relations “require[s] that we know something about thoughts that we have not yet thought” (p. 96), by which he means logical laws apply to future thoughts, hence thoughts we have not yet had. But this is another irrelevant complaint. Of course, knowledge is not the same thing as information. We can have all the letters in the right sequence (information) and still not know that they spell “stop” (knowledge). To extract knowledge from information requires analysis (computation), and that entails a procedure. Second, and more relevant to Reppert’s concern, the reason we can “know” that a procedure that applies to a thought today will apply to a thought tomorrow is the same reason we can know that a procedure that applies to growing corn today, or building an airplane today, or sharpening a spear today, or starting a fire today, will also apply to the same activity tomorrow.

We can certainly model in our imagination conditions in which those procedures would stop working (can’t grow corn on the sun; can’t build an airplane without anything to make a wing; can’t sharpen a spear in a two-dimensional space; can’t start a fire in a vacuum), and thus we can “know” that it’s possible to end up somewhere where they don’t work. But this reasoning doesn’t follow for the Law of Non-Contradiction because the only way to have any condition it does not describe is to be where no distinctions exist—which means nowhere. And that is how we know it will always apply, and thus any procedure relying on it will always work—unlike growing corn, building planes, sharpening spears, or lighting fires.

The reason we know any procedure applies anywhere at all is that we have learned from observation and practice that given a certain set of relevant conditions (like having some sticks of dry wood and kindling, in habitable atmospheric conditions, with low wind, and so on), a certain procedure will work (i.e. produce the result intended: like starting a fire). Therefore, we “know” that whenever those conditions obtain, tomorrow or a hundred years from now, the procedure will still work. Introducing new conditions, taking conditions away, can of course change that fact, and that is the only reason there could ever be any doubt about the future being the same as the past. But there are no conditions that can be added or taken away that will cause the LNC to stop working—as in, to stop correctly describing any actual or potential reality. The only move that can get rid of it is getting rid of distinctions. Which means getting rid of every possible state of existence. That’s why there are no states of existence that will not be described by the LNC.

So in the end, Victor Reppert has done nothing to show that physicalism is incapable of producing a fully explained ontology of logic. And neither has anyone else. But what we have also learned is how valuable and important it is to have worked out why that is. Reppert’s ilk have done us a favor: their failure to grasp why things are the way they are, and then using that ignorance to try and prove their ancient primitive superstition is true, inspires us to succeed at grasping what they have failed at, and thus settling and thereby learning something important about the world—or indeed, in this case, all possible worlds.

Conclusion

All logics reduce ultimately to one fundamental Law of Logic, the Law of Non-Contradiction. Maintain that, and every other logical “law” or “rule” can be built out. And the Law of Non-Contradiction is simply a literal description of any state of affairs in which distinctions exist. And “a state of affairs in which distinctions exist” is simply a description of what it means to exist. Only the complete absence of anything existing can “get rid of” the existence of distinctions—and yet not even an actual state of absolutely nothing does this, for in order for such a state to ever exist, distinctions must be made (as “nothing” is obviously quite distinct from “something,” and thus is definitely the existence of a distinction). That means that the only kind of thing that lacks all distinctions is anything that will never and can never exist. And that is simply what it means to say that some thing, call it P, can’t ever exist: as P lacks all distinctions, and distinctions must be made for something to exist, P simply per description lacks the property of existence. Whereas once something exists, distinctions exist; and the LNC simply is a description of all states of affairs where distinctions exist.

Physicalism therefore has no difficulty explaining why “Laws of Logic” exist, and why they will always govern everything that could ever exist. We also have no difficulty explaining how human beings, even other animals, can discover this fact—by intelligent learning through an active application of their exploring mind, or by the natural selection of their genes encoding the construction of their physical information-processing brain—and then use this fact—by incorporating it as a rule in a learned or intuitive procedure—to get better at discovering true facts about the world, and indeed even merely possible worlds—from which we can construct or rule out new ways the world could be, thus producing all human progress. All this requires is a physical procedure of computation; and any physical system realizing physical procedures of computation can do that; and all evidence points to human brains being just such a system, while we have entirely confirmed this of digital computers, which can be built or taught to compute every rational inference there is. And since the observable utility of rational inferences is an obvious target for selection, natural or sagacious, that we’d arrive at it eventually is unremarkable.

There is nothing left to explain.