Bill Vallicella has contributed his commentary to Victor Reppert's exchange with Richard Carrier on the true nature of the laws of logic in three separate posts. I respond to Vallicella's critique of Carrier's original response to Reppert below. Also included at the end, I respond to Vallicella's critique of Reppert's email exchange with Carrier since there are only a few issues involved before Vallicella gives up. My response to Vallicella's commentary on Reppert's original response to Carrier can be found elsewhere.


...naturalism, as Reppert understands it, cannot countenance any nonspatial and nontemporal realities.
The reason that someone might not be able to countenance nonspatial "realities" is the same reason they cannot countenance circular squares. Immaterial things are conceptually impossible things which are definitionally indistinguishable from non-existent things. Nothingness isn’t going to change any time soon. Nothingness has no beginning. Nothingness is uncaused. Nothingness isn’t concrete. Nothingness has no height, length, width, depth, or location. Nothingness can’t participate in causal networks. We only understand nothingness in terms of what it isn’t. Nothingness isn’t anything in particular. We can’t tell one nothingness from another nothingness. Etc. Nothingness has all the same “characteristics” that immaterial entities have and there is nothing that people can possibly be referring to when they talk about them “existing.” It seems to be just a trick of rhetoric (resulting in a lingual phantom or a type of philosophical error theory) to pretend to still be talking about something when we've eliminated all of its somethingness up front by definition.

Similarly, how can a nontemporal mind think!? Thinking at its most generic metric requires that this mind have one state and then transition to another. If that most rudimentary parameter cannot be satisfied, what kind of a "mind" can we possibly be talking about? Otherwise, if we aren't talking about atemporal minds like the Christian god is supposed to be, then I see no problem with the concept of static existences that aren't on timelines. This is especially true for naturalism given that I think our timeline can be understood as a static four dimensional object which is then "nontemporal" in the sense that its entire history will never change. So Vallicella is wrong in more than one way here.


...the difference between physical and logical laws are not 'trivial and obvious.'

Carrier's point is that both logical laws and physical laws merely describe the way things actually work and can claim nothing else. Putting more into it than that presupposes Platonism, assumes things simply must be the way they are as a result of these "laws" and therefore goes beyond what we can confidently claim to know.


Laws of nature are logically contingent.

It is a violation of the law of non-contradiction for "contingency" to be ontologically meaningful since that would entail that something literally does and doesn't exist simultaneously from the grandest possible frame of reference (i.e. a god's eye view). Therefore anything that exists is a permanent "addition" to reality and never not was in just the way it is. It follows that contingency is just an arbitrary frame of reference that is convenient to make use of from our perspective. Vallicella:

...the laws of logic are necessarily true, whereas the laws of physics are not.
If anything that exists in whatever way necessarily exists as I argued above, then it follows that the laws of physics have to be exactly as they are even if we may not understand why that is in the grand scheme of things.


...the laws of logic are prescriptive rather than descriptive: they prescribe how we ought to think if we want to arrive at truth in our reasoning. They do not “describe the way reason works” since reason often malfunctions.
I imagine Carrier would have no trouble saying that the laws of logic are both prescriptive and descriptive. Incidentally, part of the description can be that reason doesn't always work. Similarly the laws of physics are prescriptive in much the same way, since they tell scientists how to build things. Vallicella:

The world does not get its modal structure from the meat between our ears.
Vallicella gets Carrier's claims backwards since the claim would be that the meat between our ears reflects the modal structure of reality at large. Evolution or an intelligent designer could not make a brain that can imagine a circular square, for instance, and that's Carrier's basic point. The two are synonymous at least to the practical extent brain power can take us.


Now if P is undecidable relative to that axiom set, then there is a sense in which P is not 'computable.'
If Godel's variable P is not computable, then it is not meaningful. Either there is something to compute or there isn't. Whatever "sense" Vallicella is referring to must mean that something is not computable practically based on what we currently know or understand, but not in principle. What is it mean to say something is both meaningful and does not compute even in principle? That's meaningless by definition.


It is also false that 'computation itself is literally logic....' Computation is a process while logic is a set of truths. Computation exists contingently; the truths of logic exist necessarily. Computation is going on in the CPU in front of me now, but not in other places such as my left foot. The truths of logic are not locatable.
As I demonstrated contingency is an irrelevant distinction. Also, there are two different understandings of the referent "logic" going on here. Rather than host an assert-a-thon, it seems important to look at logic from Carrier's perspective in order to see why he says what he says and connect that to Vallicella's assertion to the contrary. If logic is a set of truths as Vallicella claims, and truth is relational as Carrier claims elsewhere, and relations in physicalism only exist in terms of actual computation, then Carrier can claim that logic is literally computation. CPUs would compute just as well in solely materialistic terms in either worldview. There would be the material world and then there would be the pattern of the computer computing. Nothing else. That's Carrier's view since the brain is just a more sophisticated biological computer. Nothing makes a pit-stop in magical logic land.


Carrier is missing a very important difference between physical laws and logical laws, namely, that one can violate logical, but not physical, laws.
One can misapply logical procedures in their thinking just as easily as they can misapply physics equations. Not everyone gets an A in physics class after all.


A program [...] presupposes the truths of mathematics.
Programs are physical systems and don't do any "presupposing" as far as I know. Though I guess I shouldn't take Vallicella so literally as he tends to do with Carrier to a fault.


I see no clear sense in which the infinity of mathematical truths (many of them undiscovered) can be described as a program.
Discovering mathematical truths is only a relative perspective. We can discover new math much like we discover any new procedures for doing anything. Did the instructions for baking a new recipe have to "pre-exist" as well? Math is certainly more rigorous and detailed than the procedures for cooking, but that's about all we can say about it.


[Carrier's] ...argument is this:

1. Logical laws derive from communication and computation.
2. Physics (i.e. the physical world) is all that is needed for communication and computation.
3. Physics (the physical world) is all that is needed for logical laws.

I see no reason at all to accept premise (1). First of all, it is not clear what ‘derive’ means here. Does it mean that logical laws are empirical generalizations from the way people reason as a matter of fact? But if LNC were an empirical generalization, it might be falsfied by future experience – which is absurd. Logical laws do not derive from communication and reasoning: they are imposed on them. They are criteria of what is to count as true, and what is to count as real; as such, they cannot be said to derive from existing physical facts.

One could not hope to falsify a true description of the physics of the past if it actually was a true description of the past. Since descriptions of things do not entail that they will necessarily continue to hold true into the future, and since we aren't actually dealing with some extraneous magical law that makes it so, true descriptions of the past are just as unfalsifiable as the law of non-contradiction. It is only our relative frame of reference going along ignorantly of the static full frame of reference that tends to lead us to believe the one is more contingent than the other.

**More on the Status of Logical Laws**

Here, Bill Vallicella seems to be taking the position that identifying the laws of physics is the same thing as identifying what the long term nature of the universe will be (and therefore presupposing that we really are dealing with literal "laws" which dictate the physics of the future).

Carrier says:

By definition, the "laws" of logic are the procedures by which one can arrive at true conclusions from true premises. Those procedures are fixed by the nature of the universe--just as all physical laws are.
But Vallicella says:

The laws of physics are logically contingent: they hold in some but not all logically possible worlds.
I have argued above that the "contingency" language is meaningless, but there are meaningful levels of articulation here. Laws of physics hold true given the particular physical geometry they describe and the laws of logic hold true in a more universal way regardless of what geometry we are talking about. Not sure why that matters. Both are descriptions of actual existence and so there's no reason to jump to metaphysical conclusions.

Carrier responds:

Vallicella is arguing in a circle. "Logically possible worlds" just are, by definition, worlds in which logical laws obtain. Thus his remark above is like saying "the laws of gravity are logically necessary, because they hold in all worlds that obey laws of gravity." You would reply, "but they don't hold in worlds thatdon't obey the laws of gravity, so they can't be logically necessary." Thus also here: "the laws of logic don't hold in worlds that don't obey the laws of logic, so the laws of logic are just as contingent as the laws of gravity." To which he'd reply, "but worlds that don't obey the laws of logic are not possible," which merely presupposes as a premise the conclusion he is attempting to arrive at. Classical circularity. The analogy to laws of gravity is entirely straightforward: to define a set as "worlds that obey laws of gravity" you are selecting worlds structured a certain way. Likewise "worlds that are logically possible": you are just selecting worlds that share the same physical property, namely that of obeying the laws of logic, which means, as I showed originally, that of possessing distinctions, which is all the physical property is that is described by the laws of logic, analogous to gravity being described by laws of gravity. He cannot escape this. A certain physical property entails obedience to the laws of logic in exactly the same way as entails obedience to laws of gravity--the only difference being which physical property we're talking about. He might in the end insist that a world without distinctions is not a world at all, but then that's simply my point, i.e. we clearly aren't in such a place, nor could we be, and indeed if such a world is impossible, we don't need to propose God to explain why we're not in one.
Vallicella has said:

This obviously begs the question against Reppert.
He may like to believe that, but Carrier is appealing to two facts that are true in Reppert's worldview. There is a physical world and there are descriptions of it. As Carrier shows, he can explain everything with those mutual facts and supernaturalism is left trying to justify a third fact. It is very typical for both sides in a debate like this to accuse the other of "begging the question," however it is very easy for Carrier and myself to ground our accusation. And not so easy for the supernaturalists who have to appeal to an unsubstantiated inference that is not shared.


Physical and logical laws in the way Vallicella and Reppert conceive of them are compatible with reality, but are not necessarily entailed by it. Although as immaterial entities that exist in that non-existent kind of way, their version of logical laws is incoherent. Carrier's perspective accounts for the mutual facts coherently without introducing ad hoc assumptions and is therefore a better explanation.