Logic and Material Reality

Does the existence of logic undermine physicalism?

Logic sometimes seems mysterious, permeating different subject areas and governing human thinking. It carries with it both the gravitas of intimidating intellectual rigour and a supernatural power shaping human endeavours toward inevitable progress through the miracles of our innate reasoning minds and the intelligibility of our ordered world. It’s even in The Bible!

Ἐν ἀρχῇ ἦν ὁ Λόγος, καὶ ὁ Λόγος ἦν πρὸς τὸν Θεόν, καὶ Θεὸς ἦν ὁ Λόγος.

In the beginning was The Logical Principle, and The Logical Principle was with God, and The Logical Principle was The God. - John 1:1 (my own translation)

A Variety of Logics

To the programmer, ‘logic’ means things like flow control statements

if( condition == true ) {
return true;
} else if ( condition == false ) {
return false;
}

(that snippet is a joke!!), or, even in this context, something looser — for example, requirements-talk consists of “business logic” or architecture talks of “logical layers” and so on.

To the online, red-pilled debate-me-bro, “logic” means something like “I am right, very smart and you are wrong and emotional”. In this context “logic” is a rhetorical device. The intellectual equivalent of beating one’s chest or giving themselves a pat on the back for being intellectually intimidating and better than their disputants. Don’t you know that “the libs” just can’t “use logic” and that’s why they have the views they do on mRNA vaccines and Trump!

In other contexts, such as to a Mathematician, “logic” means something else: a universe of discourse containing provable statements, and inductive proofs of results.

To a philosopher, it means something else yet again - the difference between modal semantics in S4 and S5, gluts gaps and paraconsistency, and the formal validity of argumentation (to name a few things). Something to do with philosophy of mind, and thought, something we owe an account of.

“Logic” is a word that has a life of its own spanning multiple subjects and being used in a variety of different ways.

A Bad Argument Against Physicalism

Due to its polysemy, mysterious nature, gravitas and seeming ability to govern all things, some people have developed what I consider to be unrefined and unreflective positions on what logic is that I consider to be mistaken in a number of ways. The most frustrating of these for me being arguments which allege to establish that logic is incompatible with a physicalist paradigm.

Christian Apologist “Made by Jimbob” offers one such argument in his video “Fatal argument against naturalism” — I shall hope it isn’t fatal as I am in my twenties, a naturalist and hope I have a few more years left.

P1) If something is a physical “effect” [event] then it is not a truth-apt proposition
P2) If naturalism is true then reality is exhausted by physical “effects” [events]
IC1) Therefore, if naturalism is true then there are no truth-apt propositions
P3) But there are truth-apt propositions
C) Therefore, naturalism is false

I’ve not quoted Jimbob directly here, I’ve done him the courtesy of making the argument logically (badum tss) valid and of translating “effects” to “events” which is more amiable philosojargon to an evil physicalist like myself.

The only commitment that I would assent to as a naturalist is actually P2. I basically agree that naturalism (or physicalism, I personally use the terms interchangeably) is the belief that reality is exhausted by physical events. P3 is either blazingly obvious or iffy depending on something that I will talk about shortly. What I can’t see is why any reasonably informed and reflective naturalist would accept P1 - so let’s look at P1 and then use that to launch into a discussion of P3.

Suppose someone is a naturalist and thinks that there are truth-apt propositions. I mean that’s the sort of “data point” or explananda that the argument is appealing to and saying that naturalists can’t provide an account of, right? Well, presumably given that someone is a naturalist, AND that they think there are truth-apt propositions, it’s not too far-fetched to form the belief that maybe they have some natural account of what truth-apt propositions are. This might mean any number of things, and I will briefly outline my views shortly, but that is all that is required for a naturalist to very very clearly reject P1. As such, it isn’t really clear to me why any well-considered naturalist would accept P1 if they’ve thought about logic or their own views in any kind of capacity at all!

If some physical states are not true or false, then aren’t they all?

Now, I can readily imagine Jimbob turning around at this point and saying “that’s not [your account isn’t] a truth-apt proposition, that’s a false theory"!” Here’s why that won’t do. Jimbob is appealing to his own beliefs that the theory is false, but not those of the person he is trying to convince — there isn’t any inconsistency in their beliefs though of course their beliefs disagree with Jimbob’s! At this point there’s a dispute about who has the better account of what a truth-apt proposition is and that’s where the discussion should go, but that kind of theory comparison requires sitting down at the table with the party you disagree with to carefully compare and contrast explanations, not brandishing the first bit of philosophy you came across like a Wunderwaffe and acting like some mad philosophy tyrant!

We can also even imagine a naturalist coming around to JimBob’s point — “ah, you mean by truth-apt proposition a “bearer of truth”, a mind-independent metaphysical entity that “has intentionality”, well if that’s what you mean of course I don’t believe in that and P3 is false, so I don’t accept your argument and it’s no problem that I kind provide an account of something that I don’t think exists on naturalism.” The hypothetical naturalist here has rightly pointed out that Jimbob is simply question-begging in P3 by meaning “something non-natural exists” in P3. Jimbob will of course object and say things like “well logic exists, every proposition is true or false” and so on but all this does nothing for the naturalist because when this naturalist says “logic exists” they just mean people saying it, making markings on pages like ‘p→q, p |- q’, truth tables (which exist on physical pages), words people say like “conditional”, “syntax”, “semantics”, “metalogical proofs” which people perform with a pen on paper, physically. They don’t deny that logic exists, they deny that there are spooky and mysterious truth-apt entities that are in any way connected to these things that people do with pencils in their hands, operated by nerves and muscles, and by creating sounds with their vocal cords.

Naturalists who believe that reality is exhausted by physical events have the following options available to them to reasonably reject this argument against naturalism. Suppose they accept P2, that If naturalism is true then reality is exhausted by physical “effects” [events]. They either believe (P3) in truth-apt propositions, in which case they understand truth-apt propositions to be natural things (i.e. being fully grounded in physical events like typing with your fingers in space-time causing electricity to go through wires and make markings that are language on a page etc.) and hence deny P1, that if something is a physical “effect” [event] then it is not a truth-apt proposition, so the argument is unsound. Or they do not believe (P3) in truth-apt propositions (because they understand such things to be non-natural spooks that have no place in their metaphysics), so the argument is unsound. And whichever way you cut it, the argument is just not going to work for naturalists.

Going forward…

Im writing this to clarify some thoughts I have on a popular-level apologetics argument that irks me. I also plan to write some more about the history of logic, what I think of logic and how I think it fits quite nicely in a naturalist paradigm and how that coheres nicely with contemporary views in statistics, computer science, linguistics and philosophy of mind. If that sounds of interest then please do subscribe or become a follower of my substack to help encourage me to write more short pieces on this topic.