First-order naturalism

In a lovely paper, Leon Porter shows that semantic naturalism is false. One way to put the argument is as follows:

1. If semantic naturalism is true, truth is a natural property.

2. All natural properties are first order.

3. Truth is not a first order property.

4. So, truth is not a natural property.

5. So, semantic naturalism is not true.

One can show (3) by using the liar paradox or just take it as the outcome of Tarski’s Indefinability of Truth Theorem.

Of course, naturalism entails semantic naturalism, so the argument refutes naturalism.

But it occurred to me today, in conversation with Bryan Reece, that perhaps one could have a weaker version of naturalism, which one might call first-order naturalism that holds that all first order truths are natural truths.

First-order naturalism escapes Porter’s argument. It’s a pretty limited naturalism, but it has some force. It implies, for instance, that Zeus does not exist. For if Zeus exists, then that Zeus exists is a first-order truth that is not natural.

First-order naturalism is an interestingly modest naturalist thesis. It is interesting to think about its limits. One that comes to mind is that it does not appear to include naturalism about minds, since it does not appear possible to characterize minds in first-order language (minds represent the world, etc., and talk of representation is at least prima facie not first-order).

First-orderism

It’s notoriously hard to characterize the physical precisely enough to attack or defend physicalism. To attack physicalism, however, it is enough to attack a characterization broader than physicalism, and to defend physicalism, a narrower characterization will do.

Here’s a suggestion along the “broader” lines. We can characterize reductive physicalism over-broadly as:

• Reductive first-orderism: All facts about the concrete (variants: contingent, spatiotemporal) features of the world reduce to first-order facts.

This may take in some theories other than what one intuitively counts as reductive physicalism, but if the object is ciriticism, that’s all we need.

Note how this characterization nicely shows how paradigm examples of magic would violate reductive physicalism: for paradigm examples of magic involve causation irreducibly by virtue of the meaning of a spell, gesture, etc., and meaning is a higher-order property. It also shows why irreducible Aristotelian teleology has no place in a reductive physicalist story: for teleological properties are second-order (I think).

Moreover, if we see reductive physicalism in the above way, it’s also easy to see that it’s false, by an argument of Leon Porter. For any first-order fact can be expressed in a first-order language. But, famously, the property of truth cannot be reduced to properties expressible in a first-order language (Tarski’s indefinability of truth; or, more simply, note that if you could express something equivalent to the property of truth in a first-order language, you could express the Liar Sentence in a first-order language). And some concrete objects, namely inscriptions, have this property of truth. Hence, some concrete objects have a property that cannot be expressed in first-order terms, contrary to reductive first-orderism.

Causal closure of first-order facts

Consider the following doctrine: First-order facts are causally closed. This doctrine neither entails nor is entailed by the doctrine that the realm of the physical is closed under causation, but it is a doctrine of a similar sort. It might, in fact, be preferable as a statement of the causal closure condition that naturalism is committed to, because the notion of a "first-order fact" seems to be clearer than that of a "physical fact".

If semantic properties of beliefs enter into causal explanations of physical facts, then first-order closure is false, unless semantic properties of beliefs reduce to first-order facts. But it is unlikely that they reduce to first-order facts. One reason to think that they don't reduce is that semantic properties such as truth and reference, if they are expressible in first-order terms, will give rise to liar-type paradoxes within the realm of the first-order. But, plausibly, the realm of the first-order is free of such paradoxes.

In any case, seeing the dualist as someone who denies the causal closure of the realm of first-order facts, as someone who thinks that mental states can cause effects in virtue of their properly semantic properties, seems to me to be illuminating.