Thursday, February 11, 2010

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.


enigMan said...

It seems to me that we know quite a lot about what we mean by "physical fact", from ordinary life and physical science, for all that such things are a bit vague (what isn't?); there is a natural kind there, which we can discover stuff about. But I've no idea what a first-order fact is. My first guess is that they like that mouse (by my computer) being black? But if so then why is the meaning of a sentence that I read not a first-order fact about the writing before me? Or why not, instead of that mouse being black, that bit of my visual field being black (a mental fact), or that piece of plastic having a surface that reflects light in such a way (a physical fact)? What you say in this post interests me, but I've no idea what you're saying.

Alexander R Pruss said...

How about: Non-first-order facts are facts that involve quantification over relations (with propositions being 0-ary relations and properties being unary relations)?

Heath White said...

I too was puzzled by "first order facts." The last comment sheds more light. But why not: non-first-order facts are facts that involve quantification? I would think that quantified facts do not add any causal juice to what's already there in particular facts.

Heath White said...

Also: why are we so sure that, say, facts about reference or truth are non-first order? E.g. the fact that 'frogs' refers to frogs; or the fact that 'snow is white' is true. Is there some hidden quantification here?

Alexander R Pruss said...


Maybe these don't involve quantification. But things like "Most of our beliefs are true" do seem to.

The suggestion that quantified facts add no explanatory juice seems to conflict with the fact that, say, the statistically-understood reliability of some faculty (epistemic or not) might explain some evolutionary facts. Though maybe reliability needs to be understood non-statistically even for evolutionary purposes.

John said...

Also: why are we so sure that, say, facts about reference or truth are non-first order? E.g. the fact that 'frogs' refers to frogs; or the fact that 'snow is white' is true. Is there some hidden quantification here?

Well, the definite descriptor (as in, "The [blank] such that [blank]") is a quantifier, so if we fill out your examples, they will quantify over propositions (or sentences, or whatever):

"'Snow is white' is true" := The proposition denoted by the sentence 'Snow is white' is true.

enigMan said...

Hmm... if I was more sure about the role of physical laws (which seem prima facie to involve quantification) in Naturalistic causation, I might agree with this post; but as it is, I'm still not sure what the first-order facts are: Why could God not have created the world without quantifying over relations?

Alexander R Pruss said...

Well, a part of the theistic explanation of the world will make reference to some principle like: For all propositions p, if God wills that p, then and therefore p.

enigMan said...

...and a naturalistic explanation may well include such laws as: "For all particles p, p will move with constant velocity unless it is a charged particle within the force-field of another particle with the same kind of charge (of either sign)."

Michael said...

The notion of a natural fact is puzzling, maybe because Naturalism is. If God created nature, then that is a fact about nature, a natural fact. If the ratio of circumference to diameter is Pi, then that is a fact about nature, a natural fact too. The Naturalist always needs an "only" or "nothing but" in their exposition, and then an irony comes into play: the "only" is unwarranted on admissible Naturalistic methods.

If a first order fact is a fact about nature, and a second order fact is a fact about facts, and a Naturalist accepts "only" facts about nature, there can be no distinction between orders of facts: facts are parts of nature too, so a fact about them is first order, about a part of nature.

But if there are facts at all, they are not "natural beings" (spatio-temporal causes). Can a naturalist even accept the existence of facts, much less multiple orders of facts ?

Does the Naturalist say that the only causes are natural (physical ?) causes ? Or do they say that the only causes of physical events are physical ? Both are compatible with epiphenomenalism, a dualistic theory. Do they say the only things (states, facts, events, properties, relations) are physical things ? So that states, facts, events, properties, and relations themselves are physical things ? I can make no sense of saying that space-time, theories, numbers, functions, Lorentz transformations, are "physical things". Consider:

"By analogy with classical mechanics, the Hamiltonian is commonly expressed as the sum of operators corresponding to the kinetic and potential energies of a system, in the form H = T + V (although this is not the technical definition of the Hamiltonian in classical mechanics, it is the form it most commonly takes). The potential operator V typically takes the form of a function V(r,t) of position and time, which simply acts on states as a multiplicative factor. The operator T corresponding to kinetic energy is constructed by analogy with the classical formula"

Here we have ostensive quantification over analogies, mechanics, sums of operators, potentials, forms, definitions, functions, positions, times, states, mulitplicative factors, formulas. Just what are these things on a "Naturalist" view of nature ? Naturalism appears for all the world to be incompatible with the science of Nature.

But these are not causes of physical things we might be told. But then some things we are acquainted with are not causes of our acquaintance (assuming that's natural, or physical). So our acquaintance is not physical, or we are not acquainted.