Wolfgang Schwarz

More on Logicalism, Physicalism and Frank Jackson

Let logicalism ("logicism" was already taken) be the claim that all truths supervene upon purely logical truths, where a purely logical truth is a truth that contains only logical terms, including terms from second order modal logic.

Logicalism immediately follows from this purely logical truth ('[]' is the box, 'ACT' the actually operator):

p <-> []((x)(F)(Fx <-> ACT(Fx)) -> p)

While all truths therefore supervene upon the purely logical truths, not all truths are a priori deducible from the purely logical truths. For instance, that water covers most of the earth isn't. So we have a counterexample to the claim that whenever all truths supervene on the F-truths, then all truths are a priori deducible from the F-truths.

However, Frank Jackson seems to have argued for just this claim. Here is his argument (From Metaphysics to Ethics, pp.81-83).

Suppose all truths are necessitated by the physical truths, as physicalists say. Then there is some physical truth P such that the conditional

if P then water covers most of the earth

is necessarily true. Suppose that it isn't a priori. By the two-dimensional analysis of a posteriori necessity (which I find completely convincing), the conditional then has a contingent A-intension, and enough information about the current context suffices to know that it is true. That is, some statement of the form

if P and C then water covers most of the earth

is a priori, where C gives information about the current context. It could e.g. say that H2O is the watery stuff, or that H2O stands at the beginning of some causal chain to our current use of "water".

Applied to logicalism, this means that some statement of the form

if (x)(F)(Fx <-> ACT(Fx)) and C then water covers most of the earth

is a priori. So far so good. Now comes the mistake:

But if physicalism is true, all the information needed to yield the proposition being expressed about what the actual world is like in various physical sentences [i.e. all the context-specifying information given by C] can be given in physical terms, for the actual context is givable in physical terms according to physicalism. (p.83)

In two-dimensional jargon, Jackson here assumes that according to physicalism, the A-intension of the complete physical truth is the set of perfect duplicates of the actual world. For suppose it isn't. Suppose it also contains various other worlds. Then information given in physical terms doesn't suffice to tell us whether we are in one of these other worlds. This is what happens with purely logical truths: the A-intension of the complete purely logical truth is the set of all worlds. Therefore purely logical truths are unable to tell us anything about the current context. Nevertheless, all truths supervene upon the purely logical truths.

On the two-dimensional analysis, sentence S a priori entails sentence T iff S's A-intension is a subset of T's A-intension. So if the A-intension of the complete physical truth is the set of perfect duplicates of the actual world, then all (non-haecceistic) truths are a priori entailed by the physical truths. So when Jackson says that the actual context is givable in physical terms according to physicalism, he in effect presupposes that according to physicalism, all truths are a priori entailed by the physical truths. But this is not how he defined physicalism. He defined it as a metaphysical supervenience thesis, and claims to have an argument why this leads to the a priori entailment thesis.