A priority, deducibility and understanding
Back to the question of deducibility.
According to the deducibility thesis, the fundamental truths (plus
indexicals, plus a 'that's all' statement) a priori entail every truth.
More precisely, when P is a complete description of the fundamental
truths and M any other truth, then, according to the deducibility thesis,
the material conditional 'P
M' is a priori.
§4 of this paper by Chalmers and Jackson contains a sketch of how the deduction could proceed. The sketch rests on two interesting assumptions. The first is that there are fundamental phenomenal truths, that is, that minimal physicalism is false. This of course makes things much easier, as witness the phenomenalist idea that all truths may be entailed by phenomenal truths alone. I would really like to do without this assumption.
The second assumption is a certain understanding of understanding. A
sentence is a priori if it can be known just by understanding it, by
grasping its meaning. Unfortunately, it is not entirely clear what
it is to grasp the meaning of 'PM'.
Suppose I come across a book containing the complete description P of microphysical reality. I don't know much about spin, mass, etc., not much more than that these are microphysical properties called 'spin', 'mass', etc. Still there is a good sense in which I understand the book -- the sense in which ordinary people understand sentences about elms and Feynman even if they don't know much about elms and Feynman. Obviously, no amount of rational reflection will allow me to infer M from P. What I lack is not just cognitive capacities, but also information about spin and mass (and 'spin' and 'mass'). Sure, all this information is implicit in P, but that doesn't help, because I can't deduce it.
So it is not true that anyone who grasps the meaning of 'PM' is
able in principle to know it. Is it true that there is at least somebody
who can know PM just by rational reflection?
I don't think so, for several reasons. Firstly, it is possible that, by a strange law of nature, everyone who entertains P immediately dies or goes mad. Secondly, and more probably, nobody might be an expert on all the concepts involved in P. For example, perhaps no spin expert knows more than I about charge, and no charge expert about spin (like in the second elm experts story). Thirdly and fourthly, even the experts' knowledge together could be insufficient to derive M from P. Of course, to fix the extension of 'spin', the experts must know more than that it is some physical property or other. But (thirdly) this extension-fixing does not require an elaborate descriptive theory. It would suffice if the experts know that spin is the property that differs now between these and those particles. That would suffice to fix the extension, but it probably wouldn't suffice to deduce M from P. Moreover (fourthly), the extension-fixing does not require a true theory. I take it that, within limits, it is possible to understand a concept even though one has false believes containing it. So even if the experts have an elaborate theory, that theory might be false. Then P, according to the theory, might actually imply Not-M.
Maybe all the deducibility thesis claims is that there is some
possible way of understanding 'PM' on which it comes out a priori.
This, I think, is true, and necessarily true. But it may be trivial. At
any rate, it depends on what to count as a way of understanding a sentence.
I'm not sure about Chalmers and Jackson's criteria here. Maybe to
understand S, your A-intension of S must simply determine the C-intension
conventionally associated with S. (This is too weak, I think. Public
meaning puts constraints on A-intensions, too: Imagine somebody's A-intension
for 'water' is the same as that for 'H2O'.) Then the thesis is trivial:
Simply add (or include) all true micro-macro conditionals 'PM' to your
A-intension of P. Any more interesting suggestions?