A priori deducibility and fundamental facts
When I tried to spell out the 'modus tollens' I mentioned on monday, I came across something that may be interesting.
Frank Jackson argues that facts about water are a priori deducible from facts about H2O:
1. H2O covers most of the earth.
2. H2O is the watery stuff.
3. The watery stuff (if it exists) is water.
C. Therefore, water covers most of the earth.
1 and 2 are a posteriori physical truths, 3 is an a priori conceptual truth.
Now let P be a complete description of fundamental reality, specifying e.g. the distribution of spin, mass and charge over points in spacetime.
1'. P.
Can we deduce that water covers most of the earth? The obvious problem is that we would have to analyze 'water' (and, for that matter, 'covering' and 'earth') in the vocabulary of P. The obvious way to try would be a stepwise (and ramsified) analysis: Water is the stuff in the lakes, a lake is a large collection of liquid (or of water), etc. But it is unlikely that any of this will take us down to the language of P. It is just incredible a conceptual analysis of 'water' could be entirely framed in terms of distributions of spin, mass, and charge.
On the other hand, everything supervenes on the fundamental facts, that is, on the P-facts. So some P-fact determines that water covers most of the earth in the sense that necessarily, this P-fact holds iff water covers most of the earth. (The necessity has to be restricted, but set that aside for the moment.) Let S be a sentence in the language of P expressing this P-fact. Since it is true, it will be deductively implied by P. Then the deduction can be completed as follows:
2'. (Necessarily) S iff water covers most of the earth.
C. Therefore, water covers most of the earth.
Note that it isn't important that we don't know what S looks like. Suppose physicists tell you. Still, the location problem is solved not by conceptual analysis, but by the necessary a posteriori 2'. And, most unfortunately, it seems that here we cannot break 2' into a part that is contingent a posteriori and another part that is necessary a priori.
Note also that the problem gets easier if the reference-fixing descriptions contain indexicals and demonstratives. Because then premise 2 also has to contain indexicals and demonstratives. E.g. it might say 'H2O is the predominant stuff in our surrounding', or 'H2O is that stuff'. (That's why, to make the problem harder, I dropped Jackson's 'of our acquaintance' in 2 and 3.)
What about this? Let D be a complex description in the language of P that necessarily denotes water. Then it is contingent a posteriori that D is what we denote by 'water'. And it is a priori that what we denote by 'water' is water. Likewise for 'covering' and 'earth'. The location problem is solved.