Tuesday, December 15, 2009

"No Fact of the Matter" Paradox?

Here's a line of reasoning I just came up with, that seems paradoxical.

(1) Quine points out that there's a kind of Sorieties series of different theories posting "atoms", ranging from Democritus' theory where the whole point of something being an atom was that atoms are indivisible to the current theories on which atoms are in fact divisible. (Let's use "atom0" to express Democtitus' notion of atoms.)

(2) This suggests that when you are far enough away from having a correct overall theory some phenomemon, the truth value of your scientific words can be vague. For, if it is vauge whether someone intermediate scientist counted as meaning atom by "atom" rather than atom0 or some other notion, then it is vague whether their assertion "there are atoms" expressed a truth.

(3) Science progresses, and we clearly have more to learn about fundamental physics (e.g. how to reconcile QM and Relativity), so we are probably in the same boat with regard to some of our current theoretical terms, maybe "quark" or "superstring". Suppose (without loss of generality) this is true of "quark".

(4) If (3) is right, there's no fact of the matter about whether "there are quarks" (as said by me now) expresses a truth.

(5) But (assuming we can apply Tarksi's T schema to an ordinary looking case like this), "there are quarks" expresses a truth if and only if there are quarks.

(6) So, there's no fact of the matter about whether there are quarks. (!)

(Conclusion) Either there's no fact of the matter about whether there are quarks, or there's no fact of the matter about whether there are strings or etc. for some term with a similar role in phyiscs.

At least, if the conclusion is true, this would be very surprising since when someone says "there's no fact of the matter as to whether" X we usually take them to be suggesting that we dismiss the question, while, presumably, scientists studying whether there are quarks/strings is a paradigm of the kind of question we DO want to invest energy in discussing.

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