Marc Horowitz 24.151 May 8, 1992

I

(A) 42 + 0 = 42 It is necessary that 0 be the additive inverse, for addition to work as conventionally defined. It is also knowable a-priori, as it does not depend on any physical evidence.

(B) The exact values of very large primes.

People have used computers to determine the valyes of prime numbers hundreds of thousands of digits long. These numbers are necessarily primes, but it is not evident a-priori that such a number is prime.

(C) I do not believe in the standard meter example.

If the scratches in the standard meter in Paris are, a-priori, one meter long, this implies that if it were determined somehow that the meter was a different length, then the stick would be wrong. This is not possible, since it is known a-priori that the scratches are one meter apart. But, the stick is wrong. The meter was redefined as a function the wavelength of one frequency of light emitted from krypton, which is a physical quantity which must be measured, and cannot be known a-priori. In fact, this new definition of the meter is different from the meterstick definition. So much for the a-priori meterstick.

(D) I am 1.68 meters tall today.

This is contingent on many things, including all events prior to the time of measurement (what if I had lost my legs in a car accident?). It is also aposteriori, as it is not something which can be deduced analytically.

V

Kripke spends several pages describing identity statements between names, and it seems that his arguments, if applied to the propositional attitude problem, serve to make the problem a non-issue. He spends a great deal of time showing that ‘Hesperus’ and ‘Phosphorus’ always pick out the same reference, no matter what universe we are referring to. The sentence ‘John believes that Phosphorus is a planet’ is uttered by a speaker in our universe. As Kripke puts it, “we use English with our meanings and our references. So, ‘Phosphorus’ has the referent it would have in our universe. Now, substitute ‘Hesperus’ in that sentence. Since ‘Phosphorus’ and ‘Hesperus’ have the referents of the speaker, not of John, the sentences keeps the same truth value and truth conditions. There is no difficulty.

This does not affect the propositional attitude problem, but there does seem to be a difficulty in that there does not seem to be any way to discuss John’s language. I’m not sure how Kripke would explain a sentence like ‘John believes that the heavenly body which he calls ‘Hesperus’ is a planet.’ In this case, he is not referring to Hesperus when he says ‘Hesperus’. I’m not convinced Kripke can discuss this.