Lecture 1 (some notes) part ii

Necessity

One of Kripke's major distinctions in necessity/contingent is that the necessary/contingent distinction is a metaphysical distinction. Whereas the a prior/a posteriori distinction is epistemological. Also, certainty, is an epistemological term. So for an x to be necessary, means that in any possible world W, x exists in W. An example of this is the Goldbach Conjecture, which states that any number n, greater than 2 that is a prime is odd. So for any two prime numbers that are greater than 2, p1 & p2, p1 + p2 does not equal n. If Goldbach's Conjecture is true, it is necessarily true, and if false, necessarily false. Yet, we don't have a priori knowledge of Goldbach's conjecture. If we ever do learn whether Goldbach's conjecture is true, we will know it a posteriori.

Kripke claims that a priori and necessity have been associated for two reasons. First, if something is is true in the actual world and true in all possible worlds, then we can see that in the other possible worlds that this statement is also a priori in other possible worlds. Although this does not seem correct. Second, if something is known a priori, then it must be necessary, since it was known without looking at the world. So Kripke's conclusion is that it isn't trivial to state that something is a priori necessary or to state that something is a posteriori contingent.

Kripke establishes the distinction between de re and de dicto modality by claiming that de re is essentialism. (I have never thought of de re in this way before.)

Here is an interesting puzzle, take the following two sentences:
'Nine is necessarily odd.'
'The number of planets is necessarily odd.'
Of course the first is true and the second is false.

Again, if we say that 'Nixon' was necessarily the president of the U.S. that is false. However, if we utter "'the man who won the election in 1968' is necessarily the winner of the election in 1968" this is true. Kripke will elaborate on this later, but this has something to do with fixing a referent. We cannot decide upon whether a property is essential or contingent without knowing the description, it is a meaningless question. Essential properties are what are used to establish identity across possible worlds, i.e. trans-world identity.

Names
What is the difference between the following two questions:
Is it necessary that 9 is greater than 7?
Is is necessary that the number of planets is greater than 7?
'9' is a rigid designator, meaning that in every possible world '9' designates the same object. Whereas descriptions, i.e. 'the number of planets', are contingent.

There is a non-circularity claim by Kripke for philosophical theories:
(C) For any useful theory, the accont must not be circular. The properties which are used in the vote must not themeselves involve the notion of reference in a way that is ultimately impossible to eliminate.
This principle seems to be aimed at Russell. For Russell defines a description as 'the so-and-so' (Kripke puts it as, 'the man called such and such'). Kripke doesn't elaborate much, and I may not understand Russell well enough to understand what is going on here. However, if one says, 'the man called "Walter Scott"', this violates (C).