Today, we're switching from metametaphysics to "straight" metaphysics, or at least so it should seem. Instead of talking about how to tell what exists, we are talking about whether there is such a thing as de re necessity.

In fact, the issues today will, later in the semester, get connected back up with metametaphysical issues, since identity is so fundamental to metaphysics.

What is necessity?

There are many kinds of necessity, even in the philosophers' sense of the word: physical necessity, practical necessity, moral necessity, mathematical necessity, logical necessity, metaphysical necessity, to name a few. Sentences are the kinds of things that are necessary (necessary in the sense of necessary truth).

Anything that is logically necessary is necessary in every other sense. Metaphysical necessity, which is what Kripke is interested in, is, roughly, logical necessity plus definitions. Thus, it is logically and metaphysically necessary that a bachelor is either married or unmarried. It is metaphysically but not logically necessary that a bachelor is unmarried. Thus, logical necessity holds only logical terms fixed, metaphysical necessity holds the language fixed, physical necessity holds language and the physical laws fixed.

A sentence P is impossible if not P is necessary. A sentence P is possible if its negation is not necessary; a sentence P is possible if it is not the case that necessarily not P; and a sentence P is necessary if not possibly not P.

As you can see, the language rapidly gets tangled, and so it is useful to abbreviate with symbols. We use box %$\square$% (or L) for necessity and diamond %$\diamond$% (or M) for possibility, and so, for example, %$\square P$% if and only if %$\lnot\diamond\lnot P$%.

A sentence is contingent if it is neither necessary nor impossible. Equivalently, a sentence is contingent if it is possible that it is true and possible that it is false.

De re vs. de dicto necessity

De re "in reality"; de dicto "as said."

Here is an example, due to Quine, that makes the idea clear enough: Suppose that Ralph Ortcutt is the shortest spy. It is necessary de dicto that the shortest spy is the shortest spy, but it is not necessary de dicto that Ralph Ortcutt is the shortest spy. Because that is true, many more people know that the shortest spy is the shortest spy than know that Ralph is the shortest spy. The knowledge that the shortest spy is the shortest spy is knowledge de dicto, about the words, but the (much rarer) knowledge that Ralph is the shortest spy is knowledge about Ralph (not his name, but the guy himself).

The philosopher's perversion of "possible worlds"

Ordinarily, we say that something is possible. Philosophers often say instead that it is true in some possible world. When talking about complex iterated modalities or many possibilities at once, that makes life easier. It is possible to eliminate such talk at the expense of some awkwardness. Example: In ordinary English, If Bush had bribed the right senators, he would have gotten Meiers through the confirmation process. In possible world talk: There is some set of senators such that Meiers gets confirmed in every possible world in which Bush bribed those senators.

Having been deflationary about possible worlds, I should point out that many philosophers view them as more than just a convenient manner of speaking: they are committed to the existence of possible worlds.

Are there contingent identity statements?

In English, are there statements of the form A=B that are possibly true and possibly false?

Why is this important?

There are many attempts in science philosophy, and everyday life to understand one kind of thing in terms of what is apparently another:

water is %$\mathrm{H}_2\mathrm{O}$%

heat is the motion of molecules

pain is the firing of afferent C fibers

necessity is truth in all possible worlds

The evening star is the morning star
or
Hesperus is Phosphorus.

mind body.

What is the nature of these identities?

Why is this hard?

Example of a contingent identity? Shakespeare is the author of Hamlet.

Proof that there are no contingent identities?

• • Shakespeare is the author of Hamlet.
  • Therefore, for any property F, Shakespeare has F if and only if the author of Hamlet has F.
  • Shakespeare has the following property: he is necessarily identical to Shakespeare.
• Therefore, the author of Hamlet is necessarily identical to Shakespeare.

-- ShaughanLavine - 09 Sep 2008

Kripke's Answer

Kripke claims that there are two ways in which words can be attached to an object:

1. Descriptively: the words describe the object, and, hence, in states of affairs in which the object lacks the described properties, they do not attach to the object.
2. Rigidly: the words merely tag the object, not in virtue of any property of the object, merely because it is the object tagged.

Example:

Abraham Lincoln might not have been named 'Abraham Lincoln,' and so the man called 'Abraham Lincoln' might not have been him.

That solves our problem: the proof works for rigid designators, and the examples are all descriptive.

necessary is not the same as a priori.

-- ShaughanLavine - 11 Sep 2008