Phi 346 S07, reading guide

The issue that is indicated by Kripke’s title and which he begins addressing is whether there can be identity statements—i.e., statements of the form a = b—that are true only contingently, not as a matter of necessity. This is an important issue, but Kripke’s views on this issue are no more important than many of the things he says in the course of explaining and justifying them. These other topics tend to be the focus of particular parts of the paper, and I’ll suggest the ones that will be most important for us in the outline sketched below.

One difficulty the paper may present to you is the amount of logical notation. I’ve included some notes explaining it (and correcting the many printing errors in the anthology); but it will generally be safe to ignore it. That’s partly because Kripke almost always also says in plain English what he writes in symbolic notation and partly because he uses this notation mainly in connection with topics that we will not focus on (especially, in his introductory remarks about the issue of contingent identity).

• Kripke introduces the topic of contingent identity by surveying commonly held views (pp. 393-399). Some of these concern statements of identity between proper names or between terms referring to kinds of things, but others concern generalizations that make no specific reference. He begins with the latter and this is where most of the symbolic notation appears. Kripke introduces a number of examples on pp. 395-399, and they are what will be most important for our purposes. In connection with the idea that names like “Cicero” are not really proper names, recall Russell’s discussion (on p. 167 in Klemke) and Quine’s discussion of “Pegasus” (Klemke, p. 322).

• When Kripke turns to his own ideas, he begins with the concept of “rigid designator” (pp. 400-403). Indeed, much of what Kripke has to say is tied to his claim that ordinary proper names are rigid designators. The importance of this claim derives in part from the fact that it is in direct conflict with the sort of analysis Russell has in mind (e.g., in his discussion of “Picadilly” on p. 160 in Klemke).

• Another idea of Kripke’s has more obviously broad implications: he claims that the distinction between necessary and contingent truths is independent of the distinction between things known a priori and things known a posteriori (pp. 404-407). In particular, there can be knowledge of necessary truths that is dependent on empirical experience.

• Kripke has more to say about the meaning of proper names when we considers what might lead people to think necessary truths can only be known a priori (pp. 407-410). He had more to say about their meaning in the other discussion of these topics that he mentions in note 1. Here are a couple of samples of what he has to say there.

Someone, let’s say, a baby, is born; his parents call him by a certain name. They talk about him to their friends. Other people meet him. Through various sorts of talk the name is spread from link to link as if by a chain. A speaker who is on the far end of this chain, who has heard about, say Richard Feynman, in the market place or elsewhere, may be referring to Richard Feynman even though he can’t remember from whom he first heard of Feynman or from whom he ever heard of Feynman. He knows that Feynman is a famous physicist. A certain passage of communication reaching ultimately to the man himself does reach the speaker. He then is referring to Feynman even though he can’t identify him uniquely. He doesn’t know what a Feynman diagram is, he doesn’t know what the Feynman theory of pair production and annihilation is. Not only that: he’d have trouble distinguishing between Gell-Mann and Feynman. So he doesn’t have to know these things, but, instead, a chain of communication going back to Feynman himself has been established, by virtue of his membership in a community which passed the name on from link to link, not by a ceremony that he makes in private in his study: ‘By “Feynman” I shall mean the man who did such and such and such and such’.

Naming and Necessity (Cambridge: Harvard University Press, 1980), pp. 91f.

You can associate “calling … by a certain name” with what he speaks of in “Identity and Necessity” as “fixing reference.” In Naming in Necessity, he says fixing the reference of a name might involve a definite description but it might instead involve simple pointing.

• Kripke turns next to the necessary identities that he thinks are found between certain terms referring to kinds of things (pp. 410-412). In thinking about the importance of this topic, notice that the sort of examples he uses are similar to the ones used in connection with 17th and 18th century discussions of “secondary qualities” and other aspects of the relation between our experience and the external world.

• Kripke ends with a discussion of the implications of what he has said for the mind-body problem (pp. 412-413). Even in the longer work, his discussion of topic is very compressed, and I doubt that we will do much with what he says here.

The symbols below are the ones Kripke intended; but, in the Klemke anthology, the dot ‘·’ appears as ‘*’, the turned iota ‘℩’ as ‘^’, and the exclamation point ‘!’ in the uniqueness quantifier as ‘|’.

Operation	Symbol	English	Meaning in context
Conjunction	·	and	“A · B” amounts to “A and B”
Negation	~	not	“~ A” amounts to “it is not the case that A” and says that A is false
Conditional	⊃	if … then …	“A ⊃ B” amounts to “if A then B”
Necessity operator	□	it is necessary that	“□ A” amounts to “necessarily, A”
Possibility operator	◇	it is possible that	“◇ A” amounts to “possibly, A”
Universal quantifier	(x)	everything, x, is such that	“(x) ...x...” amounts to “everything, x, is such that ...x...”
Existential quantifier	(∃x)	something, x, is such that	“(∃x) ...x...” amounts to “something, x, is such that ...x...”
Uniqueness quantifier	(∃!x)	exactly one thing, x, is such that	“(∃!x) ...x...” amounts to “exactly one thing, x, is such that ...x...”
Description operator	℩x	the thing, x, such that	“F(℩x Gx)” amounts to “the property F holds of the thing that has property G”

The dot ‘·’ is also used as an alternative to parentheses to mark scope (see below): in particular, of the two conditionals in ‘x=y·⊃·Fx⊃Fy’, the first has the second in its scope (as if the formula were written ‘x=y⊃(Fx⊃Fy)’).

De dicto/de re distinction: necessity de dicto is the necessary truth of a statement while necessity de re is necessity “of the thing”—i.e., it concerns a necessary property. While “The number of planets is less than the number of planets + 1" is necessarily true, it is not a necessary property of the thing that is the number of planets—i.e., the number 9—that it is less than the number of planets + 1 (since this would not be true if there were 8 planets). On the other hand, it is a necessary property of 9 or so of the number of planets that it is odd, but “The number of planets is odd” is not a necessary truth.

Leibniz’s law: this concerns the relation between identity and indiscernibility (i.e., having the same properties). It is obvious that identity implies indiscernibility—that, if x = y, then x and y have the same properties. Leibniz held also that indiscernibility implies identity, that you couldn’t have two different things whose properties were the same.

Cicero and Tully: Kripke (following Quine) uses the example of the Roman orator and philosopher Marcus Tullius Cicero (106-43), who is sometimes referred to as Tully.

Scope: sentences are analyzed as the result of applying logical operators successively. An operator that applies to expressions that already contain other operators has them in its scope and is said to have wider or larger scope than they do.

• Formula (3) is missing a set of parentheses: it should be (x)(y)((x=y) ⊃ [□(x=x) ⊃ □(x=y)])

• In note 13, the first expression should be ‘□((∃x)(x=a) ⊃ Fa)’ and the second should be ‘□(x)(~Fx ⊃ ~x=a)’. The first says “Necessarily, if a exists then it has property F” and the second says “Necessarily, if anything fails to have property F then it is not a.”