In this chapter he wants to extend his theory of proper names to deal with other parts of speech.
 

120  We can imagine dictionary definitions to be false-- either failing to specify necessary or failing to specify sufficient conditions.

one might normally take this as evidence for a cluster theory of concepts.

or one might take this as evidence for a natural kind theory.

given that one can imagine that tigers, for example, have none of the properties stated by a dictionary definitions, this is more evidence for a natural kind theory.

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side note: The strangest thing about Kripke's view is that, if the dictionary definition is true (and it describes the natural kind in question), then it is necessarily true.

This seems to contradict Kripke's appeal to the possible falsity of the dictionary definition in his argument for the natural kind view!  There  is no real problem here though, because Kripke would, if careful say something like, "It is possible that the animal we pick out with the word "tiger" is of a different natural kind."  Here, by Kripke's theory he is imagining that the meaning of the word "tiger" is different.

My intuitions get less clear at this point.  Kripke addresses this problem around pages 141-144, where he brings in epistemic possibility.
 

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123
starts to deal with this problem when he argues that it is a necessary property of gold that it has atomic number 79, but that it is also a posteriori.

to motivate this he asks us how we would describe possible worlds where the stuff that is gold here is of a different composition.  He thinks we would not say that the stuff in those worlds is gold.  But then the composition of gold is a necessary property of it.

125
He contrasts physical necessity from metaphysical necessity, arguing that (on the assumption that chemical theory is correct) it is not just physically necessary that gold has atomic number 79, but also metaphysically necessary (because we can't even image a coherent possible world where gold is a different substance), even a possible world where the laws of nature are different.

129
Discussion of heat and light in terms of phenomenological versus scientific characterizations.

Asks how you would describe a world where everyone is blind and the phenomenological properties of light are never instantiated.  Here he argues the world would be described as one where there was still light.  This is completely different from how we would describe the fools gold world.

So this is to show that the phenomenological properties really are not necessary for light (whereas the substance the stuff is composed out of really is necessary for gold).

We need to ask, are our intuitions really so clear about how we ought to describe such cases?  Kripke on heat,

Nevertheless, the term `heat' doesn't mean `whatever gives people these sensations.'  For first, people might not have been sensitive to heat, and yet the heat still have existed in the external world.  Secondly, let us suppose that somehow light rays, because of some difference in their nerve endings, did give them these sensations.  It would not the be heat but light which gave people the sensation which we call the senation of heat.  (Kripke, 131)

So the phenomenological properties of heat are not essential properties.  On the other hand, the physical properties are,

Can we then imagine a possible world in which heat was not molecular mositon?  We can imagine, of course, having discovered that it was not.  It seems to me that any case which someone will think of, which he thinks at first is a case in which heat-contrary to what is actually the case-would have been something other than molecular motion, would actually be a case in which some creatures with diffferent nerve endings from ours inhabit the planet (maybe even we, if it's a contingent fact about us that we have this partiuclar neural structure), and in which these creatures were sensitive to that something else, say light, in such a way that they felt the same thing that we feel when we feel heat.  But this is not a situation in which, say, light would have been heat, or even in which a stream of photons would have been heat, but a situation in which a stram of photons would have produced athe characteristic sensations which we call `sensations of heat'.  (Kripke, 132)

So here's the clear distinction he wants.
(1) We imagine a claim false if we are holding the meaning of the claim fixed, then we are showing the claim to be contingent.
    If we are not holding the meaning fixed, then we haven't really shown the claim to be contingent.

As a good Quinean I''m very sceptical about there being a hard and fast fact of the matter concerning which is being altered in these situations.

Note- In  "What is this thing called pain?" Mark Wilson shows that heat is not identified with mean molecular motion in physics and that something like the cluster theory is in fact what's going on.  Maybe Kripke just picked a bad example. . .
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Again this all make sense on Kripke's two factor view.  One factor of meaning allows us to refer to things (here the phenomonological properties of heat) this is the reference fixing factor.  Kripke holds that the reference fixing factor is almost never holds of a thing at all possible worlds.  Whatever holds of a kind of thing at all possible worlds is the essence of that kind of thing.  Kripke identifies this essence with "the meaning" of a term, since it is what is responsible for correct evaluation of modal claims involving the term.
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134-140
Four point Recap
134
First
He again states that he has applied his Millean view of proper names to other parts of speech such as count and mass nouns and some adjectives.

135
Second
He shows how descriptions we use to fix the reference can be contingent and a priori.

He also admits that sometimes there may not be a unified natural kind that we have baptized.

137
Third
He admits that we do use clusters of identifying properties to group things into the same kind.  However, again, this doesn't mean that it because of satisfaction of some set of the cluster that something is a member of the kind.  Again, a member of the kind might have none of the stereotypical properties, and something with all of the stereotypical properties might not be a member of the kind.

138
Fourth
Scientific investigation determines much better properties to consult when determining whether or not something is in the kind.  Science can determine necessary truths that really do describe the essence of the kind in question.  These are often necessary and a posteriori.

139
Fifth
Again, Kripke says that someone who knows very little about the essence of something can use the name of that kind of thing competently.  He appeals to the "chain" metaphor.
 

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142-144
deals with possible objection in very important way.
When I say something like "Gold could have had atomic number 13."  What I'm really saying is, "it is logicallly possible that there should have been a compound with all the properties originally known to hold of gold."

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144 type-token distinction
1st part of argument-
He argues that the phrase "brain event of type C" and "being in pain" both rigidly designate.  Thus, if one identified them, the identity would have to hold necessarily.  But clearly we can imagine zombies which have brain events of type C without instantiating "being in pain."  We can also imagine angels who are in pain, but do not have brain events of type C.  Therefore, the identity does not hold necessarily, and hence (since the mere identity entailed the necessity) the identity doesn't hold at all.

I think the place to balk here is the claim that the two types of events rigidly designate.

146
2nd part of argument-
Perhaps the materialist will bite the bullett and claim that the mind-body identity is a posteriori necessary.  Here Kripke provides a pretty good argument.  He argues that the strategy of dealing with  a posteriori necessity that we used before simply won't work here.  In earlier cases, when we thought we were, for example, imagining gold to be not equal to the natural kind it is in fact equal to, we were imagining situations epistemically indistinguisable from our own, where non-gold satisfies all of the phenomenological properties of gold.

Can we do this with "pain?"  Kripke points out that we can't.  The thing about pain is that anything with the phenomenological properties of pain has to be pain.
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Again, the only part I balk at is thinking that "brain event of type C being equal to being in pain" entails that "brain event of type C = being in pain" is necessarily true.
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