I am still reading Jason Stanley’s paper. I think that in the end the position he comes to is something close to frigidity which is nice. But first I want to discuss his characterizion of rigidity.

He says,  

Rigidity is a semantic property of an expression. More specifically, it has to do with evaluation of that expression with respect to other possible situations (or ‘worlds’).

I think this is right. Rigidity is not only a semantic property, it is the kind of property wich only shows up in modal contexts. There are many varieties of rigidity out there and he goes on to distinguish them from each other.

1.) Neutral charaterization of rigidity-

a designator d of an object x is rigid, if it designates x with respect to all possible worlds where x exists, and never designates an object other than x with respect to any possible world.

This characterizationis neutral over the issue of what the designator will designate with respect to a possible world where its actual designation does not exist. But it is also neutral between rigidity and frigidity because it is neutral over what counts as a designator. So according to frigidity (1) can be true if the designators are mental names and false if they are linguistic names.  

 2.) Persistent rigid designators- Those

 4.) Strongly rigid designators-

those designators d of an object x which exists in all possible worlds, which designate the same thing in all possible worlds (viz. x).

As I have been arguing in the last post, I do not think it is a trivial question whether anything necessarliy exists and so I doubt that there are any strongly rigid designators.

5.) De Jure rigid designators-

An expression is a de jure rigid designator of an object just  in case the semantical rules of the language unmediately link it to that object.

 6.) De Facto rigid designators-

All other rigid designators [i.e. not de jure rigid designators]

Kripke himself casts the distinction in terms of stipulating the reference. A designator is de jure rigid when “the reference is stipulated to be a single object whether we are speaking of the actual world or of a counter-factual situatiuon”. This is the thing that he is actually interested in. A de facto rigid designator is one where a desription ‘happens’ to pick out one unique object in all possible worlds (e.g. ‘the smallest prime number’ picks out The Number Two in all possible worlds.)

Are there such things as de facto rigid designators? I hear ‘the smallest prime number’ used to pick out The Number One back in the Olden Days when people (mistakenly?) thought that The Number One was prime…so maybe what ‘the smallest prime’ designates depends on what we stipulate…I tend to think that all rigid designation (were there any)would be the de jure kind.

At any rate, how doe sthis notion of stipulating the reference connect with (5)’s talk of ‘unmediate links’? Take logic as an example. In logical theory the reference of a given constant C is given by stipulation. We say ‘let C be …’ where ‘…’ is the referent. This stipulative act is licensed by a semantical rule which says that the way the constants reference is determined is via stipulation. We, as it were, just hook the constant onto the thing we want to talk about. In other cases there is a semantical rule which says that the referent is determined by the object(s) that satisfy some description. So, the constants of logic are supposed to be prime examples of de jure rigid designators. And in fact Stanley goes on in thenext section to chronicle how this is in fact historically the way that rigidity first arose, as a theory about the semantics of modal logic.

The real question then is whether or not this story as just told for logic works for English as well. Is ‘Richard’ like C? This brings us to the question of what the job of semantics is and the distinction between P-semantics and L-semantics I introduced earlier but this is already long. Iwill come back to it in another post.

In the discussion of my post I Necessarily Exist Jason Zari pointed out Timothy Williamson’s paper Necessary Existants as a way of explaining how he was led to questions about logic and the proof of necessary existence. I had never read the Williamson paper and I made some comments/responses to his argument that I would be curious to know what people thought about, so I reproduce them here.

Hey thanks forthe link to the Williamson paper…I read through it and while I think that his argument depends on a lot of very questionable assuptions (my mind is not one of the open ones that he has written the paper for :)) I now better see where you were comming from…

A couple of thoughts…It seems to me that Kripke’s version of modal logic avoids the argument that he gives in the begining of the paper. So let’s look at it real fast

(1) Necessarily, if I do not exist then the proposition that I do not exist is true.
(2) Necessarily, if the proposition that I do not exist is true then the proposition that I do
not exist exists.
(3) Necessarily, if the proposition that I do not exist exists then I exist.
(4) Necessarily, if I do not exist then I exist.

Switching from proof-theoretic talk lto model-theoretic talk, we can see that there is a model where (1)-(3) are true but do not entail (4) and so do not entail that I necessarily exist…Let the domain be the actual world and let ‘JZ” name you. So (2), and (3) are true at the actual world (in virtue of your acceptance of Russellian propositions and I am not challenging that (though I might) since the actual world contains you and so contains propositions about you.

The question then is ‘how is the proposition that JZ does not exist get to be true’? How is (1) true at the actual world? It is true just in case there is a possible world where you don’t exist (that is we adopt the Kripkean notion that a proposition is true at a world if there is some world where it is true. That would make (1) true in the actual world just in case there is some possible world where you do not exist, and we agreed earlier that there is such a possible world (trivially, the empty world). So (1)-(3) are true but in a model where we do not get the result that ‘if you exist then you don’t exist’

Now though Williams doesn’t mention Kripke by name, I take it that he is addressing this sort of move when he says the following.

It is sometimes said that a proposition can be true of a possible world without being true in that world. We can express propositions in one world about another world. Thus a proposition might be true of a possible world without existing in that world. But this idea does not address the case for (2+) [’Necessarily, if the proposition that P is true then the proposition that P exists’], for (2+) does not say that the proposition exists in any possible world of which it is true. We could paraphrase (2+) thus: for any possible world w, if the proposition that P would have been true if w had obtained, then the proposition that P would have existed if w had obtained. We can abbreviate that by saying that for any possible world w, if the proposition is true in w then the proposition exists in w. The antecedent concerns truth in w, not truth of w, so the distinction poses no threat to (2+).

but this doesn’t really address the Kripke move. Kripke says that a proposition is true in a world if it is true at some possible world. So the proposition that you do not exist is true at the actual world because it is true at (or ‘of’ if you prefer) some world. So it is true in this world and you exist in this world. We can agree with everything that he says except the bit about how the distinction poses no threat. It is true in w (the actual world) in virtue of it being true of some possible world.

He goes on to consider whether this distinction poses a problem for premise (1), which I will skip since the above seems enough to get by the argument (you may argue that I assume a negative answer to the next challenge, but if so, then I will give the argument against it)…what about his general problem with the distinction? The argument from failure to grasp contingency? He says,

Consider the contingently true proposition that Blair was Prime Minister in 2000. It is supposed to be true of the actual world @ and false of some other possible world w. On the model, the sentence contains a tacit variable; if @ is assigned to the variable, a truth results, if w is assigned, a falsehood. But that does not make the resulting propositions contingent. There is genuine contingency in how things are only if, once values have been assigned to all variables, the resulting proposition could still have differed in truth-value. It is not contingent that Blair was Prime Minister in 2000 in @ and that he was not Prime Minister in 2000 in w. What is contingent is simply that Blair was Prime Minister in 2000. Its contingency requires it not to have a variable waiting to be assigned a world. The reply ‘But contingency just is variation in truth-value with variation in the value of the world variable’ betrays a failure to grasp what contingency is.

Well right off the bat he has misrepresented the position since he says that the proposition is true of the actual world. Rather it is that the proposition is true in the actual world because it is true at/of some possible world…so I of course agree that what is contingent is the proposition that Blaire was Prime Minister in 2000…that proposition is true in the actual world and contingent because it is possible that it could have been false (though not expressible on your and Williams’ view) in the actual world…

Finally the business about the ‘illusion’ of a distinction doesn’t seem to me to work either. He says.

There is the illusion of a distinction between truth in a world and truth of a world for propositions because we appear to be able to model such a distinction on a corresponding distinction for utterances, forgetting that the presence of the latter depends on the absence of the former.

What he means by that last bit is that the intuitive claim about utterances (i.e. that the utterance ‘there are no utterances’ is true in this world because it is true of some wold) depends on our having the notion of truth in a world for propositons. As he says,

The utterance need not exist in that world in order to be true of it because the proposition which it expresses in this world exists in that one. We need not carry the utterance across from this world to that one precisely because we can carry the proposition across instead.

But this is nothing more than question begging…why isn’t the proposition that the utterance expresses true in this world because it is true of some world, just like the utterance? So, anyways, all of this is along winded way of saying that you don’t need to adopt your paraphrase as a way of avoiding the argument if one accepts Kripke semantics for modal languages like I do…

But of course the argument of the post, and the one you mention, is meant to show that this is not good enough, one also needs to jettison the idea that our semantics inculedes singular terms. Williamson explicity appeals to singular terms in his defense of premise (3)…it is that defense which my argument is aimed at…

…except there is this very odd phenomenon that for me showing that logic leads to the claim that I necessarily exist is reason to think that we have got something wrong, while for him it shows that he necessarily exists!!

When one wants to give a theory of language the natural place to start is the sentence. When one wants to give a theory of the mind the natural place to start is the thought. Given that both thoughts and sentences are said to have meanings and that semantics is the study of meaning we can see that there is a potential ambiguity in defining the semantic task.

One might take the semantic task to be that of giving the meaning of and truth-conditions for thoughts, as Michael Devitt does. On the other hand, when one asks what the point of a language is, the natural answer to give is that it is used to express thoughts. This leads us to ask just what the relation is between our thoughts and the sentences that we use to express them and one striking result from the philosophy of language in the last century is the realization that often times the content of the sentence does not capture the content of the thought. One might then take the semantic task to be that of giving the meaning of sentences independently of their being used to express any thought. Broadly speaking this is the conception of semantics that P. F. Strawson had.

I will use ‘P-semantics’ for semantics in the psychological sense that we want to give a theory of the meaning of thoughts and ‘L-semantics’ for semantics in the liguistic sense that we want to give a theory of the meaning of sentences considered apart from their being used to express any given thought. This lets me be neutral on issues about semantic and pragmatics and also recognizes that each deals with meaning and truth conditions.

Each of these two views will be interested in sentences. So, for instance take the sentence

(S) Saul Kripke, the world’s greatest living philosopher, likes tea.

When we want to know what the truth conditions for this sentence are we could mean one of two things. We could be taking this sentence to represent an utterance, an actual saying of it or a writing of it, and therefore be using it to evaluate a certain thought or we could take it as a linguistic type and be trying to evaluate its truth conditions independantly of any thought it may be used to express.

I can then neutrally formulate the distinction between rigidity and frigidity by saying that there is no such L-semantic property of rigidity. There are no singular terms in English; there is no L-semantic property that some English expressions have and that others lack such that they pick out the same object in all modal contexts. When we contruct a linguistic theory of natural languages (as opposed to a physcological theory of thoughts) we should do it so that it is free of singular terms. Our L-semantic theory should contain only descriptions.

The causal theory of reference that Kripke intiates and the Devitt develops is to be taken as a P-semantic theory. It explains how it is that we can have singular thoughts, given that the right kinds of causal/historical connections hold between ceratin thought contents and the world, but we express those thoughts using a language that itself does not have singular terms. Something like this kind of view is developed in Kent Bach’s Thought and Reference. I have coined the term ‘frigidity’ to designate this kind of view to contrast it with rigidity have tried to develop three lines of argument to prefer frigidity to rigidity.

1.) In the first place the truth conditions of sentences with names (or natural kind terms, like above) in them will change depending on who (or what) the person ‘has in mind’. We cannot determine who a name picks out independently of evaluating what thought it is being used to express (Introducing Frigidity). In the normal course of communicating who or what someone is thinking about when entertaining a singular thought is determined by the relation that the thought has to some thing or stuff in the world. Thus when evaluating a sentence like (S) we have to stipulate that we mean to be talking about Saul Kripke.

One response to this argument that I have heard from people, among them Michael Devitt, is that it fails to take serious the argument that names are ambigiuous. So, it is urged, ‘Saul Kripke’ is ambiguious in as many ways as there are people, places, and things called ‘Saul Kripke’. Thus we take each actual thing named ‘Saul Kripke’ ans collect all of teh tokens of ‘Saul Kripke’ that causally/historically ground out in the philosopher and call that a type. There will be one type for each person place or thing that tokens of ‘Saul Kripke’ causally/historically trace back to. So the truth conditions will change because the token sentence will have a token name that traces back to different objects in the world. This answer in effect denies that there is a viable distinction between L-semantics and P-semantics.

But even if we grant this point it will be the case that there is a linguistic type ‘personal name’ and that ‘Saul Kripke’ is an instance of that type as well. So there is a sense of type for which it makes sense to say that there is only one name, ‘Saul Kripke’ in English and every person who says ‘Saul Kripke’ is using that type. This is the type as considered apart from its individual uses to name particular people, the L-semantic type. What would a person have to know in order to use it correctly or understand an instance of it? They would arguably only need to know that it was used to refer to persons who bear that name or ‘are called that’. This just is its L-semantic meaning so Devitt’s objection is not really an objection.  

2.) In the second place frigidity can make sense of the debate about whether and which expressions are rigid designators that is not mere ‘intuition mongering’. How could anything solve the dispute between David Lewis and Kripke on whether ‘pain’ is a rigid designator that did not appeal to stipulations about what ‘pain’ was suppose to refer to? (Applying Frigidity)

3.) More recently I have been pushing an argument that when our logical theory incoperates the idea that linguistic names are rigid designators we end up with some counter-intuitive logical results, like that I (or you or unicorns) necessarily exist (Logic, Language, and Existence).

Now one might object to this argument because one thinks that it shows too much. One natural way to show this is by pointing out that since we can have singular thoughts we can take the singular terms in logical theory to be modeling the contnet of a singular thought. So when I think that Saul Kripke likes tea I have a thought that has some content part of which is a mental name for Saul Kripke in virtue of it tracing back to him. So I can stipulate that by ‘Saul Kripke’ I mean that guy (pointing at Saul Kripke), and I can then represent this as T(sk) where I stipulate that SK stands for that guy, Saul Kripke, and T stands for ‘likes tea’. So the argument of Logic, Language, and Existence, seems to work equally well against a P-semantic theory that has something like rigid designators.

Now, this would be nothing more than an inconvienence if we took SK to be short hand for (Ex) (SK(x)) where SK is a predicate and means ‘bears the name “Saul Kripke”‘ or ‘is called “Saul Kripke”‘ and so T(sk) to really mean (Ex) (SK(x) & T(x)). The problem only arises when we want to say that SK directly picks out a certain person of which (Ex) (x=sk) is true and so T(sk) really says (Ex) ((x=sk) & T(sk)). The question here is ‘what is the right way to capture the content of the thouoght?’ and that is a question about how to express it in language. So, it is a question of what the best L-semantic theory is, and we have many reasons, some of which I have talked about and others that are well known and time worn, for not including singular terms in our L-semantic theory.