Two Kinds of Semantics

In an earlier post I introduced a distinction between what I call P-semantics and L-semantics as a way of neutrally formulating the contrast between frigidty and rigidity.  The distinction between P and L semantics corrosponds to what one takes the semantic task to be. One might take the semantic task to be that of giving the meaning of and truth-conditions for thoughts, as Michael Devitt does. For instance, here is how he characterizes the semantic task in the precis to Coming to our Senses: A Naturalistic Program for Semantic Localism.

In Coming I seek a solution to this problem [i.e. identifying the semantic task] by focusing on the purposes for which we ascribe meanings (or contents) using `that’ clauses (“t-clauses”) in attitude ascriptions: in particular, the purposes of explaining intentional behavior and of using thoughts and utterances as guides to reality. I call these purposes “semantic.” I say further that a property plays a “semantic” role if and only if it is a property of the sort specified by t-clauses, and, if it were the case that a token thought had the property, it would be in virtue of this fact that the token can explain the behavior of the thinker or be used as a guide to reality. We are then in the position to add the following explication to the statement of the basic task: A property is a meaning if and only if it plays a semantic role in that sense. And the basic task is to explain the nature of meanings in that sense (Devitt 1997)

For Devitt meaning is primarily a property of thoughts and the semantic task is to explain what property they have which allows them to play the role in behavior that they do. This is what I call P-semantics.

On the other hand, one might take the semantic task to be that of giving the meaning of sentences independently of their being used to express any thought. This way of thinking about semantics has it as simply a part of grammar. To illustrate, if I say ‘Saul Kripke likes tea’ talking about my dog and you say it talking about Saul Kripke we both use the same sentence, though we refer to different objects (Strawson 1950/1985). We do so in the sense that we use something with the same physical structure but we also use something with a certain syntactic structure, something that has a noun phrase and a verb phrase as part of its structure like (1)

(1) [S [NP [proper noun, Saul Kripke]], [VP [verb, likes], [np, tea]]]

This is roughly Kent Bach’s position. According to Bach the job of semantics is to provide an interpretation of (1) that explains how it can be used to do the things that people do with it. Here are a couple of quotes from his 1999 paper “The Semantic Pragmatic Distinction: What it is and Why it Matters” and his 2002 paper “Semantic, Pragmatic”

I take the semantics of a sentence to be a projection of its syntax. That is, semantic structure is interpreted syntactic structure. Contents of sentences are determined compositionally; they are a function of the contents of the sentence’s constituents and their syntactic relations. (Bach 2002)

Semantic information about sentences is part of sentence grammar, and it includes information about expressions whose meanings are relevant to use rather than to truth conditions. Linguistically encoded information can pertain to how the present utterance relates to the previous, to the topic of the present utterance, or to what the speaker is doing. That there are these sorts of linguistically encoded information shows that the business of sentence semantics cannot be confined to giving the proposition it expresses. (Bach 1999)

This is what I call L-semantics. It seems to me that both of these conceptions are legitimate conceptions of something that should be called ‘semantics’. Both kinds of theories will be interested in giving the truth-conditions of sentences. One then is faced with a choice between three options.

1. L-semantics just is P-semantics

2. P-semantics just is L-semantics

3. L-semantics and P-semantics are distinct and need distinct theories

1 is perhaps the most popular. Jerry Fodor (Fodor 1998) endorses 1 when he says “…English has no semantics. Learning English…[is] learning how to associate its sentences with the corresponding thoughts.” 2 is perhaps less popular but it is the kind of view that followers of Seller’s will likely endorse. Frigidity claims 3.

Varieties of Rigidity

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

designators d of an object x, which designate x in all worlds in which x exists, and designate nothing in worlds in which x does not exist.

3.) Obstinate rigid designators- Those

designators d of an object x, which designate x in all worlds in which x exists, and designate x in all worlds in which x does not exist; or, more simply, designate x with respect to every possible world.

(2) and (3) differ in the way that they want to treat the designator with respect to a possible world where the designated thng does not exist. The names themselves come from Salmon. Some of the debate that has been going on around here lately can be seen to be over this issue. Kripke’s own view, as Stanley notes, is (3).

 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.


Truth and Necessity

I have been reading Jason Stanely’s paper on names and rigid designation from the Oxford Companion to the Philosophy of Language in the course of doing some research for my frigidity v. rigidity axe-grinding. It is an interesting and informative, though technical, introduction to issues about rigidity and I will come back to its relation to frigidity in a later post… but one thing caught my attention early on. He says, 

consider Kripke’s class of strongly rigid designators (Kripke, 1980, p. 48). This class contains the rigid designators of necessary existents. That is, this class contains all and only those designators d of an object x which exists in all possible worlds, which designate the same thing in all possible worlds (viz. x). For example, the descriptive phrase “the result of adding two and three” is a strongly rigid designator, since its actual denotation, namely the number five, exists in all possible worlds, and the phrase denotes that number with respect to all possible worlds.

Is it really the case that ‘the number five exists in all possible worlds’? Isn’t there a possible world where fictionalism about math is true? In that world 2+2=4 is not true because ‘2’ stands for an existing object, viz. The Number Two, it is true because ‘in the story we tell about mathematics’ ‘2’ stands for The Number Two in just the same way that ‘Santa wears a red suit’ is true, not because ‘Santa’ picks out some guy who wears a red suit but because ‘in the story about Santa’ ‘Santa’ picks out a guywho wears a red suit. Maybe fictionalism about math isn’t actual, but surely it’s possible, isn’t it? 

We can give the same kind of argument for any proposed ‘strongly rigid’ designator. Take God for instance. It take it that Atheism is a legitimate possibility for the actual world. That is, it migt actually turn out to be the case that there is no God. Of course it might also turn out to be the case that there isn’t one. Each of these seems to me to be a metaphysical possibility, not merely an epistemic possibility. If so then there is a possible world where God does not exist (it may or may not be the actual world). Isn’t this some reason to prefer, when faced with the possiblility of a proof of necessary existence, to take my view (fix it) rather than Williamson’s (accept it)? That is, isn’t there an issue here about whether there are any ‘strongly rigid’ designators? 

Timothy Williamson on Necessary Existents

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!!

Language, Thought, and Logic

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.

50th Philosophers’ Carnival

Welcome to the July 16, “Dog Days of Summer ’07” edition of the philosophers’ carnival.

The theme, as advertized, is: Mind, Meaning and Morals. I hope you find some interesting articles below and manage to avoid work for a litle while longer 🙂


Ivana Simic addresses an issue in modal epistemology introduced by Crispen Wright in The Cautious Man Problem posted at Florida Student Philosophy Blog

Gualtiero Piccinini asks Two Questions About the Origins of Connectionism posted at Brains.

Avery Archer examines a classic debate in 20th Century Analytic philosophy in Naturalised Epistemology: Quine vs. Stroud posted at The Space of Reasons.

Tanasije Gorgoski tries to figure out what in the hell philosophers are talking about when they talk about experience in The Meaning of ‘Experience’ posted at A brood comb.

Thad Guy gives us another classic philosophy cartoon: Witness My Power and Be Awed posted at Thad Guy


Jason Kuznicki presents Open Society IV: That Which Melts Into Air posted at Positive Liberty, saying, “I’m reading Karl Popper’s The Open Society and Its Enemies, as well as much of the supporting philosophy. Along the way, I’m blogging my observations.”

For some reason I recently had a discussion about what it meant to be an American and who the greatest American was. Well, after reading Charles Modiano’s History’s Hit Job on Thomas Paine I say Thomas Paine is a strong candidate! posted at CLEAN OUR HOUSE! – Killing the Bigotry in all of US

Richard Brown continues to pit the pragmatic thesis of frigidity against against the semantic thesis of rigidity and to argue for the supiority of frigidity both theoretically and in capturing the spirit of Kripke’s picture, in Logic, Languange, and Existence posted at Philosophy Sucks!


Brian Berkey argues that the demandingness of ethics is not an objection to an ethical theory in What is a Moral Demand? posted at Philosophy from the Left Coast.

Steve Gimbel asks When Is Good Enough, Good Enough? posted at Philosophers’ Playground, saying, “Most classical ethical theories include some sort of maximization notion in the definition of moral rightness. This post asks Susan Wolf’s question, “isn’t there some point where an act is morally good enough?””

Rebecca Roache reflects on the lessons that debates in ethics can take from Hempel in Hempel’s Dilemma and Human Nature posted at Ethics Etc

David Hunter continues his examination of The Human Tissue Act: When should applications to not require consent be approved? posted at Philosophy and Bioethics

Matt Brown suggests that the thought experiments employed in our introductory courses on ethics may be doing more harm than good in cooked up thought experiments and the viciousness of ethics posted at Weitermachen!

Enigman wonders who the moral experts are in Physics and Ethics posted at Enigmania

And finally, Thom Brooks invites you to look at the introduction to his book The Global Justice Reader posted at The Brooks Blog.

That concludes this edition. Submit your blog article to the next edition of philosophers’ carnival using our carnival submission form. Past posts and future hosts can be found on our blog carnival index page.

Technorati tags:
, .

Logic, Language, and Existence

I have been thinking a lot about the argument of an earlier post (I Necessarily Exist), due to some excellent comments on the post and because I have been having some discussion via email with Kent Bach about it, and I think I understand what the argument is supposed to look like now. So what I want to do is take some time to show how this argument for frigidity goes and how it ultimately supports what I say about What Kripke Really Thinks.

The argument, to remind you, is one that David Rosenthal presented in a Quine class I had with him and and is a proof by reductio that the existence of any object that one desires is a theorem of first-order logic. All that one has to do to get the proof going is to agree that to say that it exists is to say something with the logical form Ex (x=c) where ‘c’ is a singular terms that refers to the object in question. Here is a version that prooves that Saul Kripke’s existence is a theorem. Let ‘SK’ name the actual Saul Kripke.

1. –(Ex) (x=SK)                     assumption for reductio
2. (x) –(x=SK)                       equivalent to 1.
3. (x) (x=x)                            axiom of identity
4. (SK=SK)                             UI of 3.
5. –(SK=SK)                           UI of 2.
6. (SK=SK) & -(SK=SK)       4, 5

This argument is valid and is supposed to illustrate the problems that Quine discussed in his famous article ‘On What There Is’ involving existence statements. Some people have objected that since the first premises assumes that SK does not exist then he is not in the domain of the quantifier and so something fishy is going on in step 5 (and possibly step 4. as well). But this is not right because the argument is supposed to illustrate that something funny happens when you try to say that something doesn’t exist and you use a logic with singular terms. So, SK must refer (in first-order logic) and it does refer. We then show that since it refers it is a theorem of first-order logic that SK exists. So the ultimate aim of Rosenthal’s argument is to show that if we have singular terms in our logic, as opposed to just variables, then it turns out that it is a theorem of first-order logic that Saul Kripke exists, or that you do, or that I do, or that unicorns do…something has gone wrong and the natural candidate is the use of the singular term.

Quine’s solution to this problem is to suggest that we use Russell’s theory of descriptions so that when we analyze sentences like ‘Saul Kripke Exists’ we get a logical statement free of singular terms. He, of course, recommended that we invent a description like ‘the thing that Kripkisizes’, or ‘the Kripkisizer’ so that we would render ‘Kripke exists’ as Ex (Kx) where ‘K’ stands for the invented description. This is kind of weird and off-putting but the argument is good and so we should see if there is some more natural way to treat (linguistic) names as descriptions.

The Bachian strategy that I endorse is to use the description that mentions the name. So according to this view the linguistic name ‘Saul Kripke’ is semantically equivelent to “The bearer of ‘Saul Kripke'”. So we render ‘Kripke exists’ into first-order logic as Ex (Kx), where ‘K’ stands for the description that mentions the name (Bach calls this a nominal description). So, this part of the argument shows that we should rid first-order logic of singular terms and if one takes first-order logic to be in the business of giving a formal semantics then we should rid our semantic theory of singular terms, and this is just what frigidity does.

Now in the earlier post I suggested that we could adapt Rosenthal’s proof to a modal proof that Kripke (or you, or me, or unicorns) necessarily exists which to remind you again went as follows.

(2) Saul Kripke necessarily exists: □Ex (x=SK))
1. ◊ –Ex (x=SK)           assumption for reductio
2. ◊ (x) –(x=SK)          equivalent to 1.
3. (x)□ (x=x)                modal axiom of identity
4. □ (SK=SK)                UI of 3.
5. ◊ -(SK=SK)               UI of 2.
6. –□ (SK=SK)              equivalent to 5.
7. □ (SK=SK) & -□ (SK=SK)           4,6

Now, in the course of doing some research about this I made an interesting discovery.

It turns out that the problem of necessary existence has some history in modal logic. In fact it turns out that Kripke is famous for formulating a system of quantified modal logic that is supposed to block proofs of necessary existence (as well as some other pesky things like the Barcan formula). So how does Kripke do this? Well, in his 1963 paper “Semantical Considerations on Modal Logic” he modifies standard quanitified modal logic in two ways. The first is by requiring that there be no free variables in any of the axioms or theroems that we use.

The Stanford Encyclopedia entry on actualism has a nice Proof of necessary existence in S5 if one wants to look at it and the same article has some discussion of how Kripke’s move blocks the inference, but as is usually the case with papers in html the quantifiers do not show up and so it is hard to follow the discussion (in the article that is, the proof above is an image and so one can see the quantifiers)…so I will reproduce the proof with the ‘typwritter notation’ that I have been using here.

So the claim of necessary existence is taken to be the claim that everything that exists necessarily exists or, (x)□Ey (y=x) the proof of this proceeds as follows

1. x=x axiom of identity
2. (y) -(y=x) –> -(x=x) instance of quantifier axiom
3. (x=x) –> -(y) -(y=x) from 2 by contraposition
4. (x=x) –> Ey (y=x) from 3 quantifier exchange
5. Ey (y=x) from 1 &4 by modus Ponens
6. □Ey (y=x) from 5 by rule of necessitation
7. (x)□Ey (y=x) from 6 by rule of universal generalization

Ok, so now notice that the axioms 1 and 2 above have free variables which have to be bound in Kripke’s system. So we get 1′. (x) (x=x) and 2′. (x) ((y) -(y=x) –> -(x=x)) and so we cannot derive the problematic theorem. Instead we get the following.

1′. (x) (x=x)
2′. (x) ((y) -(y=x) –> -(x=x)
3′. (x) ((x=x) –> Ey (y=x) From 2′ by contraposition and quantifier exchange
4′. (x) (x=x) –> (x)Ey (y=x) From 3′ by quantifier distribution rule
5′. (x)Ey (y=x) From 1′ & 4′ by modus ponens
6′. □(x)Ey (y=x) From 5′ by rule of necessitation

But 6′ is harmless as it just says that necessarily, everything that exists is self identical. In order to get the pesky result that everything that exists necessarily exist we need a theorem that says □(x)Ey (y=x) –> (x)□Ey (y=x) (which is the so-called converse Barcan formula). If we had this we could derive the offending theorem from 6′ and the converse Barcan formula by modus ponens. “But,” the article continues,

as Kripke points out, the usual…proof of [the converse Barcan formula] also depends essentially on an application of Necessitation to an open formula derived by universal instantiation — the same “flaw” that infects the proof of [necessary existence]. (See the inference from line 1 to line 2 in the supplementary document Proof of the Converse Barcan Formula in S5.) Hence, it, too, fails under the generality interpretation of free variables.

But notice that the modal proof that I gave does not fail under the generality constraint.  The axiom of identity that I appeal to contains no free variables.

So what is going on here? Well, as the article continues by pointing out that we can still prove the offending theorems simply by replacing the free variables in the original proof by constants (this is in effect what the proof I offered did), and so,

The second element of Kripke’s solution, therefore, is to banish constants from the language of quantified modal logic; that is, to specify the language of quantified modal logic in such a way that variables are the only terms.

In other words Kripke thinks that we should eliminate singular terms from our quantified modal logic and so by extension from our semantical theory; in other words it looks like this is further support for my claim that Kripke really has something like frigidity in mind rather than rigidity.

Now there is more that needs to be said here, but this post is already way too long so I will save it for another time…

Emotive Realism

In some earlier posts I have been clearing the way for presenting the metaethical view that I defend (The Meaning and Use of ‘is True’, Truth, Justification, and the Quasi-Realist Way, Meaning and Justification, Reason and the Nature of Obligation, and A Simple Argument for Moral Realism). What I want to do now is to introduce Emotive Realism which is supposed to be a way of combining classical emotivism with moral realism.

The basic idea is simple enough. When I say that something is right/wrong/good/bad I express my moral sentiment in just the way that the classical emotivists thought and at the same time I assert (that is express my belief) that my moral sentiment is the correct way to feel about the person/act in question. As an example, when I say something like ‘suicide bombing is wicked’ I express my moral condemnation of suicide bombing; that is I express my moral feeling about suicide bombing. This is the illocutionary act. It is successful just in case you recognize that I intend to be expressing my moral condemnation. I also at the same time express the belief that moral condemnation is the correct attitude to have towards suicide bombing. I (usually, but by no means always) do this with the perlocutionary goal of trying to get you have the same attitude. Whether we are successful in this perlocutionary goal has no bearing on whether or not we are successful in our illocutionary act. In other words, you may ‘grasp’ the attitude that I express (namely that I morally disapprove and think this is the correct way to feel) without your thereby coming to share my attitude.

There are of course bells and whistles that have to be added to the theory (like an account of the semantics of moral sentences) which I intend to talk about later. But here what I want to point out is that this kind of theory is in principle compatible with any theory of justification. The issues of justification, on this view boils down to answering the question ‘is the belief that I express ever true?’ The answer to this question could be ‘no’ in which case you would have something like Ayer’s version of emotivism. It could also be ‘yes’ at which point we have further questions, like is the truth of the belief robust or not? If we say no to this question then we would have a version of expressivism like Blackburn’s. But it should also be clear that we can say ‘yes’ to this last question, in which case we would have an emotive realism and the belief will be true in virtue of the correct theory of moral justification.

I Necessarily Exist

In several earlier posts I introduced and defended what I call Frigid Stipulation as an alternative to Rigid Designation (Introducing Frigidity, Applying Frigidity, What Kripke Really Thinks). The basic claim is that in natural languages (as opposed to in thoughts)there are no logically proper names at all, no singular terms what so ever. Every sentence with what looks grammatically like a singular term is really a disguised quantifier at the level of logical form and truth conditions and so can be analysed via Russell’s theory of descriptions.

Aside for the argument that I gave for frigidity from the fact that the truth conditions of sentences with so-called rigid designators in them change depending on who the speaker had in mind, there are also all kinds of well-known problems with construing linguistic names as logical constants, in fact with the whole idea of logical constants in the first place. These problems range from the normal ones about identity and existence statements, and belief attributions involving co-referential terms, to the bizarre logical result that we can prove that any given individual exists as a matter of first-order logic. The proof is actually quite simple and takes the form of a reductio of the assumption that the individual in question does not exist.

Here is a version of the proof that Rosenthal once presented in a Quine class I had with him.

(1) Proof by reductio that Saul Kripke exists: ((Ex) (x=SK))

            1. –(Ex) (x=SK)                     assumption for reductio

            2. (x) –(x=SK)                       equivalent to 1.

            3. (x) (x=x)                            axiom of identity

            4. (SK=SK)                             UI of 3.

            5. –(SK=SK)                           UI of 2.

            6. (SK=SK) & -(SK=SK)       4., 5.

As you can see, we derive the contradiction that Saul Kripke is both self-identical and not self-identical from the assumption that he does not exist and the axiom of identity with just two uses of universal instantiation. So we can prove that any given object exists as a matter of first-order logic with identity. But surely that is absurd! We may be able to live with the result that some object or other exists (Ex (Fx)), which naturally follows in standard first-order logic, but we cannot live with the fact that we can prove that any given particular object exists.

Even worse it seems to me that we can give an analogous proof that the object in question necessarily exists!

(2) Proof that Saul Kripke necessarily exists: □Ex (x=SK))
                1. ◊ –Ex (x=SK)          assumption for reductio

                2. ◊ (x) –(x=SK)         equivalent to 1.

                3. (x)□ (x=x)               modal axiom of identity

                4. □ (SK=SK)               UI of 3.

                5. ◊ -(SK=SK)              UI of 2.

                6. –□ (SK=SK)              equivalent to 5.

                7. □ (SK=SK) & -□ (SK=SK)           4,6

But surely this is even more absurd than the last! How can I necessarily exist? These kinds of results offer good reason to adopt frigidity.

Meaning and Justification

So, I am finally done working on my paper ‘Consciousness, Higher-Order Thoughts, and What It’s Like‘. It has been converted into both PowerPoint and Poster format and I am looking forward to presenting it in the upcoming Weeks…but before I do I want to start what will be a series of posts on Emotive Realism, the metaethical view that I defend.

In some earlier posts (The Meaning and Use of ‘is True’, and ‘Truth, Justification and the Quasi-Realist Way‘) I argued against Simon Blackburn’s Quasi-Realism by showing that the deflationary account of truth that he relies on is unmotivated and cannot be support a satisfying account of justification. Ultimately what I want to do is to argue for a view that is emotive but that is also a kind of realism and which does nto hide behind the smoke and mirrors of deflationsim.

In this post I want show that Emotivism, and views like it, are actually two claims that can come apart; one about the meaning of ethical terms, the other about the justification of moral judgments. Emotivism is so often thought of as an anti-realist view mostly as a matter of the historical accident that its earliest defenders happened to be irrealists. If this is true then they is no principled reason why an emotive theory could’t also be a kind of realism. Along the way I wantto say something about what moral realism is.

The claim that these two issues (i.e. of th meaning of moral words and the justification of moral judgements) are seperate is not a popular view. In fact it is often thought that your views on one force your views on the other. In particular it is often argued that a philosopher’s theory of justification determines her theory of semantics and that this semantic theory is the only way to tell the difference between someone who is a ‘real-realist’ and quasi-realists like Simon Blackburn.  

David Copp (Copp 2001) is a nice example of this. He says that the distinctive doctrine of moral realism is that the moral realist thinks that the moral predicates refer to robust moral properties. So to say that suicide bombing is morally wrong is to assert that suicide bombing has the robust moral property of being wrong. To say that moral properties are ‘robust’ is to say that “[they] have the same basic metaphysical status as ordinary non-moral properties,” (p 4). It is of course a matter of some controversy just what the status of ordinary non-moral properties is. But in moral contexts there are, broadly speaking, two candidates and an ethical realist like Copp is committed to one of them. On the one hand we might think that there are non-natural properties and that ‘good’ and other moral words pick some of those properties out, or we might think that non-natural properties don’t exist and insist that moral properties must be natural properties and ‘good’ and other moral words pick some of those out.

The irrealist, on this view, is one who denies that the moral predicates refer to robust moral properties of either variety. It is, in fact, a huge mistake according to the irrealists to think that moral predicates act like non-moral predicates and refer to, or denote, or whatever, some kind of property. Moral predicates are in a different kind of business all-together and only look as though they stand for properties. What they really do is serve to express our moral sentiments, in much the same way that ‘ouch!’ express pain.

Notice though that even though we are told that we can differentiate these views by their semantics this is really supposed to be diagnostic of their views about the justification of moral judgments. The robust moral properties that moral predicates refer to are supposed to be the truthmakers for moral judgments in exactly the same way that non-moral properties are supposed to be the truthmakers for non-moral judgments. The irrealist denies that there are such properties and instead claims that moral judgments are justified by the emotional, conative, or motivational states of people. This leads us to the real distinction between realism and irrealism: If two people disagree over some fundamental moral claim, like whether unjustified killing is morally permissible, can, in some sense, both be right? A realist will claim that only one of them can be right, whereas an irrealist will claim that they can both be right. One way to secure this is by appealing to the kind of semantics already talked about, that is, by appealing to moral properties and claiming that the task of the moral predicates is to refer or denote those properties.

But there are really two questions that have been so far unaddressed in the meaning side of the question. Since we want to seperate meaning from use it then becomes important to assess whether the meaning claim that the emotivists made was really a claim about the meaning of the words or whether it was a claim about how the word was used independently of its meaning. It seems to me to be hostorically correct to say the latter, but even if it weren’t it is clearly possible to modernize the theory by saying that moral utterances are used to express our moral sentiments independently of their meaning, in much the same way that ‘I feel like a burrito’ (said in response to ‘what do you want for lunch? or something) expresses my desire to have a burrito for lunch independently of its meaning.

This could be the case even if the sentence that we said was literally false (as is the case when I say, of a talkitive friend, “he never shuts up”) This means that the issue of the meaning of the sentence that I say and the issue of the justification of the moral judgment I thereby express are completely seperate. There is no reason to think that in order to be a moral realist you must be committed to moral properties and to a semantics of moral words that has them referring to thos moral properties.