Spam A Lot

Ever since I found Richard’s comment in the spam section and noticed that there has been a big increase in spam comments blocked lately I started getting worried that people’s comments aren’t getting posted. If you try to post something that doesn’t show up email me and I will check the spam box (email on my website)

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.

The Introspective HOT Zombie Problem

Photo from http://www.zombiepinups.com/

normal_laurenbarnett02.jpg

Usually you will find me defending Rosenthal’s version of the higher-order thought theory of consciousness but today I want to raise what might be a problem. In an earlier post (Varieties of Higher-Order Zombie) I introduced what I call an Introspective HOT Zombie, which is

a creature who lacked all of my first-order states and all of my second-order states but which had all of my third-order [i.e. introspective] states. This is the introspective HOT zombie. This creature has no conscious states even though it seems to him [introspectively] as though he does. When I see red I will be conscious of the red and conscious of myself as seeing red and were I to introspect I would be conscious of myself as being conscious of myself as seeing red, but the introspective HOT zombie is just conscious of itself as being conscious of itself as seeing red.

So what is it like for the Introspective HOT Zombie? The answer,according to higher-order theory, must be that it is like consciously seeing red. Why? Here is a relevant passage from Rosenthal’s “Introspection and Self-Interpretation”

When we introspect a state, we are conscious of it in a way that seems attentive, focused, deliberate, and reflective. When a state is conscious but not introspectively conscious, by contrast, we are conscious of it in a way that is relatively fleeting, diffuse, casual, and inattentive. Introspective and introspective consciousness do not seem to differ in any other ways. There is no phenomenological or subjective difference, and no theoretical reason to posit any difference. (p. 110 in Consciousness and Mind)

Since there is no phenomenological or subjective difference between having a conscious state and introspecting that state what it is like for a creature to have a conscious mental state and what it is like for that creature to introspect its conscious mental state will be the same, albeit with the caveat that in introspection we will be conscious of the first-order state in a way that is attentive, focused, etc. So the Introspective HOT Zombie will seemingly have a conscious experience that it does not in fact have.

Now, this in and of itself is not necessarily a problem for Rosenthal’s account, though it does show that he has some explaining to do. But whatever his explanation is of how the Introspective HOT Zombie is possible it immediately leads us to what we might call an Introspective Intra-subjective Qualia Inversion Problem. In the previous post that I mentioned, I posed the problem as follows. Imagine

a creature who had a first-order state that was a seeing of red and that had a HOT misrepresenting this first-order state as a seeing of green. What it is like for this creature to have the first-order state will be like seeing green so it will be like seeing green for this creature. Now suppose that this creature introspects its conscious mental states and (for some reason) has a third-order state that represents the second-order state as a seeing of red (that is it accidentally gets things right). What will it be like for this creature?

According to the argument above Rosenthal is committed to saying that it will be like seeing red for this creature since being conscious of myself as being conscious of myself as seeing red just is like seeing red for me. But, as I point out, Rosenthal is also committed to saying that it will be like seeing green for this creature since what it is like to have the first-order state is determined by the HOT. So it looks like we have to say that what it is like for this creature is simultaneously like seeing red and seeing green.

But that would mean that the creature represents some object or area of space as both red and green at the same time. Does this mean that it is then like seeing the object as yellow for the creature? Or are we to say that somehow the object both looks red and green (but not yellow) at the same time? How can one object both appear to be green and appear to be red at the same time? This seems absurd. What’s worse it seems like we could run the same argument on any experiences we want, so it might be the case that something looks both like a square and like a circle at the same time in virtue of having ones HOT represent some object as a square and then having an introspective 3rd order HOT that represents the second-order HOT as an experience as of a circle…

It is starting to look like the Introspective HOT Zombie is a real problem for Rosenthal’s view…

Evidence for something String-ish

There has been a lot of debate lately about string theory and testability (see for instance Hanging on by a Thread) . It seems to be one of the only theories in the modern time that is taken seriously by physicists in spite of the fact that it cannot be empirically tested, and in fact it is hard to see how it could be so tested. This gets a lot of people upset as it looks like string theory can’t be falsified and so shouldn’t count as a scientific theory.

Ed Witten is famous for, among other things, arguing that string theory does make one prediction. It predicts gravity. It is concievable, he argues, that some alien society discovered string theory before they discovered gravity. In that world gravity is a prediction of string theory and not of quantuum mechanics. So it merely an historical accident that in our actual world we discovered gravity first and string theory second. So there is a sense in which string theory has already made one bery important ‘prediction’ albeit one that is already established.

Is this all the evidence for string theory that we can muster? I have been thinking lately that perhaps we can get some evidence for something that is at least more string-ish than particle physics if we think about special relativity….So perhaps the most famous result of the special theory of relativity is the equivelance of mass and energy captured by E=MC^2. There have been two philosophical interpretations of this equivelance (see the Stanford Encyclopedia entry linked to above). There are those who take it to show that the properties picked out by ‘energy’ and ‘mass’ turn out to be the same property, and those who take it to show that there is no ontological distinction between fields and matter, or in other words that there is just one kind of stuff out there. It seems to me that either way one interprets the equivelance of mass and energy it provides some reason for thinking that a theory like string thoery will turn out to be correct (as opposed to a theory like particle physics).

So, say that you take it to show that there is only one kind of fundamental stuff out there that we can describe as either energy or mass. This is evidence for something string-ish in that string theory posits only on fundamental entity, viz. the string. Particle physics, on the other hand, posits a zoo of particles that are all made from different stuff. Electrons are made from one kind of stuff quarks from another kind of stuff. Thus particle physics as standardly construed seems fundamentally at odds with the ‘one stuff’ interpretation of E=MC^2.

On the other hand, let’s say that you take the equivelance to show that energy and mass are the same property, though that property may be had by several different kinds of stuff. This is evidence for something string-ish in that string theory posits that the one property is actually string vibration and so can explain what the property is as well as how it will seem to us that one converts into the other (i.e. the pattern of vibration changes).  What is the candidate property that particle physics offers? It’s only answer is ‘a property, we know not what’. Thus the two fundamental properties of physics are rendered completely mysterious.

Now, I don’t think this second argument is as decisive as the first, and I also think that the property interpretation is more likely to be true, so I tentatively conclude that special relativity does give us some reason to prefer a string-ish theory over particle physics…but I will have to think about it some more…