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)
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.
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.
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?
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.
Photo from http://www.zombiepinups.com/
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…
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…
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
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!
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?”"
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!
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.
Mandik seems to think that if he deletes my arguments and threatens to ban me from his blog then he doesn’t have to address the issues…that’s fine. But there is an issue to address that I think is worth spelling out, as I think it generalizes a bit.
So, then what exactly is the disagreement?
In some other posts (Implementing the Transitivity Principle, and Is There Such a Thing as a Neurophilosophical Theory of Consciousness?) I have been arguing that theories like Mandik’s (which include, I think, people like Churchland and Prinz as well) must really be implementing some actual theory about what conscious states are rather than actually giving a distinctly new kind of theory. The notion of what a conscious state is seems to be somehow theoretically/copnceptually prior to neural investigation.
So take Mandik’s version of the theory. On his view you have a sensory state which carries information about the outside world and which triggers an ‘egocentric conceptul’ state. An egocentric conceptual state is a state that has two kinds of content. It has objectively third person concepts and concepts that single out the thinker as the one having the experience. When these two states start to causally interact a conscious state is born. So, as an example take me having a conscious experience of seeing a red ball. Then I have a sensory state which carries information about the red ball (whatever that means…it probably means something like ‘there are properties that the objects in the world have and there are there cells in the retina, LGN, and V1, etc, which are ‘tuned’ to those properties’ and then there is a causal story about how those physical objects cause those things that are tuned to them to operate) and that sensory state triggers a egocentric conceptual state, perhaps something like ‘there is a red ball in that direction from me’ or perhaps more simply, ‘red ball in front of me’. These two states start to causally interact (whatever that means) and then, for some unexplained reason, there is a conscious seeing of a red ball.
Now when one hears this, one naturally sees a lot of parrellels with Rosenthal’s version of higher-order thought theory. On that theory there is a first-order state which has qualitative properties, these properties represent the perceptible properties of physical objects. So on both views we have some states and those states are in the business of representing physcial properties. Rosenthal wants to call the properties of the sensory states ‘sensory qualities’ or ‘qualitative properties’ and Mandik doesn’t, but other than that purely terminological point there is no difference at this point. Ok, so then the first-order sensory state ‘triggers’ (not really for Rosenthal, but let’s let that slide since Pete and I can both agree on it) a higher-order thought. The higher-order thought is something like ‘I am, myself, seeing a red ball’. The person is now conscious of themselves as seeing a red ball and so is consciously seeing a red ball.
So then one might be tempted to say ‘so, Mandik, you’re conceptualized egocentric states sound a lot like higher-order thoughts’ since they are basically states that conceptually characterize the sensory state. So, though it is not exacly Rosenthal’s higher-order theory, it is a theory that implements the transitivity principle and that takes care of the mystery about why having these states causally interact results in a conscious state. To which Mandik responds, ‘no, if they were higher-order thoughts then I would be conscious of the first-order sensory state, but on my theory I am only conscious of the red ball’. Mandik seems to think that that constitutes an argument that his view doesn’t implement transitivity (well, to be fair, I guess you need the premise ‘and I am only conscious of the red ball’ to make it an argument). I claim that it is something that itself needs an argument; it is the thing that you need to establish via an argument and so is not an argument that his view doesn’t implement transitivity, for the following reasons.
First, according to Rosenthal’s version of the theory it will in fact seem to you as though all you are aware of is the red ball because the higher-order thought conceptualizes the first-order state as having properties that belong to the tomatoe. But you become so conscious by being conscious of the first-order state. For it is the properties of the first-order state that you are conceptualizing! How could we conceptualize the object itself? We would not be conscious of the object if we did not have some first-order state that represented it. So to simply say ‘oh, on my view I am only conscious of the tomatoe, so it is not a higher-order view’ is to beg the question at hand. One needs to explain how it is that the egocentric ceonceptual state gets to be about the red ball without utilizing the sensory state. This is what I meant when I said that Mandik had not given an argument. He has not given an account of how it is that his ‘but I am only conscious of the tomatoe’ is true in a way that isn’t the above way.
And we do sometimes have the kinds of higher-order thoughts that Rosenthal affirms and Mandik denies. So for instance, I might think ‘I am having a really bad migrane right now’ (I am thinking about my experience) or ‘I felt really nausaus last night’ (I am thinking about when the experience occurred) or looking at a stick in some water ‘the way that stick looks is not the way that it is’ (I am thinking about the experience as different from reality)…We do think about vehicular properties of the experience (in Mandik’s terms). The claim that Rosenthal makes is that we are actually doing it all the time, though we are not conscious of doing it. So again Mandik needs to spell out how his view isn’t the above kind of view, which he hasn’t done.
When you point out that his evidence isn’t really evidence and whithout it he is simply insisting that his view is different without justification (again how else could it work if not in the way talked about above?) so it would be nice if he could be explicit and give an argument as to why it is different (that is, answer the above question), he refuses to answer. Now, I didn’t think that was such a big deal…in fact I was hoping that he would just give me an argument that showed me how I was wrong…But he didn’t…instead he deleted the post where I made the case just as I did above and threatened to ban me. Surely this is Cyber Sophistry!
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…