Consider the sentences 'Caissa is a cat' and 'Every cat is an animal.' Edward the Nominalist made two claims in an earlier comment thread that stuck in my Fregean craw:
1. The relation between 'Caissa' and 'cat' is the same as the relation between 'cat' and 'animal'.
2. The relation between *Caissa* and *cat* is the same as the relation between *cat* and *animal.*
Single quotes are being used in the usual way to draw attention to the expression enclosed within them. Asterisks are being used to draw attention to the concept expressed by the linguistic item enclosed within them. I take it we agree that concepts are mental in nature in the sense that, were there no minds, there would be no concepts.
Affirming (2), Edward commits himself to individual or singular concepts. I deny that there are individual concepts and so I reject (2). Rejecting (2), I take the side of the Fregeans against the traditional formal logicians who think that singular propositions can be analyzed as general. Thus 'Caissa is a cat' gets analyzed by the TFL-ers as 'Every Caissa is a cat.'
To discuss this profitably we need to agree on the following definition of 'individual concept':
D1. C is an individual concept of x =df x is an instance of C, and it is not possible that there be a y distinct from x such that y is an instance of C.
So if there is an individual concept of my cat Caissa, then Caissa instantiates this concept and nothing distinct from Caissa does or could instantiate it. We can therefore say that individual concepts, if there are any, 'capture' or 'grasp' or 'make present to the mind' the very haecceity (thisness) of the individuals of which they are the individual concepts.
We can also speak of individual concepts as singular concepts and contrast them with general concepts. *Cat* is a general concept. What makes it general is not that it has many instances, but that it can have many (two or more) instances. General concepts are thus multiply instantiable.
The concept C1 expressed by 'the fattest cat that ever lived and ever will live' is also general. For, supposing that Oscar instantiates this concept, it is possible that some other feline instantiate it. Thus C1 does not capture the haecceity of Oscar or of any cat. C1 is general, not singular. C1 is multiply instantiable in the sense that it can have two or more instances, though not in the same possible world.
And so from the fact that a concept applies to exactly one thing if it applies to anything, one cannot validly infer that it is an individual or singular concept. Such a concept must capture the very identity or thisness of the thing of which it is a concept. This is an important point. To push further I introduce a definition and a lemma.
D2. C is a pure concept =df C involves no specific individual and can be grasped without reference to any specific individual.
Thus 'green,' 'green door,' 'bigger than a barn,' 'self-identical,' and 'married to someone' all express pure concepts. 'Taller than the Washington Monument,' 'married to Heidegger,' and 'identical to Heidegger' express impure concepts.
Lemma 1: No individual concept is a pure concept.
Proof. By (D1), if C is an individual concept of x, then it is not possible that there be a y distinct from x such that y instantiates C. But every pure concept, no matter how specific, is possibly such as to have two or more instances. Therefore, no individual concept is a pure concept.
Consider the famous Max Black example of two iron spheres alike in all monadic and relational respects. A pure concept of either, no matter how specific, would also be a pure concept of the other. And so the haecceity of neither would be captured by that pure concept.
Lemma 2. No individual concept is an impure concept.
Proof. An individual concept is either pure or impure. If C is impure, then by (D2) it must involve an individual. And if C is an individual concept it must involve the very individual of which it is the individual concept. But individuum ineffabile est: no individual can be grasped as an individual. But that is precisely what one would have to be able to do to have an impure concept of an individual. Therefore, no individual concept is an impure concept.
Putting the lemmata together, it follows that an individual concept cannot be either pure or impure. But it must be one or the other. So there are no individual concepts. Q. E. D.!
Three points to make.
The first is to thank you for posting this – it’s so useful to have comments and critique and criticism of an idea as it goes through the ‘birthing’ process.
The second is a request for clarification. A few months back I discussed the idea of a ‘logically intransitive verb’. Such a verb is one which has a grammatical accusative but no ‘logical’ accusative, i.e. such that ‘aRb’ can be true, without ‘Ex x=b’ being true. ‘Refers to’, in my view, is such a verb. Thus
(1) ‘Frodo’ refers to Frodo.
Is true. And so is
(2) ‘Frodo’ refers to someone.
Is true. But
(3) Someone is such that ‘Frodo’ refers to them.
Is not true. This is relevant to your definition of a pure concept C - “C involves no specific individual and can be grasped without reference to any specific individual.” You have the two verbs ‘involves’ and ‘grasped with reference to’. Thus the name ‘Frodo’ (meaning the character in LOTR, the hobbit) does naturally involve Frodo. And you cannot grasp the concept of Frodo (according to me) without reference to Frodo. But there is no strong sense in which this concept involves Frodo, or any real reference relation to any existing individual (for there is no such person as Frodo, and no such things as hobbits. So you it would be useful to clarify in what sense you intend to use these verbs. (Or to challenge the idea of ‘logically intransitive verb’ as incoherent or false or whatever).
Third point – to clarify, I hold that you can only grasp the concept of Frodo if you have read ‘Lord of the Rings’ (or some other book or text or body of information that references Frodo). It’s analogous ‘the former’ and ‘the latter’. These are descriptions which appear to be first-level, and to qualify the individuals referred to, but really, as it were, qualify the text itself (or the information received). This may help to resolve the difficulty with Max Black’s example. Borgesque thought-experiment: a Chinese author, who has never read Lord of the Rings, writes a very similar or identical work. Then I say that when people read this work and talk about the characters – say the one corresponding to Frodo – then they are not talking about Frodo. The right kind of causal connection to the work is not available. By contrast, if I read a sequel to LOTR in which Frodo appears as a character, and if I make it explicit the reference to Tolkien’s text, then I am referring to Frodo, and people who talk about my character are referring to him also. Thus, by the right kind of causal connection to a particular text (or mass-produced copies of it) we acquire individual concepts – in this case, individual concepts corresponding to things that do not exist.
The case of real history (e.g. Julius Caesar) is in my view no different. There is no semantic connection between my individual concept of Julius C. and Julius C. himself. But there is a connection between this concept and the historical texts I learned at school, or from books I read. It is this specific connection to items of information, texts etc. that guarantees the acquisition of individual concepts by different people, and their successful use to make individuating reference. What guarantees that we are all thinking about Julius Caesar is the right kind of relation to a certain set of texts – not a relation to any existing person, which is irrelevant. What guarantees that we are all thinking about Frodo is exactly the same kind of relation. The existence of the individual referred to, and even their causal relation to the text, is irrelevant.
Posted by: Edward the nominalist | Monday, July 25, 2011 at 02:44 AM
You're welcome.
But I don't think we will make any progress at all if we bring the problems associated with fictional discourse into this discussion. This will only muddy the waters hopelessly.
Here is a cat. An existing cat. A presently existing cat. Two feet from my face. Her name is 'Caissa.' The question is this: Does this name express an individual concept or not? That's the issue.
The answer depends on how 'individual concept' is defined. And I now see that my (D1) needs to be explained and perhaps modified.
Briefly, 'concept of x' in the definition is to be read as a subjective genitive, not as an objective genitive.
Posted by: Bill Vallicella | Monday, July 25, 2011 at 04:17 AM
>>But I don't think we will make any progress at all if we bring the problems associated with fictional discourse into this discussion. This will only muddy the waters hopelessly.
Individual thoughts about fictional characters are crucial to my account. The argument I am trying to forestall runs
1. A purely mental concept (or brain state) is inherently general (think of a reduplication of the world, such that the same mental state applies to both – this would be your ‘pure concept’)
2. Ergo, a truly singular concept must involve some relation to the external world
3. Such a relation can only be instantiated by the individual the mental state is ‘about’
4. But there can be no such relation, therefore there can be no impure singular concept.
The point of invoking thoughts about fictional characters is to block step 3. I concede step 1. Mental states/brain states are inherently general, and have no ‘singular aboutness’. Therefore I concede step 2. But the singular relation does not have to be terminated by the individual the thought is ‘about’. Rather, it can be related to a specific source of information. So I reject 3.
>>Here is a cat. An existing cat. A presently existing cat. Two feet from my face. Her name is 'Caissa.' The question is this: Does this name express an individual concept or not?
It does. But the concept involves no kind of relation with the individual cat. Proof: I have also acquired this individual concept *Caissa*, since you talk about Caissa quite often on your blog. I.e. when you use the name, I know which animal you are talking about. But it is quite possible (for sake of example) you made the existence of this cat up. But that does not matter: I still have the individual concept ‘Caissa’, which, if there were no such cat, would be accessible only to readers of your blog.
Posted by: Edward the nominalist | Monday, July 25, 2011 at 06:48 AM
PS note that in Direct Reference theory, there must be individual concepts. In that theory, the meaning of a singular term is the object it refers to. Therefore - assuming we can equate a singular meaning to a singular concept - such concepts exist.
Posted by: Edward the nominalist | Monday, July 25, 2011 at 07:49 AM
Bill,
A few more or less general comments.
1) “I take it we agree that concepts are mental in nature in the sense that, were there no minds, there would be no concepts.”
I assume you are aware that the above is not a classic Fregean view. According to Frege, concepts, unlike ideas, are not mental; they have an objective existence quite independently of the existence of minds and they are the constituents of propositions, which also exist independently of the existence of any minds.
This being said, your argument heavily depends upon the assumption that concepts are mental in character insofar as it depends upon the contention that individual concepts cannot be grasped in isolation from the individuals they are concepts of.
2) There is a tradition going back to Church, Carnap, and more recently Kripke where individual concepts are taken to be certain kind of intensions; i.e., functions from possible worlds to individuals, so that in each world the function picks out one, and only one, individual; although it may not be the same individual across possible worlds. So stated, the contrast with general concepts is clear; a general concept (e.g., ‘a cat’) is a function from possible worlds to one, more than one, or no individuals.
An example of such an individual concept would be “The first person to enter the room is very likely to be a woman.” I could even label this person by the name ‘Desdemona’. Clearly, in different worlds there is going to be a different individual woman who enters the room first. In worlds in which a man enters the room first (or no one enters), the function fails to pick out a value. Thus, Desdemona refers to different individuals in different worlds (i.e., it is not rigid). It seems that your D1 is quite different from this traditional conception of an individual concept.
3) Ed’s conception of individual concepts you are criticizing in the present post is not the same as the one briefly cited above. In fact, I fail to understand it. Let me explain. Consider your example regarding Caissa the cat according to TFL:
“Thus 'Caissa is a cat' gets analyzed by the TFL-ers as 'Every Caissa is a cat.'”
But this is a bogus analysis (i.e., no analysis at all). For ‘Every Caissa is a cat’ in turn means:
(E) (x)(If x=Caissa, then x is a cat).
But, now, how does (E) clarify the logical contribution of ‘Caissa’ in sentences such as ‘Caissa is a cat’? The generality expresses by (E) has nothing to do with an analysis of ‘Caissa’ as an individual versus a general term. (E) simply assigns the logical form of a universally quantified sentence to ‘Caissa is a cat’, but it still uses the term ‘Caissa’ as a constant. How else would one understand the contribution of ‘Caissa’ in the antecedent ‘x=Caissa’? Where is the analysis here? Compare this to Russell’s analysis of ‘the’, where the analysis eliminates the expression ‘the’ altogether. Whether you like Russell’s analysis or not, it is a genuine proposal; (E) is not.
4) According to D1, c is an individual concept of x just in case x is an instance of c in w1 (you may view w1 as the actual world, although this is not necessary) and for every w distinct from w1, if there exists a y in w such that y is an instance of c, then y=x. But now according to this understanding of D1, individual concepts turn out to be simply concepts expressed by rigid designators.
So understood, individual concepts turn out to be a special class of functions that are constant across possible worlds; i.e., if the function maps the actual world into a given individual o, then it maps every possible world into the same individual o, provided the individual o exists; if o fails to exist in a given world, then the function has no value in that world.
The above shows that your proof of Lemma 1 is unsound. Consider the individual concept c* expressed by the numeral '2' as follows: The only even prime. Clearly, c* is a pure concept, for no other individual concept is involved in its description. But it is also false that c* “is possibly such as to have two or more instances.” c* can have only one instance and that is the number two.
Posted by: Account Deleted | Monday, July 25, 2011 at 07:51 AM
>>The generality expresses by (E) has nothing to do with an analysis of ‘Caissa’ as an individual versus a general term.
You are failing to understand that in TFL there is no distinction between singular and general term.
>> (E) simply assigns the logical form of a universally quantified sentence to ‘Caissa is a cat’, but it still uses the term ‘Caissa’ as a constant.
This is your translation, from a language that does not distinguish between singular and general terms, to one that does.
Posted by: Edward nominalist | Monday, July 25, 2011 at 01:18 PM
Ah, my mistake Peter, and apologies. You are criticising the attempted translation of 'Caissa is a cat' into 'every Caissa is a cat'. This is obviously defective, for the very reasons you state.
Apologies.
Posted by: Edward nominalist | Monday, July 25, 2011 at 01:20 PM
Well, gentlemen, I can see there is little point is discussing this further. Neither of you are responding to the argument I gave, but instead are going off on tangents of your own. You are also ignoring the context of this post which was the whole series starting with the one on whether singular existentials can be understood as expressing the instantiation of a property.
Posted by: Bill Vallicella | Monday, July 25, 2011 at 02:01 PM
Bill,
I'm afraid you lost me at "no individual can be grasped as an individual." Would you mind elaborating on that point a bit?
Posted by: Spencer | Monday, July 25, 2011 at 04:54 PM
Hi Spencer,
Suppose you have two numerically distinct individuals that share all pure properties, whether monadic or relational. Your concept of the one will not be different from your concept of the other even if your concept is complete. Now since the individuals are numerically diverse but not conceptually diverse, that which makes each the very individual that it is -- call it its haecceity
-- cannot be conceptualized, 'grasped.'
If there are are genuine individuals -- individuals not reducible to bundles of properties -- then they are ineffable as individuals. *Individuum ineffabile est.* The thought goes back to Aristotle. And as Aristotle says in another place, though not in Latin!, *De individuo nulla scientia,* there is no science of the individual. Science is of the universal, the repeatable. Individuals are unrepeatable.
And so no individual can be grasped as an individual. I can grasp an individual as an instance of properties, but there is more to an individual than its being an instance of properties.
Does that help?
Posted by: Bill Vallicella | Monday, July 25, 2011 at 06:33 PM
>> Neither of you are responding to the argument I gave, but instead are going off on tangents of your own.
OK let’s take the argument on its own terms.
1. You define an individual concept C of x as where x is an instance of C, and it is not possible that there be a y distinct from x such that y is an instance of C. My first problem with this is that you seem be assuming that to have an individual concept of an individual, it must be of an existing individual. As I have pointed out, there can be individual concepts of fictional characters.
2. You then define a pure concept C as one which ‘involves’ no specific individual. An impure concept is therefore one which is not pure, and by implication does involve a specific individual
3. You argue that an individual concept C cannot be pure, because by definition (from 1 above) C cannot have more than one instance. However, your definition of ‘pure concept’ was one which ‘involves’ no specific individual, so the respective middle terms don’t quite match. You could simply have defined a pure concept as one which could have multiple instances.
4. Therefore, if there is an individual concept, it cannot be pure, i.e. it cannot have multiple instances. OK, fair enough, but this doesn’t get us very far.
5. Finally you argue that if C is impure, it must ‘involve’ some individual. So now we are reverting back to the ‘involve’ definition, rather than the ‘multiple instance’ definition of ‘pure’
6. Finally, you say that no concept can ‘involve’ an individual because individuals are ‘ineffable’ or whatever. I think this assumption needs more evidence. It’s not enough to say ‘Aristotle hath said it’ (even the scholastics challenged Aristotle’s claims). Although I probably do accept this.
My main worry is the apparent equivocation between concepts that ‘involve’ individuals, and concepts that cannot be multiply instantiated. Peter seems to have given an adequate counter-example in the case of the number 2. “Consider the individual concept c* expressed by the numeral '2' as follows: The only even prime. Clearly, c* is a pure concept, for no other individual concept is involved in its description. But it is also false that c* “is possibly such as to have two or more instances.” c* can have only one instance and that is the number two. “
Posted by: Edward the nominalist | Tuesday, July 26, 2011 at 01:27 AM
Edward,
Now you are confronting my points directly, which is helpful. I will reply to your points seriatim. But I have time for only one at the moment.
Ad (1). You say that there can be individual concepts of fictional characters. I deny that. As I argued in earlier posts, there are no future individuals and no nonexistent individuals. Since a fictional individual is a nonexistent individual, there are no fictional individuals.
But do we really need to discuss this for present purposes? We both admit that there exist concrete individuals. Why can't we focus on the question whether there are individual concepts of these individuals? As I said earlier, bringing in the problems of fictional discourse only makes this murky discussion murkier. Murkier than the Thames at midnight after a London plumbing crisis.
Note that I am issuing a double denial. I deny that there are fictional individuals (whence it follows that there are no individual concepts of fictional individuals) and I deny that there are individual concepts of existent individuals.
Posted by: Bill Vallicella | Tuesday, July 26, 2011 at 04:36 AM
>>You say that there can be individual concepts of fictional characters. I deny that. As I argued in earlier posts, there are no future individuals and no nonexistent individuals. Since a fictional individual is a nonexistent individual, there are no fictional individuals.
Agree with the latter - there are no fictional individuals. But this is consistent with there being concepts of fictional individuals. Just as there can be desires for cigarettes, without there being cigarettes. I've explained this many times before.
>>But do we really need to discuss this for present purposes?
I was forestalling an objection that I thought might be relevant to your concern, but wasn't.
The relevant question is whether your argument in the post above involves equivocation on the middle term ('pure concept'). If the middle term is 'concept that cannot have multiple instances', it is not clear how your conclusion follows. If the middle term is 'concept that involves an individual', it is not clear how this relates to your definition D1.
Posted by: Edward the nominalist | Tuesday, July 26, 2011 at 05:21 AM
I can desire a cigarette without (i) there being any particular cigarette that I desire and without (ii) there being any cigarettes at all. And so you want to say that I can have an individual concept of Frodo without there being Frodo.
But your analogy fails. Desire for a cigarette is general: it is for some cigarette or other. It is a desire for the co-instatiation of certain pure properties. But an individual concept of Frodo requires the existence of Frodo -- otherwise the concept of Frodo would would not be individual or singular.
Posted by: Bill Vallicella | Tuesday, July 26, 2011 at 10:21 AM
I am having trouble understanding your 'equivocation on middle term' objection. Can you lay out the syllogism on whose middle term I am supposed to be equivocating?
Posted by: Bill Vallicella | Tuesday, July 26, 2011 at 10:54 AM
Yes, I think so. I've been thinking a lot about haecceity and ethics recently. I'll send you an email about it.
Posted by: Spencer | Tuesday, July 26, 2011 at 04:33 PM
>>But an individual concept of Frodo requires the existence of Frodo
Proof required! The Greeks prayed to Zeus, surely? Is that true or false?
>>I am having trouble understanding your 'equivocation on middle term' objection. Can you lay out the syllogism on whose middle term I am supposed to be equivocating?
As I understand it, your argument is this:
1. An individual concept cannot be multiply instantiated
2a A pure concept can be multiply instantiated
2b A pure concept involves no specific individual and can be grasped without reference to any specific individual.
3 An individual concept cannot be pure because an individual concept cannot (from 1) be multiply instantiated but (from 2a) a pure concept can be multiply instantiated. It cannot be not-pure because (from 2b) a not-pure concept would have to be grasped by reference to a specific individual and (per Aristotle and ineffability) this is impossible. Ergo etc.
You are ‘cherry picking middles’. One half of the disjunction in (3) depends on 2a, the other on 2b. What you need to prove is that a concept which does not involve reference to any specific individual is inherently multiply instantiable. So I think your argument should be this
*1. No individual concept can be multiply instantiated
*2. No concept can have reference to an individual
*3. A concept that does not have reference to an individual, is inherently capable of being multiply instantiated.
*4. Therefore there can be no individual concept
I have left the logic out, but it should be plain. Any individual concept C either has reference to an individual or not. But no concept has reference to an individual (per 2). Therefore C does not have reference to an individual. It follows (per 3) that it is inherently capable of being multiply instantiated. But this is ruled out by (1). Therefore there is no such C.
However, you need to prove (3). Note that Scotus, in the work that I am translating, denies something like (3). He says that it is possible to conceive a common nature in different ways, namely in one way as predicable of more than one thing, i.e. as essentially common, or in another way as not predicable of more than one thing, i.e. to conceive the nature as a ‘this’. Sed possibile est apud intellectum eodem modo concipere naturam ut dicibilis est de pluribus, et eandem ut non est dicibilis de pluribus … semper enim in natura communi concepta ut ‘haec’, intelligitur per se natura concepta absolute. In the same context, he also discusses Aristotle’s thesis that there can be no science of individuals.
Posted by: Edward the nominalist | Wednesday, July 27, 2011 at 01:14 AM
Here is the argument I gave, though modified somewhat:
1. An individual concept C is either pure or impure.
2. C cannot be a pure concept. (Because pure concepts are multiply instantiable, and no individual concept is multiply instantiable.)
3. C cannot be an impure concept (Because there are no impure individual concepts. Concepts reproduce in the mind the qualitative aspects of things only. They cannot reproduce or 'capture' the nonqualitative thisness of a thing. If there were impure individual concepts, however, then they would have to capture that nonqualitative thisness.
Therefore
4. There are no individual concepts.
There is no problem with the logic here. So if you care to disagree you must reject one of my premises or the definitions that are being employed. Perhaps you mean something different by 'concept' or by 'individual concept' etc. It appears you reject (3). But why?
Is it because you accept the Identity of Indiscernibles? Then we must discuss that.
Do you perhaps think that the entire being of a concrete individual can be grasped conceptually by a finite mind? Its essence, all its nonessential properties, its existence, its thisness? The whole 'kit and caboodle'?
Do you disagree with Aristotle and hold that the individual qua individual is not conceptually ineffable? Do you think one can have total scientia of an individual?
Posted by: Bill Vallicella | Wednesday, July 27, 2011 at 04:23 AM
Spencer,
Please do send me your e-mail.
Posted by: Bill Vallicella | Wednesday, July 27, 2011 at 04:24 AM
Edward,
Yes, the Greeks prayed to Zeus. But Zeus neither exists nor is an individual. Only what exists or existed is an individual. That's what I have been arguing.
Posted by: Bill Vallicella | Wednesday, July 27, 2011 at 04:28 AM
<<
1. An individual concept C is either pure or impure.
2. C cannot be a pure concept. (Because pure concepts are multiply instantiable, and no individual concept is multiply instantiable.)
3. C cannot be an impure concept (Because there are no impure individual concepts. Concepts reproduce in the mind the qualitative aspects of things only. They cannot reproduce or 'capture' the nonqualitative thisness of a thing. If there were impure individual concepts, however, then they would have to capture that nonqualitative thisness.
Therefore
4. There are no individual concepts.
>>
With all respects, you still have a ‘gap in the middle’. The definition of ‘pure concept’ from 2 is “multiply instantiable”. But then you don’t mention multiple instantiability in (3). You move to the terms ‘qualitative aspect’, or ‘nonqualitative thisness’. So you need a premiss that makes that connection.
You need something like ‘whatever is inherently non-multiply instantiable is inherently non-qualitative, and captures thisness, but concepts in the mind are qualitative only, ergo etc’. But then I might challenge that. Exactly why can’t a concept be inherently non-qualitative? As Scotus says, we can perhaps conceive a thing under the aspect of ‘not predicable of more than one thing’. Why not?
>>Do you perhaps think that the entire being of a concrete individual can be grasped conceptually by a finite mind? Its essence, all its nonessential properties, its existence, its thisness? The whole 'kit and caboodle'?
Its thisness, according to me, is a simple quality. I can understand which person is being referred to, knowing hardly anything about that person. We do not need total scientia individui.
Posted by: Edward Ockham | Wednesday, July 27, 2011 at 09:37 AM
And you still haven't answered Peter's point above about the concept of the number 2 (as the first even prime). That is clearly instantiable only by one object, moreover the same object in every possible world, and is therefore an individual concept. And I think it is a concept that we can have.
Posted by: Edward Ockham | Wednesday, July 27, 2011 at 09:39 AM
As for Peter's objection, it is irrelevant because the question concerns concrete contingent individuals. That was clear from the context, starting with the post about the correct analysis of 'I might not have existed.'
Posted by: Bill Vallicella | Wednesday, July 27, 2011 at 10:27 AM
I didn't *define* a pure concept as one that is multiply instantiable, but as one that does not require for its content the existence of any specific individual. Multiple instantiability is a *consequence* of the definition.
The logic of my argument is impeccable. Your problem is with my premises or my definitions or with my supporting arguments for the premises.
>>Exactly why can’t a concept be inherently non-qualitative? As Scotus says, we can perhaps conceive a thing under the aspect of ‘not predicable of more than one thing’. Why not?<<
Say what? First of all, an individual cannot be predicated, so of course no individual is predicable of more than one thing. I just don't follow you.
Posted by: Bill Vallicella | Wednesday, July 27, 2011 at 10:51 AM
>>The logic of my argument is impeccable.
Not as it stands. Only if we supply a missing premiss, which corresponds to premiss 3 in my new version here.
1. An individual concept is not multiply instantiable [your definition]
2. A pure concept involves no specific individual [your definition]
3. A concept that involves no specific individual is multiply instantiable (missing assumption)
4. A pure concept is multiply instantiable (from 2, 3)
5. An individual concept (if such exists) is not a pure concept (from 1, 4)
6. An individual concept (if such exists) involves some specific individual (3, 5)
7. No concept can involve a specific individual
8. If an individual concept C exists, it is false that C is pure, and false that C is not pure
9. Therefore (skipping some elementary logic) there is no individual concept
I question 3. Is it a logical or analytic truth? If it were analytic, your argument could be a lot simpler. If not analytic, what justifies premiss 3?
Posted by: Edward nominalist | Wednesday, July 27, 2011 at 01:22 PM
PS suppose premiss 3 is analytic. Suppose e.g. 'involves a specific individual' means 'not multiply instantiable'. Then premiss 7 is equal to 'all concepts are multiply instantiable'. So your whole argument amounts to 'individual concepts are not multiply instantiable, all concepts are multiply instantiable, therefore no concepts are individual'. That's a valid argument, but did you mean that? Probably not, therefore premiss 3 is not analytically true. So what makes it true?
Posted by: Edward nominalist | Wednesday, July 27, 2011 at 01:35 PM
>>3. A concept that involves no specific individual is multiply instantiable <<
Do you have a reason to think that this is not true?
I'll give you a (bad) reason. Consider a concept that only one individual in the actual world instantiates, e.g., the concept of the fastest London marathoner of all time. You might be tempted to say that that concept is not multiply instantiable but does not involve any specific individual.
I would reply that it is multiply instantiable in that someone other than the person who instantiates it could have instantiated it.
Is (3) analytic? Maybe it is a synthetic apriori truth of metaphysics. Whatever, it strikes me as true. Or do have a good reason for saying it is not true?
Posted by: Bill Vallicella | Wednesday, July 27, 2011 at 04:03 PM
Thank you for these useful points. We now understand the locus of the dispute. We should return to the subject soon.
Meanwhile, changing the subject completely, I fail to understand the game of 'chicken' that the two houses are playing over debt. (Wasn't there a James Dean film that started that way, with bad results?). I would be interested in hearing your views in a post.
Posted by: Edward Ockham | Thursday, July 28, 2011 at 12:15 AM
PS I agree the reason you give above is a bad reason.
Posted by: Edward Ockham | Thursday, July 28, 2011 at 12:16 AM
Edward,
Yes we will return to this topic and others in the vicinity. You've got me fired up over individuation.
That was automotive as opposed to legislative 'chicken' in the Dean flick. Thanks for crediting me with views worth hearing on the budget debate. I'll see if I have anything worth posting.
Posted by: Bill Vallicella | Thursday, July 28, 2011 at 07:03 AM
>>That was automotive as opposed to legislative 'chicken' in the Dean flick.
Same thing really.
http://www.youtube.com/watch?v=u7hZ9jKrwvo
I like the way he drives and smokes at the same time.
Posted by: Edward nominalist | Thursday, July 28, 2011 at 01:27 PM
The quintessence of cool.
Posted by: Bill Vallicella | Friday, July 29, 2011 at 09:57 AM
Reply to Bill on Individual Concepts,
In the above post Bill gave an argument that purports to show that there cannot be individual concepts. In order to assess Bill’s argument we need to be clear about the concept of *individual concepts* under consideration. As I noted in my previous comment, there is a tradition going back to Church, Carnap, and more recently Kripke which construes individual concepts as functions from possible worlds to individuals. Clearly, this is not the conception which Bill’s argument attacks. Bill’s argument is directed against a notion of individual concept that he associates with the so-called Traditional-Formal-Logician (TFL) and that appears to be defended on these pages by Ed-the-Nominalist.
What is the TFL-ers conception of an individual concept? It appears that TFL-ers hold that certain sentences which according to modern logicians are thought of as expressing singular propositions in fact express general propositions. An example that Bill cites is the following:
(*) “'Caissa is a cat' gets analyzed by the TFL-ers as 'Every Caissa is a cat.'
It is worth noting that according to modern logic the sentence ‘Caissa is a cat’ has the logical form of ‘Fa’, where ‘F’ is the predicate ‘…is a cat’ and ‘a’ is a singular term. Now the analysis stated by (*) is ambiguous between two different readings:
(a) ‘Caissa is a cat’ is true iff (x)(If x=Caissa, then x is a Cat);
(b) ‘Caissa is a cat’ is true iff (x)(If x is Caissasing, then x is a Cat), where ‘Caissasing’ is taken to be a predicate.
I do not know which one, (a) or (b), TFL-ers endorse, and this goes for our resident TFL-er Ed as well. As I noted in my previous post, (a) will not work because the antecedent of (a) contains the term ‘Caissa’ as a singular term. Therefore, (a) cannot serve as an analysis of ‘Caissa is a cat’ which eliminates the singular term ‘Caissa’. While (b) does indeed replace the singular term ‘Caissa’ and replaces it with a predicate by way of a formal stipulation a la Quine, this does not show that (b) is a correct account of ordinary sentences such as ‘Caissa is a cat’. Merely because we can introduce a formal trick that converts singular terms into predicates it does not mean that ordinary names function in ordinary discourse as predicates.
Let me now turn to Bill’s argument. First, Bill makes a very significant assumption about the nature of concepts. He says: “I take it we agree that concepts are mental in nature in the sense that, were there no minds, there would be no concepts.”
This assumption that concepts are mental in nature is anti-Fregean. I think that one could very well undermine Bill’s argument by simply denying this anti-Fregean premise, since Bill depends upon it heavily in his argument.
Secondly, definition D1 needs to be modified so as to restrict the range of ‘x’ and ‘y’ to contingent existents. Otherwise, counterexamples to D1 involving necessary entities such as the number two or God will arise (see an argument based on the only even prime in my previous post).
Third, D1 offers a definition of putative individual concepts in terms of what we might call *rigid instantiation*: i.e., if x instantiates C in the actual world, then whatever instantiates C in any other possible world, if anything, is identical to x. While this definition is relatively clear as far as it goes, Bill seems to draw a consequence from D1 which neither follows from D1 nor is it clear. He says:
(**) “We can therefore say that individual concepts, if there are any, 'capture' or 'grasp' or 'make present to the mind' the very haecceity (thisness) of the individuals of which they are the individual concepts.”
I do not see how this follows from D1. D1 is stated in terms of instantiation, identity, and possibility. (**), on the other hand, expresses what I take to be the phenomenology of grasping an individual concept. I do not see how concept phenomenology that is articulated in (**) is supposed to follow from D1 without some additional assumptions.
Consider the general concept *cat*. We can give an definition of the general concept *cat* analogous to D1 in terms of multiple instantiation such that two entities instantiate *cat* only if they are kind-similar, etc. Would such a definition license us to infer that a general concept presents to our mind the nature of the kind instances of which instantiate the concept *cat*? Not at all; o/w the discovery of the nature of things would have required nothing more than reflection on concepts. So Bill needs to justify why does he have this special requirement from individual concepts, when no analogous requirement would be appropriate in the case of general concepts.
Posted by: Account Deleted | Friday, July 29, 2011 at 06:29 PM
Peter,
I thank you for these comments. I hope to respond in new posts.
Posted by: Bill Vallicella | Saturday, July 30, 2011 at 04:31 AM