Category: Haecceity

Singular Concepts and Singular Negative Existentials

A re-post  from 15 May 2012. Reproduced verbatim.

………………………………….

London Ed seems to be suggesting that we need irreducibly singular concepts (properties, propositional functions) if we are properly to analyze grammatically singular negative existence statements such as

1. Vulcan does not exist.

But why do we need to take 'Vulcan' to express a singular concept or haecceity property?  Why isn't the following an adequate analysis:

1A. The concept Small, intra-Mercurial planet whose existence explains the peculiarities of Mercury's orbit is not instantiated.

Note that the concept picked out by the italicized phrase is general, not singular.  It is general even though only one individual instantiates it if any does.  The fact that different individuals instantiate it at different possible worlds suffices to make the concept general, not irreducibly singular.

Singular Concepts Again

Ed writes,

Your counter-arguments are very useful but I find some of them puzzling. One argument that repeatedly occurs is that a concept cannot contain the object that it is a concept of. Our concept of Venus (if we have one) cannot contain Venus, for example.

My difficulty is that I agree with this argument, indeed it’s a cornerstone of the thesis in the book. See e.g.

The standard theory is a development of Mill’s theory, and is attended by the same difficulties. It explains properness by a semantic connection between proper name and bearer whereby the name can only signify that thing, but this leads to all the well-known difficulties mentioned in the last chapter, for example (i) how a large planetary body like Jupiter could be a part of a meaning or a thought, (ii) how identity statements involving different names for the same thing, such as “Hesperus is Phosphorus” can sometimes be informative, and (iii) how negative existential statements, which apparently deny a meaning for the name, are possible at all.

My emphasis. So where are we disagreeing I wonder? Is it that I claim a singular term has a meaning or sense? But in other posts of yours, you seem to agree that singular terms have a sense.

Or is it that you think that the sense of a singular term is ‘general’?

BV: Yes, that is what I claim. A singular term such as a name has a sense, but its sense is general. But I note that you switched from 'concept' to 'sense.'  They are closely related. We may have to examine whether they are equivalent.  

If so, you need to define what ‘general’ means. I define it as repeatable. A repeatable concept is one that we can without contradiction suppose to be instantiated by more than one individual, perhaps by individuals in different possible worlds. A singular concept by contrast is one where we cannot suppose repeatability without contradicting ourselves. For example, I cannot rationally entertain the thought that there could have been someone else who was Boris Johnson in 2021. That is because ‘someone else’ in this context means ‘someone other than Boris Johnson’, but ‘who was Boris Johnson’ means ‘someone who was no other than Boris Johnson’.

Thus to suppose that there could have been someone else who was Boris Johnson in 2021 is to suppose that there could have been someone who was both (1) other than Boris Johnson and (2) not other than Boris Johnson.

BV: I accept your definitions of 'general concept' and 'singular concept' pending some caveats to come.  We agree that there are general concepts.  We also agree that there are general terms and that there are singular terms. Presumably we also agree that a term is not the same as the concept the term expresses.  The English word 'tree' and the German word 'Baum' are both token-distinct and type-distinct. But they express the same concept. Therefore, a word and the concept it expresses are not the same.  And the same goes for sense: a word is not the same as its sense.

We disagree about whether there are singular concepts. You say that there are and I say that there aren't.   

I think the onus is on you to establish that there cannot be unrepeatable concepts in the sense defined above.

BV: Why is the onus probandi on me rather than on you? Why is there a presumption in favor of your position that I must defeat, rather than the other way around? But let's not worry about where the burden of proof lies. We are not in a court room.  You want an argument from me to the conclusion that there are no singular/individual/unrepeatable concepts. The demand is legitimate regardless of burden-of-proof considerations.

We agree that a first-level singular concept C, if instantiated, is instantiated by exactly one individual in the actual world and by the very same individual in every merely possible world in which C is instantiated.  This is essentially your definition of 'singular concept.' I don't disagree with it but I say more. 

I say that every concept is a mental grasping by the person who deploys the concept of the thing or things that instantiate (fall under, bear) the concept.  A concept of an individual, then, would have to be a mental grasping of what makes that individual be the very individual it is and not some other actual or possible individual.  So if there is the irreducibly singular concept Socrateity, then my deployment of that concept would allow we to grasp the haecceity (thisness) of Socrates which is precisely his and 'incommunicable' (as a schoolman might say) to any other individual actual or possible.  But this is what minds of our type cannot grasp. Every concept we deploy is a general concept, and it doesn't matter how specific the concept is. Specificity no matter how far protracted never gets the length of singularity.

All of our concepts are mental representations of the repeatable features of things.  It follows that all of our concepts are general. The individual, however, is essentially unrepeatable. For that very reason there cannot be a concept of the individual qua individual.

Consider Max Black's world in which there are exactly two iron spheres, alike in all monadic and relational respects, and nothing else. If there were an individual concept of the one sphere, then it would also be an individual concept of the other.  But then it would not be an individual or singular concept: it would be general.  It would be general because it would have two instances. The only way there could be two individual concepts is if each had as a constituent an iron sphere — which is absurd.  Therefore, there cannot be any individual concepts.

 

A Proof of Individual Concepts?

This just in from Edward:

Proof that singular concepts (aka individual concepts) exist.

1. Common terms (‘cat’) and singular terms (‘this cat’, ‘Max’) exist.

2. These terms are meaningful, i.e. their meanings exist.

3. A concept is the meaning of a term.

4. Thus (from 1,2, 3) singular concepts, aka singular meanings, exist.

QED

This argument equivocates on 'meaning.' There are of course general and singular terms and they both have meanings if the meaning of a term is its extension, the (set of) things to which it applies. Accordingly, the meaning/extension of 'cat' is (the set of)  cats, and the meaning/extension of 'Max' is Max, or his singleton.  General terms also have meaning in the sense of intension.  'Cordate' and 'renate' are general terms that have the same extension but differ in intension.  But the singular term 'Max,' while it has an extension, lacks an intension.

So for both (1) and (2) to be true, the meaning of a term must be its extension. But for (3) to be true, the meaning of a term must be its intension. So the argument trades on an equivocation and is for that reason invalid.

Here is a sound argument:

5. A concept is the intension of a term.

6. Singular terms lack intensions.

7. If a term lacks an intension, then there is no concept the term expresses.

Therefore

8. Singular terms do not express concepts. (From 5, 6, 7)

9. If a term does not express a concept, then there exists no concept the term expresses.

Therefore

10. There are no singular/individual concepts.

Just ask yourself: how could there be a concept of precisely Max and nothing actually or possibly different from Max? Suppose that there is a definite description that Max alone satisfies in the actual world.  That description would express a concept that only one thing could bear or instantiate. But such a concept would not be singular but general since something else might have satisfied the description.   For there to be an individual concept of Max, Max himself would somehow  have to be a constituent of the concept. But that is impossible and for two reasons.  First, concepts reside in the mind but no cat is a constituent of anything in my mind.  Second, a concept is distinct from its bearer and can exist whether or not its bearer exists.  But the concept MAX, if there were such a concept, would not be wholly distinct from its bearer and could not exist without its bearer.

The individual qua individual cannot be conceptualized. My conceptual grasp of an individual such as Max is always and necessarily by way of general concepts: cat, domestic cat, black cat, Tuxedo cat, black male Tuxedo cat five years old and weighing 20 lbs,  cat presently in my visual field, this cat to which I am now pointing.  Note that Max need not be this cat to which I am presently pointing, whence it follows that the haecceity of Max himself  cannot be reached or grasped or conceptualized in the concept this cat to which I am presently pointing.

Intentionality, Singularity, and Individual Concepts

Herewith, some notes on R. M. Sainsbury, Intentionality without Exotica.  (Exotica are those items  that are "nonexistent, nonconcrete, or nonactual." (303) Examples include Superman and Arcadia.)

'Jack wants a sloop' could mean three different things. (a) There is a particular sloop Jack wants.  In this case, Jack's desire is externally singular.  Desire is an object-directed mental state, and in this case the object exists and is singular.

(b) There is no particular sloop Jack wants; what he wants is "relief from slooplessness" in Quine's phrase. In this case the desire, being "wholly non-specific," is not externally singular.  In fact, it is not singular at all.  Jack wants some sloop or other, but no particular sloop whether one that exists at present or one that is to be built.

(c) Jack wants a sloop of a certain description, one that, at the time of the initial desire, no external object satisfies. He contracts with a ship builder to build a sloop to his exact specifications, a sloop he dubs The Mary Jane. It turns out, however, that the sloop is never built.  In this case, Sainsbury tells us, the desire is not externally singular as in case (a), but internally singular:

The concept The Mary Jane that features in the content of the desire is the kind of concept appropriate to external singularity, though that kind of singularity is absent, so the desire counts as internally singular. The kind of concept that makes for singularity in thought is one produced by a concept-producing mechanism whose functional role is to generate concepts fit for using to think about individual things. I call such a concept an ‘‘individual concept’’ (Sainsbury 2005: 217ff). Individual concepts are individuated by the event in which they are introduced. In typical cases, and when all goes well, an act of attention to an object accompanies, or perhaps is a constituent of, the introduction of an individual concept, which then has that object as its bearer. In cases in which all does not go well, for example in hallucination, an individual concept is used by the subject as if it had an object even though it does not; an act internally indistinguishable from an act of attending to an object occurs, and in that act an individual concept without a bearer comes into being. A concept so introduced can be used in thought; for example an individual concept C  can be a component in wondering whether C is real or merely hallucinated. In less typical cases, it is known to the subject that the concept has no bearer. An example would be a case in which I know I am hallucinating.     
    External singularity is relational: a subject is related to an object. Internal singularity is not relational in this way. (301, bolding added.)
 
What interests me here is the notion of an individual concept (IC). We are told above that an IC is distinct from its bearer and can exist without a bearer.  So the existence and identity of an IC does not depend on its having a bearer. We are also told that one and the same IC can figure in both a veridical and a non-veridical  (hallucinatory) experience, the seeing of a dagger, say.  So it is not the bearer that individuates the IC. What individuates it is the mental event by which it is introduced.
 
To these two points I add a third: it is built into the sense of 'individual concept' that if an individual concept C has a bearer, then it has exactly one bearer in the actual world, and the same bearer in every  possible world in which it has a bearer.  So if there is an individual concept SOCRATES, and it has a bearer, then it has exactly one bearer, Socrates, and not possibly anything distinct from Socrates.  This implies that individual concepts of externally singular items are as singular in content as the items of which they are the concepts. This in turn implies that no individual concept of an externally singular item is general:  no such concept is multiply instantiable or multiply 'bearable.'
 
I now add a fourth point: concepts are mental entities in the sense that they cannot exist apart from minds. Concepts are representations and therefore mental entities in the sense indicated.  A fifth point is that our minds are finite and our powers of conceptualization correspondingly limited. One obvious limit on our power to conceptualize is that no concept of ours can capture or grasp the haecceity (thisness) of any externally singular item.  We ectypal intellects cannot conceptually eff the ineffable, where what is ineffable is the individual in its individuality or singularity or haecceity, i.e.,  in that which makes it be this individual and no other actual or possible individual.  God, the archetypal intellect, may be able to grasp the haecceity of an individual, but this is clearly beyond our 'pay grade.' If God can do it, this is presumably because he creates the individual ex nihilo.
 
It follows from the fourth and fifth points that all of our concepts are general.  Suppose that the concept FASTEST MARATHONER (FM) applies to Jones. That concept is general despite the fact that at any given time t only one person can instantiate or bear it.   For at times earlier and later than t, some other runners were and will be the FM.  Therefore, FM does not capture Jones' haecceity. But even if Jones is the FM at every time in the actual world, there are possible worlds in which some other person is the FM at every time. What's more, at any time at which Jones is the FM, he might not have been the FM at that time.
 
Sainsbury's theory of individual concepts strikes me as incoherent.  The following cannot all be true:
 
1) There are individual concepts.
2) Concepts are representations in finite minds, and our minds are finite.
3) Individual concepts of externally singular items must be as singular in content as the items of which they are the concepts.
4) Every externally singular item exists. (There are no 'exotica.')
5) Every externally singular item is wholly determinate or complete where x is complete =df x  satisfies the property version of the Law of Excluded Middle (tertium non datur).
6) No concept in a finite mind of an externally singular item is singular in content in the sense of encoding every property of the wholly determinate or complete thing of which it is the concept.
7) One and the same individual concept can figure in both a veridical and a non-veridical  (hallucinatory) experience.
 
Sainsbury is committed to each of these seven propositions, and yet they cannot all be true. The first five propositions, taken in conjunction, entails the negation of (6).   Or if (6) is true, then (1) is false.  (6) and (7) cannot both be true.
 
I conclude that there are no individual concepts, and that the distinction between externally singular and internally singular object-directed mental states cannot be upheld.