Why I Reject Individual Concepts

This entry was first posted on 24 July 2011. Time for a repost with minor modifications. I find that I still reject individual concepts. Surprise!

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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 that 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 (TFL-ers) 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 (non-qualitative 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, although it dos have 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 or at the same time. 

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 non-qualitative 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, if they express concepts at all. 

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, even unto maximal specificity, 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 non-qualitative 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 precisely 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.!

Comments

[oz]

we have discussed this before. i distinguish haecceity properties (which are implausible) from haecceity predicates.

lemma 1 is false.

[oz]

"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."

this needs modifying to allow individual concepts of fictional beings such as frodo. perhaps "C is an individual concept if for all x, if x is instance of C, it is not possible there be a y etc."

[oz]

It looks as though you borrowed, or reinvented Strawson’s distinction between pure individuating descriptions (“the first dog born at sea”), and individuating descriptions (“the first dog born in London”) that contain a singular term such as a place name (‘London’) or temporal name (‘19th century’). See Individuals p.26. Strawson (who was well versed in the traditional logic) may have got it from John Stuart Mill, who distinguishes between ‘king’ and ‘king who succeeded William the Conqueror’.

Your distinction between pure and impure therefore is the distinction between a concept expressed using a general term or set of general terms, and a concept which cannot be expressed except by using singular terms, perhaps as part of a description. But singular terms express singular concepts, so you have apparently disproved the existence of singular concepts by invoking singular concepts! Where has your argument gone wrong?

The paragraph after Lemma 2 seems to do all the heavy lifting.

You say “If C is impure, then by (D2) it must involve an individual.” Why is that? An impure concept can only be expressed by using a singular term (‘first elf born in Hobbiton’, ‘first man to forge the Ring of Power’). In what sense do concepts expressed using empty names ‘involve’ an individual, given that there is no such individual?

You say “if C is an individual concept it must involve the very individual of which it is the individual concept. In what sense does the name ‘Sauron’ involve Sauron? You go on “no individual can be grasped precisely as an individual”. I could reasonably complain that I don’t understand what is going on here.

Singular (or ‘individual’) concepts are not difficult to explain. I begin a story “there was a hobbit called ‘Frodo’”, and I continue “Frodo lived in a hole”. My first (indefinite) sentence introduces the singular concept *Frodo*, which I then go on to use, by a term (‘Frodo’) that signifies that concept. By grasping that concept, I am grasping the idea that if there were such a being as Frodo, then no other being could be Frodo: in every possible world in which the concept of ‘being Frodo’ were instantiated, it would be instantiated by the same being that it instantiates now.

“Individuum ineffabile est” – I don’t think this is a scholastic maxim. But in any case ‘ineffabile’ means ‘unutterable’ or ‘unpronouncable’ so I don’t know in what sense individuals are unutterable. Singular/individual concepts are certainly not unutterable, for we express them by uttering singular terms. A singular concept is simply the meaning of a singular term such as ‘Socrates’ or ‘Frodo’.

[oz]

Reference and Identity p.33:

... a proper name cannot have a plural. Or suppose it had. Then we could use the name to signify both that the same thing is such-and-such, and that a different thing is such-and-such. But a proper name cannot signify identity and difference at the same time, so it cannot have a plural. A common name, by contrast, can be used to signify both “the same F” and “another F,” because its purpose is not to continue an anaphoric chain. The anaphoric account has no philosophical difficulties at all. We run into such difficulties only if we suppose that a name signifies some essential property of an individual, or the individual itself, rather than a property of the language alone.