Identity of Indiscernibles and Haecceities

According to the identity of indiscernibles, as a matter of necessity, no two things can share all their properties. If a and b share all their properties then they are not two things, but one: they are numerically identical. You can’t have qualitative identity without thereby having numerical identity.

Why think the identity of indiscernibles is true? Well, suppose it’s false; in that case there is a possible world containing two entities, a and b, which share all their properties. And the uncomfortable thought is meant to be that in that world there is nothing that makes these entities distinct.

This thought proceeds from the idea that, for every object o, something grounds the identity of o: there is a metaphysical explanation for o’s being that very object, and not some other thing. What could do this grounding other than some subset of o’s properties? But if o is the thing it is in virtue of having some subset of its properties, then any thing which had all and only o’s properties would have its identity determined in the same way as o, and hence would be numerically identical to o.

That, I take it, is the intuitive thought behind the identity of indiscernibles. Any defender of that thought has to say something about Max Black’s world consisting solely of the two homogenous iron spheres Castor and Pollux. One thing to say is that the objects have different haecceitistic properties. Castor is distinct from Pollux because one has the property being identical to Castor and the other the property being identical to Pollux. Something seems unsatisfying about that. John Heil describes it somewhere as “the sort of move that gives philosophy a bad name.” But what’s wrong with it?

Firstly, you might not like the admission of such a ‘property’ into your ontology. Our grasp of what properties are seems to be tied to qualitative ways for things to be – such as being red or being round etc; the introduction of mere haecceitistic properties might be thought to have stretched the concept of property beyond breaking point.

But suppose you accept the existence of properties of the form being identical to x; there is a deeper problem. We are told that Castor and Pollux are distinct because Castor has the property being identical to Castor and Pollux has the property being identical to Pollux. But that only serves to ground the distinctness of Castor and Pollux if these properties are themselves distinct. If ‘the property being identical to Castor’ and ‘the property being identical to Pollux’ are two names for the same property then the fact that Castor has the former property and Pollux the latter doesn’t serve to ground their distinctness. So we need to ensure that these haecceitistic properties are distinct if their admission into our ontology is going to help us with Black’s example. But then, by the same reasoning that led us to the identity of indiscernibles in the first place, there must be something that grounds the distinctness of these properties. Now what do we usually think are the individuation conditions for properties? One might try: P and Q are the same property iff they make the same contribution to the qualitative nature of their bearer. But of course, this will only do for qualitative properties; applying it to mere haecceitistic properties would make them all identical, since mere haecceitistic properties don’t make any contribution to the qualitative nature of their bearers (that’s precisely why it rankles to call them ‘properties’). So for mere haecceitistic properties it seems we should have instead: P and Q are the same haecceitistic property iff they belong to the same thing.

But if that’s right then being identical to Castor is distinct from being identical to Pollux in virtue of the bearer of the former being distinct from the bearer of the latter. In which case we can hardly appeal to the distinctness of the properties to ground the distinctness of the bearers.

One who invokes mere haecceitistic properties to deal with Black’s world wants to hold that [Castor is distinct from Pollux] in virtue of the distinctness of being identical to Castor and being identical to Pollux; but it seems that they should be committed to [being identical to Castor is distinct from being identical to Pollux] holding true in virtue of the distinctness of Castor and Pollux. But these ‘in virtue of’ claims can’t both be true, since in-virtue-of is asymmetric. So the introduction of mere haecceitistic properties doesn’t seem to help: to ground the distinctness of Castor and Pollux the distinctness of the properties would apparently need to be taken as brute; and if we’re prepared to do that, why not just accept the distinctness of Castor and Pollux as brute in the first place?

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3 responses to “Identity of Indiscernibles and Haecceities

  1. Aha. Another example, if I am not mistaken, of how philosophers are doomed for all eternity to use up taxpayers money by endlessly repeating their past. This sort of stuff was extensively discussed in the middle ages. See my latest posting on Jean Buridan here, for example. http://ocham.blogspot.com/2006/12/buridan-on-individuation.htmlYou say ” Our grasp of what properties are seems to be tied to qualitative ways for things to be – such as being red or being round etc; the introduction of mere haecceitistic properties might be thought to have stretched the concept of property beyond breaking point.” But what counts as being a qualitative way to be? Why is being round qualitative, and being Socrates not? On the second difficulty you raise, surely the answer is quite simple. What distinguishes property words (i.e. common nouns) from proper nouns, is that for any noun phrase of the form ‘an F’ we can also say ‘another F’, i.e. it is essential to the grammar of common nouns that there can be another of whatever they signify to be F. With proper names, by contrast, their function is simply to indicate we are talking about the same individual, i.e. there cannot be ‘another N’. This, as you imply, requires a definition of ‘the same’ that is not circular. But that is quite simple. When there are two occurrences of the same name in different sentences, e.g. ‘N is P’ and ‘N is Q’, the repetition of the name allows us to infer from the truth of both sentences that a single thing is both P and Q. And thus no property or haecceity is signified. We infer that a single thing has P, and has Q: no other property is to be inferred, no property of being N or anything like that. The proper name is just a bit of linguistic glue that ties different sentences together. Nothing more.

  2. Am I right in think that the challenge for the proponent of the Identity of Indiscernibles (II) is to show that the Black World (BW) is consistent with (II)? If so, then I’m not sure I see why an appeal to haecceitistic properties is problematic in your second way (I understand but don’t sympathize with the first complaint you mention). (II) Necessarily, for all x and all y, if for all F, Fx if and only if Fy, then x = y.Let ‘C’ be the property ‘being identical to Castor’. Let ‘P’ be the property ‘being identical to ‘Pollux’. Then, if (BW) is a world in which there are two spheres that are qualitatively identical with one another, then (BW) does not falsify (II) because there is a property (a non-qualitative property), C, exemplified by Castor but not Pollux. Your complaint, I take it, is that (II) should be taken to apply to properties, too. And, if (II) applies to properties, then (II)as applied to C and P has as a result that C and P are the same property. First, I’m not sure why we should think that (II) applies to properties. But, even if we do think that, I don’t see why we should think that (II) as applied to C and P has as a result that C and P are the same property. The proponent of (II) isn’t committed to accepting any claim about identity facts holding ‘in virtue of’ facts concerning the exemplification of properties. Maybe that’s a view held by a number of proponents of (II), but (II) itself doesn’t commit one to that claim. But, suppose that you do want to claim that identity facts hold ‘in virtue of’ facts concerning the exemplification of properties. Why can’t the proponent of this view (and (II)) claim that C and P are non-identical in virtue of the fact that C, but not P, has the second order property of ‘being the property of being identical to Castor’?

  3. I think you’re right that if it’s legitimate to appeal to haecceities to distinguish C and P, then, since according to the haecceitist, the having of these properties will not be in virtue of anything more basic, a haecceitist should just hold that it’s a brute fact that C is distinct from P (if that is in fact the case). But this is fully consonant with the haecceitist view of identity as brute. And I think the upshot is probably just that Black examples cannot be employed persuasively to put pressure haecceitists or anti-haecceitists with their wits about them. Fortunately there’s more that can be said. (Isn’t there always?) If there’s nothing in virtue of which x = x (apart from, perhaps, x’s possible existence), and distinctness facts depend on identity facts, we shouldn’t expect there to be any illuminating non-brute answer to the question ‘in virtue of what is C distinct from P?’ (provided that C is distinct from P).

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