Contingent Examples of Term-Relative Intrinsicality?

Zylstra's work shows that, if we are going to try to analyze essence in terms of necessity and intrinsicality and deliver the goods on Fine's celebrated Socrates/{Socrates} example (Socrates does not belong essentially to {Socrates}, but {Socrates} essentially contains Socrates), we had better understand intrinsicality as term-relative, at least in the case of relations. That is, we can't just say that some relations are intrinsic and others are extrinsic and that's it - rather, some two-place relations are, so to speak, intrinsic on one side but extrinsic on the other.

But can we really explicate such a concept of intrinsicality? Or is this really just going to be the concept of essence which we end up explicating? If we can do the job, then we should get something that, when supplemented with necessity, yields the notion of essence. This suggests that we should be able to find contingent cases of such asymmetric intrinsicality. And so that now seems to be the big question, if we're wondering whether essence should be accounted for in terms of necessity and something else, or the other way around. (Or at least whether intrinsicality should be involved if we pursue the first strategy.)

Thinking about parts of things, where those things could nevertheless have had different parts, may be one way of looking. For instance, perhaps 'My laptop contains the chip C' provides such an example. If the chip is intrinsic to the laptop, then we can say that the laptop intrinsically contains the chip, but that the chip is not intrinsically inside the laptop. But the laptop could have had another chip or perhaps no chip in that place, so it does not contain the chip necessarily.

I wonder how solid and convincing this sort of example is, though, and I wonder if there are other sorts available.

An Attempt to Diagnose the Disagreement over the Relational Explanation of Identity

Here is what I have to say in response to the schmidentity challenge as posed to the sui generis view of identity statements. (See also these two related posts from several years ago.)

OK, so we can grant that you can introduce a 'schmidentity' predicate in the way Kripke describes. We can also grant that this predicate could then get used to do what we do with identity statements. But can we, having granted these things, nonetheless deny that the meaning and function of identity statements is explained with the object-relation story?

I am strongly inclined to do all of this. Why? Because the characteristic function of informative identity statements and their denials - the way they get us to merge and separate mental files, or concepts of individuals - is passed over in this explanation. Going along with the object-relation explanation seems to render this incidental, instead of the main point. That explanation makes it look as though the main function of an 'a is b' statement is also fulfilled by the corresponding 'a is a' statement, which of course it is not.

But, someone may argue, does the object-relation explanation really create this false appearance? And here it would be easy to be dogmatic. There would be something silly about insisting that yes, this sort of explanation really does create this false appearance. After all, my opponent - the philosopher who wants to say that the object-relation story is perfectly adequate, and that there's no problem here, and that anyone who thinks there is is in a muddle - doesn't actually seem to be confused about the fact that 'a is b' statements are often useful in a way that the corresponding 'a is a' statements are not. They would happily admit that. So the difference between us seems to be in whether we are happy to leave this out in our primary explanation, so to speak, of identity statements.

And it is important that I allow that the object-relation explanation of identity statements does show something. It's not as if it is a sheer mistake. It shows that we can so to speak depict identity statements as a special case of relational statements, i.e. statements like 'John loves Mary'. I do not want to deny this, or deny that it is of philosophical interest.

There is something neat or cool about this sort of observation, too. It has a charm to it, similar to the charm possessed by clever hacks (in the sense of computer culture). I think that the philosopher who wants to defend the object-relation story lacks a proper place to put this. They feel the charm, the strikingness, of the explanation, and - not wanting this to elude them - wrongly place it in the "primary explanation" place in their thinking, instead of a place marked something like "striking and potentially instructive thing you can say". So long as we only focus on the "primary explanation" place, it looks like the defender of the object-relation story is missing something and proposing something maddeningly objectionable, but it also looks like the antagonist of the object-relation story is missing something. It is not until we consider other possibilities for the significance of the object-relation story that we are able to give both parties their due.

This, I now think, is a very important point (even though I may not have expressed it very well). I regret that I didn't manage to arrive at this point in my paper on this topic. I also think my predecessors were missing something in this regard.

So, we can grant the possibility of the schmidentity predicate, and the possibility of it coming to be used to do the characteristic work of identity statements, but nonetheless deny that the object-relation story should take pride of place in our explanation of the meaning and function of identity statements. A leftover question here is: should we also deny that the meaning and function of statements made with the 'schmidentity' predicate, if they are being used in the way we use identity statements, is explained by their stipulated semantics? And the answer, I think, is Yes. If they are being used in that way, then the object-relation story should not take pride of place in their explanation. But it is understandable that we should hesitate here, since 'schmidentity' was introduced and defined by means of the object-relation story, and this invites us to look at their use - when they are being used in the characteristic way we use identity statements - as a kind of secondary thing, a happy side-effect.

(I feel like saying something more at this point, which may be more objectionable, about what other use (schm)identity statements may have, apart from their practical use which has to do with merging and separating. A metaphysical use, so to speak. And about what attitude we take to this use, or whether it might be a kind of illusion. And this relates to one of the old posts linked to at the beginning. But I won't do more than make this hint, since these are treacherous waters and I wouldn't want to abuse the goodwill of a differently-minded reader.)

Notes on Identity (and the idea of a 'law of metaphysics' concerning it)

(I) Everything is identical with itself and with no other thing.

Consider what results when we try to express (I) in first-order logic:

(FOL I) (x) x = x  ~ (y)(y = x  ~ y = x)

For a closer articulation, let us introduce a function SelfOf() - the identity function – and a distinctness relation D, yielding

(FOL I 2) (x){ x = SelfOf(x)  ~ (y)(y = x  y D x)}

This shows what we are doing in the case where we use something like (I) to introduce 'identity' and cognates, e.g. making sure it's not taken qualitatively. We are presupposing, using, the notions of self and distinctness/otherness, and showing how identity connects with them; if we had fixed interpretations for 'D' and 'SelfOf', we could use (FOL I 2) to define '='. And we could of course reverse this, presupposing '='. (In the first use, we would naturally emphasise 'self' and 'no other thing', or just 'other', in pronunciation. In the second, we would emphasise the word 'identical'.) We can also presuppose nothing, and take these propositions as just specifying how these notions are to relate to each other.

All these construals can be called grammatical in Wittgenstein's sense. But now, is there some other way of taking (I)? It can certainly look that way in philosophy. ('Law of Metaphysics'.)

It can look as though (I) is ruling out worlds where the identity relation looks like this:

 

or like this:

and ruling in this sort of picture:

 

But no one wants to say that these worlds are real, or even possible. So then can't we – mustn't we - take this ruling in and out as grammatical too?

Somehow, instead of seeing it that way, philosophical thinkers try to give it another, impossible sort of application – or so I want to say. But what is this other application, and how am I to describe it without falling prey to the sort of confused thinking I am trying to correct?

What makes these mistakes, or confusions, hard to correct is their slippery, elusive character. (This no doubt has to do with the way so many of our key terms slip and slide so naturally between slightly different uses.)

It is not as if my opponent thinks their Law of Metaphysics is empirical, or anything like that. Rather, they have a spurious category for it, I want to say – or, at the very least, they spuriously categorize it.

They fail to make a category at the right level, so to speak – fail to regard identity statements as being sufficiently special in their fundamental workings. Instead, they are assimilated to other relational statements, giving rise to the conception of a special sort of fact (which we have some kind of special access to, perhaps).

A purported picturing of the world as being one way rather than another. A purported division in some space of representations. Also, perhaps some vague conception of an analogue of empirical verification – as it were, rational perception (cf. Plato, Goedel, the notion of an “eye of Reason”). The sort of thing no one would ever feel like positing for 'Bachelors are unmarried' (except perhaps in a heroic effort to be consistent).

How is it that this comes about here, and not, say, with 'Bachelors are unmarried'? I believe it arises from the mixture of two modes of representation. This should become clear in a moment.

* * *

It is odd the way (I) can inspire phrases like 'Law of Metaphysics' while 'Everything exists' is much less likely to. Of course, for the latter to be false, there would have to be things which do not exist, which is obviously contradictory. OK, but isn't that also true of the following natural description of “what it would take for (I) to be false”?: there would have to be things which do not bear the identity relation to themselves, or distinct objects between which it holds.

It is as though the two conflicting things here are less similar, a bit further apart in language, than in the existence case.

What if I had said 'there would have to be things which aren't themselves, or things which are other things'? That sounds more flatly contradictory; no one, unless doubly perverse, would formulate a “Law of Metaphysics” running 'Things are themselves'. (Butler's Dictum is not generally presented as a Law of Metaphysics.) The flavour changes markedly when we bring in 'identical', talk of 'bearing the identity relation' etc. That is where we begin to get the mixture of modes of representation.

A natural picture to illustrate, or put by, 'Everything is what it is' would be:

Things are represented as dots and are shown “just being themselves”. Whereas the natural picture to put by (I) is: 

 

And here we get the feeling of a contrast, of substance, of something being ruled out. Namely stuff like:

 

The mixture of two modes of representation here consists in the fact that each dot in the picture is taken to represent a different object, and yet lines are drawn indicating the identity relation – lines which could only be of use if two dots sometimes represented one object.

* * *

With identity statements, merely specifying the relation in question (identity) and the pair of objects involved in the ascription (assuming the names involved refer) fails to specify 'what is said' in any natural sense, however minimal. This problem cannot be avoided either by expelling repetitive identities from language – there can be multiple different non-repetitive identities concerning one and the same object.

If you find this strange or unacceptable, I suggest you have in the back of your mind a conception of relations which identity does not really fall under. Perhaps you are picturing something like the dots above, and imagining relations as encoding further information on top of that structure. This may be a good conception, in which case you should stop classifying identity as a relation, stop classifying identity statements along with propositions like 'John loves Mary'. This, rather than, e.g., moving to an unnatural conception of 'what is said' – which is, I think, what hard-line Millians such as Scott Soames do.

This move in semantics to an unnatural conception of what is said, then, may have an origin related to that of the conception of a Law of Metaphysics discussed critically above. Also, they can be made to support each other: if it's a 'substantial metaphysical fact' that everything is identical to itself, then a repetitive identity is an instance of this, and so perhaps it inherits some metaphysical substantiality for itself, in which case perhaps there is an informative, substantive extensional core to extensionally equivalent identity statements – something which they all say. Conversely, if we take this last thing for granted: what sort of thing does a repetitive identity say which an empirically informative counterpart also says? It had better not be something trivial, since the latter doesn't seem to say anything trivial, in any sense of 'say'. And so what sort of thing is this non-trivial thing which repetitive identities say? Perhaps we could call it 'an instance of a Law of Metaphysics'!