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Saturday, August 28, 2010


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This difficulty was not unfamiliar to Aristotle and his scholastic followers. Aristotle distinguished between 'essential' and 'accidental' features. Accidental features are those which a substance may lose. Aristotle's example is Socrates getting tanned in the sun. The description 'tanned person' may denote Socrates on some occasion, but not on others. So the identity 'Socrates = tanned person' is a sort of accidental identity (and thus not necessary). By contrast 'Socrates = rational animal' is essential, and thus necessary.

Mill discusses a similar issue in chapter 6 ('Verbal and Real Propositions') of the first book of A System of Logic. He entirely rejects the essential/accidental distinction and argues that it is all a matter of definition. We have the following definition (adapting to your example)

A fist =def a clenched hand

Thus while it is not necessary that a hand remains clenched, it is necessary that a clenched hand cannot be unclenched.

This doesn't quite address the difficulty you mention here, which is apparently that "the hand can, while the fist cannot, survive adoption of a different 'posture.' " I reply: this hand, if clenched, is necessarily clenched, as things are now. If the hand is going to be unclenched, then time must pass, of course. But then it is no contradiction to say that this hand, while clenched now, will be unclenched. This hand is currently identical with this fist. That identity, at this point in time t, is entirely necessary. The proposition 'this hand was identical with that fist at t' will always be true. But the hand remaining under the description 'clenched' is clearly not necessary.

Can this fist become unclenched? Can this clenched hand become unclenched? Yes of course. The proposition 'this F is not F' is of course necessarily untrue. There is no point in time which, uttered in the present tense, it can be true. But 'this F will not be F' is certainly possible. Perhaps, one day, I will not be poor. Perhaps this poor person will one day be rich. But on that day, 'this poor person is not poor' will fail to be true because 'this poor person' will no longer pick out me.

Hope that makes sense, and hope it engages your question.

Oops I messed up the html. Ignore the italics.

Can we escape this impasse by semantic ascent? You say at one point "if two items are numerically identical, then this is necessarily the case." Surely no *two* things can be identical because then there'd be just one of them. Is then numerical identity perhaps a binary relation over referring terms?

Hesperus and Phosphorus are numerically identical
is a shorthand way of saying
Both 'Hesperus' and 'Phosphorus' refer to a single thing.
Suppose that 'the hand' refers to my hand and that 'the fist' also refers to my hand when it's clenched but has no referent when my hand is unclenched. If I wave an open palm and say 'Look at the fist!' you'd reasonably reply 'What fist?' So while my hand is clenched 'the fist' and 'the hand' refer to the same thing and so we would say in our shorthand, 'the fist is numerically identical to the hand' or 'the fist has every property that the hand has and vice versa.' With just one object under consideration the arguments from persistence conditions and from discernibility drop out. The asymmetry between our two referring terms is apparent. The remaining objection is that nothing new comes into existence. I'd have to say that when the mason finishes rearranging the stones what comes into existence is a referent for 'the wall' construed as the description 'the stones arranged wall-wise'.
'the wall' has/had a referent
is what we mean when we say
the wall exists/existed.

Test to remove italics.

Surely this is just another example of the famous puzzle we were taught as undergraduates about 'the number of planets = 9'. If 'the number of planets' is a referring expression, as is '9', then we have strict identity, and it seems that some merely contingent fact like the number of planets is necessary.

The commonly accepted solution is that 'the number of planets' is not a strictly referring expression (or 'rigid designator') but a description.

It makes sense to me to speak of two distinct things sharing parts. The mereological sum a + R + F-ness has the same parts as the fact a's being F, but they're distinct things. Why not also with the statue and the bronze examples?

BV: "But this is also counterintuitive. Consider the potter at his wheel. As the lump of clay spins, the potter shapes the lump into a series of many (continuum-many?) intermediate shapes before he stops with one that satisfies him. Thus we have a series of objects (proto-pots) each of which is a concrete individual numericallt distinct from the clay yet (i) spatially conicident with it, and (ii) sharing with it every momentary property. And that is hard to swallow, is it not?"

I'm not sure what the force of this is supposed to be. Is there any theory in metaphysics that doesn't have "hard to swallow" consequences? Isn't just a fact of the philosophical endeavor that somewhere down the line, you have to accept something a bit counterintuitive to be consistent?

In any case, it seems better to me to just accept possibly crazy consequences of your solution to a philosophical problem than hold that the problem is genuinely insoluble.

It seems to me (and please excuse me for any naiveté) that in all your examples one of the items is hierarchically below the other. What I mean by that is that the hand (and you said hand, not opened hand, or flattened palm) can be made into any number of poses, while the fist is but one of those poses. Similarly with the clay (again, clay, not a slab or lump of clay), it can be fashioned into a variety of shapes, each distinct from, though subsidiary to, the block of clay they were made of. It is a form of potentiality, with the hierarchically superior object able to form any number of the hierarchically inferior objects, but not vice versa. Perhaps therein lies their difference?
The other difference between hand and fist; stones and wall; clay and bowl, is about use. The fist can punch, the hand cannot; the wall can protect, the stones cannot; etc. So while physically composed of the same 'stuff' their potential use, or actions are different.
So if you use hierarchically different objects then my first argument stands. And if you change the wording and use hierarchically similar objects (fist vs open palm, clay bowl vs clay slab) then the second argument holds.
This all seems a little obvious though so perhaps I'm missing the point?.

David Brightly,

You are right, two things cannot be one thing. So it is better to say: for any x, y, if x = y, then necessarily x = y.

You suggest that
1. Hesperus = Phosphorus
is shorthand for
2. 'Hesperus' and 'Phosphorus' refer to a single thing.

(2) entails (1), but (1) does not entail (2). For (1) is true at times and in possible worlds at which (2) is not true. Similalrly,

3. The wall exists
is entailed by but does not entail
4. 'The wall' has a referent.

What allows you to assume that at a time at which 'the fist' and 'the hand' each have a referent that they have the same referent? Could the terms not refer to two different spatially coincident objects that share all the same momentary properties but are different in respect of modal and historical properties?

I don't think semantic ascent allows us to evade the problem.


I turned off the italics you left on by typing left angle bracket forward slash i right angle bracket. The forward slash is the switch that turns off an HTML command.

Hello Bill,
I agree that it's an assumption that 'the fist' and 'the hand' are co-referential, but (a) it seems a reasonable assumption that doesn't do any damage to my notion of 'object' and (b) if it leads to a dispelling of the aporetic discomfort, that is all well and good. But if I have you right, you are saying that, on modal and temporal grounds,

(1) Hesperus is identical to Phosphorus,
(2) 'Hesperus' and 'Phosphorus' refer to a single thing
are not equivalent. You allow that (2)-->(1). Here's an argument that ~(2)-->~(1) and hence (1)-->(2). If ~(2) then 'H' and 'P' refer to two different things. (We must assume that both refer to something, or is it that we cannot perhaps your point?) But we agree that two different things cannot be identical. So it is not the case that H is identical to P. At the moment I can't see how this argument fails on modal or temporal grounds.

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