1. Some maintain that a hand, and that same hand made into a fist, are identical. And there are those who would say the same about a piece of bronze and the statue made out of it, namely, that they are identical at every time at which both exist. This is not an unreasonable thing to say. After all, fist and hand, statue and bronze, are spatially coincident and neither has a physical part the other doesn't have. A fist is just a certain familiar arrangement of hand-parts. There is no part of the fist that is not part of the hand, and vice versa. So at looks as if first and hand are identical. But we need to be clear as to what identity is.
2. Identity is standardly taken to be an equivalence relation (reflexive, symmetrical, transitive) governed by the Indiscernibility of Identicals (InId) and the Necessity of Identity (NecId). The first principle says that, if two items are numerically identical, then they share all properties. The second says that if two items are numerically identical, then this is necessarily the case. Both principles strike me as beyond epistemic reproach. 'Identity' is short for 'numerical identity.'
3. Despite the considerations of #1, it looks as if fist and hand, statue and hunk of bronze, cannot be identical since they differ in their persistence conditions. The hunk of bronze can, while the statue cannot, survive being melted down and recast in some other form. The hand can, while the fist cannot, survive adoption of a different 'posture.' In both cases, something is true of the one that is not true of the other. So even at the times at which the fist is the hand, and the bronze is the statue, the two are not identical: the 'is' is not the 'is' of identity. It is the 'is' of composition and what you have are two things, not one.
What I have just given is a modal discernibility argument. Let me spell it out. Consider a time t at which the hand is in the shape of a fist. At t, the hand, but not the fist, has the modal property of being possibly such as to to be unfisted. So the hand cannot be identical to the fist given that, for any x, y, if x = y, then x, y share all properties.
But there is also this nonmodal discernibility argument. The hunk of bronze existed long before the statue came into existence, and the hunk of bronze exists while the form of a statue. So the hunk of bronze exists at more times that the statues does, which implies the the hunk of bronze is not identical to the statue.
There is also this consideration. Identity is symmetrical. So we can say either fist = hand or hand = fist. But is it the fist or the hand that both are? Intuitively, it is the hand. The hand is the fundamental reality here, not the fist. So how can fist and hand be identical? It seems that fist and hand are numerically distinct, albeit spatially coincident, concrete individuals.
4. The Law of Excluded Middle seems very secure indeed, especially in application to presently existing things. So either the fist is identical to the hand, and there is just one thing, a fisted hand, or the fist is not identical to the hand and there are two spatially coincident things, a fist and a hand. So which is it?
5. If you say that the fist = the hand, then when you make a fist nothing new comes into existence, and when the potter makes a pot out of clay, nothing new comes into existence. And when a mason makes a wall out of stones, nothing new comes into existence. He started with some stones and he ended with some stones. Given that the stones exist, and that the mason's work did not cause anything new to come into existence, must we not say that the single composite entity, the wall, does not exist? (For if it did exist, then there would be an existent in addition to the stones.) But it sounds crazy to say that the wall the mason has just finished constructing does not exist.
6. If, on the other hand, you say that the fist is not identical to the hand, then you can say that the making of a fist causes a new thing to come into existence, the fist. And similarly with the statue and the wall. After the mason stacks n stones into a wall, he has as a result of his efforts n +1 objects, the original n stones and the wall.
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?
7. We appear to be at an impasse. We cannot comfortably say that the fist = the hand, nor can we comfortably say that the fist is not identical to the hand. Nor can we comfortably give up LEM. If there are no fists, statues, walls, artifacts generally, then there cannot be any puzzles about their composition. But we cannot comfortably say that there are no such things either.
Do we have here an example of a problem that is both genuine but insoluble?
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.
Posted by: William | Sunday, August 29, 2010 at 02:23 AM
Oops I messed up the html. Ignore the italics.
Posted by: William | Sunday, August 29, 2010 at 02:24 AM
Bill,
is a shorthand way of saying 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'. is what we mean when we sayCan 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?
Posted by: David Brightly | Sunday, August 29, 2010 at 04:45 PM
Test to remove italics.
Posted by: William | Monday, August 30, 2010 at 02:40 AM
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.
Posted by: William | Monday, August 30, 2010 at 02:47 AM
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?
Posted by: Steven | Monday, August 30, 2010 at 09:41 AM
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.
Posted by: Steven | Monday, August 30, 2010 at 02:12 PM
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?.
Posted by: Daevid | Monday, August 30, 2010 at 05:40 PM
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.
Posted by: Bill Vallicella | Monday, August 30, 2010 at 07:58 PM
William,
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.
Posted by: Bill Vallicella | Monday, August 30, 2010 at 08:01 PM
Hello Bill,
and 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.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,
Posted by: David Brightly | Wednesday, September 01, 2010 at 01:46 AM