Thursday, August 26, 2010

More on 'Replacement Identity'

Not everyone is sure about replacement identity, the assumption that when a component of some artefact (or at least a very small component such as a brick) is replaced, the artefact remains the same. Some of these arguments are qualified by the assumption that the components are 'simple'. But what components are simple? An artefact like a bike is made from artefacts such as mudguards, wheels, brakes and so on. These artefacts (a brake e.g.) are built from other artefactual components such as rubber blocks, steel wingnuts, plastic cables and so on. An artefact such as a plastic cable is made of molecules. A molecule is not an artefact, of course, but it is complex, being made of atoms. An atom is made of sub-atomic particles and so on.

It seems entirely implausible that when a small sliver of material, or molecule or sub-atomic particle is shaved off the bike, the bike is no longer identical with the bike that existed before. So some qualified version of Replacement Identity must be true. But then the Transitivity of Identity kicks in. If the bike is the same bike after a tiny part has been removed and then replaced, then it is the same bike. And still the same bike after another part has been shaved off and replaced. And so on until the whole bike has been completely replaced. The enemies of (A) must bite the bullet. Either it is false, even for sub-atomic changes in composition. That seems implausible. Otherwise Replacement Identity + Transitivity gets us to the paradoxical conclusion. More on Transitivity later, as I promised.

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3 Comments:

Blogger Erik said...

This is also in response to some of what you said in the previous posts comments (identity in replacement)

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My argument withstands your removing atoms argument; the mudguard example was, like the SoT, just to bring out the idea expressed, we can intelligibly talk about some infinitesimal being removed.

As I indicated in a previous comment, the relationship between the objects is one of equivalence, not identity. This allows us to be more imprecise in saying that it is the "same" object. Your logical objections about the phrases themselves are more obscuring than helpful. They are, I argue, relying on an inaccuracy, one that does not actually speak to the fact(s) of the matter.

Where you might press me is to say what the relationship is between these "equivalent" objects. This is the least clear part of my argument, and I can't say I really have a coherent explanation, only the intuition that this is, on the thesis of artefact identity, better at bring out what is puzzling about the SoT problem.

Part of my suggestion is that at the level of ordinary discourse about identity, we don't need the precision of saying that 'the bike before' and 'the bike after' are different; they are for ordinary purposes trivial changes to a mudguard or seat or tire or some arbitrary atomic/sub-atomic bits. This says nothing however about whether they are actually identical.

2:17 pm  
Blogger Ocham said...

>>As I indicated in a previous comment, the relationship between the objects is one of equivalence, not identity. This allows us to be more imprecise in saying that it is the "same" object. Your logical objections about the phrases themselves are more obscuring than helpful. They are, I argue, relying on an inaccuracy, one that does not actually speak to the fact(s) of the matter.

On the contrary, the relation is of identity, *as I have defined it*. It is a very simple notion: we have numerical identity when two predicates apply to single subject. I.e. if we can truly say 'X is both A and B', then we have an identity between what 'is A' is predicated of, and what 'is B' is predicated of. That is how I am defining identity. Thus, when I say 'this bike had the old mudguard yesterday, and has the new mudguard today', there is identity (in the sense I have precisely and rigorously defined) between what 'had the old mudguard yesterday' is predicated of, and what 'has a new mudguard today' is predicated of.

If you deny identity *in this sense*, you are forced to deny that it is ever true to say that, e.g. I replaced a brick in this house, or that the bike has a new mudguard, and things like that. Are you denying that?

2:34 pm  
Blogger Erik said...

I am trying to offer a thesis that the notion of logical identity, in the sense you use it, is not one that we can use in this case (insofar as it is relating to the form against the actual content i.e. validity vs soundness).

Am I then denying this use of identity for approaching SoT, yes. For now I am prepared to bite that bullet, I want an argument that gives me, for artefacts, an unsavory consequence.

(If you do want to use it, then we are having a different argument, and we actually don't really disagree.

The sort of argument Mr. Brightley is offering can be interesting but I think pushes at the boundary of whether what we are arguing is coherent.)

Again, as far as old and new, these terms don't really have the temporal content we give them, in the example described, they are just handles we use to make intelligible the way we speak of objects that undergo changes like replacing a mud guard.

Now whether this is some sort of creation, I haven't puzzled out. I hope though to see whether I can use this kind of argument for puzzling this out.

4:04 pm  

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