[ontolog-forum] Relative Identity

[Simon Spero <sesuncedu@xxxxxxxxx>]

On Mon, May 27, 2013 at 8:41 PM, Christopher Menzel <chris.menzel@xxxxxxxxx> wrote:

On May 18, 2013, at 5:30 PM, William Frank <williamf.frank@xxxxxxxxx> wrote:

x is the same as y 

is not meaningful in itself, in that it lacks the context of a qualifier T, where T is a type of thing, so that the full _expression_ is

x is the same T as y.

This is of course the theory of relative identity. I myself think the view is fatally flawed as a comprehensive account of identity (notably, it seems to presuppose absolute identity: x is the same T as y if and only if there are F and G such that F is a T and G is a T and F = G). Problems and virtues of the view aside, however, it is much too strong to say that absolute identity "is not meaningful". It may have its quirks and limitations, but meaningless it is not; we can axiomatize it, provide a clear extensional semantics for it, etc.

I strongly agree that absolute identity is highly meaningful, but would disagree that relative identity presupposes absolute identity.

If absolute LL is

   `=`(x, y)  → (∀φ. φ(x) → φ(y))

then a relative  RLL can be defined by restricting which predicates must be identical for x and y to be the same F, e.g. 

`=`(F,x,y)  → (∀φ.  RI(F,φ) → (φ(x) → φ(y))

There are stronger questions regarding whether the term "identity" should be reserved for absolute identity, but relative identity can be a useful way of identifying useful (equivalence) classes when analyzing a domain.  

For example, a library may own several physical copies of the same print run of a "book" (multiple Items exemplifying the same Manifestation in terms of the FRBR model).   The Items owned by a particular Library are referred to as Holdings.

If we relax the conditions of identity to exclude those properties related to physical identity (e.g. made of same atoms, occupying identical regions of space-time, etc), apart from the property of being located at the same library,  we can come up with a new (equivalence) class that collapses all Holdings of the same Manifestation at the same library.  

If someone is looking to obtain any physical copy of a book via Inter Library Loan, then these "Hasings" are quite salient. 

By successively reducing the properties that must be identical, one can ascend from particulars (Items) to Works and above.  

Simon

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