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## Re: [ontolog-forum] Relative Identity

 To: "[ontolog-forum]" "doug foxvog" Thu, 30 May 2013 23:24:49 -0400
 ```On Tue, May 28, 2013 12:20, Simon Spero wrote: > On Mon, May 27, 2013 at 8:41 PM, Christopher Menzel > wrote: > >> On May 18, 2013, at 5:30 PM, William Frank >> 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.    (01) > 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))    (02) How does this apply to properties measured at different times? Instantaneous identity is not as useful as identity over time. Do you consider the only case of absolute identity to be instantaneous identity?    (03) > 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.    (04) > `=`(F,x,y) → (∀φ. RI(F,φ) → (φ(x) → φ(y))    (05) > 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.    (06) > 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.    (07) > 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),    (08) If ObjectA at time t1 has 99.9999% of the atoms that ObjectB at time t2 has, is it the identical object? If ObjectC at time t3 has the 30 times the rest mass that ObjectD does at time t4 is it necessarily a different object? If ObjectE has twice the length, but half the width at time t5 that ObjectF has at time t6, are they necessarily not absolutely identical? If an unexcited neutral atom of H4 at time t7 is in the exact same place with the exact same momentum as an unexcited neutral atom of H4 at time t8, are they absolutely identical?    (09) > 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.    (010) It collapses them into being instances of the identical class; but i suggests that they shouldn't be considered to be the identical thing.    (011) -- doug foxvog    (012) > If someone is looking to obtain any physical copy of a book via Inter > Library Loan, then these "Hasings" are quite salient.    (013) > By successively reducing the properties that must be identical, one can > ascend from particulars (Items) to Works and above.    (014) > Simon    (015) _________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/ Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx Shared Files: http://ontolog.cim3.net/file/ Community Wiki: http://ontolog.cim3.net/wiki/ To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J    (016) ```
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