Occasions of Identity_ A Study in the Metaphysics of Persistence, Change, and Sameness Part 3

Occasional Identity (E): States that an entity X has the time-indexed property of being at time t' if and only if something identical with X at time t also has the property of being at t'.
Occasional Identity (E)*: Suggests that for any object X, it is identical with something at t if and only if that object also has the time-indexed property at some other time t'.

The Leibniz's Law argument posits that statements (1), (3), and (4) cannot all be true simultaneously:
- (1) states that POND is in a pond at time T2.
- (3) asserts that SLIDE is not in a pond at that time.
- The argument suggests that if something identical with SLIDE at T1 is in a pond at T2, then SLIDE must also be in a pond at T2, violating the truth of (3).
Critics of OIT (Occasional Identity Thesis) may try to dispute (E) but it is more promising for them to target (E*).

Advocates of the Leibniz’s Law argument should focus on the distinction between the sufficiency for (6) (X has the property of being in a pond at T2) and (12) (there is something in a pond at T2 which is also identical with SLIDE at T1).
There exists a potential conflation between the conditions that ensure (7) (SLIDE is in the pond) versus (12).
An occasional identity theorist could potentially switch from the traditional view of (E) to (A), arguing that the latter provides necessary criteria for the analysis of time-indexed properties that do not contradict earlier interpretations of identity.

(A) states X has the time-indexed property of being o at t' if and only if everything identical with X at t is o at t'.
By accepting (A), it follows that if POND is in a pond at T2, then the conclusion is that SLIDE necessarily has to also be in the pond at T2, leading the occasional identity theorist to the conclusion that the statement (5) is false.
Such interchange of identities places pressure on the argument against OIT by questioning the validity of self-consistent identity within divisions like amoebic fission.

An intriguing aspect of occasional identities is the instability implication. This holds that SLIDE may be true at one time while simultaneously not exhibiting that property at another point.
OIT claims that identity is contingent — X may identify with Y at specific times but not across all temporal states.
This raises questions on identity and how one views traits such as height—if X is the same height at one moment as Y, it does not require X and Y be identical throughout their existence and is non-theoretically derived.

OIT's claims must grapple with identity-ensuring relations that should ideally establish the sameness of identities over time.
Furthermore, the distinction remains robust that OIT must be internally consistent; if it can assert identity at one point in time while contesting that identity at another time, then it can segment notions of sameness into discrete moments of existence.
The interplay between SLIDE and POND at each time stamp emphasizes this tenuous edge of identity; SLIDE could be invalidated as an identity with POND at T2 without contradicting the assertion made at T1.

The core argument surrounding Leibniz's Law intersects critically with notions of occasional identity. By emphasizing the necessity of contextual conditions for identities to hold or, conversely, to cease holding its implications for metaphysical discussions on identity grow nuanced.
OIT can assert identities while embracing inherent contradictions; it embraces a flexible view of identity that augments philosophical discussion on what it means to exist across different times.