The nontransitivity of the contingent and occasio

Authors: Ralf M Bader

Publish Date: 2010/10/16

Volume: 157, Issue: 1, Pages: 141-152

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Abstract

This paper establishes that the occasional identity relation and the contingent identity relation are both nontransitive and as such are not properly classified as identity relations This is achieved by appealing to cases where multiple fissions and fusions occur simultaneously These cases show that the contingent and occasional identity relations do not even satisfy the timeindexed and worldindexed versions of the transitivity requirement and hence are nontransitive relationsIt might be asked why the fissions and fusions must occur simultaneously In order to see why this has to be so it is best to consider a case analogous to Case 1 but where the fissions and fusions are not simultaneous and then explain why such a case failsAt t B and D both undergo fission B splitting into A and x while D fissions to form y and E At t′ we have a fusion of x and y that forms C Exactly like in Case 1 it seems that we now have the following temporary identities A and C as well as C and E are identical at t but A and E are not identical at t thereby undermining the transitivity of identity A and E are only identical at t to things that are identical to each other at t′ It is only true that at t at t′ A = E but this is not equivalent to at t A = E since the temporal qualifiers are not redundant Thus it seems that Case A1 constitutes a situation where at t C = A and at t C = E but A is not identical to E at t Open image in new windowSince A and C as well as C and E are connected by a chain of identityatt statements it might seem that we can get the required at t A = C and at t C = E When looking at Case A1 we see that hboxA= thboxB hboxB= thboxx hboxx= thboxC hboxC= thboxy hboxy= thboxD and hboxD= thboxE However we cannot get at t A = C and at t C = E given that the identityatt relation put forward by Gallois is nonsymmetrical cf Gallois 1998 p 116 Accordingly in Case A1 we have hboxB= thboxx and hboxx= thboxC but neghboxB= thboxC without a violation of transitivity Since x = B at t and since x = C at t′ and since the identityatt relation is not symmetrical we do not get at t C = BWe can salvage the idea underlying Case A1 by slightly modifying the example In Case A1 we can rule out hboxC= thboxD by means of the hboxC= thboxx relation At t′ C = x and at t negD = x Accordingly hboxC= thboxD does not satisfy IT and is hence ruled out The same applies to hboxC= thboxB since at t′ C = y but at t negB = y However this problem can be fixed by appealing to cases where fissions and fusions occur simultaneously These cases are such that at one instant we have B and D and at the next instant we have A C and E There are no intermediary objects such as x and y that are identical to C at t′ that could be used to rule out hboxC= thboxB and hboxC= thboxD Accordingly we get the following identityatt relationsIn a normal case of fusion we can use the identityatt relation going in one direction from B to C ie mathophboxB= tlimitslongrightarrowhboxC in order to establish the identity B = C at t′ This occasional identity can then be used to rule out the identityatt relation from C to D going in the other direction ie mathophboxD= tlimitslongleftarrowhboxC since at t negD = B which is required by IT However in Case A2 we have no identityatt relation going to C that could be used to rule out identityatt relations going away from C This is because the fission cases ensure that no such relations obtain since the occasional identity at t A = B rules out mathophboxB= tlimitslongrightarrowhboxC since this identityatt relation would require C to be identical to A at t′ The same holds for the relation between D and C insofar as the occasional identity at t E = D rules out mathophboxD= tlimitslongrightarrowhboxC since this identityatt relation would require C to be identical to E at t′7 This is what is special about simultaneous fissions and fusions namely that both the branches connecting C to B and C to D are such that there are no identityatt relations ‘going to’ C that could be used for ruling out identityatt relations ‘going away’ from C The identitysustaining relation between C and B is sufficient for the identityatt relation mathophboxB= tlimitslongleftarrowhboxC to hold in the absence of there being something at t′ to which C is identical and to which B is not identical at t At t′ C is only identical to C and hence any object standing in an identitysustaining relation to C will be related to C by IT Since both B and D stand in identitysustaining relations to C they are both identicalatt to C ie mathophboxB= tlimitslongleftarrowhboxC and mathophboxD= tlimitslongleftarrowhboxC 8 Open image in new windowThus we can conclude that Case A1 fails due to the nonsymmetry of the identityatt relation However we can save the argument by appealing to cases involving simultaneous fissions and fusions In Case A2 it is the case that at t A = C and at t C = E but at t negA = E which implies that the occasional identity relation is nontransitive

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