If Murphy's favourite hammer has had both its head and its haft replaced several times over its long lifetime - is this still Murphy's favourite hammer? Or is it really a completely different hammer?
I think the 'dilemma', here, is between what we feel, as an unexamined intuition ('it's the same hammer'); and the difficulty of framing an abstract philosophical justification for why it is indeed still the same hammer - despite that everything about it has been replaced.
Properly considered, this is a very deep question indeed; and unless we have a 'theory' that explains why it is still the same hammer, then our metaphysics Must Be wrong.
Because what applies to the hammer applies to persons: applies to specific men and women Christianly-considered. We know that nothing makes sense about anything unless we are the same person through time; yet we also know that potentially everything about us may change, probably should change, as we undergo theosis - as we progress towards deity.
Probably, nearly all of our microscopic body is replaced through life; and even the cells that do last 'a lifetime' (neurons, myocytes) were not there at conception. The entire body is presumably replaced at the chemical level. And the mind of a zygote, morula, embryo, neonate, child, adult, senescent person... well this may have transformed wholly and more than once; leaving aside the re-formation of death and resurrection.
One attempted solution that is proposed by Owen Barfield - following Rudolf Steiner, is to posit an eternal and unchanging 'spirit' that persists through all physical and psychological changes. But this, I believe, rules out any fundamental change. If the Spirit is to carry a single identity it cannot change. All change is rendered superficial (i.e. a matter of body and soul, which are aspects of temporary incarnations) - while our core 'spirit' essence is static, by definition - or else it would not be The Same. This renders theosis trivial - hence I reject it.
There is, however (you will not be surprised to hear) a metaphysical philosophy that can readily explain why Murphy's hammer is still his favourite, and why a person can have literally everything about him (body and soul) replaced (in the process of spiritual progression to full deity) - and yet he or she will still remain the same person.
Mormon theology is based on evolutionary development as a core assumption, which entails that Time is always included in any ultimate analysis, which means (to jump a few steps) that every 'thing' is 'defined' as an uninterrupted lineage, extending through-time.This is one of its great strengths.
So that fact that at two different cross-sectional moments, the same 'thing' may have Nothing in-common, does not matter.
This is an aspect of what I understand by 'polarity' based on process of '-ing'. Or, more simply, a conscious and explicit version of the spontaneous 'animistic' spirituality of children and hunter-gatherers; a metaphysics based on Beings and Relationships in Time.
The above is based on a recent post at Junior Ganymede.