The following argument is an application of the problem of identity to the theory of evolution. It is not an extensive treatment of the concept, but that is because it doesn’t need to be ;) Apologist Mike Robinson of www.thelordgodexists.com has an excellent variation on a similar problem facing naturalists at this link. If you want a more in depth logical criticism of the naturalistic worldview, I think his article is a great help.
My argument is simple:
If all living organisms perpetually evolve, then no living organism is ever self-identical.
But the perpetual evolution of a given organism presupposes its self-identity.
Therefore, perpetual evolution is impossible.
That is all.
Soli. Deo. Gloria.