Jack forwarded me last week an intriguing message from Chris Landauer, from some non-public forum, dealing with identity and undecidability.
"Another question came up about recognizing when two objects are the same. Since that question is formally undecidable even in polynomial expressions over the integers (Hilbert's 10th problem), I don't see it as being possible in the more complicated spaces of computing systems (...) without some kind of "cheating", to use the usual mathematical parlance.
In this case, one useful kind of cheating is to provide some very carefully engineered introspective processes that let the computing objects help to analyze and combine themselves with others. This notion of "Computational Reflection'' is one of the main principles that underlie Kirstie Bellman's and my theoretical computing research, which has shown that we can build such computing systems"
A quick search about Launder and Bellman led me to a very rich list of publications .
But further searching for "identity + undecidable", I stumbled on this amazing paper written in early Web days (Oct '93) by Henry G. Baker. Although written for the context of distributed computing, quite technical, dealing in-depth with various flavours of identity/equality of objects in object-oriented languages such as LISP, many excerpts of the paper make sense even for the non-programmer:
Of course, to behave supposes a context of behaviour ... this conforts me in the line of thought that there is no identity, only identification process."Our model for object identity is similar to the concept of "operational identity", in which objects which behave the same should be the same."