There’s an interesting debate between Bryan Caplan and Robin Hanson on their respective blogs. Caplan writes:

… Robin didn’t care about biological survival.  He didn’t need his brain implanted in a cloned body.  He just wanted his neurons preserved well enough to “upload himself” into a computer.

To my mind, it was ridiculously easy to prove that “uploading yourself” isn’t life extension.  “An upload is merely a simulation.  It wouldn’t be you,” I remarked.  “It would if the simulation were accurate enough,” he told me.

He finds that point of view illogical:

If I’m whatever I define as me, why bother with cryonics?  Why not “define myself” as my Y-chromosome, or my writings, or the human race, or carbon?  By Robin’s standard, all it takes to vastly extend your life is to identify yourself with something highly durable.

His reply: “There are limits to what you can choose to identify with.”

And finally rejects the notion:

Fascination with technology crowds out not just philosophy of mind, but common sense.

Robin responds:

Bryan, you are the sum of your parts and their relations.  We know where you are and what you are made of; you are in your head, and you are made out of the signals that your brain cells send each other.

I find it interesting that it was Caplan who mentioned philosophy of mind, because the reigning philosophy of mind today is functionalism:

Functionalism in the philosophy of mind is the doctrine that what makes something a mental state of a particular type does not depend on its internal constitution, but rather on the way it functions, or the role it plays, in the system of which it is a part. This doctrine is rooted in Aristotle’s conception of the soul, and has antecedents in Hobbes’s conception of the mind as a “calculating machine”, but it has become fully articulated (and popularly endorsed) only in the last third of the 20th century. Though the term ‘functionalism’ is used to designate a variety of positions in a variety of other disciplines, including psychology, sociology, economics, and architecture, this entry focuses exclusively on functionalism as a philosophical thesis about the nature of mental states.

Functionalism is in a sense the modern version of dualism, the philosophy of mind that holds there are two basic kinds of things, mind and matter.  However, it overcomes a host of the logical problems of naive dualism in understanding what “mindstuff” actually is.  In older versions, you had the key problem that if the mind wasn’t physical, it didn’t make sense that it could affect what a physical system did; so what difference did it make if there was a mind or not?  This led to craziness such as epiphenomenalism.

Robin’s answer is essentially that the mind, as well as the body, is autopoietic: a stable pattern maintained in a flow of actual matter and energy, in which the substrate of real physical stuff keeps changing but the real you, the pattern, remains.  It is in fact the pattern that is the “mindstuff” in functionalism.

One of the big intellectual foundations of functionalism is the work in computability theory that form the core of computer science and modern metamathematics. This is commonly thought of as Turing completeness, but the universal Turing machine shares its seminal position with other models of computability such as Post production systems and partial recursive functions.  Even Conway’s game of Life turns out to be computationally universal.

50 years of computer science have given us a strong understanding of substrates, emulation, implementation compatibilities, and a host of related phenomena.  To those of have spent most of our lives working with it, the notion that physical brains are a computational substrate and that our identities are the currently running program and data — the autopoietic process — is the intuitively obvious common sense.

As such, we can answer Caplan’s question somewhat more precisely.  What you can choose to define as you is limited to a computationally universal substrate (mod storage limits) that is running a process that has various elements of memory and algorithm in common with the ones in the process currently running in your head.  How many elements and how closely they have to match is up to, well, you.