Algorithms and mathematical functions CANNOT be material
And here's a proof:
"Every physical process, no matter how long (even infinite), is indeterminate among incompatible pure functions; (2) so, no such process can be IDENTICAL with any of them, nor can it uniquely determine a function among processes that is IDENTICAL with any pure function. [That follows from the arguments used by Wittgenstein, Goodman, Kripke and many others.] (3) But we know beyond any doubt that WE think in forms that are pure functions (addition, squaring, conjunction, modus ponens) and are not indeterminate among incompatible functions. THEREFORE, our thinking, in so far as it is the realization of a determinate pure function, cannot be any material process or any function among material processes. Thus, human thought, as intelligent, is immaterial." (https://www.sas.upenn.edu/~jross/aristotlesrevenge.htm)
In short, an algorithm cannot possibly be a material thing, as any physical process whatsoever could represent infinitely many algorithms, and so can't possibly uniquely pin down any of them. But we humans can do so: we can say that is an implementation of quick sort!
So algorithms and our thoughts about them must be immaterial.
"Every physical process, no matter how long (even infinite), is indeterminate among incompatible pure functions; (2) so, no such process can be IDENTICAL with any of them, nor can it uniquely determine a function among processes that is IDENTICAL with any pure function. [That follows from the arguments used by Wittgenstein, Goodman, Kripke and many others.] (3) But we know beyond any doubt that WE think in forms that are pure functions (addition, squaring, conjunction, modus ponens) and are not indeterminate among incompatible functions. THEREFORE, our thinking, in so far as it is the realization of a determinate pure function, cannot be any material process or any function among material processes. Thus, human thought, as intelligent, is immaterial." (https://www.sas.upenn.edu/~jross/aristotlesrevenge.htm)
In short, an algorithm cannot possibly be a material thing, as any physical process whatsoever could represent infinitely many algorithms, and so can't possibly uniquely pin down any of them. But we humans can do so: we can say that is an implementation of quick sort!
So algorithms and our thoughts about them must be immaterial.
so riddle me this:
ReplyDeleteA computer can do addition (a pure function I learn) with 100^% reliability but (as I earlier learned from Freser) is a mere artifact. How can a computer - a material artifact - run an algorithm if that algorithm is not capable of being encapsulated in an entirely material way ? And further - how could it possibly be encapsulated in a non-material way?
I don't think you've understood the well-proven point (and this is something that even materialist philosophers have come to admit): it is not that the algorithm can be instantiated, it is that any material instantiation is always indeterminate between any number of algorithms. It is only *we* who can judge that the computer indeed implements an algorithm. In fact, it is only human judgment that can decide that a computer actually implements addition at all, rather than is playing chess, etc.
DeleteThat's a goods clarification - thanks, I did indeed need to go back and take a longer look at the piece your quote come from.
DeleteBut why is it only humans who can judge that the computer indeed implements an algorithm? Surely we ourselves are running an algorithm to make this determination ? So this view that some things that run algorithms have intrinsically a higher level of judgement than other things seemed flawed.
"Surely we ourselves are running an algorithm to make this determination ?"
DeleteNo, rob, the whole point is that surely we are NOT running an algorithm to make that determination: because then we would need to run an algorithm to determine if that algorithm is correct. And we would need to check that algorithm with an algorithm. And this would never stop.
I don't deny there needs to be a term for something that transcends the mere specific instance - but 'abstract' seems a way better term than ';immaterial' since every single implementation instance is (at least in my world) 100% material.
ReplyDeleteSince abstract things ARE immaterial I am fine with that. And yes, to manifest in the material world, the logos must be "made flesh": we've had that bit down for a couple of thousand years, rob!
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