Friday, February 20, 2015
the iffity of reducibility
lately, i've been dealing with the idea of irreducibility.
what does it mean?
p is irreducible in system S when one cannot fully explain p from the set of principles given in S.
there are several examples of this:
1- in mathematics, gödel's famous incompleteness theorem.
2- in computer science, stephen wolfram's computational irreducibility principle.
3- intentionalität in the philosophy of mind.
i'm no physicist, but i'd like to advance a general idea about irreducibility in physics.
we have different systems to explain different physical phenomena: newtonian mechanics to explain macro phenomena in general, einstein (general) relativity being a definite refinement to newton's classical mechanics, and quantum mechanics, a refinement to einstein's theory (now to explain the micro phenomena), and then the various string theories to reconcile einstein's general relativity with quantum mechanics, etc.
let's suppose in some future we have S the set of all systems (S1, S2, Si...Sn), to explain physical phenomena.
(a trivial question): will S ever explain all of physical phenomena?
lets ask the question differently. is physical phenomena completely reducible to physics?
(if it did, there would be nothing new, deeper or different to explain, )
yet, what vouchsafes such possibility --of closure-- could only come from within S, since any Si is precisely defined within S!
but nothing in the already existing set (S1, S2, Si...Sn) prevents a new Sj from revising Si and so forth...