Thursday, February 19, 2015
the iffity of reducibility
lately, i've been stressing 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.
is theoretical physics incomplete? i'd say yes.
we have different systems to explain different physical phenomena: newtonian mechanics to explain macrophenomena in general, einstein (general) relativity being a definite refinement to newton's classical mechanics, and then quantum mechanics a refinement to einstein's theory and then the various string theories to reconcile einstein's theories with quantum mechanics theories, etc.
let's suppose in some future we have S the set of all systems (S1, S2, Si...Sn), to explain physical phenomena.
will S explain all of physical phenomena?
if it did there would be nothing new to explain, nothing deeper or different.
if so, what vouchsafes such possibility could not be merely theoretical, since "theoretical" is precisely defined as a realm within S!
(hint: we can conceive of a new Sj being added as a revision of a previously thought complete set S. why? because theories are necessarily falsifiable!