|
|
Re: Whitehead & Russell on Reductio A.A. and when Constructivism is
mainstream #200; 2nd ed; Correcting Math
Posted:
Oct 16, 2009 12:49 AM
|
|
On Oct 12, 8:07 am, Marshall <marshall.spi...@gmail.com> wrote:
|I guess what I'm fixating on is what kind of values the
|logic is manipulating.
It depends on what you mean.
Propositional or predicate calculus is always manipulating
propositions or predicates, whether you are thinking of it
as classical or intuitionistic. You get away with supposing
in the classical case that "ultimately" the propositions
all have "truth value" either "true" or "false" because
you have assumed (pretty much by fiat) that they do, but
it's not clear what the really gets you. Constructivists
sometimes think differently about what propositions are,
but it's somewhat difficult to convey. The kind of
verificationist philosophy described in Dummett's Elements
of Intuitionism might give you an idea.
For some purposes you can think of classical logic as
having "values" in Boolean algebras and intuitionistic
logic as having "values" in Heyting algebras. (That's
essentially just a restatement of certain logical laws
in algebraic form, though.)
Kripke models provide a way to think about intuitionistic
logic. Instead of thinking about what is true now, think
about what might or might not be discovered at future
stages in the game. Then without taking off your classical
thinking cap you can get a prosaic way of thinking about
intuitionistic logic.
Keith Ramsay
|
|
