On 26 Apr 2017, at 23:32, Brent Meeker wrote:
On 4/26/2017 10:21 AM, Bruno Marchal wrote:
Maybe I will just ask you this. 1) Do you agree that consciousness
is a form of knowledge? 2) that knowable obeys the S4 axioms?
S4 =
[](A->B) -> ([]A -> []B) K
[]A->A T
[]A -> [][]A 4
Then incompleteness explains why this works with "[]" payed by
provability, and gives a temporal non nameable subject, which
cannot identify itself with any third person notion.
Are you saying that if [] is interpreted as "knowable" then these
axioms completely characterize "knowable"?
Not necessary completely. You will have to add Grz to get the complete
characterization in the mechanist frame: []([](A -> []A) -> A) -> A
And then you reason that "provable" is characterized by these
axioms hence "knowable" and "provable" are the same thing??
On the contrary. By incompleteness "provable" obeys a quite different
logic(s) (G and G*). But provable and true ([]p & p) obeys the S4
logic, indeed, the S4Grz.
Machine self-provable Incompleteness refutes Socrates and Gettier
critics of Theaetetus' idea.
Bruno
Brent
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