Logik wrote: ↑Wed May 01, 2019 1:57 pm
PeteOlcott wrote: ↑Wed May 01, 2019 3:33 am
(F ⊢ x) means ◻x
I am going to remove myself from these discussions because you seem to be dogmatically doubling down on deduction as some absolute ideal for reasoning.
Radical skepticism or radical scepticism is the philosophical position that knowledge is most likely impossible. Radical skeptics hold that doubt exists as to the veracity of every belief and that certainty is therefore never justified. To determine the extent to which it is possible to respond to radical skeptical challenges is the task of epistemology or "the theory of knowledge".
I agree that nothing empirical can be known with 100% perfectly justified complete certainty.
There is nothing empirical about ¬(1 = 0).
There is no chance what-so-ever that living_thing->animal->dog is really an office_building,
these are not beliefs they are definitions.
Axioms are nothing more than expressions of language that have been defined to have
the semantic value of Boolean True.
I don't know how Quine can think that analytical truth is circular when analytical truth is this:
Analytical truth is simply truth that can be totally verified as completely
true entirely based on the meaning of the words in the sentence.
Copyright 2012 Pete Olcott
The fundamental nature of Truth has been my philosophical quest since I was a young boy
peeved by the inability of people to properly distinguish between opinions and established facts.
Since that time I have raised the bar and eliminated empirical "facts" from the set
of 100% justified complete certainty. Only fact that can be verified as completely
true entirely based on the meaning of their words count as actual truth.
I was so pleased the very first time that I found this:
◇P ↔ ¬◻¬P Possibly(P) <--> Not(Necessarily(Not(P))
◻P ↔ ¬◇¬P Necessarily(P) <--> Not(Possibly(Not(P)))
Now I finally had a way to formally express the distinction between
possible and impossible.
Possible(p) is any expression of language p that
HAS NOT BEEN proved Necessarily(Not(P)) based on the meaning of the words of p.
Impossible(p) is any expression of language p that
HAS BEEN proved Necessarily(Not(P)) based on the meaning of the words of p.