surreptitious57 wrote:
It is possible that a proposition is only assumed to be known with certainty. Now an axiomatically deductive system of logic like mathematics
can determine the truth value of a proposition as it uses proof to validate its conclusions. But an inductive system like science uses evidence
that is less rigorous than proof so more susceptible to error. It does use proof too but only in the form of negative proof or disproof however
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I think everything you've said above is exactly right, with the exception of the very last sentence, and despite what Karl Popper may have said about
deductive falsification (as opposed to
inductive confirmation which he eschewed).
Once again Quine's name comes up in the form of the so-called 'Duhem-Quine thesis'. In its less radical formulations at least, I believe it's universally accepted these days that scientific hypotheses are never tested in isolation, but rather as part of a package of theories, hypotheses and background assumptions. When observation conflicts with the particular theory/hypothesis under scrutiny all we can say for sure is that
something is wrong somewhere in the package. Logic alone cannot tell us where the problem lies: it may lie with the hypothesis under test; it may lie elsewhere. There can be no definitive (i.e. logical) refutation or disproof; at the end of the day a judgement call is still required -- what Duhem refers to as 'good sense'.
Your first sentence is very significant, I think. For example, if Bob claims to know a certain proposition, perhaps that his wife is faithful to him, and later it becomes clear to all, including poor cuckolded Bob himself, that things are not so, we can say either:
(1) Bob knew his wife was faithful, but he was wrong
or
(2) Bob
thought he knew he wife was faithful, but he was wrong
I'm guessing most of us would intuitively select (2) as the appropriate response. Likewise, and referring back to my comments in my post at the bottom of the previous page, if Bob claimed (mistakenly) to know
with certainty that a proposition P was true, it seems to me the appropriate response would be to say that since he was wrong, he did not know P
at all; a fortiori he did not know it
with certainty.
If a proposition is indeed (really, actually, absolutely, right-on man) known with certainty, or just
known simpliciter, then the proposition
cannot be wrong.