From Newsgroup: sci.math
On 6/25/2026 2:43 AM, Mikko wrote:
On 24/06/2026 22:31, olcott wrote:
On 6/24/2026 3:08 AM, Mikko wrote:
On 23/06/2026 17:26, olcott wrote:
On 6/23/2026 12:32 AM, Mikko wrote:
On 22/06/2026 17:45, olcott wrote:
On 6/22/2026 2:30 AM, Mikko wrote:
On 22/06/2026 02:47, olcott wrote:
On 6/21/2026 5:37 AM, Mikko wrote:
On 21/06/2026 03:41, olcott wrote:
Knowledge is not merely a justified true belief.
Knowledge is a sufficiently justified true belief such
that the justification is sufficient reason to conclude
that the belief is true. Copyright PL Olcott 2026
The problem is what justification is sufficient to call the >>>>>>>>> conclusion
"knowledge". That problem is a consequence to some peoples
desire to
have a word for a concept that is hard to define and hard to >>>>>>>>> use without
mistakes.
When we use the court's "reasonable person"
standard we know that no reasonable person
would ever construe number of coins in the
pocket as having anything at all to do with
getting the job. (the first Gettier case)
https://iep.utm.edu/gettier/
On the other hand the company president's opinion
about who would be hired might be construed as a
sufficiently justified belief.
It is hard to construct a rule that simulates a "reasonable person". >>>>>>> And also hard to test how well some proposed rule achieves that.
None-the-less the Gettier cases are conquered.
Merely ad hoc solutions, no computable method.
I am not aware of any alternative solution to Gettier
where the judgement of human minds is involved that is
better than mine.
Gettier is fairly unimportant. THe important problem is fo find an
algrithm to simulate a "reaonable person" as clisely as possibly.
My augmentations to PTS approximate on infallibility
within the atomic base.
No reason to think in does.
Only because you don't even understand how PTS
differs from TCS.
Irrelevant. Apparently you don't know how PTS differs from useful.
*Proof Theoretic Semantics as a new Foundation*
*for Mathematics, Logic and the Theory of Computation*
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS).
Essentially PTS just coherently connects the
semantic meanings expressed in language together
into one coherent body of general knowledge.
It does this without undecidability or mathematical
incompleteness.
https://philpapers.org/archive/OLCPTS-2.pdf
In proofrCatheoretic semantics an expression has
semantic meaning only if there is a chain of
canonical inference steps from some atomic base
to that expression. If no such chain exists,
the expression does not inherit meaning from the base.
A consequnce of that restriction is that it often excludes what> is
actually needed for solving some problem. For example, consider
the calssical prblem of trisecting an angle. How does PTS help
with that?
--
Copyright 2026 Olcott
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
The complete structure of this system is now defined.
The entire body of knowledge expressed in language is
comprised of two types of relations between finite strings:
(a) *Axioms* Expressions of language that are stipulated to be true.
My system bridges the analytic/synthetic distinction by
expressly encoding all empirical "atomic facts" in a formal
language such as CycL of the Cyc project.
(b) *Inference Rules* Expressions of language that are semantically
entailed syntactically from (a) and/or (b).
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