On 8/20/24 10:07 AM, olcott wrote:
On 8/20/2024 5:30 AM, Mikko wrote:
On 2024-08-19 12:48:08 +0000, olcott said:
On 8/19/2024 3:07 AM, Mikko wrote:
On 2024-08-18 12:18:02 +0000, olcott said:
On 8/15/2024 4:01 AM, Mikko wrote:
On 2024-08-13 12:43:16 +0000, olcott said:
In epistemology (theory of knowledge), a self-evident proposition >>>>>>> is a proposition that is known to be true by understanding its
meaning
without proof https://en.wikipedia.org/wiki/Self-evidence
Self-evident propositions are uninteresting.
It turns out that self-evident <is> the notion of {analytic truth}
and all of math and logic only deals in {analytic truth}.
A large part of what math and logic deals in is not self-evident.
For examle, most people would not regard it self-evident that in
classical geometry it is impossible to construct a square that
has the same area as a given circle.
By self-evident I do not mean that people can understand it.
I only mean that it is semantically entailed by a set of axioms.
A better term than self-evident is semantic tautology.
Which dictionary has that as the first meaning of "self-evident"?
In epistemology (theory of knowledge), a self-evident
proposition is a proposition that is known to be true
by understanding its meaning without proof. https://en.wikipedia.org/wiki/Self-evidence
I am establishing it as Analytic(Olcott) when I define
the predicate True(L,x):
Unless expression x has a connection (through a sequence
of true preserving operations) in system F to its semantic
meanings expressed in language L of F then x is simply
untrue in F.
Whenever there is no sequence of truth preserving from
x or ~x to its meaning in L of F then x has no truth-maker
in F and x not a truth-bearer in F. We never get to x is
undecidable in F.
And this is part of your problem, as it isn't applicable to Formal
Systems as they have clearly defined meanings for what is "True" and
what is "Known".
The Formalism of the system gets around the problems that epistemology
tries to handle.
Also, the Analytic/Synthetic distinction doesn't apply to Formal
Systems, as "observation" isn't a source of truth in a Formal System,
only what derives from the rules of the system.
But then, you never really understood what Formal Systems are, and how
they are NOT tied to "the real world" at all, and thus not really
applicable to your idea of truth detecting.
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