> Pedantically, axioms by definition are assumed/defined without proof and not provable ...
(Bishop from c1 to d2).
Quite true in one form of its use:
In mathematics or logic, an axiom is an unprovable rule or
first principle accepted as true because it is self-evident
or particularly useful. “Nothing can both be and not be at
the same time and in the same respect” is an example of an
axiom. The term is often used interchangeably with
postulate, though the latter term is sometimes reserved for
mathematical applications (such as the postulates of
Euclidean geometry). It should be contrasted with a
theorem, which requires a rigorous proof.[0]
However, notice the interchangeable use with "postulate", defined thusly:
a hypothesis advanced as an essential presupposition,
condition, or premise of a train of reasoning[1]
And, of course, a hypothesis is capable of being proven. Given the original use of "axiom" when responding to a quote referencing "common understanding", not a mathematical context, is it reasonable to interpret this usage as a postulation?
It's just not what the word axiom means nor how anyone uses it. An axiom is unprovable by definition - is it a thing we accept to be true because it is useful to do so (e.g. there exists an empty set)
"Provably Correct Axiom" is nonsense. An axiom is unprovable.
Just "provably correct" would've been fine. This chess stuff is hilariously pretentious.
Sorry but the entire line of argumentation and all it’s chess flavor is miles off the mark. This is not the sound of arguing with someone who studied what they talked about.
(Queen from d8 to a5) check.
> Pedantically, axioms by definition are assumed/defined without proof and not provable ...
(Bishop from c1 to d2).
Quite true in one form of its use:
However, notice the interchangeable use with "postulate", defined thusly: And, of course, a hypothesis is capable of being proven. Given the original use of "axiom" when responding to a quote referencing "common understanding", not a mathematical context, is it reasonable to interpret this usage as a postulation?(Queen from a5 to e5) check.
;-)
0 - https://www.merriam-webster.com/dictionary/axiom
1 - https://www.merriam-webster.com/dictionary/postulate