XPost: sci.logic
On 6/2/24 1:36 PM, olcott wrote:
Because of Quine's paper: https://www.ditext.com/quine/quine.html most philosophers have been confused into believing that there is no such
thing as expressions of language that are {true on the basis of their meaning}.
Except that, in FORMAL LOGIC SYSTEMS, the ONLY definition of "meaning"
is what is derived from the formal definitions and axioms of the system.
The unique contribution I have made to this is that the semantic meaning
of these expressions is always specified by other expressions. When we
can derive x or ~x by applying truth preserving operations to a set of semantic meanings then this perfectly aligns with Wittgenstein's concise critique of Gödel: https://www.liarparadox.org/Wittgenstein.pdf
Unless P or ~P has been proved in Russell's system P has no truth value
and thus cannot be a proposition according to the law of the excluded
middle.
As Richard keeps pointing out:
Sometimes this "proof" may require an infinite sequence of steps.
But the problem is that if it takes an "infinite sequence of steps" to
make it true, that set of steps is NOT a PROOF, as proof is defined as a
FINITE number of steps.
Thus, there exists statement that are TRUE (by being established by an
infinite sequence of steps) but can not be PROVEN (which requires
finding a finite number of steps to show it)
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