On Sunday, August 20, 2023 at 9:28:42 PM UTC-7, Ross Finlayson wrote:

On Sunday, August 20, 2023 at 9:21:53 PM UTC-7, olcott wrote:

On 8/20/2023 11:18 PM, Ross Finlayson wrote:

On Sunday, August 20, 2023 at 9:00:56 PM UTC-7, olcott wrote:

On 8/20/2023 9:43 PM, Ross Finlayson wrote:

On Sunday, August 20, 2023 at 4:22:24 PM UTC-7, olcott wrote:

https://iep.utm.edu/liar-paradox/#:~:text=Strawson%20has%20argued%20that%20the,fails%20to%20express%20a%20proposition.

x := y means x is defined to be another name for y
https://en.wikipedia.org/wiki/List_of_logic_symbols

LP := ~True(LP) // formalizes "This sentence is not true"

*Diagonal lemma*
Let S be a theory extending first-order arithmetic. For every formula >>>> ϕ(x) there is a sentence ψ such that S ⊢ ψ ↔ ϕ⟨ψ⟩.

*The sentence ψ is of course not self-referential in a strict sense* >>>> https://plato.stanford.edu/entries/self-reference/

Because it has always been the convention to formalize self-reference >>>> inaccurately using the ↔ symbol it was never clear enough that the >>>> formalized Liar Paradox has cycle in its evaluation directed-graph. >>>>

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

Logic sort of belongs to philosophy, after all.

Yes.
--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius >> hits a target no one else can see." Arthur Schopenhauer

There really is a thing called "technical philosophy", and it's really mostly about the instruments of reason, and especially about the
roots of the foundation of reason, and, its place in a universe.

Over time it's varied quite a bit in its focus and schools related with it,
schools of thought and schools of men (inclusive, great philosophers), often about the bounds and limits of the phenomological, and whether there's object-sense or number-sense resulting from reason itself, beyond
the pings and needles of stimules-response, or the physical sensory, that
beyond the phenomenous, is the nous, then whether it's real, and, whether
it's real.

Then, paradox and reason go together with paradox as unresolved reason, and resolved paradox, as reason.

Where, philosophers like Leibniz and Nozick and so on agree that "the fundamental question of metaphysics is 'where is there something, rather than nothing, at all', it's a usual deliberation on universals and none of them.

Then, it sort of arises that there are various principles of constancy and consistency,
and, diversity and variety, that represent complementary duals, what results from
a sort of inverse or generalized inverse, in that insofar as the objects of reason
are both definable and indefinable and effable and ineffable, that it sorts itself
out how it's so from nothing/everything together that its constancy/variety
and how ordering/numbering sort of justly result from it, in the extension of
the rulial, the regular, the ordinary, in that formless and amorphous and extraordinary.

This is a sort of "axiomless natural deduction" then for making there's a universe of
elements, and, they're logical and they're mathematical, embodying relation, a
universe of primeval mathematical objects or ur-elements, then that it just sort of
results that definition itself, sees arise schema and relation and type and so on.

So, that's one reason why reasoning about reason results strong platonists find
there's a platonic universe like a Leibniz' monadology, or what Nozick discusses
approaching pragmatically, then that usual mathematics like geometry and set theory
just sort of "perceived" in the universe of mathematical objects.

As a true foundation for logical discourse it's quite well explored since antiquity
by everybody with reasoning faculties, and, made declared in most traditional forms
of organized reasoning like religions and what goes into answering questions of existence.

Then, logic is just a sort of result of "resolved paradoxes", that there are none, then
about the deconstructive accounts of what are usually pragmatic working theories
including the quite low-level, finding the attachments from those to a universe of objects,
and cultivating for reason an object-sense and number-sense that it results from the
dialectic as it's conditioned and completed, about then why this further nous is also
as well phenomenological, and sits to suffice for otherwise all the poor materialists
and what's given down as definitions.

Truthmaker theory seems to provide excellent insights
into the nature of truth and its foundation.
--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer

Where model theory and proof theory are the same, or, "equi-interpretable", one in
example or structurally or geometrically and the other after the abstract and derivation
and the resulting context and as what's followed in context, model theory and proof theory,
there's a general notion that a universe of logical object is "true" already, then that pondering
it results what would be the "paradox of quantification, about x = x or x =/=x or x < x", that
the outlier of sorts results for that what those objects _are_ is a body of the formulas in the
proofs in the proof theory, and, only truisms are well-formed formula, though one might
aver that it starts negatory and results affirmatory, then that "that's truth, it's a theory of
truth, already", this makes for an ideal existing "true theory", then, that all efforts in reasoning
or well-formed formulas or definition and the unambiguous, are simply as exercise in recognizing
what must be structure of same, then that the better and lower and stronger theories, are closer,
while all sorts matters of speculation, are free.

So, it's more truth "finder" than "maker", which is a usual aspect of platonism that truth is
discovered, not invented, including the discovery of how to invent things. (Or for that
matter dissemble.)

Such language here is called a "Comenius language".

"Equi-interpretable", ....

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