On 07/01/2026 07:59 AM, olcott wrote:
On 7/1/2026 7:13 AM, Ross Finlayson wrote:
On 06/30/2026 08:01 PM, olcott wrote:
On 6/30/2026 9:47 PM, Ross Finlayson wrote:
On 06/30/2026 10:36 AM, Ross Finlayson wrote:
On 06/30/2026 07:53 AM, olcott wrote:
On 6/30/2026 8:23 AM, Ross Finlayson wrote:
So, if you want to know more about my theory, which is an account >>>>>>>> of reason, and for Foundations, then I'd suggest first making for >>>>>>>> yourself a "universal education", then finding resolutions to the >>>>>>>> "paradoxes" of mathematical logic,
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Olcott's Minimal Type Theory
G rao -4Prov_PA(riLGriY)
Directed Graph of evaluation sequence
00 rao-a-a-a-a-a-a-a-a-a-a-a-a-a-a 01 02
01 G
02 -4-a-a-a-a-a-a-a-a-a-a-a-a-a-a 03
03 Prov_PA-a-a-a-a-a-a-a-a 04
04 G||del_Number_of 01-a // cycle indicates no well-founded
justification
tree exists.
ZFC already handled Russell's Paradox converting set
theory into Naive set theory.
It is important to keep computation in the loop
because computation exposes the hidden assumptions
that math makes.
CurryrCoHoward correspondence
In programming language theory and proof theory,
the CurryrCoHoward correspondence is a direct relationship
between computer programs and mathematical proofs.
https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence >>>>>>>
then revealing the "super-classical"
results of classical mathematics, then for the "extra-ordinary" the >>>>>>>> "great atlas of mathematical independence", then for "higher
mathematics", and quite about "continuity" and "infinity",
then there's also "the physics" after "the logic" and "the
mathematics".
"Curry's poor substitute" at least rejects material implication.
Matters of meaning or the epistemological is a field called
"semiotics".
Semantics after syntax is properly logical, that's all.
Cycle-detection is a usual routine involving memory and time, the
resources.
The Liar Paradox is just a template of what would be a fallacy:
two wrongs don't make a right.
unify_with_occurs_check(and(false(LP), true(LP)))
Two wrongs don't make a right.
Russell's retro-thesis is hypocrisy veiled as authority.
Where's the GUID for "dictionary", or "vocabulary", and what's in it. >>>>>> "Cat" is a word.
It's fair to say "the Liar Paradox is false",
then that the negation translates through the copula "is"
to result "this sentence is true", a meaningless, empty tautology
(except as quoted a meaningless, empty, tautology).
It doesn't work on other "paradoxes", though.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics almost gets there
through an enormously more convoluted process.
They almost always utterly avoid any nuance of
true. Instead they focus on meaning.
Finlayson's paradox: there are none.
That quote of Wittgenstein's just a weak echo of Leibnitz' "principle of >>> sufficient reason" about what an inference is. The Tractatus
Correct reasoning is not correctly evaluated on the
basis of who came up with the ideas. These ideas either
has a sound basis or not.
It just the same thing that I have been saying fir years.
True on the basis of meaning expressed in language must
have a direct semantic connection to those things in the
directly in the formal system of this language that make it
true.
(a) Cats are animals
(b) Animals are living things
(c) re| Cats are living things
No jumping outside of the language to a separate model.
Logicophilosophicus starts alright then Wittgenstein wimps out while
being all hot-headed about it later. Russell's favorite philosophers,
Plotinus after Philo, are early weak nominalist fictionalists, and
having material implication in their vacuous implicits and so on,
Chrysippus could throw them from the boat since neither are they
Pythagoreans.
A much simpler process arrives at a "principle of _thorough_ reason",
where not only are affirmatory and negatory inferences found,
also in the diligence any their contradictions.
That is what I just showed.
Russell's retro-thesis simply can't make the extra-ordinary go away.
It's considered a quasi-modal variety of the weaker sort of the
logicist positivism, which has a stronger variety after a strong
mathematical platonism which invigorates it as "must be science".
Old schlock wrapped as new, ....
The only way to obtain a correct foundation of these
things is to reverse-engineer them from first principles.
If one does not do that then the extraneous baggage
of the differing human perspectives prevent a fully
coherent view.
That's just syllogism, and makes for constructivism
since any sort stipulation, like an axiom, is unfounded.
The "axiomless natural deduction" to arrive at "axiomless
geometry" and "axiomless arithmetic" is a usual notion that
mathematical platonists have, though these days sometimes
they call themselves structural realists to not concern
dear old Bertrand, then though logicist positivists take
that label without fulfilling its definition.
Syllogism is subject ordering, and Aristotle reads every
syllogism its statements in every order, for example to
detect cycles and disambiguate them, which otherwise a
linear reader will fail to detect.
The "principle of _thorough_ reason" is more than the
"principle of 'sufficient' reason", then that in a
wider account of a wider, fuller dialectic, what's
sound, thorough, fulfilling, and fair.
Mentioning something like Prawitz' "inversion principle"
and about both the restriction _and_ the recovery, and
more than Russell's mere "isolation in significance and
significance in isolation", means that restricting (ignoring)
the resolution of any and all paradoxes leaves the door ajar
just like quasi-modal logic and principle of explosion.
So, maybe readers and researchers in foundations should start
with outlining the requirements and desiderata of a theory
that's constant, consistent, complete, and concrete,
and see how axiomless natural deduction fulfills that
with a comprehensive yet paradox-free account, and
that's the usual account since antiquity and even since
before recorded times, then it's called "mathematical platonism",
since issues of the human condition itself are subjective,
and whether Thoth or Hermes Trismagistus has an ankh for reason
or spiral for infinity, in at least one account there's both.
Thoth -> thought
Logos -> logic
Ma'at -> math
Aristotle won't be made a fool, and more than merely
half-Aristotleans have always both prior and posterior accounts.
On 7/1/2026 12:00 PM, Ross Finlayson wrote:
On 07/01/2026 07:59 AM, olcott wrote:
On 7/1/2026 7:13 AM, Ross Finlayson wrote:
On 06/30/2026 08:01 PM, olcott wrote:
On 6/30/2026 9:47 PM, Ross Finlayson wrote:
On 06/30/2026 10:36 AM, Ross Finlayson wrote:
On 06/30/2026 07:53 AM, olcott wrote:
On 6/30/2026 8:23 AM, Ross Finlayson wrote:
So, if you want to know more about my theory, which is an account >>>>>>>>> of reason, and for Foundations, then I'd suggest first making for >>>>>>>>> yourself a "universal education", then finding resolutions to the >>>>>>>>> "paradoxes" of mathematical logic,
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Olcott's Minimal Type Theory
G rao -4Prov_PA(riLGriY)
Directed Graph of evaluation sequence
00 rao 01 02
01 G
02 -4 03
03 Prov_PA 04
04 G||del_Number_of 01 // cycle indicates no well-founded
justification
tree exists.
ZFC already handled Russell's Paradox converting set
theory into Naive set theory.
It is important to keep computation in the loop
because computation exposes the hidden assumptions
that math makes.
CurryrCoHoward correspondence
In programming language theory and proof theory,
the CurryrCoHoward correspondence is a direct relationship
between computer programs and mathematical proofs.
https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence >>>>>>>>
then revealing the "super-classical"
results of classical mathematics, then for the "extra-ordinary" >>>>>>>>> the
"great atlas of mathematical independence", then for "higher >>>>>>>>> mathematics", and quite about "continuity" and "infinity",
then there's also "the physics" after "the logic" and "the
mathematics".
"Curry's poor substitute" at least rejects material implication. >>>>>>>
Matters of meaning or the epistemological is a field called
"semiotics".
Semantics after syntax is properly logical, that's all.
Cycle-detection is a usual routine involving memory and time, the >>>>>>> resources.
The Liar Paradox is just a template of what would be a fallacy:
two wrongs don't make a right.
unify_with_occurs_check(and(false(LP), true(LP)))
Two wrongs don't make a right.
Russell's retro-thesis is hypocrisy veiled as authority.
Where's the GUID for "dictionary", or "vocabulary", and what's in >>>>>>> it.
"Cat" is a word.
It's fair to say "the Liar Paradox is false",
then that the negation translates through the copula "is"
to result "this sentence is true", a meaningless, empty tautology
(except as quoted a meaningless, empty, tautology).
It doesn't work on other "paradoxes", though.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics almost gets there
through an enormously more convoluted process.
They almost always utterly avoid any nuance of
true. Instead they focus on meaning.
Finlayson's paradox: there are none.
That quote of Wittgenstein's just a weak echo of Leibnitz'
"principle of
sufficient reason" about what an inference is. The Tractatus
Correct reasoning is not correctly evaluated on the
basis of who came up with the ideas. These ideas either
has a sound basis or not.
It just the same thing that I have been saying fir years.
True on the basis of meaning expressed in language must
have a direct semantic connection to those things in the
directly in the formal system of this language that make it
true.
(a) Cats are animals
(b) Animals are living things
(c) re| Cats are living things
No jumping outside of the language to a separate model.
Logicophilosophicus starts alright then Wittgenstein wimps out while
being all hot-headed about it later. Russell's favorite philosophers,
Plotinus after Philo, are early weak nominalist fictionalists, and
having material implication in their vacuous implicits and so on,
Chrysippus could throw them from the boat since neither are they
Pythagoreans.
A much simpler process arrives at a "principle of _thorough_ reason",
where not only are affirmatory and negatory inferences found,
also in the diligence any their contradictions.
That is what I just showed.
Russell's retro-thesis simply can't make the extra-ordinary go away.
It's considered a quasi-modal variety of the weaker sort of the
logicist positivism, which has a stronger variety after a strong
mathematical platonism which invigorates it as "must be science".
Old schlock wrapped as new, ....
The only way to obtain a correct foundation of these
things is to reverse-engineer them from first principles.
If one does not do that then the extraneous baggage
of the differing human perspectives prevent a fully
coherent view.
That's just syllogism, and makes for constructivism
since any sort stipulation, like an axiom, is unfounded.
The "axiomless natural deduction" to arrive at "axiomless
geometry" and "axiomless arithmetic" is a usual notion that
mathematical platonists have, though these days sometimes
they call themselves structural realists to not concern
dear old Bertrand, then though logicist positivists take
that label without fulfilling its definition.
Syllogism is subject ordering, and Aristotle reads every
syllogism its statements in every order, for example to
detect cycles and disambiguate them, which otherwise a
linear reader will fail to detect.
The "principle of _thorough_ reason" is more than the
"principle of 'sufficient' reason", then that in a
wider account of a wider, fuller dialectic, what's
sound, thorough, fulfilling, and fair.
Mentioning something like Prawitz' "inversion principle"
and about both the restriction _and_ the recovery, and
more than Russell's mere "isolation in significance and
significance in isolation", means that restricting (ignoring)
the resolution of any and all paradoxes leaves the door ajar
just like quasi-modal logic and principle of explosion.
So, maybe readers and researchers in foundations should start
with outlining the requirements and desiderata of a theory
that's constant, consistent, complete, and concrete,
The entire body of knowledge expressed in language
(a) Encodes all of the empirical "atomic facts" as axioms
this merges the analytic/synthetic distinction into one
analytic system. https://plato.stanford.edu/entries/analytic-synthetic/
(b) Provide a finite list of the possible semantic relations
between/among the elements of (a) and these are specified
syntactically using a system similar to CycL. https://en.wikipedia.org/wiki/CycL
(c) This whole thing is stored in a knowledge ontology https://en.wikipedia.org/wiki/Ontology_(information_science)
Hierarchy of simple type theory. https://en.wikipedia.org/wiki/History_of_type_theory#G%C3%B6del_1944
Now we have the entire body of general knowledge that
can be expressed in language as a set of stipulated
semantic relations between finite strings.
and see how axiomless natural deduction fulfills that
with a comprehensive yet paradox-free account, and
that's the usual account since antiquity and even since
before recorded times, then it's called "mathematical platonism",
since issues of the human condition itself are subjective,
and whether Thoth or Hermes Trismagistus has an ankh for reason
or spiral for infinity, in at least one account there's both.
Thoth -> thought
Logos -> logic
Ma'at -> math
Aristotle won't be made a fool, and more than merely
half-Aristotleans have always both prior and posterior accounts.
On 07/01/2026 10:57 AM, olcott wrote:
On 7/1/2026 12:00 PM, Ross Finlayson wrote:
On 07/01/2026 07:59 AM, olcott wrote:
On 7/1/2026 7:13 AM, Ross Finlayson wrote:
On 06/30/2026 08:01 PM, olcott wrote:
On 6/30/2026 9:47 PM, Ross Finlayson wrote:
On 06/30/2026 10:36 AM, Ross Finlayson wrote:
On 06/30/2026 07:53 AM, olcott wrote:
On 6/30/2026 8:23 AM, Ross Finlayson wrote:
So, if you want to know more about my theory, which is an account >>>>>>>>>> of reason, and for Foundations, then I'd suggest first making for >>>>>>>>>> yourself a "universal education", then finding resolutions to the >>>>>>>>>> "paradoxes" of mathematical logic,
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Olcott's Minimal Type Theory
G rao -4Prov_PA(riLGriY)
Directed Graph of evaluation sequence
00 rao-a-a-a-a-a-a-a-a-a-a-a-a-a-a 01 02
01 G
02 -4-a-a-a-a-a-a-a-a-a-a-a-a-a-a 03
03 Prov_PA-a-a-a-a-a-a-a-a 04
04 G||del_Number_of 01-a // cycle indicates no well-founded
justification
tree exists.
ZFC already handled Russell's Paradox converting set
theory into Naive set theory.
It is important to keep computation in the loop
because computation exposes the hidden assumptions
that math makes.
CurryrCoHoward correspondence
In programming language theory and proof theory,
the CurryrCoHoward correspondence is a direct relationship
between computer programs and mathematical proofs.
https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence >>>>>>>>>
then revealing the "super-classical"
results of classical mathematics, then for the "extra-ordinary" >>>>>>>>>> the
"great atlas of mathematical independence", then for "higher >>>>>>>>>> mathematics", and quite about "continuity" and "infinity", >>>>>>>>>> then there's also "the physics" after "the logic" and "the >>>>>>>>>> mathematics".
"Curry's poor substitute" at least rejects material implication. >>>>>>>>
Matters of meaning or the epistemological is a field called
"semiotics".
Semantics after syntax is properly logical, that's all.
Cycle-detection is a usual routine involving memory and time, the >>>>>>>> resources.
The Liar Paradox is just a template of what would be a fallacy: >>>>>>>> two wrongs don't make a right.
unify_with_occurs_check(and(false(LP), true(LP)))
Two wrongs don't make a right.
Russell's retro-thesis is hypocrisy veiled as authority.
Where's the GUID for "dictionary", or "vocabulary", and what's in >>>>>>>> it.
"Cat" is a word.
It's fair to say "the Liar Paradox is false",
then that the negation translates through the copula "is"
to result "this sentence is true", a meaningless, empty tautology >>>>>>> (except as quoted a meaningless, empty, tautology).
It doesn't work on other "paradoxes", though.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics almost gets there
through an enormously more convoluted process.
They almost always utterly avoid any nuance of
true. Instead they focus on meaning.
Finlayson's paradox: there are none.
That quote of Wittgenstein's just a weak echo of Leibnitz'
"principle of
sufficient reason" about what an inference is. The Tractatus
Correct reasoning is not correctly evaluated on the
basis of who came up with the ideas. These ideas either
has a sound basis or not.
It just the same thing that I have been saying fir years.
True on the basis of meaning expressed in language must
have a direct semantic connection to those things in the
directly in the formal system of this language that make it
true.
(a) Cats are animals
(b) Animals are living things
(c) re| Cats are living things
No jumping outside of the language to a separate model.
Logicophilosophicus starts alright then Wittgenstein wimps out while >>>>> being all hot-headed about it later. Russell's favorite philosophers, >>>>> Plotinus after Philo, are early weak nominalist fictionalists, and
having material implication in their vacuous implicits and so on,
Chrysippus could throw them from the boat since neither are they
Pythagoreans.
A much simpler process arrives at a "principle of _thorough_ reason", >>>>> where not only are affirmatory and negatory inferences found,
also in the diligence any their contradictions.
That is what I just showed.
Russell's retro-thesis simply can't make the extra-ordinary go away. >>>>> It's considered a quasi-modal variety of the weaker sort of the
logicist positivism, which has a stronger variety after a strong
mathematical platonism which invigorates it as "must be science".
Old schlock wrapped as new, ....
The only way to obtain a correct foundation of these
things is to reverse-engineer them from first principles.
If one does not do that then the extraneous baggage
of the differing human perspectives prevent a fully
coherent view.
That's just syllogism, and makes for constructivism
since any sort stipulation, like an axiom, is unfounded.
The "axiomless natural deduction" to arrive at "axiomless
geometry" and "axiomless arithmetic" is a usual notion that
mathematical platonists have, though these days sometimes
they call themselves structural realists to not concern
dear old Bertrand, then though logicist positivists take
that label without fulfilling its definition.
Syllogism is subject ordering, and Aristotle reads every
syllogism its statements in every order, for example to
detect cycles and disambiguate them, which otherwise a
linear reader will fail to detect.
The "principle of _thorough_ reason" is more than the
"principle of 'sufficient' reason", then that in a
wider account of a wider, fuller dialectic, what's
sound, thorough, fulfilling, and fair.
Mentioning something like Prawitz' "inversion principle"
and about both the restriction _and_ the recovery, and
more than Russell's mere "isolation in significance and
significance in isolation", means that restricting (ignoring)
the resolution of any and all paradoxes leaves the door ajar
just like quasi-modal logic and principle of explosion.
So, maybe readers and researchers in foundations should start
with outlining the requirements and desiderata of a theory
that's constant, consistent, complete, and concrete,
The entire body of knowledge expressed in language
(a) Encodes all of the empirical "atomic facts" as axioms
this merges the analytic/synthetic distinction into one
analytic system. https://plato.stanford.edu/entries/analytic-synthetic/
(b) Provide a finite list of the possible semantic relations
between/among the elements of (a) and these are specified
syntactically using a system similar to CycL.
https://en.wikipedia.org/wiki/CycL
(c) This whole thing is stored in a knowledge ontology
https://en.wikipedia.org/wiki/Ontology_(information_science)
Hierarchy of simple type theory.
https://en.wikipedia.org/wiki/History_of_type_theory#G%C3%B6del_1944
Now we have the entire body of general knowledge that
can be expressed in language as a set of stipulated
semantic relations between finite strings.
and see how axiomless natural deduction fulfills that
with a comprehensive yet paradox-free account, and
that's the usual account since antiquity and even since
before recorded times, then it's called "mathematical platonism",
since issues of the human condition itself are subjective,
and whether Thoth or Hermes Trismagistus has an ankh for reason
or spiral for infinity, in at least one account there's both.
Thoth -> thought
Logos -> logic
Ma'at -> math
Aristotle won't be made a fool, and more than merely
half-Aristotleans have always both prior and posterior accounts.
That's not "a priori truth".
That's just a "convenient" lie to make some system of inference
considered itself compelled complete yet make it slavish while
really it's merely a model of a partial half-account of reason,
that fragmented synthetic pluralism and inconstancy in definition.
Adding an element to another element is synthetic
(where did it come from?), partitioning an element
into two is analytic (how was it already there?).
The usual account of mathematical platonism is analytic,
the usual account of logicist positivism is synthetic,
they are two different things.
Usual accounts of incompleteness like the Hilbert-Bernays paradox
confirm and certify that "logicist positivist nominalist theories"
are at best "merely and completely science".
Then, the account that it's not a science, is wrong.
Anybody can have a quite thorough body of knowledge -
if it doesn't change it's considered they stopped learning,
not that there isn't anything left to learn.
Quit trying to tell people they can't learn, it's insulting.
On 07/01/2026 10:57 AM, olcott wrote:
On 7/1/2026 12:00 PM, Ross Finlayson wrote:
On 07/01/2026 07:59 AM, olcott wrote:
On 7/1/2026 7:13 AM, Ross Finlayson wrote:
On 06/30/2026 08:01 PM, olcott wrote:
On 6/30/2026 9:47 PM, Ross Finlayson wrote:
On 06/30/2026 10:36 AM, Ross Finlayson wrote:
On 06/30/2026 07:53 AM, olcott wrote:
On 6/30/2026 8:23 AM, Ross Finlayson wrote:
So, if you want to know more about my theory, which is an account >>>>>>>>>> of reason, and for Foundations, then I'd suggest first making for >>>>>>>>>> yourself a "universal education", then finding resolutions to the >>>>>>>>>> "paradoxes" of mathematical logic,
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Olcott's Minimal Type Theory
G rao -4Prov_PA(riLGriY)
Directed Graph of evaluation sequence
00 rao-a-a-a-a-a-a-a-a-a-a-a-a-a-a 01 02
01 G
02 -4-a-a-a-a-a-a-a-a-a-a-a-a-a-a 03
03 Prov_PA-a-a-a-a-a-a-a-a 04
04 G||del_Number_of 01-a // cycle indicates no well-founded
justification
tree exists.
ZFC already handled Russell's Paradox converting set
theory into Naive set theory.
It is important to keep computation in the loop
because computation exposes the hidden assumptions
that math makes.
CurryrCoHoward correspondence
In programming language theory and proof theory,
the CurryrCoHoward correspondence is a direct relationship
between computer programs and mathematical proofs.
https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence >>>>>>>>>
then revealing the "super-classical"
results of classical mathematics, then for the "extra-ordinary" >>>>>>>>>> the
"great atlas of mathematical independence", then for "higher >>>>>>>>>> mathematics", and quite about "continuity" and "infinity", >>>>>>>>>> then there's also "the physics" after "the logic" and "the >>>>>>>>>> mathematics".
"Curry's poor substitute" at least rejects material implication. >>>>>>>>
Matters of meaning or the epistemological is a field called
"semiotics".
Semantics after syntax is properly logical, that's all.
Cycle-detection is a usual routine involving memory and time, the >>>>>>>> resources.
The Liar Paradox is just a template of what would be a fallacy: >>>>>>>> two wrongs don't make a right.
unify_with_occurs_check(and(false(LP), true(LP)))
Two wrongs don't make a right.
Russell's retro-thesis is hypocrisy veiled as authority.
Where's the GUID for "dictionary", or "vocabulary", and what's in >>>>>>>> it.
"Cat" is a word.
It's fair to say "the Liar Paradox is false",
then that the negation translates through the copula "is"
to result "this sentence is true", a meaningless, empty tautology >>>>>>> (except as quoted a meaningless, empty, tautology).
It doesn't work on other "paradoxes", though.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics almost gets there
through an enormously more convoluted process.
They almost always utterly avoid any nuance of
true. Instead they focus on meaning.
Finlayson's paradox: there are none.
That quote of Wittgenstein's just a weak echo of Leibnitz'
"principle of
sufficient reason" about what an inference is. The Tractatus
Correct reasoning is not correctly evaluated on the
basis of who came up with the ideas. These ideas either
has a sound basis or not.
It just the same thing that I have been saying fir years.
True on the basis of meaning expressed in language must
have a direct semantic connection to those things in the
directly in the formal system of this language that make it
true.
(a) Cats are animals
(b) Animals are living things
(c) re| Cats are living things
No jumping outside of the language to a separate model.
Logicophilosophicus starts alright then Wittgenstein wimps out while >>>>> being all hot-headed about it later. Russell's favorite philosophers, >>>>> Plotinus after Philo, are early weak nominalist fictionalists, and
having material implication in their vacuous implicits and so on,
Chrysippus could throw them from the boat since neither are they
Pythagoreans.
A much simpler process arrives at a "principle of _thorough_ reason", >>>>> where not only are affirmatory and negatory inferences found,
also in the diligence any their contradictions.
That is what I just showed.
Russell's retro-thesis simply can't make the extra-ordinary go away. >>>>> It's considered a quasi-modal variety of the weaker sort of the
logicist positivism, which has a stronger variety after a strong
mathematical platonism which invigorates it as "must be science".
Old schlock wrapped as new, ....
The only way to obtain a correct foundation of these
things is to reverse-engineer them from first principles.
If one does not do that then the extraneous baggage
of the differing human perspectives prevent a fully
coherent view.
That's just syllogism, and makes for constructivism
since any sort stipulation, like an axiom, is unfounded.
The "axiomless natural deduction" to arrive at "axiomless
geometry" and "axiomless arithmetic" is a usual notion that
mathematical platonists have, though these days sometimes
they call themselves structural realists to not concern
dear old Bertrand, then though logicist positivists take
that label without fulfilling its definition.
Syllogism is subject ordering, and Aristotle reads every
syllogism its statements in every order, for example to
detect cycles and disambiguate them, which otherwise a
linear reader will fail to detect.
The "principle of _thorough_ reason" is more than the
"principle of 'sufficient' reason", then that in a
wider account of a wider, fuller dialectic, what's
sound, thorough, fulfilling, and fair.
Mentioning something like Prawitz' "inversion principle"
and about both the restriction _and_ the recovery, and
more than Russell's mere "isolation in significance and
significance in isolation", means that restricting (ignoring)
the resolution of any and all paradoxes leaves the door ajar
just like quasi-modal logic and principle of explosion.
So, maybe readers and researchers in foundations should start
with outlining the requirements and desiderata of a theory
that's constant, consistent, complete, and concrete,
The entire body of knowledge expressed in language
(a) Encodes all of the empirical "atomic facts" as axioms
this merges the analytic/synthetic distinction into one
analytic system. https://plato.stanford.edu/entries/analytic-synthetic/
(b) Provide a finite list of the possible semantic relations
between/among the elements of (a) and these are specified
syntactically using a system similar to CycL.
https://en.wikipedia.org/wiki/CycL
(c) This whole thing is stored in a knowledge ontology
https://en.wikipedia.org/wiki/Ontology_(information_science)
Hierarchy of simple type theory.
https://en.wikipedia.org/wiki/History_of_type_theory#G%C3%B6del_1944
Now we have the entire body of general knowledge that
can be expressed in language as a set of stipulated
semantic relations between finite strings.
and see how axiomless natural deduction fulfills that
with a comprehensive yet paradox-free account, and
that's the usual account since antiquity and even since
before recorded times, then it's called "mathematical platonism",
since issues of the human condition itself are subjective,
and whether Thoth or Hermes Trismagistus has an ankh for reason
or spiral for infinity, in at least one account there's both.
Thoth -> thought
Logos -> logic
Ma'at -> math
Aristotle won't be made a fool, and more than merely
half-Aristotleans have always both prior and posterior accounts.
That's not "a priori truth".
That's just a "convenient" lie to make some system of inference
considered itself compelled complete yet make it slavish while
really it's merely a model of a partial half-account of reason,
that fragmented synthetic pluralism and inconstancy in definition.
Adding an element to another element is synthetic
(where did it come from?), partitioning an element
into two is analytic (how was it already there?).
The usual account of mathematical platonism is analytic,
the usual account of logicist positivism is synthetic,
they are two different things.
Usual accounts of incompleteness like the Hilbert-Bernays paradox
confirm and certify that "logicist positivist nominalist theories"
are at best "merely and completely science".
Then, the account that it's not a science, is wrong.
Anybody can have a quite thorough body of knowledge -
if it doesn't change it's considered they stopped learning,
not that there isn't anything left to learn.
Quit trying to tell people they can't learn, it's insulting.
On 7/1/2026 12:31 PM, Ross Finlayson wrote:
On 07/01/2026 10:57 AM, olcott wrote:
On 7/1/2026 12:00 PM, Ross Finlayson wrote:
On 07/01/2026 07:59 AM, olcott wrote:
On 7/1/2026 7:13 AM, Ross Finlayson wrote:
On 06/30/2026 08:01 PM, olcott wrote:
On 6/30/2026 9:47 PM, Ross Finlayson wrote:
On 06/30/2026 10:36 AM, Ross Finlayson wrote:
On 06/30/2026 07:53 AM, olcott wrote:
On 6/30/2026 8:23 AM, Ross Finlayson wrote:
So, if you want to know more about my theory, which is an >>>>>>>>>>> account
of reason, and for Foundations, then I'd suggest first making >>>>>>>>>>> for
yourself a "universal education", then finding resolutions to >>>>>>>>>>> the
"paradoxes" of mathematical logic,
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Olcott's Minimal Type Theory
G rao -4Prov_PA(riLGriY)
Directed Graph of evaluation sequence
00 rao 01 02
01 G
02 -4 03
03 Prov_PA 04
04 G||del_Number_of 01 // cycle indicates no well-founded >>>>>>>>>> justification
tree exists.
ZFC already handled Russell's Paradox converting set
theory into Naive set theory.
It is important to keep computation in the loop
because computation exposes the hidden assumptions
that math makes.
CurryrCoHoward correspondence
In programming language theory and proof theory,
the CurryrCoHoward correspondence is a direct relationship >>>>>>>>>> between computer programs and mathematical proofs.
https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence >>>>>>>>>>
then revealing the "super-classical"
results of classical mathematics, then for the "extra-ordinary" >>>>>>>>>>> the
"great atlas of mathematical independence", then for "higher >>>>>>>>>>> mathematics", and quite about "continuity" and "infinity", >>>>>>>>>>> then there's also "the physics" after "the logic" and "the >>>>>>>>>>> mathematics".
"Curry's poor substitute" at least rejects material implication. >>>>>>>>>
Matters of meaning or the epistemological is a field called
"semiotics".
Semantics after syntax is properly logical, that's all.
Cycle-detection is a usual routine involving memory and time, the >>>>>>>>> resources.
The Liar Paradox is just a template of what would be a fallacy: >>>>>>>>> two wrongs don't make a right.
unify_with_occurs_check(and(false(LP), true(LP)))
Two wrongs don't make a right.
Russell's retro-thesis is hypocrisy veiled as authority.
Where's the GUID for "dictionary", or "vocabulary", and what's in >>>>>>>>> it.
"Cat" is a word.
It's fair to say "the Liar Paradox is false",
then that the negation translates through the copula "is"
to result "this sentence is true", a meaningless, empty tautology >>>>>>>> (except as quoted a meaningless, empty, tautology).
It doesn't work on other "paradoxes", though.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics almost gets there
through an enormously more convoluted process.
They almost always utterly avoid any nuance of
true. Instead they focus on meaning.
Finlayson's paradox: there are none.
That quote of Wittgenstein's just a weak echo of Leibnitz'
"principle of
sufficient reason" about what an inference is. The Tractatus
Correct reasoning is not correctly evaluated on the
basis of who came up with the ideas. These ideas either
has a sound basis or not.
It just the same thing that I have been saying fir years.
True on the basis of meaning expressed in language must
have a direct semantic connection to those things in the
directly in the formal system of this language that make it
true.
(a) Cats are animals
(b) Animals are living things
(c) re| Cats are living things
No jumping outside of the language to a separate model.
Logicophilosophicus starts alright then Wittgenstein wimps out while >>>>>> being all hot-headed about it later. Russell's favorite philosophers, >>>>>> Plotinus after Philo, are early weak nominalist fictionalists, and >>>>>> having material implication in their vacuous implicits and so on,
Chrysippus could throw them from the boat since neither are they
Pythagoreans.
A much simpler process arrives at a "principle of _thorough_ reason", >>>>>> where not only are affirmatory and negatory inferences found,
also in the diligence any their contradictions.
That is what I just showed.
Russell's retro-thesis simply can't make the extra-ordinary go away. >>>>>> It's considered a quasi-modal variety of the weaker sort of the
logicist positivism, which has a stronger variety after a strong
mathematical platonism which invigorates it as "must be science".
Old schlock wrapped as new, ....
The only way to obtain a correct foundation of these
things is to reverse-engineer them from first principles.
If one does not do that then the extraneous baggage
of the differing human perspectives prevent a fully
coherent view.
That's just syllogism, and makes for constructivism
since any sort stipulation, like an axiom, is unfounded.
The "axiomless natural deduction" to arrive at "axiomless
geometry" and "axiomless arithmetic" is a usual notion that
mathematical platonists have, though these days sometimes
they call themselves structural realists to not concern
dear old Bertrand, then though logicist positivists take
that label without fulfilling its definition.
Syllogism is subject ordering, and Aristotle reads every
syllogism its statements in every order, for example to
detect cycles and disambiguate them, which otherwise a
linear reader will fail to detect.
The "principle of _thorough_ reason" is more than the
"principle of 'sufficient' reason", then that in a
wider account of a wider, fuller dialectic, what's
sound, thorough, fulfilling, and fair.
Mentioning something like Prawitz' "inversion principle"
and about both the restriction _and_ the recovery, and
more than Russell's mere "isolation in significance and
significance in isolation", means that restricting (ignoring)
the resolution of any and all paradoxes leaves the door ajar
just like quasi-modal logic and principle of explosion.
So, maybe readers and researchers in foundations should start
with outlining the requirements and desiderata of a theory
that's constant, consistent, complete, and concrete,
The entire body of knowledge expressed in language
(a) Encodes all of the empirical "atomic facts" as axioms
this merges the analytic/synthetic distinction into one
analytic system. https://plato.stanford.edu/entries/analytic-synthetic/
(b) Provide a finite list of the possible semantic relations
between/among the elements of (a) and these are specified
syntactically using a system similar to CycL.
https://en.wikipedia.org/wiki/CycL
(c) This whole thing is stored in a knowledge ontology
https://en.wikipedia.org/wiki/Ontology_(information_science)
Hierarchy of simple type theory.
https://en.wikipedia.org/wiki/History_of_type_theory#G%C3%B6del_1944
Now we have the entire body of general knowledge that
can be expressed in language as a set of stipulated
semantic relations between finite strings.
and see how axiomless natural deduction fulfills that
with a comprehensive yet paradox-free account, and
that's the usual account since antiquity and even since
before recorded times, then it's called "mathematical platonism",
since issues of the human condition itself are subjective,
and whether Thoth or Hermes Trismagistus has an ankh for reason
or spiral for infinity, in at least one account there's both.
Thoth -> thought
Logos -> logic
Ma'at -> math
Aristotle won't be made a fool, and more than merely
half-Aristotleans have always both prior and posterior accounts.
That's not "a priori truth".
That's just a "convenient" lie to make some system of inference
considered itself compelled complete yet make it slavish while
really it's merely a model of a partial half-account of reason,
that fragmented synthetic pluralism and inconstancy in definition.
Adding an element to another element is synthetic
(where did it come from?), partitioning an element
into two is analytic (how was it already there?).
The usual account of mathematical platonism is analytic,
the usual account of logicist positivism is synthetic,
they are two different things.
Usual accounts of incompleteness like the Hilbert-Bernays paradox
confirm and certify that "logicist positivist nominalist theories"
are at best "merely and completely science".
Then, the account that it's not a science, is wrong.
Anybody can have a quite thorough body of knowledge -
if it doesn't change it's considered they stopped learning,
not that there isn't anything left to learn.
Quit trying to tell people they can't learn, it's insulting.
Well, we have to remember that Olcott has claimed to be god.
On 07/01/2026 12:37 PM, Chris M. Thomasson wrote:
On 7/1/2026 12:31 PM, Ross Finlayson wrote:
On 07/01/2026 10:57 AM, olcott wrote:
On 7/1/2026 12:00 PM, Ross Finlayson wrote:
On 07/01/2026 07:59 AM, olcott wrote:
On 7/1/2026 7:13 AM, Ross Finlayson wrote:
On 06/30/2026 08:01 PM, olcott wrote:
On 6/30/2026 9:47 PM, Ross Finlayson wrote:
On 06/30/2026 10:36 AM, Ross Finlayson wrote:
On 06/30/2026 07:53 AM, olcott wrote:
On 6/30/2026 8:23 AM, Ross Finlayson wrote:
So, if you want to know more about my theory, which is an >>>>>>>>>>>> account
of reason, and for Foundations, then I'd suggest first making >>>>>>>>>>>> for
yourself a "universal education", then finding resolutions to >>>>>>>>>>>> the
"paradoxes" of mathematical logic,
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Olcott's Minimal Type Theory
G rao -4Prov_PA(riLGriY)
Directed Graph of evaluation sequence
00 rao-a-a-a-a-a-a-a-a-a-a-a-a-a-a 01 02
01 G
02 -4-a-a-a-a-a-a-a-a-a-a-a-a-a-a 03
03 Prov_PA-a-a-a-a-a-a-a-a 04
04 G||del_Number_of 01-a // cycle indicates no well-founded >>>>>>>>>>> justification
tree exists.
ZFC already handled Russell's Paradox converting set
theory into Naive set theory.
It is important to keep computation in the loop
because computation exposes the hidden assumptions
that math makes.
CurryrCoHoward correspondence
In programming language theory and proof theory,
the CurryrCoHoward correspondence is a direct relationship >>>>>>>>>>> between computer programs and mathematical proofs.
https://en.wikipedia.org/wiki/
Curry%E2%80%93Howard_correspondence
then revealing the "super-classical"
results of classical mathematics, then for the "extra-ordinary" >>>>>>>>>>>> the
"great atlas of mathematical independence", then for "higher >>>>>>>>>>>> mathematics", and quite about "continuity" and "infinity", >>>>>>>>>>>> then there's also "the physics" after "the logic" and "the >>>>>>>>>>>> mathematics".
"Curry's poor substitute" at least rejects material implication. >>>>>>>>>>
Matters of meaning or the epistemological is a field called >>>>>>>>>> "semiotics".
Semantics after syntax is properly logical, that's all.
Cycle-detection is a usual routine involving memory and time, the >>>>>>>>>> resources.
The Liar Paradox is just a template of what would be a fallacy: >>>>>>>>>> two wrongs don't make a right.
unify_with_occurs_check(and(false(LP), true(LP)))
Two wrongs don't make a right.
Russell's retro-thesis is hypocrisy veiled as authority.
Where's the GUID for "dictionary", or "vocabulary", and what's in >>>>>>>>>> it.
"Cat" is a word.
It's fair to say "the Liar Paradox is false",
then that the negation translates through the copula "is"
to result "this sentence is true", a meaningless, empty tautology >>>>>>>>> (except as quoted a meaningless, empty, tautology).
It doesn't work on other "paradoxes", though.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics almost gets there
through an enormously more convoluted process.
They almost always utterly avoid any nuance of
true. Instead they focus on meaning.
Finlayson's paradox: there are none.
That quote of Wittgenstein's just a weak echo of Leibnitz'
"principle of
sufficient reason" about what an inference is. The Tractatus
Correct reasoning is not correctly evaluated on the
basis of who came up with the ideas. These ideas either
has a sound basis or not.
It just the same thing that I have been saying fir years.
True on the basis of meaning expressed in language must
have a direct semantic connection to those things in the
directly in the formal system of this language that make it
true.
(a) Cats are animals
(b) Animals are living things
(c) re| Cats are living things
No jumping outside of the language to a separate model.
Logicophilosophicus starts alright then Wittgenstein wimps out while >>>>>>> being all hot-headed about it later. Russell's favorite
philosophers,
Plotinus after Philo, are early weak nominalist fictionalists, and >>>>>>> having material implication in their vacuous implicits and so on, >>>>>>> Chrysippus could throw them from the boat since neither are they >>>>>>> Pythagoreans.
A much simpler process arrives at a "principle of _thorough_
reason",
where not only are affirmatory and negatory inferences found,
also in the diligence any their contradictions.
That is what I just showed.
Russell's retro-thesis simply can't make the extra-ordinary go away. >>>>>>> It's considered a quasi-modal variety of the weaker sort of the
logicist positivism, which has a stronger variety after a strong >>>>>>> mathematical platonism which invigorates it as "must be science". >>>>>>>
Old schlock wrapped as new, ....
The only way to obtain a correct foundation of these
things is to reverse-engineer them from first principles.
If one does not do that then the extraneous baggage
of the differing human perspectives prevent a fully
coherent view.
That's just syllogism, and makes for constructivism
since any sort stipulation, like an axiom, is unfounded.
The "axiomless natural deduction" to arrive at "axiomless
geometry" and "axiomless arithmetic" is a usual notion that
mathematical platonists have, though these days sometimes
they call themselves structural realists to not concern
dear old Bertrand, then though logicist positivists take
that label without fulfilling its definition.
Syllogism is subject ordering, and Aristotle reads every
syllogism its statements in every order, for example to
detect cycles and disambiguate them, which otherwise a
linear reader will fail to detect.
The "principle of _thorough_ reason" is more than the
"principle of 'sufficient' reason", then that in a
wider account of a wider, fuller dialectic, what's
sound, thorough, fulfilling, and fair.
Mentioning something like Prawitz' "inversion principle"
and about both the restriction _and_ the recovery, and
more than Russell's mere "isolation in significance and
significance in isolation", means that restricting (ignoring)
the resolution of any and all paradoxes leaves the door ajar
just like quasi-modal logic and principle of explosion.
So, maybe readers and researchers in foundations should start
with outlining the requirements and desiderata of a theory
that's constant, consistent, complete, and concrete,
The entire body of knowledge expressed in language
(a) Encodes all of the empirical "atomic facts" as axioms
this merges the analytic/synthetic distinction into one
analytic system. https://plato.stanford.edu/entries/analytic-synthetic/ >>>>
(b) Provide a finite list of the possible semantic relations
between/among the elements of (a) and these are specified
syntactically using a system similar to CycL.
https://en.wikipedia.org/wiki/CycL
(c) This whole thing is stored in a knowledge ontology
https://en.wikipedia.org/wiki/Ontology_(information_science)
Hierarchy of simple type theory.
https://en.wikipedia.org/wiki/History_of_type_theory#G%C3%B6del_1944
Now we have the entire body of general knowledge that
can be expressed in language as a set of stipulated
semantic relations between finite strings.
and see how axiomless natural deduction fulfills that
with a comprehensive yet paradox-free account, and
that's the usual account since antiquity and even since
before recorded times, then it's called "mathematical platonism",
since issues of the human condition itself are subjective,
and whether Thoth or Hermes Trismagistus has an ankh for reason
or spiral for infinity, in at least one account there's both.
Thoth -> thought
Logos -> logic
Ma'at -> math
Aristotle won't be made a fool, and more than merely
half-Aristotleans have always both prior and posterior accounts.
That's not "a priori truth".
That's just a "convenient" lie to make some system of inference
considered itself compelled complete yet make it slavish while
really it's merely a model of a partial half-account of reason,
that fragmented synthetic pluralism and inconstancy in definition.
Adding an element to another element is synthetic
(where did it come from?), partitioning an element
into two is analytic (how was it already there?).
The usual account of mathematical platonism is analytic,
the usual account of logicist positivism is synthetic,
they are two different things.
Usual accounts of incompleteness like the Hilbert-Bernays paradox
confirm and certify that "logicist positivist nominalist theories"
are at best "merely and completely science".
Then, the account that it's not a science, is wrong.
Anybody can have a quite thorough body of knowledge -
if it doesn't change it's considered they stopped learning,
not that there isn't anything left to learn.
Quit trying to tell people they can't learn, it's insulting.
Well, we have to remember that Olcott has claimed to be god.
Seems more like a sock-puppet chat-bot with a stolen identity.
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