On 07/14/2026 05:07 AM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 7/13/2026 4:09 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
[ .... ]
That remains to be shown.
Maybe you think that actual facts might not be true?
Facts are true by definition.-a A "complete set of atomic facts" is not >>>> even conceivable.-a We know such a set, if consistent, would be
incomplete by G||del's Incompleteness Theorem.-a So such a set cannot
exist.
All undecidability is unmasked as semantic
incoherence or outside of the body of knowledge.
Meaningless word salad.
When we stupidly have fucked up ways for determining
what is true we get fucked up results.
You should revert to expressing your thoughts in less offensive terms.
P reo Q means syntactic derivation implements semantic
entailment encoded in syntactically the language.
It doesn't.
This is the only inference steps allowed.
Grammatically ill-formed.-a But it's probably wrong, anyway.
By this measure PA reo G is simply false.
You aren't using that symbol with its standard meaning, so there's
nothing to reply to.
That you make sure to refuse to begin to understand
any of the details of this is no rebuttal at all.
You should learn G||del's Incompleteness Theorem, accept that it is
proven, and amend your somewhat ridiculous claims to take it into
account.
Since you refuse to accept any of the definitions
of my terms I can't begin to show how they work.
You're attempting to replace precise terms of the art with vague
half-definitions, probably to be able to equivocate, and never to be
pinned down to a precise meaning.
--
Copyright 2026 Olcott
That seems one of the problems with something like "Hobbes' nominalism", which beyond "extreme fictionalism" is like "the Red Queen's" entirely caprious judgment, one wondering whether Carroll's court-erie is a
parody of Hobbes.
Here instead there's perceived the, "requirements and desiderata",
of the theory, before getting into "architecture and implementation",
of a, "extreme rationalism", into thinks like "axiomless arithmetic"
and "axiomless geometry" that gives both the Archimedean and Euclidean
and the sub- and super- Archimedean and Euclidean, about deconstructive accounts then about what arrives for universals.
Carroll or Dodgson's mathematical infinitesimals are rather as like the cumulative hierarchy of ordinals in reverse, ....
On 7/14/2026 4:39 PM, Ross Finlayson wrote:
On 07/14/2026 05:07 AM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 7/13/2026 4:09 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
[ .... ]
That remains to be shown.
Maybe you think that actual facts might not be true?
Facts are true by definition. A "complete set of atomic facts" is not >>>>> even conceivable. We know such a set, if consistent, would be
incomplete by G||del's Incompleteness Theorem. So such a set cannot >>>>> exist.
All undecidability is unmasked as semantic
incoherence or outside of the body of knowledge.
Meaningless word salad.
When we stupidly have fucked up ways for determining
what is true we get fucked up results.
You should revert to expressing your thoughts in less offensive terms.
P reo Q means syntactic derivation implements semantic
entailment encoded in syntactically the language.
It doesn't.
This is the only inference steps allowed.
Grammatically ill-formed. But it's probably wrong, anyway.
By this measure PA reo G is simply false.
You aren't using that symbol with its standard meaning, so there's
nothing to reply to.
That you make sure to refuse to begin to understand
any of the details of this is no rebuttal at all.
You should learn G||del's Incompleteness Theorem, accept that it is
proven, and amend your somewhat ridiculous claims to take it into
account.
Since you refuse to accept any of the definitions
of my terms I can't begin to show how they work.
You're attempting to replace precise terms of the art with vague
half-definitions, probably to be able to equivocate, and never to be
pinned down to a precise meaning.
--
Copyright 2026 Olcott
That seems one of the problems with something like "Hobbes' nominalism",
which beyond "extreme fictionalism" is like "the Red Queen's" entirely
caprious judgment, one wondering whether Carroll's court-erie is a
parody of Hobbes.
Here instead there's perceived the, "requirements and desiderata",
of the theory, before getting into "architecture and implementation",
of a, "extreme rationalism", into thinks like "axiomless arithmetic"
and "axiomless geometry" that gives both the Archimedean and Euclidean
and the sub- and super- Archimedean and Euclidean, about deconstructive
accounts then about what arrives for universals.
Carroll or Dodgson's mathematical infinitesimals are rather as like the
cumulative hierarchy of ordinals in reverse, ....
P <semantically entails> Q means syntactic derivation
implements semantic entailment encoded in syntactically
the language. This is the only inference steps allowed.
Very difficult can understand yet the above completely
proves my whole point. As a concrete example of semantic
entailment specified syntactically we have expressions
written in the CycL ontology language.
To everyone that cannot possibly begin to understand
anything about semantics outside of model theory, you
just don't have a single clue about the actual full
field of semantics.
On 07/14/2026 02:56 PM, olcott wrote:
On 7/14/2026 4:39 PM, Ross Finlayson wrote:
On 07/14/2026 05:07 AM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 7/13/2026 4:09 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
[ .... ]
That remains to be shown.
Maybe you think that actual facts might not be true?
Facts are true by definition.-a A "complete set of atomic facts" is >>>>>> not
even conceivable.-a We know such a set, if consistent, would be
incomplete by G||del's Incompleteness Theorem.-a So such a set cannot >>>>>> exist.
All undecidability is unmasked as semantic
incoherence or outside of the body of knowledge.
Meaningless word salad.
When we stupidly have fucked up ways for determining
what is true we get fucked up results.
You should revert to expressing your thoughts in less offensive terms. >>>>
P reo Q means syntactic derivation implements semantic
entailment encoded in syntactically the language.
It doesn't.
This is the only inference steps allowed.
Grammatically ill-formed.-a But it's probably wrong, anyway.
By this measure PA reo G is simply false.
You aren't using that symbol with its standard meaning, so there's
nothing to reply to.
That you make sure to refuse to begin to understand
any of the details of this is no rebuttal at all.
You should learn G||del's Incompleteness Theorem, accept that it is
proven, and amend your somewhat ridiculous claims to take it into
account.
Since you refuse to accept any of the definitions
of my terms I can't begin to show how they work.
You're attempting to replace precise terms of the art with vague
half-definitions, probably to be able to equivocate, and never to be
pinned down to a precise meaning.
--
Copyright 2026 Olcott
That seems one of the problems with something like "Hobbes' nominalism", >>> which beyond "extreme fictionalism" is like "the Red Queen's" entirely
caprious judgment, one wondering whether Carroll's court-erie is a
parody of Hobbes.
Here instead there's perceived the, "requirements and desiderata",
of the theory, before getting into "architecture and implementation",
of a, "extreme rationalism", into thinks like "axiomless arithmetic"
and "axiomless geometry" that gives both the Archimedean and Euclidean
and the sub- and super- Archimedean and Euclidean, about deconstructive
accounts then about what arrives for universals.
Carroll or Dodgson's mathematical infinitesimals are rather as like the
cumulative hierarchy of ordinals in reverse, ....
P <semantically entails> Q means syntactic derivation
implements semantic entailment encoded in syntactically
the language. This is the only inference steps allowed.
Very difficult can understand yet the above completely
proves my whole point. As a concrete example of semantic
entailment specified syntactically we have expressions
written in the CycL ontology language.
To everyone that cannot possibly begin to understand
anything about semantics outside of model theory, you
just don't have a single clue about the actual full
field of semantics.
Doesn't say much, that's just the definition of entailment,
and omits monotonicity, which makes for the not the inconstancy.
On 7/14/2026 5:38 PM, Ross Finlayson wrote:
On 07/14/2026 02:56 PM, olcott wrote:
On 7/14/2026 4:39 PM, Ross Finlayson wrote:
On 07/14/2026 05:07 AM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 7/13/2026 4:09 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
[ .... ]
That remains to be shown.
Maybe you think that actual facts might not be true?
Facts are true by definition. A "complete set of atomic facts"
is not
even conceivable. We know such a set, if consistent, would be
incomplete by G||del's Incompleteness Theorem. So such a set cannot >>>>>>> exist.
All undecidability is unmasked as semantic
incoherence or outside of the body of knowledge.
Meaningless word salad.
When we stupidly have fucked up ways for determining
what is true we get fucked up results.
You should revert to expressing your thoughts in less offensive terms. >>>>>
P reo Q means syntactic derivation implements semantic
entailment encoded in syntactically the language.
It doesn't.
This is the only inference steps allowed.
Grammatically ill-formed. But it's probably wrong, anyway.
By this measure PA reo G is simply false.
You aren't using that symbol with its standard meaning, so there's
nothing to reply to.
That you make sure to refuse to begin to understand
any of the details of this is no rebuttal at all.
You should learn G||del's Incompleteness Theorem, accept that it is
proven, and amend your somewhat ridiculous claims to take it into
account.
Since you refuse to accept any of the definitions
of my terms I can't begin to show how they work.
You're attempting to replace precise terms of the art with vague
half-definitions, probably to be able to equivocate, and never to be >>>>> pinned down to a precise meaning.
--
Copyright 2026 Olcott
That seems one of the problems with something like "Hobbes'
nominalism",
which beyond "extreme fictionalism" is like "the Red Queen's" entirely >>>> caprious judgment, one wondering whether Carroll's court-erie is a
parody of Hobbes.
Here instead there's perceived the, "requirements and desiderata",
of the theory, before getting into "architecture and implementation",
of a, "extreme rationalism", into thinks like "axiomless arithmetic"
and "axiomless geometry" that gives both the Archimedean and Euclidean >>>> and the sub- and super- Archimedean and Euclidean, about deconstructive >>>> accounts then about what arrives for universals.
Carroll or Dodgson's mathematical infinitesimals are rather as like the >>>> cumulative hierarchy of ordinals in reverse, ....
P <semantically entails> Q means syntactic derivation
implements semantic entailment encoded in syntactically
the language. This is the only inference steps allowed.
Very difficult can understand yet the above completely
proves my whole point. As a concrete example of semantic
entailment specified syntactically we have expressions
written in the CycL ontology language.
To everyone that cannot possibly begin to understand
anything about semantics outside of model theory, you
just don't have a single clue about the actual full
field of semantics.
Doesn't say much, that's just the definition of entailment,
and omits monotonicity, which makes for the not the inconstancy.
It all a {meaning of words} thing that everyone here
cannot begin to understand because they are totally
stuck on numbers.
Formal semantics of linguistics of formalized natural
language does not have one damn thing to do with numbers. https://en.wikipedia.org/wiki/Montague_grammar
I avoided all of those big words so that I would not make
everyone here look like a complete ignoramus.
On 07/14/2026 03:49 PM, olcott wrote:
On 7/14/2026 5:38 PM, Ross Finlayson wrote:
On 07/14/2026 02:56 PM, olcott wrote:
On 7/14/2026 4:39 PM, Ross Finlayson wrote:
On 07/14/2026 05:07 AM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 7/13/2026 4:09 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
[ .... ]
That remains to be shown.
Maybe you think that actual facts might not be true?
Facts are true by definition.-a A "complete set of atomic facts" >>>>>>>> is not
even conceivable.-a We know such a set, if consistent, would be >>>>>>>> incomplete by G||del's Incompleteness Theorem.-a So such a set cannot >>>>>>>> exist.
All undecidability is unmasked as semantic
incoherence or outside of the body of knowledge.
Meaningless word salad.
When we stupidly have fucked up ways for determining
what is true we get fucked up results.
You should revert to expressing your thoughts in less offensive
terms.
P reo Q means syntactic derivation implements semantic
entailment encoded in syntactically the language.
It doesn't.
This is the only inference steps allowed.
Grammatically ill-formed.-a But it's probably wrong, anyway.
By this measure PA reo G is simply false.
You aren't using that symbol with its standard meaning, so there's >>>>>> nothing to reply to.
That you make sure to refuse to begin to understand
any of the details of this is no rebuttal at all.
You should learn G||del's Incompleteness Theorem, accept that it is >>>>>> proven, and amend your somewhat ridiculous claims to take it into
account.
Since you refuse to accept any of the definitions
of my terms I can't begin to show how they work.
You're attempting to replace precise terms of the art with vague
half-definitions, probably to be able to equivocate, and never to be >>>>>> pinned down to a precise meaning.
--
Copyright 2026 Olcott
That seems one of the problems with something like "Hobbes'
nominalism",
which beyond "extreme fictionalism" is like "the Red Queen's" entirely >>>>> caprious judgment, one wondering whether Carroll's court-erie is a
parody of Hobbes.
Here instead there's perceived the, "requirements and desiderata",
of the theory, before getting into "architecture and implementation", >>>>> of a, "extreme rationalism", into thinks like "axiomless arithmetic" >>>>> and "axiomless geometry" that gives both the Archimedean and Euclidean >>>>> and the sub- and super- Archimedean and Euclidean, about
deconstructive
accounts then about what arrives for universals.
Carroll or Dodgson's mathematical infinitesimals are rather as like >>>>> the
cumulative hierarchy of ordinals in reverse, ....
P <semantically entails> Q means syntactic derivation
implements semantic entailment encoded in syntactically
the language. This is the only inference steps allowed.
Very difficult can understand yet the above completely
proves my whole point. As a concrete example of semantic
entailment specified syntactically we have expressions
written in the CycL ontology language.
To everyone that cannot possibly begin to understand
anything about semantics outside of model theory, you
just don't have a single clue about the actual full
field of semantics.
Doesn't say much, that's just the definition of entailment,
and omits monotonicity, which makes for the not the inconstancy.
It all a {meaning of words} thing that everyone here
cannot begin to understand because they are totally
stuck on numbers.
Formal semantics of linguistics of formalized natural
language does not have one damn thing to do with numbers.
https://en.wikipedia.org/wiki/Montague_grammar
I avoided all of those big words so that I would not make
everyone here look like a complete ignoramus.
Saying "Montague grammar" picks up "material implication"
and "ex falso quodlibet" a.k.a. "principle of explosion",
so, it's your own foot you're shooting.
Instead here there are considered "Herbrand semantics".
Montague was just a party-boy flake in the orbit of Tarski.
On 7/14/2026 7:29 PM, Ross Finlayson wrote:
On 07/14/2026 03:49 PM, olcott wrote:
On 7/14/2026 5:38 PM, Ross Finlayson wrote:
On 07/14/2026 02:56 PM, olcott wrote:
On 7/14/2026 4:39 PM, Ross Finlayson wrote:
On 07/14/2026 05:07 AM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 7/13/2026 4:09 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
[ .... ]
That remains to be shown.
Maybe you think that actual facts might not be true?
Facts are true by definition. A "complete set of atomic facts" >>>>>>>>> is not
even conceivable. We know such a set, if consistent, would be >>>>>>>>> incomplete by G||del's Incompleteness Theorem. So such a set >>>>>>>>> cannot
exist.
All undecidability is unmasked as semantic
incoherence or outside of the body of knowledge.
Meaningless word salad.
When we stupidly have fucked up ways for determining
what is true we get fucked up results.
You should revert to expressing your thoughts in less offensive
terms.
P reo Q means syntactic derivation implements semantic
entailment encoded in syntactically the language.
It doesn't.
This is the only inference steps allowed.
Grammatically ill-formed. But it's probably wrong, anyway.
By this measure PA reo G is simply false.
You aren't using that symbol with its standard meaning, so there's >>>>>>> nothing to reply to.
That you make sure to refuse to begin to understand
any of the details of this is no rebuttal at all.
You should learn G||del's Incompleteness Theorem, accept that it is >>>>>>> proven, and amend your somewhat ridiculous claims to take it into >>>>>>> account.
Since you refuse to accept any of the definitions
of my terms I can't begin to show how they work.
You're attempting to replace precise terms of the art with vague >>>>>>> half-definitions, probably to be able to equivocate, and never to be >>>>>>> pinned down to a precise meaning.
--
Copyright 2026 Olcott
That seems one of the problems with something like "Hobbes'
nominalism",
which beyond "extreme fictionalism" is like "the Red Queen's"
entirely
caprious judgment, one wondering whether Carroll's court-erie is a >>>>>> parody of Hobbes.
Here instead there's perceived the, "requirements and desiderata", >>>>>> of the theory, before getting into "architecture and implementation", >>>>>> of a, "extreme rationalism", into thinks like "axiomless arithmetic" >>>>>> and "axiomless geometry" that gives both the Archimedean and
Euclidean
and the sub- and super- Archimedean and Euclidean, about
deconstructive
accounts then about what arrives for universals.
Carroll or Dodgson's mathematical infinitesimals are rather as
like the
cumulative hierarchy of ordinals in reverse, ....
P <semantically entails> Q means syntactic derivation
implements semantic entailment encoded in syntactically
the language. This is the only inference steps allowed.
Very difficult can understand yet the above completely
proves my whole point. As a concrete example of semantic
entailment specified syntactically we have expressions
written in the CycL ontology language.
To everyone that cannot possibly begin to understand
anything about semantics outside of model theory, you
just don't have a single clue about the actual full
field of semantics.
Doesn't say much, that's just the definition of entailment,
and omits monotonicity, which makes for the not the inconstancy.
It all a {meaning of words} thing that everyone here
cannot begin to understand because they are totally
stuck on numbers.
Formal semantics of linguistics of formalized natural
language does not have one damn thing to do with numbers.
https://en.wikipedia.org/wiki/Montague_grammar
I avoided all of those big words so that I would not make
everyone here look like a complete ignoramus.
Saying "Montague grammar" picks up "material implication"
and "ex falso quodlibet" a.k.a. "principle of explosion",
so, it's your own foot you're shooting.
Not when you think these things all the way through.
Instead here there are considered "Herbrand semantics".
Montague was just a party-boy flake in the orbit of Tarski.
Gemini thinks that you are very good with computation.
It looked up your professional work. If this is so and
not just bullshit then you could actually understand the
details of the structure of the Cyc Project and the CycL
language.
On 07/14/2026 05:38 PM, olcott wrote:
On 7/14/2026 7:29 PM, Ross Finlayson wrote:
On 07/14/2026 03:49 PM, olcott wrote:
On 7/14/2026 5:38 PM, Ross Finlayson wrote:
On 07/14/2026 02:56 PM, olcott wrote:
On 7/14/2026 4:39 PM, Ross Finlayson wrote:
On 07/14/2026 05:07 AM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 7/13/2026 4:09 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
[ .... ]
That remains to be shown.
Maybe you think that actual facts might not be true?
Facts are true by definition.-a A "complete set of atomic facts" >>>>>>>>>> is not
even conceivable.-a We know such a set, if consistent, would be >>>>>>>>>> incomplete by G||del's Incompleteness Theorem.-a So such a set >>>>>>>>>> cannot
exist.
All undecidability is unmasked as semantic
incoherence or outside of the body of knowledge.
Meaningless word salad.
When we stupidly have fucked up ways for determining
what is true we get fucked up results.
You should revert to expressing your thoughts in less offensive >>>>>>>> terms.
P reo Q means syntactic derivation implements semantic
entailment encoded in syntactically the language.
It doesn't.
This is the only inference steps allowed.
Grammatically ill-formed.-a But it's probably wrong, anyway.
By this measure PA reo G is simply false.
You aren't using that symbol with its standard meaning, so there's >>>>>>>> nothing to reply to.
That you make sure to refuse to begin to understand
any of the details of this is no rebuttal at all.
You should learn G||del's Incompleteness Theorem, accept that it is >>>>>>>> proven, and amend your somewhat ridiculous claims to take it into >>>>>>>> account.
Since you refuse to accept any of the definitions
of my terms I can't begin to show how they work.
You're attempting to replace precise terms of the art with vague >>>>>>>> half-definitions, probably to be able to equivocate, and never >>>>>>>> to be
pinned down to a precise meaning.
--
Copyright 2026 Olcott
That seems one of the problems with something like "Hobbes'
nominalism",
which beyond "extreme fictionalism" is like "the Red Queen's"
entirely
caprious judgment, one wondering whether Carroll's court-erie is a >>>>>>> parody of Hobbes.
Here instead there's perceived the, "requirements and desiderata", >>>>>>> of the theory, before getting into "architecture and
implementation",
of a, "extreme rationalism", into thinks like "axiomless arithmetic" >>>>>>> and "axiomless geometry" that gives both the Archimedean and
Euclidean
and the sub- and super- Archimedean and Euclidean, about
deconstructive
accounts then about what arrives for universals.
Carroll or Dodgson's mathematical infinitesimals are rather as
like the
cumulative hierarchy of ordinals in reverse, ....
P <semantically entails> Q means syntactic derivation
implements semantic entailment encoded in syntactically
the language. This is the only inference steps allowed.
Very difficult can understand yet the above completely
proves my whole point. As a concrete example of semantic
entailment specified syntactically we have expressions
written in the CycL ontology language.
To everyone that cannot possibly begin to understand
anything about semantics outside of model theory, you
just don't have a single clue about the actual full
field of semantics.
Doesn't say much, that's just the definition of entailment,
and omits monotonicity, which makes for the not the inconstancy.
It all a {meaning of words} thing that everyone here
cannot begin to understand because they are totally
stuck on numbers.
Formal semantics of linguistics of formalized natural
language does not have one damn thing to do with numbers.
https://en.wikipedia.org/wiki/Montague_grammar
I avoided all of those big words so that I would not make
everyone here look like a complete ignoramus.
Saying "Montague grammar" picks up "material implication"
and "ex falso quodlibet" a.k.a. "principle of explosion",
so, it's your own foot you're shooting.
Not when you think these things all the way through.
Instead here there are considered "Herbrand semantics".
Montague was just a party-boy flake in the orbit of Tarski.
Gemini thinks that you are very good with computation.
It looked up your professional work. If this is so and
not just bullshit then you could actually understand the
details of the structure of the Cyc Project and the CycL
language.
I'm a qualified and experienced professional programmer/analyst,
various knowledge inference formats like KIF, RDF, OWL, or
basically usually often enough about 3-tuples of relation
yet for the temporal introducing 5-tuples, are almost never
found salient in the koolaid and the firehose.
That said, ontology is simply organization in knowledge,
it's that simple, not a guarantee itself.
On 7/14/2026 9:03 PM, Ross Finlayson wrote:
On 07/14/2026 05:38 PM, olcott wrote:
On 7/14/2026 7:29 PM, Ross Finlayson wrote:
On 07/14/2026 03:49 PM, olcott wrote:
On 7/14/2026 5:38 PM, Ross Finlayson wrote:
On 07/14/2026 02:56 PM, olcott wrote:
On 7/14/2026 4:39 PM, Ross Finlayson wrote:
On 07/14/2026 05:07 AM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 7/13/2026 4:09 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
[ .... ]
That remains to be shown.
Maybe you think that actual facts might not be true?
Facts are true by definition. A "complete set of atomic facts" >>>>>>>>>>> is not
even conceivable. We know such a set, if consistent, would be >>>>>>>>>>> incomplete by G||del's Incompleteness Theorem. So such a set >>>>>>>>>>> cannot
exist.
All undecidability is unmasked as semantic
incoherence or outside of the body of knowledge.
Meaningless word salad.
When we stupidly have fucked up ways for determining
what is true we get fucked up results.
You should revert to expressing your thoughts in less offensive >>>>>>>>> terms.
P reo Q means syntactic derivation implements semantic
entailment encoded in syntactically the language.
It doesn't.
This is the only inference steps allowed.
Grammatically ill-formed. But it's probably wrong, anyway.
By this measure PA reo G is simply false.
You aren't using that symbol with its standard meaning, so there's >>>>>>>>> nothing to reply to.
That you make sure to refuse to begin to understand
any of the details of this is no rebuttal at all.
You should learn G||del's Incompleteness Theorem, accept that it is >>>>>>>>> proven, and amend your somewhat ridiculous claims to take it into >>>>>>>>> account.
Since you refuse to accept any of the definitions
of my terms I can't begin to show how they work.
You're attempting to replace precise terms of the art with vague >>>>>>>>> half-definitions, probably to be able to equivocate, and never >>>>>>>>> to be
pinned down to a precise meaning.
--
Copyright 2026 Olcott
That seems one of the problems with something like "Hobbes'
nominalism",
which beyond "extreme fictionalism" is like "the Red Queen's"
entirely
caprious judgment, one wondering whether Carroll's court-erie is a >>>>>>>> parody of Hobbes.
Here instead there's perceived the, "requirements and desiderata", >>>>>>>> of the theory, before getting into "architecture and
implementation",
of a, "extreme rationalism", into thinks like "axiomless
arithmetic"
and "axiomless geometry" that gives both the Archimedean and
Euclidean
and the sub- and super- Archimedean and Euclidean, about
deconstructive
accounts then about what arrives for universals.
Carroll or Dodgson's mathematical infinitesimals are rather as >>>>>>>> like the
cumulative hierarchy of ordinals in reverse, ....
P <semantically entails> Q means syntactic derivation
implements semantic entailment encoded in syntactically
the language. This is the only inference steps allowed.
Very difficult can understand yet the above completely
proves my whole point. As a concrete example of semantic
entailment specified syntactically we have expressions
written in the CycL ontology language.
To everyone that cannot possibly begin to understand
anything about semantics outside of model theory, you
just don't have a single clue about the actual full
field of semantics.
Doesn't say much, that's just the definition of entailment,
and omits monotonicity, which makes for the not the inconstancy.
It all a {meaning of words} thing that everyone here
cannot begin to understand because they are totally
stuck on numbers.
Formal semantics of linguistics of formalized natural
language does not have one damn thing to do with numbers.
https://en.wikipedia.org/wiki/Montague_grammar
I avoided all of those big words so that I would not make
everyone here look like a complete ignoramus.
Saying "Montague grammar" picks up "material implication"
and "ex falso quodlibet" a.k.a. "principle of explosion",
so, it's your own foot you're shooting.
Not when you think these things all the way through.
Instead here there are considered "Herbrand semantics".
Montague was just a party-boy flake in the orbit of Tarski.
Gemini thinks that you are very good with computation.
It looked up your professional work. If this is so and
not just bullshit then you could actually understand the
details of the structure of the Cyc Project and the CycL
language.
I'm a qualified and experienced professional programmer/analyst,
various knowledge inference formats like KIF, RDF, OWL, or
basically usually often enough about 3-tuples of relation
yet for the temporal introducing 5-tuples, are almost never
found salient in the koolaid and the firehose.
That said, ontology is simply organization in knowledge,
it's that simple, not a guarantee itself.
Yes so you can understand these things. A properly
formed knowledge ontology that is sufficiently
populated does directly facilitate making some
subset of all truth expressed in language computable.
The relative taste of strawberries to blueberries
cannot be expressed in language.
On 07/14/2026 07:12 PM, olcott wrote:
On 7/14/2026 9:03 PM, Ross Finlayson wrote:
On 07/14/2026 05:38 PM, olcott wrote:
On 7/14/2026 7:29 PM, Ross Finlayson wrote:
On 07/14/2026 03:49 PM, olcott wrote:
On 7/14/2026 5:38 PM, Ross Finlayson wrote:
On 07/14/2026 02:56 PM, olcott wrote:
On 7/14/2026 4:39 PM, Ross Finlayson wrote:
On 07/14/2026 05:07 AM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 7/13/2026 4:09 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
[ .... ]
That remains to be shown.
Maybe you think that actual facts might not be true?
Facts are true by definition.-a A "complete set of atomic facts" >>>>>>>>>>>> is not
even conceivable.-a We know such a set, if consistent, would be >>>>>>>>>>>> incomplete by G||del's Incompleteness Theorem.-a So such a set >>>>>>>>>>>> cannot
exist.
All undecidability is unmasked as semantic
incoherence or outside of the body of knowledge.
Meaningless word salad.
When we stupidly have fucked up ways for determining
what is true we get fucked up results.
You should revert to expressing your thoughts in less offensive >>>>>>>>>> terms.
P reo Q means syntactic derivation implements semantic
entailment encoded in syntactically the language.
It doesn't.
This is the only inference steps allowed.
Grammatically ill-formed.-a But it's probably wrong, anyway. >>>>>>>>>>
By this measure PA reo G is simply false.
You aren't using that symbol with its standard meaning, so >>>>>>>>>> there's
nothing to reply to.
That you make sure to refuse to begin to understand
any of the details of this is no rebuttal at all.
You should learn G||del's Incompleteness Theorem, accept that >>>>>>>>>> it is
proven, and amend your somewhat ridiculous claims to take it into >>>>>>>>>> account.
Since you refuse to accept any of the definitions
of my terms I can't begin to show how they work.
You're attempting to replace precise terms of the art with vague >>>>>>>>>> half-definitions, probably to be able to equivocate, and never >>>>>>>>>> to be
pinned down to a precise meaning.
--
Copyright 2026 Olcott
That seems one of the problems with something like "Hobbes'
nominalism",
which beyond "extreme fictionalism" is like "the Red Queen's" >>>>>>>>> entirely
caprious judgment, one wondering whether Carroll's court-erie is a >>>>>>>>> parody of Hobbes.
Here instead there's perceived the, "requirements and desiderata", >>>>>>>>> of the theory, before getting into "architecture and
implementation",
of a, "extreme rationalism", into thinks like "axiomless
arithmetic"
and "axiomless geometry" that gives both the Archimedean and >>>>>>>>> Euclidean
and the sub- and super- Archimedean and Euclidean, about
deconstructive
accounts then about what arrives for universals.
Carroll or Dodgson's mathematical infinitesimals are rather as >>>>>>>>> like the
cumulative hierarchy of ordinals in reverse, ....
P <semantically entails> Q means syntactic derivation
implements semantic entailment encoded in syntactically
the language. This is the only inference steps allowed.
Very difficult can understand yet the above completely
proves my whole point. As a concrete example of semantic
entailment specified syntactically we have expressions
written in the CycL ontology language.
To everyone that cannot possibly begin to understand
anything about semantics outside of model theory, you
just don't have a single clue about the actual full
field of semantics.
Doesn't say much, that's just the definition of entailment,
and omits monotonicity, which makes for the not the inconstancy. >>>>>>>
It all a {meaning of words} thing that everyone here
cannot begin to understand because they are totally
stuck on numbers.
Formal semantics of linguistics of formalized natural
language does not have one damn thing to do with numbers.
https://en.wikipedia.org/wiki/Montague_grammar
I avoided all of those big words so that I would not make
everyone here look like a complete ignoramus.
Saying "Montague grammar" picks up "material implication"
and "ex falso quodlibet" a.k.a. "principle of explosion",
so, it's your own foot you're shooting.
Not when you think these things all the way through.
Instead here there are considered "Herbrand semantics".
Montague was just a party-boy flake in the orbit of Tarski.
Gemini thinks that you are very good with computation.
It looked up your professional work. If this is so and
not just bullshit then you could actually understand the
details of the structure of the Cyc Project and the CycL
language.
I'm a qualified and experienced professional programmer/analyst,
various knowledge inference formats like KIF, RDF, OWL, or
basically usually often enough about 3-tuples of relation
yet for the temporal introducing 5-tuples, are almost never
found salient in the koolaid and the firehose.
That said, ontology is simply organization in knowledge,
it's that simple, not a guarantee itself.
Yes so you can understand these things. A properly
formed knowledge ontology that is sufficiently
populated does directly facilitate making some
subset of all truth expressed in language computable.
The relative taste of strawberries to blueberries
cannot be expressed in language.
Ah, the old "one step forward, two steps back" -
the story being told is old as dirt, the Pythagoreans
told it when their universe of magnitudes was finite ratios,
which makes a lot of sense when there are infinite integers.
The "the relative taste of strawberries to blueberries"
_is_ already an expression in language.
Strawberries are more tart while blueberries lucious,
though both strawberries and blueberries are a bit tart
and lucious, though usually prepared blueberries need
less sugar, strawberries have more vitamin C while blueberries
have more anthocyanins, while both are nutritious and with
also non-nutritional value, less people are allergic to blueberries,
any matter of taste can be expressed in terms of strawberries and blueberries, in a limited sense.
"Colorless green" is an actual account of the dual-tri-stimulus
colorspace of the chromatic and prismatic that monochromatic:
an account that usual textbooks don't have.
I'm a researcher in Foundations not just a "full-stack enterprise dev".
On 7/15/2026 3:03 PM, Ross Finlayson wrote:
On 07/14/2026 07:12 PM, olcott wrote:
On 7/14/2026 9:03 PM, Ross Finlayson wrote:
On 07/14/2026 05:38 PM, olcott wrote:
On 7/14/2026 7:29 PM, Ross Finlayson wrote:
On 07/14/2026 03:49 PM, olcott wrote:
On 7/14/2026 5:38 PM, Ross Finlayson wrote:
On 07/14/2026 02:56 PM, olcott wrote:
On 7/14/2026 4:39 PM, Ross Finlayson wrote:
On 07/14/2026 05:07 AM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 7/13/2026 4:09 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
[ .... ]
That remains to be shown.
Maybe you think that actual facts might not be true?
Facts are true by definition. A "complete set of atomic >>>>>>>>>>>>> facts"
is not
even conceivable. We know such a set, if consistent, would be >>>>>>>>>>>>> incomplete by G||del's Incompleteness Theorem. So such a set >>>>>>>>>>>>> cannot
exist.
All undecidability is unmasked as semantic
incoherence or outside of the body of knowledge.
Meaningless word salad.
When we stupidly have fucked up ways for determining
what is true we get fucked up results.
You should revert to expressing your thoughts in less offensive >>>>>>>>>>> terms.
P reo Q means syntactic derivation implements semantic >>>>>>>>>>>> entailment encoded in syntactically the language.
It doesn't.
This is the only inference steps allowed.
Grammatically ill-formed. But it's probably wrong, anyway. >>>>>>>>>>>
By this measure PA reo G is simply false.
You aren't using that symbol with its standard meaning, so >>>>>>>>>>> there's
nothing to reply to.
That you make sure to refuse to begin to understand
any of the details of this is no rebuttal at all.
You should learn G||del's Incompleteness Theorem, accept that >>>>>>>>>>> it is
proven, and amend your somewhat ridiculous claims to take it >>>>>>>>>>> into
account.
Since you refuse to accept any of the definitions
of my terms I can't begin to show how they work.
You're attempting to replace precise terms of the art with vague >>>>>>>>>>> half-definitions, probably to be able to equivocate, and never >>>>>>>>>>> to be
pinned down to a precise meaning.
--
Copyright 2026 Olcott
That seems one of the problems with something like "Hobbes' >>>>>>>>>> nominalism",
which beyond "extreme fictionalism" is like "the Red Queen's" >>>>>>>>>> entirely
caprious judgment, one wondering whether Carroll's court-erie >>>>>>>>>> is a
parody of Hobbes.
Here instead there's perceived the, "requirements and
desiderata",
of the theory, before getting into "architecture and
implementation",
of a, "extreme rationalism", into thinks like "axiomless
arithmetic"
and "axiomless geometry" that gives both the Archimedean and >>>>>>>>>> Euclidean
and the sub- and super- Archimedean and Euclidean, about
deconstructive
accounts then about what arrives for universals.
Carroll or Dodgson's mathematical infinitesimals are rather as >>>>>>>>>> like the
cumulative hierarchy of ordinals in reverse, ....
P <semantically entails> Q means syntactic derivation
implements semantic entailment encoded in syntactically
the language. This is the only inference steps allowed.
Very difficult can understand yet the above completely
proves my whole point. As a concrete example of semantic
entailment specified syntactically we have expressions
written in the CycL ontology language.
To everyone that cannot possibly begin to understand
anything about semantics outside of model theory, you
just don't have a single clue about the actual full
field of semantics.
Doesn't say much, that's just the definition of entailment,
and omits monotonicity, which makes for the not the inconstancy. >>>>>>>>
It all a {meaning of words} thing that everyone here
cannot begin to understand because they are totally
stuck on numbers.
Formal semantics of linguistics of formalized natural
language does not have one damn thing to do with numbers.
https://en.wikipedia.org/wiki/Montague_grammar
I avoided all of those big words so that I would not make
everyone here look like a complete ignoramus.
Saying "Montague grammar" picks up "material implication"
and "ex falso quodlibet" a.k.a. "principle of explosion",
so, it's your own foot you're shooting.
Not when you think these things all the way through.
Instead here there are considered "Herbrand semantics".
Montague was just a party-boy flake in the orbit of Tarski.
Gemini thinks that you are very good with computation.
It looked up your professional work. If this is so and
not just bullshit then you could actually understand the
details of the structure of the Cyc Project and the CycL
language.
I'm a qualified and experienced professional programmer/analyst,
various knowledge inference formats like KIF, RDF, OWL, or
basically usually often enough about 3-tuples of relation
yet for the temporal introducing 5-tuples, are almost never
found salient in the koolaid and the firehose.
That said, ontology is simply organization in knowledge,
it's that simple, not a guarantee itself.
Yes so you can understand these things. A properly
formed knowledge ontology that is sufficiently
populated does directly facilitate making some
subset of all truth expressed in language computable.
The relative taste of strawberries to blueberries
cannot be expressed in language.
Ah, the old "one step forward, two steps back" -
the story being told is old as dirt, the Pythagoreans
told it when their universe of magnitudes was finite ratios,
which makes a lot of sense when there are infinite integers.
The "the relative taste of strawberries to blueberries"
_is_ already an expression in language.
Strawberries are more tart while blueberries lucious,
though both strawberries and blueberries are a bit tart
and lucious, though usually prepared blueberries need
less sugar, strawberries have more vitamin C while blueberries
have more anthocyanins, while both are nutritious and with
also non-nutritional value, less people are allergic to blueberries,
any matter of taste can be expressed in terms of strawberries and
blueberries, in a limited sense.
"Colorless green" is an actual account of the dual-tri-stimulus
colorspace of the chromatic and prismatic that monochromatic:
an account that usual textbooks don't have.
I'm a researcher in Foundations not just a "full-stack enterprise dev".
Foundations of math of numbers not Foundations
of every aspect of generic truth itself.
On 7/15/2026 3:03 PM, Ross Finlayson wrote:
On 07/14/2026 07:12 PM, olcott wrote:
On 7/14/2026 9:03 PM, Ross Finlayson wrote:
On 07/14/2026 05:38 PM, olcott wrote:
On 7/14/2026 7:29 PM, Ross Finlayson wrote:
On 07/14/2026 03:49 PM, olcott wrote:
On 7/14/2026 5:38 PM, Ross Finlayson wrote:
On 07/14/2026 02:56 PM, olcott wrote:
On 7/14/2026 4:39 PM, Ross Finlayson wrote:
On 07/14/2026 05:07 AM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 7/13/2026 4:09 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
[ .... ]
That remains to be shown.
Maybe you think that actual facts might not be true?
Facts are true by definition.-a A "complete set of atomic >>>>>>>>>>>>> facts"
is not
even conceivable.-a We know such a set, if consistent, would be >>>>>>>>>>>>> incomplete by G||del's Incompleteness Theorem.-a So such a set >>>>>>>>>>>>> cannot
exist.
All undecidability is unmasked as semantic
incoherence or outside of the body of knowledge.
Meaningless word salad.
When we stupidly have fucked up ways for determining
what is true we get fucked up results.
You should revert to expressing your thoughts in less offensive >>>>>>>>>>> terms.
P reo Q means syntactic derivation implements semantic >>>>>>>>>>>> entailment encoded in syntactically the language.
It doesn't.
This is the only inference steps allowed.
Grammatically ill-formed.-a But it's probably wrong, anyway. >>>>>>>>>>>
By this measure PA reo G is simply false.
You aren't using that symbol with its standard meaning, so >>>>>>>>>>> there's
nothing to reply to.
That you make sure to refuse to begin to understand
any of the details of this is no rebuttal at all.
You should learn G||del's Incompleteness Theorem, accept that >>>>>>>>>>> it is
proven, and amend your somewhat ridiculous claims to take it >>>>>>>>>>> into
account.
Since you refuse to accept any of the definitions
of my terms I can't begin to show how they work.
You're attempting to replace precise terms of the art with vague >>>>>>>>>>> half-definitions, probably to be able to equivocate, and never >>>>>>>>>>> to be
pinned down to a precise meaning.
--
Copyright 2026 Olcott
That seems one of the problems with something like "Hobbes' >>>>>>>>>> nominalism",
which beyond "extreme fictionalism" is like "the Red Queen's" >>>>>>>>>> entirely
caprious judgment, one wondering whether Carroll's court-erie >>>>>>>>>> is a
parody of Hobbes.
Here instead there's perceived the, "requirements and
desiderata",
of the theory, before getting into "architecture and
implementation",
of a, "extreme rationalism", into thinks like "axiomless
arithmetic"
and "axiomless geometry" that gives both the Archimedean and >>>>>>>>>> Euclidean
and the sub- and super- Archimedean and Euclidean, about
deconstructive
accounts then about what arrives for universals.
Carroll or Dodgson's mathematical infinitesimals are rather as >>>>>>>>>> like the
cumulative hierarchy of ordinals in reverse, ....
P <semantically entails> Q means syntactic derivation
implements semantic entailment encoded in syntactically
the language. This is the only inference steps allowed.
Very difficult can understand yet the above completely
proves my whole point. As a concrete example of semantic
entailment specified syntactically we have expressions
written in the CycL ontology language.
To everyone that cannot possibly begin to understand
anything about semantics outside of model theory, you
just don't have a single clue about the actual full
field of semantics.
Doesn't say much, that's just the definition of entailment,
and omits monotonicity, which makes for the not the inconstancy. >>>>>>>>
It all a {meaning of words} thing that everyone here
cannot begin to understand because they are totally
stuck on numbers.
Formal semantics of linguistics of formalized natural
language does not have one damn thing to do with numbers.
https://en.wikipedia.org/wiki/Montague_grammar
I avoided all of those big words so that I would not make
everyone here look like a complete ignoramus.
Saying "Montague grammar" picks up "material implication"
and "ex falso quodlibet" a.k.a. "principle of explosion",
so, it's your own foot you're shooting.
Not when you think these things all the way through.
Instead here there are considered "Herbrand semantics".
Montague was just a party-boy flake in the orbit of Tarski.
Gemini thinks that you are very good with computation.
It looked up your professional work. If this is so and
not just bullshit then you could actually understand the
details of the structure of the Cyc Project and the CycL
language.
I'm a qualified and experienced professional programmer/analyst,
various knowledge inference formats like KIF, RDF, OWL, or
basically usually often enough about 3-tuples of relation
yet for the temporal introducing 5-tuples, are almost never
found salient in the koolaid and the firehose.
That said, ontology is simply organization in knowledge,
it's that simple, not a guarantee itself.
Yes so you can understand these things. A properly
formed knowledge ontology that is sufficiently
populated does directly facilitate making some
subset of all truth expressed in language computable.
The relative taste of strawberries to blueberries
cannot be expressed in language.
Ah, the old "one step forward, two steps back" -
the story being told is old as dirt, the Pythagoreans
told it when their universe of magnitudes was finite ratios,
which makes a lot of sense when there are infinite integers.
The "the relative taste of strawberries to blueberries"
_is_ already an expression in language.
Strawberries are more tart while blueberries lucious,
though both strawberries and blueberries are a bit tart
and lucious, though usually prepared blueberries need
less sugar, strawberries have more vitamin C while blueberries
have more anthocyanins, while both are nutritious and with
also non-nutritional value, less people are allergic to blueberries,
any matter of taste can be expressed in terms of strawberries and
blueberries, in a limited sense.
"Colorless green" is an actual account of the dual-tri-stimulus
colorspace of the chromatic and prismatic that monochromatic:
an account that usual textbooks don't have.
I'm a researcher in Foundations not just a "full-stack enterprise dev".
Foundations of math of numbers not Foundations
of every aspect of generic truth itself.
Foundations are simple:
From nothing you can construct the empty set, which is the prototype
of the natural number zero. For every other natural number you can
construct the prototype from the prototype of the prvious one as the
union of the prefious prototype and the singlet set containing the
previous set. There are well known (and other) ways to construct the
integers from then natual numbers, the rational numbers from the
integers, and the real numbers from rationals. From reals one can
construct the unverse and all its contents and their behaviours.
On 07/16/2026 12:42 AM, Mikko wrote:
Foundations are simple:
From nothing you can construct the empty set, which is the prototype
of the natural number zero. For every other natural number you can
construct the prototype from the prototype of the prvious one as the
union of the prefious prototype and the singlet set containing the
previous set. There are well known (and other) ways to construct the
integers from then natual numbers, the rational numbers from the
integers, and the real numbers from rationals. From reals one can
construct the unverse and all its contents and their behaviours.
"Nothing" and "the empty set" aren't necessarily the same,
while it may be agreeable that "the fundamental question of
meta-physics" is "why is there something rather than nothing".
The usual notions of "empty set" and "inductive set" are
given as introducing constants into the language of ZF set theory,
yet, besides that expansion-of-comprehension, then ZF's are also restriction-of-comprehension, "ordinary empty set" and "ordinary
inductive set", when for example the empty set and the inductive
set aren't unique, and there are "extra-ordinary" empty and
inductive sets, that quantification over elements finds.
Then, the "Void" and "Universe" are "complementary duals",
reflecting on philosophy's usual account of "Nothing" and
"Being" as the considerations of those.
Foundations _are_ simple: in fact so simple that then how
they arrive and making for the approfondissement of the
objects of logic and mathematics, involves super-classical
reasoning quite directly then making for paradox-free reason
of the completeness in repleteness of infinity and continuity.
"A-Theory" it's called here, "theatheory", a "Null Axiom Theory".
On 07/16/2026 08:08 AM, Ross Finlayson wrote:
On 07/16/2026 12:42 AM, Mikko wrote:
Foundations are simple:
From nothing you can construct the empty set, which is the prototype
of the natural number zero. For every other natural number you can
construct the prototype from the prototype of the prvious one as the
union of the prefious prototype and the singlet set containing the
previous set. There are well known (and other) ways to construct the
integers from then natual numbers, the rational numbers from the
integers, and the real numbers from rationals. From reals one can
construct the unverse and all its contents and their behaviours.
"Nothing" and "the empty set" aren't necessarily the same,
while it may be agreeable that "the fundamental question of
meta-physics" is "why is there something rather than nothing".
The usual notions of "empty set" and "inductive set" are
given as introducing constants into the language of ZF set theory,
yet, besides that expansion-of-comprehension, then ZF's are also
restriction-of-comprehension, "ordinary empty set" and "ordinary
inductive set", when for example the empty set and the inductive
set aren't unique, and there are "extra-ordinary" empty and
inductive sets, that quantification over elements finds.
Then, the "Void" and "Universe" are "complementary duals",
reflecting on philosophy's usual account of "Nothing" and
"Being" as the considerations of those.
Foundations _are_ simple: in fact so simple that then how
they arrive and making for the approfondissement of the
objects of logic and mathematics, involves super-classical
reasoning quite directly then making for paradox-free reason
of the completeness in repleteness of infinity and continuity.
"A-Theory" it's called here, "theatheory", a "Null Axiom Theory".
"Being" and "Nothing", or "Sein" and "Nichtes",
these are the usual premier concepts in philosophy,
since the ancient Greeks with "Being: no Nothing",
then Hegel with "Nothing and Being", that then the
20'th century arrived at "existentialism and nihilism",
when they are flip sides of a coin each other themselves.
It's called canon, we already have one.
On 07/16/2026 08:25 AM, Ross Finlayson wrote:
On 07/16/2026 08:08 AM, Ross Finlayson wrote:
On 07/16/2026 12:42 AM, Mikko wrote:
Foundations are simple:
From nothing you can construct the empty set, which is the prototype
of the natural number zero. For every other natural number you can
construct the prototype from the prototype of the prvious one as the
union of the prefious prototype and the singlet set containing the
previous set. There are well known (and other) ways to construct the
integers from then natual numbers, the rational numbers from the
integers, and the real numbers from rationals. From reals one can
construct the unverse and all its contents and their behaviours.
"Nothing" and "the empty set" aren't necessarily the same,
while it may be agreeable that "the fundamental question of
meta-physics" is "why is there something rather than nothing".
The usual notions of "empty set" and "inductive set" are
given as introducing constants into the language of ZF set theory,
yet, besides that expansion-of-comprehension, then ZF's are also
restriction-of-comprehension, "ordinary empty set" and "ordinary
inductive set", when for example the empty set and the inductive
set aren't unique, and there are "extra-ordinary" empty and
inductive sets, that quantification over elements finds.
Then, the "Void" and "Universe" are "complementary duals",
reflecting on philosophy's usual account of "Nothing" and
"Being" as the considerations of those.
Foundations _are_ simple: in fact so simple that then how
they arrive and making for the approfondissement of the
objects of logic and mathematics, involves super-classical
reasoning quite directly then making for paradox-free reason
of the completeness in repleteness of infinity and continuity.
"A-Theory" it's called here, "theatheory", a "Null Axiom Theory".
"Being" and "Nothing", or "Sein" and "Nichtes",
these are the usual premier concepts in philosophy,
since the ancient Greeks with "Being: no Nothing",
then Hegel with "Nothing and Being", that then the
20'th century arrived at "existentialism and nihilism",
when they are flip sides of a coin each other themselves.
It's called canon, we already have one.
Researchers in Foundations since forever usually at least
once arrive at Mathematical Platonism that the universe of
mathematical objects with infinity and continuity exists
and that this brings along logic also, thus resulting for
a sort of "axiomless geometry" and "axiomless arithmetic"
to subsume and be sublime to "Archimedean arithmetic"
and "Euclidean geometry", then for algebra and DesCartes,
the arithmetic and geometry and algebra and analysis.
This is among reasons why "old wrapped as new" gets old.
This is the plain old plain old,
"Hilbert's Infinite, Living, Working Museum of Mathematics",
now with "the Great Atlas of Mathematical Independence"
in "paradox-free reason".
This sort of holistic dual monism is considered a more thorough
and mature account opposed to the fragmented synthetic pluralism
of the nominalist fictionalist variety for a mathematics replete
with infinity and continuity.
For example, bringing Pythagoreanism and Cantorianism back
together again, the Atlas makes bridges (ponts, analytical
bridges) for this.
Otherwise those competing claims of opposing views only see
each other as "Giant Monsters of Mathematical Independence".
That there's a universe at all implies that they're wrong,
or, generously, "incomplete".
On 07/16/2026 12:42 AM, Mikko wrote:
Foundations are simple:
-aFrom nothing you can construct the empty set, which is the prototype
of the natural number zero. For every other natural number you can
construct the prototype from the prototype of the prvious one as the
union of the prefious prototype and the singlet set containing the
previous set. There are well known (and other) ways to construct the
integers from then natual numbers, the rational numbers from the
integers, and the real numbers from rationals. From reals one can
construct the unverse and all its contents and their behaviours.
"Nothing" and "the empty set" aren't necessarily the same,
On 16/07/2026 18:08, Ross Finlayson wrote:
On 07/16/2026 12:42 AM, Mikko wrote:
Foundations are simple:
From nothing you can construct the empty set, which is the prototype
of the natural number zero. For every other natural number you can
construct the prototype from the prototype of the prvious one as the
union of the prefious prototype and the singlet set containing the
previous set. There are well known (and other) ways to construct the
integers from then natual numbers, the rational numbers from the
integers, and the real numbers from rationals. From reals one can
construct the unverse and all its contents and their behaviours.
"Nothing" and "the empty set" aren't necessarily the same,
They are necessarily different. In particuar, the set that contains
nothing else than the empty set is a singlet set.
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