On 12/05/2026 16:59, olcott wrote:
Olcott thesis: Every element of the body of knowledge
that can be expressed in language can be expressed as
relations between finite strings.
I propose that a concrete counter example to this these
is categorically impossible.
You should be able to prove your thesis from reasonable definitions.
On 5/26/2026 2:56 AM, Mikko wrote:
On 12/05/2026 16:59, olcott wrote:
Olcott thesis: Every element of the body of knowledge
that can be expressed in language can be expressed as
relations between finite strings.
I propose that a concrete counter example to this these
is categorically impossible.
You should be able to prove your thesis from reasonable definitions.
Then Church-Turing should prove theirs.
To the structuralists, meaning is a not an
inherent aspect of a concept, but rather a
property of the relationships between the
concept and all other concepts.
This framework originated with the Swiss
linguist Ferdinand de Saussure.
On 05/26/2026 07:01 AM, olcott wrote:
On 5/26/2026 2:56 AM, Mikko wrote:
On 12/05/2026 16:59, olcott wrote:
Olcott thesis: Every element of the body of knowledge
that can be expressed in language can be expressed as
relations between finite strings.
I propose that a concrete counter example to this these
is categorically impossible.
You should be able to prove your thesis from reasonable definitions.
Then Church-Turing should prove theirs.
To the structuralists, meaning is a not an
inherent aspect of a concept, but rather a
property of the relationships between the
concept and all other concepts.
This framework originated with the Swiss
linguist Ferdinand de Saussure.
That's usually enough model theory then, models of relations.
People in axiomatic set theory often forget or don't know
that to make all the models of relation has that there
are all the sets, and later equivalence classes, to
provide what are the sets that are the relations.
Then, in the real world, physical objects as mathematical
objects have all their relations as mathematical objects
as physical objects, infinities of them.
So, things like cardinals as "equivalence classes of sets
under bijective relation" or real numbers as "equivalence
classes of series that are Cauchy" have that those equivalence
classes are often larger than ordinary sets in the ordinary set theory.
Then, the physics of the real world is a continuum mechanics.
People who'd prefer ordinary theories have already found
that these accounts of the extra-ordinary always are so,
then "structuralists" are simply those that observe that expansion-of-comprehension always makes structures, that
making more-than-less a model-theory as with regards to
proof-theory, and a theory with a universe.
Then, whether the constructible universe is the universe,
or V = L, gets into lots of accounts of assumptions or
about Feferman's account then for whether that's hypocritical
like Russell's "axiomatized ordinary" is to Mirimanoff's
"natural extra-ordinary".
Anyways it's simple to show that P.O.'s account is
basically a fragmented pluralistic synthetic argument,
about something like the paradoxes of identity, and that
identity's defined by both x = x and x = V \ x.
On 5/26/2026 10:37 AM, Ross Finlayson wrote:
On 05/26/2026 07:01 AM, olcott wrote:
On 5/26/2026 2:56 AM, Mikko wrote:
On 12/05/2026 16:59, olcott wrote:
Olcott thesis: Every element of the body of knowledge
that can be expressed in language can be expressed as
relations between finite strings.
I propose that a concrete counter example to this these
is categorically impossible.
You should be able to prove your thesis from reasonable definitions.
Then Church-Turing should prove theirs.
To the structuralists, meaning is a not an
inherent aspect of a concept, but rather a
property of the relationships between the
concept and all other concepts.
This framework originated with the Swiss
linguist Ferdinand de Saussure.
That's usually enough model theory then, models of relations.
It is not at all conventional truth conditional semantics.
It seems to be simple type theory through the lens of
proof theoretic semantics.
People in axiomatic set theory often forget or don't know
that to make all the models of relation has that there
are all the sets, and later equivalence classes, to
provide what are the sets that are the relations.
Then, in the real world, physical objects as mathematical
objects have all their relations as mathematical objects
as physical objects, infinities of them.
So, things like cardinals as "equivalence classes of sets
under bijective relation" or real numbers as "equivalence
classes of series that are Cauchy" have that those equivalence
classes are often larger than ordinary sets in the ordinary set theory.
You seem to keep staying in your cloud of abstractions
that have nothing to do with the kind of system that can
establish the truth of real world consequences.
Then, the physics of the real world is a continuum mechanics.
People who'd prefer ordinary theories have already found
that these accounts of the extra-ordinary always are so,
then "structuralists" are simply those that observe that
expansion-of-comprehension always makes structures, that
making more-than-less a model-theory as with regards to
proof-theory, and a theory with a universe.
Then, whether the constructible universe is the universe,
or V = L, gets into lots of accounts of assumptions or
about Feferman's account then for whether that's hypocritical
like Russell's "axiomatized ordinary" is to Mirimanoff's
"natural extra-ordinary".
Anyways it's simple to show that P.O.'s account is
basically a fragmented pluralistic synthetic argument,
about something like the paradoxes of identity, and that
identity's defined by both x = x and x = V \ x.
Why don't you just STFU until you first come to know
proof theoretic semantics. Without that all you have
is prejudice and bias.
On 05/26/2026 08:50 AM, olcott wrote:
On 5/26/2026 10:37 AM, Ross Finlayson wrote:
On 05/26/2026 07:01 AM, olcott wrote:
On 5/26/2026 2:56 AM, Mikko wrote:
On 12/05/2026 16:59, olcott wrote:
Olcott thesis: Every element of the body of knowledge
that can be expressed in language can be expressed as
relations between finite strings.
I propose that a concrete counter example to this these
is categorically impossible.
You should be able to prove your thesis from reasonable definitions. >>>>>
Then Church-Turing should prove theirs.
To the structuralists, meaning is a not an
inherent aspect of a concept, but rather a
property of the relationships between the
concept and all other concepts.
This framework originated with the Swiss
linguist Ferdinand de Saussure.
That's usually enough model theory then, models of relations.
It is not at all conventional truth conditional semantics.
It seems to be simple type theory through the lens of
proof theoretic semantics.
People in axiomatic set theory often forget or don't know
that to make all the models of relation has that there
are all the sets, and later equivalence classes, to
provide what are the sets that are the relations.
Then, in the real world, physical objects as mathematical
objects have all their relations as mathematical objects
as physical objects, infinities of them.
So, things like cardinals as "equivalence classes of sets
under bijective relation" or real numbers as "equivalence
classes of series that are Cauchy" have that those equivalence
classes are often larger than ordinary sets in the ordinary set theory.
You seem to keep staying in your cloud of abstractions
that have nothing to do with the kind of system that can
establish the truth of real world consequences.
Then, the physics of the real world is a continuum mechanics.
People who'd prefer ordinary theories have already found
that these accounts of the extra-ordinary always are so,
then "structuralists" are simply those that observe that
expansion-of-comprehension always makes structures, that
making more-than-less a model-theory as with regards to
proof-theory, and a theory with a universe.
Then, whether the constructible universe is the universe,
or V = L, gets into lots of accounts of assumptions or
about Feferman's account then for whether that's hypocritical
like Russell's "axiomatized ordinary" is to Mirimanoff's
"natural extra-ordinary".
Anyways it's simple to show that P.O.'s account is
basically a fragmented pluralistic synthetic argument,
about something like the paradoxes of identity, and that
identity's defined by both x = x and x = V \ x.
Why don't you just STFU until you first come to know
proof theoretic semantics. Without that all you have
is prejudice and bias.
Well, no, here there's an account of paradox-free reason,
that there is one at all.
That's all axiomatics is is "prejudice", before-judged,
and all ordinary ruliality is, "bias", inductive bias.
Then, a usual enough account of addressing "the fundamental
question of metaphysics: why is there something rather
than nothing" gets into an account of the Void and Universe,
then for Point and Space and for Increment and Partition and
for Metaphor and Metonymy, having a theory at all.
Then, principles (not axioms, say) _describe_ that the
Inverse subsumes Contradiction and the Thorough subsumes
the Sufficient, about the principles of excluded-middle
and the principle of sufficient reason, that the Inverse
makes for Diversity among complementary duals and Variety
among like neighbors, and the Thorough makes for that
Aristotle won't be made a fool, including for his accounts
of where excluded-middle holds or doesn't and where the
inductive inference suffices or doesn't.
Thusly it's a _one_ theory, a heno-theory, in which all
the other accounts of theory get interpreted, a mono-heno-theory,
that's also conveniently an account of any theory at all.
Anyways it's simple to show that most all usual accounts
that have only the Contradiction and not the Inverse and
only the Sufficient and not the Thorough, are fragmented,
pluralistic, and synthetic (and inconsistent). So, that's
not just among retro-finitist crankety trolls, indeed it
makes for that super-classical reasoning is first-class itself,
and for ready demonstrations where yes/no questions have
"yes AND no" answers and where inductive inference not only
fails to suffice yet is shown suffices to fail.
Then all sorts super-classical reasoning have resolving
any sort of "paradox" otherwise in reasoning about the
real world given competing inductive claims, about why
for example there's calculus or even accounts of motion,
which as mentioned can otherwise be destroyed by argument.
Anyways, "two wrongs" is just more wrong.
On 5/26/2026 11:31 AM, Ross Finlayson wrote:
On 05/26/2026 08:50 AM, olcott wrote:
On 5/26/2026 10:37 AM, Ross Finlayson wrote:
On 05/26/2026 07:01 AM, olcott wrote:
On 5/26/2026 2:56 AM, Mikko wrote:
On 12/05/2026 16:59, olcott wrote:
Olcott thesis: Every element of the body of knowledge
that can be expressed in language can be expressed as
relations between finite strings.
I propose that a concrete counter example to this these
is categorically impossible.
You should be able to prove your thesis from reasonable definitions. >>>>>>
Then Church-Turing should prove theirs.
To the structuralists, meaning is a not an
inherent aspect of a concept, but rather a
property of the relationships between the
concept and all other concepts.
This framework originated with the Swiss
linguist Ferdinand de Saussure.
That's usually enough model theory then, models of relations.
It is not at all conventional truth conditional semantics.
It seems to be simple type theory through the lens of
proof theoretic semantics.
People in axiomatic set theory often forget or don't know
that to make all the models of relation has that there
are all the sets, and later equivalence classes, to
provide what are the sets that are the relations.
Then, in the real world, physical objects as mathematical
objects have all their relations as mathematical objects
as physical objects, infinities of them.
So, things like cardinals as "equivalence classes of sets
under bijective relation" or real numbers as "equivalence
classes of series that are Cauchy" have that those equivalence
classes are often larger than ordinary sets in the ordinary set theory. >>>>
You seem to keep staying in your cloud of abstractions
that have nothing to do with the kind of system that can
establish the truth of real world consequences.
Then, the physics of the real world is a continuum mechanics.
People who'd prefer ordinary theories have already found
that these accounts of the extra-ordinary always are so,
then "structuralists" are simply those that observe that
expansion-of-comprehension always makes structures, that
making more-than-less a model-theory as with regards to
proof-theory, and a theory with a universe.
Then, whether the constructible universe is the universe,
or V = L, gets into lots of accounts of assumptions or
about Feferman's account then for whether that's hypocritical
like Russell's "axiomatized ordinary" is to Mirimanoff's
"natural extra-ordinary".
Anyways it's simple to show that P.O.'s account is
basically a fragmented pluralistic synthetic argument,
about something like the paradoxes of identity, and that
identity's defined by both x = x and x = V \ x.
Why don't you just STFU until you first come to know
proof theoretic semantics. Without that all you have
is prejudice and bias.
Well, no, here there's an account of paradox-free reason,
that there is one at all.
That's all axiomatics is is "prejudice", before-judged,
and all ordinary ruliality is, "bias", inductive bias.
I will dumb it down for you.
Every expression of language that cannot possibly be
grounded in a truth value is simply not truth apt.
All undecidability has always either been a misconception
or like the truth value of the Goldbach conjecture outside
of the body of current human knowledge.
Then, a usual enough account of addressing "the fundamental
question of metaphysics: why is there something rather
than nothing" gets into an account of the Void and Universe,
then for Point and Space and for Increment and Partition and
for Metaphor and Metonymy, having a theory at all.
Then, principles (not axioms, say) _describe_ that the
Inverse subsumes Contradiction and the Thorough subsumes
the Sufficient, about the principles of excluded-middle
and the principle of sufficient reason, that the Inverse
makes for Diversity among complementary duals and Variety
among like neighbors, and the Thorough makes for that
Aristotle won't be made a fool, including for his accounts
of where excluded-middle holds or doesn't and where the
inductive inference suffices or doesn't.
Thusly it's a _one_ theory, a heno-theory, in which all
the other accounts of theory get interpreted, a mono-heno-theory,
that's also conveniently an account of any theory at all.
Anyways it's simple to show that most all usual accounts
that have only the Contradiction and not the Inverse and
only the Sufficient and not the Thorough, are fragmented,
pluralistic, and synthetic (and inconsistent). So, that's
not just among retro-finitist crankety trolls, indeed it
makes for that super-classical reasoning is first-class itself,
and for ready demonstrations where yes/no questions have
"yes AND no" answers and where inductive inference not only
fails to suffice yet is shown suffices to fail.
Then all sorts super-classical reasoning have resolving
any sort of "paradox" otherwise in reasoning about the
real world given competing inductive claims, about why
for example there's calculus or even accounts of motion,
which as mentioned can otherwise be destroyed by argument.
Anyways, "two wrongs" is just more wrong.
On 5/26/2026 2:56 AM, Mikko wrote:
On 12/05/2026 16:59, olcott wrote:
Olcott thesis: Every element of the body of knowledge
that can be expressed in language can be expressed as
relations between finite strings.
I propose that a concrete counter example to this these
is categorically impossible.
You should be able to prove your thesis from reasonable definitions.
Then Church-Turing should prove theirs.
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