Wikipedia agrees with Axiom(Olcott) and WFF directly expressing semantics

[peteolcott]

https://en.wikipedia.org/wiki/Theory_(mathematical_logic)
This article has said this since 2010, I checked the history page.

Theory_(mathematical_logic)
initial statements are often called the primitive elements or elementary
statements of the theory, to distinguish them from other statements which
may be derived from them.

A theory T is a conceptual class consisting of certain of these elementary
statements. The elementary statements which belong to T are called the
elementary theorems of T and said to be true. In this way, a theory is a
way of designating a subset of E which consists entirely of true statements.

Thus not only agreeing with Axiom(Olcott) that some expressions of the
formal language of the formal system have been defined to have the semantic
value of True, but also anchoring the semantics of the formal system directly
within its syntax.

[peteolcott]

Post by peteolcott
https://en.wikipedia.org/wiki/Theory_(mathematical_logic)
This article has said this since 2010, I checked the history page.
Theory_(mathematical_logic)
initial statements are often called the primitive elements or elementary
statements of the theory, to distinguish them from other statements which
may be derived from them.
A theory T is a conceptual class consisting of certain of these elementary
statements. The elementary statements which belong to T are called the
elementary theorems of T and said to be true. In this way, a theory is a
way of designating a subset of E which consists entirely of true statements.
Thus not only agreeing with Axiom(Olcott) that some expressions of the
formal language of the formal system have been defined to have the semantic
value of True, but also anchoring the semantics of the formal system directly
within its syntax.

<quote>
The construction of a theory begins by specifying a definite
non-empty conceptual class E, the elements of which are called
statements. These initial statements are often called the
primitive elements or elementary statements of the theory, to
distinguish them from other statements which may be derived from
them.
A theory T is a conceptual class consisting of certain of these
elementary statements. The elementary statements which belong to
T are called the elementary theorems of T and said to be true.
In this way, a theory is a way of designating a subset of E
which consists entirely of true statements.
This general way of designating a theory stipulates that the
truth of any of its elementary statements is not known without
T. Thus the same elementary statement may be true with respect
to one theory, and not true with respect to another. This is
as in ordinary language, where statements such as "He is an
honest person." cannot be judged to be true or false without
reference to some interpretation of who "He" is and, for that
matter, what an "honest person" is under this theory.
</quote>
[Haskell Curry, Foundations of Mathematical Logic, 2010.]

Ah great you anchored it in a much more credible original source.
https://en.wikipedia.org/wiki/Haskell_Curry
Curry is also known for Curry's paradox and the Curry–Howard correspondence.

It seems to me that in the third paragraph (which you omitted)
Curry makes it explicit the statements, elementary and
otherwise, dependent on the context. However Curry - and
everybody else - do not read "true" to imply the kind of "Truth"
you work with.

It is not actually anchored in the linguistic kind of context it is
only anchored in semantics specified by the of the rest of the language.

How can there possibly be more than one kind of true?

Elsewhere we find "theory" as a set of theorems (statements
accepted as "true" - actually the other way around in practice -
"true" means the statement is a theorem in T.

Exactly what I said here (and so many people violently disagreed)
∀x True(x) ↔ ⊢x // Completing the Tarski Truth predicate

The ONLY kind of True that there actually is refutes the
Tarski 1936 Undefinability Theorem.

https://www.brainyquote.com/quotes/albert_einstein_129798
Great spirits have always encountered violent opposition from mediocre minds.

[Peter Percival]

Post by peteolcott
https://en.wikipedia.org/wiki/Theory_(mathematical_logic)
This article has said this since 2010, I checked the history page.
Theory_(mathematical_logic)
initial statements are often called the primitive elements or elementary
statements of the theory, to distinguish them from other statements which
may be derived from them.
A theory T is a conceptual class consisting of certain of these elementary
statements. The elementary statements which belong to T are called the
elementary theorems of T and said to be true. In this way, a theory is a
way of designating a subset of E which consists entirely of true statements.
Thus not only agreeing with Axiom(Olcott) that some expressions of the
formal language of the formal system have been defined to have the semantic
value of True, but also anchoring the semantics of the formal system directly
within its syntax.

'All of the theorems of a theory are true' is not the same as 'all of
the truths expressible in the language of a theory are theorems of it'.

[peteolcott]

Post by peteolcott
https://en.wikipedia.org/wiki/Theory_(mathematical_logic)
This article has said this since 2010, I checked the history page.
Theory_(mathematical_logic)
initial statements are often called the primitive elements or elementary
statements of the theory, to distinguish them from other statements which
may be derived from them.
A theory T is a conceptual class consisting of certain of these elementary
statements. The elementary statements which belong to T are called the
elementary theorems of T and said to be true. In this way, a theory is a
way of designating a subset of E which consists entirely of true statements.
Thus not only agreeing with Axiom(Olcott) that some expressions of the
formal language of the formal system have been defined to have the semantic
value of True, but also anchoring the semantics of the formal system directly
within its syntax.

'All of the theorems of a theory are true' is not the same as 'all of the truths expressible in the language of a theory are theorems of it'.

Try and provide a concrete example of an expression of language that is
true in the theory and not a theorem of this same theory.

[Franz Gnaedinger]

Post by peteolcott
"Great spirits have always encountered violent
opposition from mediocre minds." Albert Einstein

Didn't you learn from your fellow kikerikee Pentcho Valev that Einstein
lived in a schizophrenic parallel world? in the real world the GPS works
without relativity theory, and Goedel was wrong. But maybe some people
counfound these two worlds?

[Helmut Richter]

Post by peteolcott
"Great spirits have always encountered violent
opposition from mediocre minds." Albert Einstein

But it is a fallacy to draw the conclusion: "Spirits that always encounter
violent opposition from mediocre minds must be great spirits."

... where "mediocre" here just means "disagreeing with the self-appointed
genius".

[Christian Weisgerber]

Post by Helmut Richter

Post by peteolcott
"Great spirits have always encountered violent
opposition from mediocre minds." Albert Einstein

But it is a fallacy to draw the conclusion: "Spirits that always encounter
violent opposition from mediocre minds must be great spirits."

As Carl Sagan put it: "They laughed at Columbus, they laughed at
Fulton, they laughed at the Wright brothers. But they also laughed
at Bozo the Clown."

[peteolcott]

Post by Christian Weisgerber

Post by Helmut Richter

Post by peteolcott
"Great spirits have always encountered violent
opposition from mediocre minds." Albert Einstein

But it is a fallacy to draw the conclusion: "Spirits that always encounter
violent opposition from mediocre minds must be great spirits."

As Carl Sagan put it: "They laughed at Columbus, they laughed at
Fulton, they laughed at the Wright brothers. But they also laughed
at Bozo the Clown."

Not very discriminating were they?

[peteolcott]

Post by Helmut Richter

Post by peteolcott
"Great spirits have always encountered violent
opposition from mediocre minds." Albert Einstein

But it is a fallacy to draw the conclusion: "Spirits that always encounter
violent opposition from mediocre minds must be great spirits."
... where "mediocre" here just means "disagreeing with the self-appointed
genius".

The instance of the fallacy and the legitimacy can only be correctly
distinguished from each other by finding actual mistakes ion what is being said.

Glancing at a few words before forming one's rebuttal is certainly not the
correct process.

[peteolcott]

Post by peteolcott

Post by Helmut Richter

Post by peteolcott
"Great spirits have always encountered violent
opposition from mediocre minds." Albert Einstein

But it is a fallacy to draw the conclusion: "Spirits that always encounter
violent opposition from mediocre minds must be great spirits."
... where "mediocre" here just means "disagreeing with the self-appointed
genius".

The instance of the fallacy and the legitimacy can only be correctly
distinguished from each other by finding actual mistakes ion what is being said.
Glancing at a few words before forming one's rebuttal is certainly not the
correct process.

THIS PROVES THAT TARSKI WAS WRONG

Here is the original source:
http://liarparadox.org/Tarski_Undefinability_Proof.pdf

On the left is what Tarski said,
On the right is the same thing using conventional notation:
(3) x ∉ Pr ↔ x ∈ Tr // ~Provable(x) ↔ True(x)

If we plug any semantic value into x such as: 3 > 5 we get:
~Provable(3 > 5) ↔ True(3 > 5)

When we generalize this we get:
The fact that an expression of language x is not provable makes
this expression of language x logically equivalent to true.

[Peter T. Daniels]

Post by peteolcott

'All of the theorems of a theory are true' is not the same as 'all of the truths expressible in the language of a theory are theorems of it'.

Try and provide a concrete example of an expression of language that is
true in the theory and not a theorem of this same theory.

No utterance in a language is a theorem (unless the utterance happens to
be a snippet of, for instance, a geometry textbook).

[Helmut Richter]

Post by Peter T. Daniels

Post by peteolcott

'All of the theorems of a theory are true' is not the same as 'all of the truths expressible in the language of a theory are theorems of it'.

Try and provide a concrete example of an expression of language that is
true in the theory and not a theorem of this same theory.

No utterance in a language is a theorem (unless the utterance happens to
be a snippet of, for instance, a geometry textbook).

Every theorem is uttered in some language. Pete Olcott seems to infer that
any reasoning about theorems belongs to linguistics. This is why he is
unable to understand why flooding this newsgroup with such reasoning is
considered very indecent by those who are interested in linguistics
proper.

Whether or not this reasoning is correct should not be discussed here but
in sci.logic or somewhere else where it could belong. (But I understand
when people interested in logic are also not keen on receiving several
repetitions of Pete Olcott's musings each day.)

I think all readers here – except one – agree on these points, and this
one is able to render this group much less usable than it would have been
without his contributions.

[peteolcott]

Post by Helmut Richter

Post by Peter T. Daniels

Post by peteolcott

'All of the theorems of a theory are true' is not the same as 'all of the truths expressible in the language of a theory are theorems of it'.

Try and provide a concrete example of an expression of language that is
true in the theory and not a theorem of this same theory.

No utterance in a language is a theorem (unless the utterance happens to
be a snippet of, for instance, a geometry textbook).

Every theorem is uttered in some language. Pete Olcott seems to infer that
any reasoning about theorems belongs to linguistics. This is why he is
unable to understand why flooding this newsgroup with such reasoning is
considered very indecent by those who are interested in linguistics
proper.
Whether or not this reasoning is correct should not be discussed here but
in sci.logic or somewhere else where it could belong. (But I understand
when people interested in logic are also not keen on receiving several
repetitions of Pete Olcott's musings each day.)
I think all readers here – except one – agree on these points, and this
one is able to render this group much less usable than it would have been
without his contributions.

In this paper I show how the term theorem is broadened to include natural language.
https://www.researchgate.net/publication/323866366_The_Notion_of_Truth_in_Natural_and_Formal_Languages
it is extended from [provable from axioms] to [provable from facts].

These two groups are dead:
https://groups.google.com/forum/#!forum/linguistic-semantics
sci.lang.semantics

That hardly anyone within linguistics cares about semantics certainly
does not entail that semantics is not an aspect of linguistics.

[Peter T. Daniels]

Post by peteolcott
https://groups.google.com/forum/#!forum/linguistic-semantics
sci.lang.semantics
That hardly anyone within linguistics cares about semantics certainly
does not entail that semantics is not an aspect of linguistics.

Many, many linguists care about semantics. They do not, however, care
about whatever it is that you've mislabeled "semantics."

[peteolcott]

Post by Peter T. Daniels

Post by peteolcott
https://groups.google.com/forum/#!forum/linguistic-semantics
sci.lang.semantics
That hardly anyone within linguistics cares about semantics certainly
does not entail that semantics is not an aspect of linguistics.

Many, many linguists care about semantics. They do not, however, care
about whatever it is that you've mislabeled "semantics."

Then why did this group die?

Post by Peter T. Daniels

Post by peteolcott
sci.lang.semantics

[peteolcott]

Post by Peter T. Daniels

Post by peteolcott

'All of the theorems of a theory are true' is not the same as 'all of the truths expressible in the language of a theory are theorems of it'.

Try and provide a concrete example of an expression of language that is
true in the theory and not a theorem of this same theory.

No utterance in a language is a theorem (unless the utterance happens to
be a snippet of, for instance, a geometry textbook).

I broaden the scope of the word theorem [provable from axioms] to
also apply to natural language [provable from facts].

So the sentence: "A cat is not a dog" is a Theorem of English and
provable in English on the basis of the properties of dogs and cats.

https://www.researchgate.net/publication/323866366_The_Notion_of_Truth_in_Natural_and_Formal_Languages

[Helmut Richter]

Post by peteolcott
I broaden the scope of the word theorem [provable from axioms] to
also apply to natural language [provable from facts].
So the sentence: "A cat is not a dog" is a Theorem of English and
provable in English on the basis of the properties of dogs and cats.

The provability of the sentence depends only on the properties of cats and
dogs irrespective of the language in which these are expressed. It has to
do with zoology but not with the English – or any other – language.

Yes, there are natural-language sentences whose logic depend on language.
For instance „The dog bit the man and ran away“ may be ambiguous as to who
ran away, the dog or the man. In *such* cases, I accept the logic of the
sentence to be discussed here. But not simple translations of formal-logic
sentences to natural language. They are true or false irrespective of the
language in which they are expressed.

[peteolcott]

Post by Helmut Richter

Post by peteolcott
I broaden the scope of the word theorem [provable from axioms] to
also apply to natural language [provable from facts].
So the sentence: "A cat is not a dog" is a Theorem of English and
provable in English on the basis of the properties of dogs and cats.

The provability of the sentence depends only on the properties of cats and
dogs irrespective of the language in which these are expressed. It has to
do with zoology but not with the English – or any other – language.

If has to do with the way that the concepts connect together as
expressed in language.

Post by Helmut Richter
Yes, there are natural-language sentences whose logic depend on language.
For instance „The dog bit the man and ran away“ may be ambiguous as to who
ran away, the dog or the man. In *such* cases, I accept the logic of the
sentence to be discussed here. But not simple translations of formal-logic
sentences to natural language. They are true or false irrespective of the
language in which they are expressed.

Higher order logic (HOL) with types (AKA Minimal Type Theory) can be
the lingua franca connecting differing expressions of natural language
to their common semantic meaning.

[peteolcott]

Post by peteolcott

Post by Helmut Richter

Post by peteolcott
I broaden the scope of the word theorem [provable from axioms] to
also apply to natural language [provable from facts].
So the sentence: "A cat is not a dog" is a Theorem of English and
provable in English on the basis of the properties of dogs and cats.

The provability of the sentence depends only on the properties of cats and
dogs irrespective of the language in which these are expressed. It has to
do with zoology but not with the English – or any other – language.

If has to do with the way that the concepts connect together as
expressed in language.

Formal languages have little to do with natural languages. Do you understand the difference between “formal” and “natural”? I doubt it.

I wrote this paper linking the commonality between natural and formal languages.
https://www.researchgate.net/publication/323866366_The_Notion_of_Truth_in_Natural_and_Formal_Languages

Post by peteolcott

Post by Helmut Richter
Yes, there are natural-language sentences whose logic depend on language.
For instance „The dog bit the man and ran away“ may be ambiguous as to who
ran away, the dog or the man. In *such* cases, I accept the logic of the
sentence to be discussed here. But not simple translations of formal-logic
sentences to natural language. They are true or false irrespective of the
language in which they are expressed.

Higher order logic (HOL) with types (AKA Minimal Type Theory) can be
the lingua franca connecting differing expressions of natural language
to their common semantic meaning.

Doubt that too. So, prove it. If you what “prove” actually means, which also I doubt.

My paper explains the gist of the commonality of the notion of Truth between
formal and natural languages.

Post by peteolcott
--
Copyright 2019 Pete Olcott All rights reserved
"Great spirits have always encountered violent
opposition from mediocre minds." Albert Einstein

Your “copyright” just makes you an asshole, you know.
ZG

[Peter Percival]

Post by peteolcott
[...]
I broaden the scope of the word theorem [provable from axioms] to
also apply to natural language [provable from facts].

When logicians show that there are theories T and sentences phi in the
language of T such that neither phi nor ~phi is a theorem of T they are
not using 'theorem' in that way. Do you really think that a truth
becomes a falsehood when people mangle the meanings of words?

[Peter Percival]

Post by peteolcott

Post by Peter Percival

Post by peteolcott
https://en.wikipedia.org/wiki/Theory_(mathematical_logic)
This article has said this since 2010, I checked the history page.
Theory_(mathematical_logic)
initial statements are often called the primitive elements or elementary
statements of the theory, to distinguish them from other statements which
may be derived from them.
A theory T is a conceptual class consisting of certain of these elementary
statements. The elementary statements which belong to T are called the
elementary theorems of T and said to be true. In this way, a theory is a
way of designating a subset of E which consists entirely of true statements.
Thus not only agreeing with Axiom(Olcott) that some expressions of the
formal language of the formal system have been defined to have the semantic
value of True, but also anchoring the semantics of the formal system directly
within its syntax.

'All of the theorems of a theory are true' is not the same as 'all of
the truths expressible in the language of a theory are theorems of it'.

Try and provide a concrete example of an expression of language that is
true in the theory

What do you mean by a sentence being true in a theory? Sentences are
true (or not) in models.

Post by peteolcott
and not a theorem of this same theory.

[peteolcott]

Post by peteolcott

Post by peteolcott
https://en.wikipedia.org/wiki/Theory_(mathematical_logic)
This article has said this since 2010, I checked the history page.
Theory_(mathematical_logic)
initial statements are often called the primitive elements or elementary
statements of the theory, to distinguish them from other statements which
may be derived from them.
A theory T is a conceptual class consisting of certain of these elementary
statements. The elementary statements which belong to T are called the
elementary theorems of T and said to be true. In this way, a theory is a
way of designating a subset of E which consists entirely of true statements.
Thus not only agreeing with Axiom(Olcott) that some expressions of the
formal language of the formal system have been defined to have the semantic
value of True, but also anchoring the semantics of the formal system directly
within its syntax.

'All of the theorems of a theory are true' is not the same as 'all of the truths expressible in the language of a theory are theorems of it'.

Try and provide a concrete example of an expression of language that is
true in the theory

What do you mean by a sentence being true in a theory?  Sentences are true (or not) in models.

Post by peteolcott

Post by peteolcott
The elementary statements which belong to T are called the
elementary theorems of T and said to be true. In this way, a theory is a
way of designating a subset of E which consists entirely of true statements.

Haskell Curry, Foundations of Mathematical Logic, 2010.

Post by peteolcott
and not a theorem of this same theory.

[Peter Percival]

Post by peteolcott

Post by peteolcott

Post by Peter Percival

Post by peteolcott
https://en.wikipedia.org/wiki/Theory_(mathematical_logic)
This article has said this since 2010, I checked the history page.
Theory_(mathematical_logic)
initial statements are often called the primitive elements or elementary
statements of the theory, to distinguish them from other statements which
may be derived from them.
A theory T is a conceptual class consisting of certain of these elementary
statements. The elementary statements which belong to T are called the
elementary theorems of T and said to be true. In this way, a theory is a
way of designating a subset of E which consists entirely of true statements.
Thus not only agreeing with Axiom(Olcott) that some expressions of the
formal language of the formal system have been defined to have the semantic
value of True, but also anchoring the semantics of the formal system directly
within its syntax.

'All of the theorems of a theory are true' is not the same as 'all
of the truths expressible in the language of a theory are theorems
of it'.

Try and provide a concrete example of an expression of language that is
true in the theory

What do you mean by a sentence being true in a theory?  Sentences are
true (or not) in models.

Post by peteolcott

Post by Peter Percival

Post by peteolcott
The elementary statements which belong to T are called the
elementary theorems of T and said to be true. In this way, a

'All of the theorems of a theory are true' is not the same as 'all of
the truths expressible in the language of a theory are theorems of it'.

You seem not tom understand the difference between 'X is a subset of Y'
and 'Y is a subset of X'.

Post by peteolcott
theory is a

Post by peteolcott

Post by Peter Percival

Post by peteolcott
way of designating a subset of E which consists entirely of true

statements.
 Haskell Curry, Foundations of Mathematical Logic, 2010.

Post by peteolcott
and not a theorem of this same theory.

[Franz Gnaedinger]

Post by peteolcott
https://en.wikipedia.org/wiki/Theory_(mathematical_logic)
This article has said this since 2010, I checked the history page.

Now you must find a Wikipedia page that says you can dismiss proven theorems
of mathematics and mathematical logic.


(Allgod, mathematical and natural logic, liar paradox, conclusion)

Meanwhile Peter Olcott officially announced that he is God. Being God,
and the only one, he can dismiss the proven theorems of Goedel and Turing
and suffocate sci.logic and sci.lang and other fora by starting ever more
parallel threads.

I see the main problem in academe that has no clear idea of logic, or rather
a one-sided one, regarding mathematical logic as logic per se. Mathematical
logic is the logic of building and maintaining based on the formula a = a
while there is a wider logic formulated by Goethe: All is equal, all unequal ...,
known to artists of all times.

Goedel is very hard to understand for laymen when you consider mathematical
logic the only real logic, but most easy when you have a look at both sides.
Goedel proved that mathematics can't really and completely be separated from
general logic and the principle of equal unequal, it can only be secured
from case to case, for example divisions by zero are forbidden. Why? these
divisions yield infinite, which is equal unequal in itself. If you restrict logic
to mathematical logic you encounter paradoxa, which are quite natural
in the real world.

The problem is academe. Universities are not really universal. Allgod tries
to solve the problem by cramming the realm of wider logic (that includes
for example language) into mathematical logic, hoping he will thus regain
totality and completeness - absolute and complete and total being his
mantra words - and does it for the price of his career and sanity.

If only he would stop cross-posting to sci.lang! (he promised to do so,
but he doesn't stand by his word).

The logic of equal unequal blossoms in language. Allgod can't have that,
He tries to force language into the logic of a = a with his "mathematics
of the meaning of words" that led him nowhere. He deprives language
of life in the name of mathematical logic, and mathematical logic
of its power by dismissing proven theorems.

I feel entitled to defend sci.lang from those who suffocate it with ever
more parallel threads.

(on the liar paradox)

A Cretan says all Cretans are liars. He is right. Psychologists found that
we are lying many times a day, and in different ways. We humans are liars,
Cretans are humans, ergo they are liars. QED. The famous liar paradox arises
when the natural logic of equal unequal is reduced to the mathematical logic
of a = a. A liar is a liar, alaways lying, only ever lying. But such a person
does not exist in the real world, on the contrary, a professional liar cares
to tell the truth as often as ever possible in order to gain the confidence
of a potential victim.

(conclusion, rigid denial vs Goedel's rigor)

Allgod tries to reduce natural logic to mathematical logic, however,
he can't escape the equal unequal, it haunts him in the form of
proven = proven = not proven. He replaces Goedel's rigor with
his naive but rigid denial. Every advice to come down from his trip
and write a modest but useful program that may then be extended
was in vain. He is a satellite that flies too low, destined to burn out
in the atmosphere. All warning failed.