Discussion:
The Notion of Truth in Natural and Formal Languages
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peteolcott
2018-10-15 16:54:21 UTC
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The purpose of this paper is to complete the RHS of Tarski's famous formula: ∀x True(x) ↔ φ(x)
For any natural (human) or formal (mathematical) language L we know that an expression X of
language L is true if and only if there are expressions Γ of language L that connect X to known
facts. By extending the notion of a Well Formed Formula to include syntactically formalized rules
for rejecting semantically incorrect expressions we recognize and reject expressions that evaluate to
neither True nor False.

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

The Notion of Truth in Natural and Formal Languages
https://philpapers.org/archive/OLCTNO.pdf
Copyright 2016, 2017 2018 (and other years since 1997) Pete Olcott
Peter Percival
2018-10-15 17:22:43 UTC
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Permalink
Post by peteolcott
The purpose of this paper is to complete the RHS of Tarski's famous
formula: ∀x True(x) ↔ φ(x)
For any natural (human) or formal (mathematical) language L we know that an expression X of
language L is true if and only if there are expressions Γ of language L
that connect X to known
facts. By extending the notion of a Well Formed Formula to include
syntactically formalized rules
for rejecting semantically incorrect expressions we recognize and reject
expressions that evaluate to
neither True nor False.
https://www.researchgate.net/publication/323866366_The_Notion_of_Truth_in_Natural_and_Formal_Languages
The Notion of Truth in Natural and Formal Languages
https://philpapers.org/archive/OLCTNO.pdf
Copyright 2016, 2017 2018 (and other years since 1997) Pete Olcott
There is nothing there that you haven't posted to sci.logic before. You
have not taken into account the criticisms you got in sci.logic.
Peter Percival
2018-10-15 17:46:35 UTC
Reply
Permalink
Post by peteolcott
The purpose of this paper is to complete the RHS of Tarski's famous
formula: ∀x True(x) ↔ φ(x)
For any natural (human) or formal (mathematical) language L we know
that an expression X of
language L is true if and only if there are expressions Γ of language
L that connect X to known
facts. By extending the notion of a Well Formed Formula to include
syntactically formalized rules
for rejecting semantically incorrect expressions we recognize and
reject expressions that evaluate to
neither True nor False.
https://www.researchgate.net/publication/323866366_The_Notion_of_Truth_in_Natural_and_Formal_Languages
The Notion of Truth in Natural and Formal Languages
https://philpapers.org/archive/OLCTNO.pdf
Copyright 2016, 2017 2018 (and other years since 1997) Pete Olcott
There is nothing there that you haven't posted to sci.logic before.  You
have not taken into account the criticisms you got in sci.logic.
You say that you require Mendelson premises to be axioms. That shows
that you have not understood the passage from Mendelson even though you
have quoted it forty two million times. (It may be that you mean that
you require the set of premises to be empty, but who cares?)
peteolcott
2018-10-16 15:58:01 UTC
Reply
Permalink
Post by peteolcott
The purpose of this paper is to complete the RHS of Tarski's famous formula: ∀x True(x) ↔ φ(x)
For any natural (human) or formal (mathematical) language L we know that an expression X of
language L is true if and only if there are expressions Γ of language L that connect X to known
facts. By extending the notion of a Well Formed Formula to include syntactically formalized rules
for rejecting semantically incorrect expressions we recognize and reject expressions that evaluate to
neither True nor False.
https://www.researchgate.net/publication/323866366_The_Notion_of_Truth_in_Natural_and_Formal_Languages
The Notion of Truth in Natural and Formal Languages
https://philpapers.org/archive/OLCTNO.pdf
Copyright 2016, 2017 2018 (and other years since 1997) Pete Olcott
There is nothing there that you haven't posted to sci.logic before.  You have not taken into account the criticisms you got in sci.logic.
You say that you require Mendelson premises to be axioms.  That shows that you have not understood the passage from Mendelson even though you have quoted it forty two million times.  (It may be that you mean that you require the set of premises to be
empty, but who cares?)
I am taking Mendelson's specification, adding a new feature and from this
creating a new idea using Mendelson as the starting point of this new idea.

All new ideas are necessarily comprised entirely of new combinations of old ideas.

I have written two published patents. The requirement for a patent is a new
(and useful) combination of old ideas.

Provable(X, Y) merely shows that Y is logically entailed from Y
Provable(X, Y) and True(X) proves True(Y)

Copyright 2016, 2017, 2018 Pete Olcott
Peter Percival
2018-10-16 16:20:58 UTC
Reply
Permalink
Post by peteolcott
Post by Peter Percival
Post by peteolcott
The purpose of this paper is to complete the RHS of Tarski's famous
formula: ∀x True(x) ↔ φ(x)
For any natural (human) or formal (mathematical) language L we know
that an expression X of
language L is true if and only if there are expressions Γ of
language L that connect X to known
facts. By extending the notion of a Well Formed Formula to include
syntactically formalized rules
for rejecting semantically incorrect expressions we recognize and
reject expressions that evaluate to
neither True nor False.
https://www.researchgate.net/publication/323866366_The_Notion_of_Truth_in_Natural_and_Formal_Languages
The Notion of Truth in Natural and Formal Languages
https://philpapers.org/archive/OLCTNO.pdf
Copyright 2016, 2017 2018 (and other years since 1997) Pete Olcott
There is nothing there that you haven't posted to sci.logic before.
You have not taken into account the criticisms you got in sci.logic.
You say that you require Mendelson premises to be axioms.  That shows
that you have not understood the passage from Mendelson even though
you have quoted it forty two million times.  (It may be that you mean
that you require the set of premises to be empty, but who cares?)
I am taking Mendelson's specification, adding a new feature and from this
Had you understood Mendelson. you'd know that your "new feature" is no
such thing.
Post by peteolcott
creating a new idea using Mendelson as the starting point of this new idea.
All new ideas are necessarily comprised entirely of new combinations of old ideas.
I have written two published patents. The requirement for a patent is a new
(and useful) combination of old ideas.
Provable(X, Y) merely shows that Y is logically entailed from Y
Provable(X, Y) and True(X) proves True(Y)
Copyright 2016, 2017, 2018 Pete Olcott
peteolcott
2018-10-17 14:46:34 UTC
Reply
Permalink
Post by peteolcott
Post by peteolcott
The purpose of this paper is to complete the RHS of Tarski's famous formula: ∀x True(x) ↔ φ(x)
For any natural (human) or formal (mathematical) language L we know that an expression X of
language L is true if and only if there are expressions Γ of language L that connect X to known
facts. By extending the notion of a Well Formed Formula to include syntactically formalized rules
for rejecting semantically incorrect expressions we recognize and reject expressions that evaluate to
neither True nor False.
https://www.researchgate.net/publication/323866366_The_Notion_of_Truth_in_Natural_and_Formal_Languages
The Notion of Truth in Natural and Formal Languages
https://philpapers.org/archive/OLCTNO.pdf
Copyright 2016, 2017 2018 (and other years since 1997) Pete Olcott
There is nothing there that you haven't posted to sci.logic before. You have not taken into account the criticisms you got in sci.logic.
You say that you require Mendelson premises to be axioms.  That shows that you have not understood the passage from Mendelson even though you have quoted it forty two million times.  (It may be that you mean that you require the set of premises to be
empty, but who cares?)
I am taking Mendelson's specification, adding a new feature and from this
Had you understood Mendelson. you'd know that your "new feature" is no such thing.
So there is no such thing as the hypothesis that premises are axioms?
Wait a minute that was a hypothesis that premises are axioms, therefore
unequivocally proving that there is such a thing.
Post by peteolcott
creating a new idea using Mendelson as the starting point of this new idea.
All new ideas are necessarily comprised entirely of new combinations of old ideas.
I have written two published patents. The requirement for a patent is a new
(and useful) combination of old ideas.
Provable(X, Y) merely shows that Y is logically entailed from Y
Provable(X, Y) and True(X) proves True(Y)
Copyright 2016, 2017, 2018 Pete Olcott
Peter Percival
2018-10-17 15:23:32 UTC
Reply
Permalink
Post by peteolcott
Post by peteolcott
Post by Peter Percival
Post by peteolcott
The purpose of this paper is to complete the RHS of Tarski's
famous formula: ∀x True(x) ↔ φ(x)
For any natural (human) or formal (mathematical) language L we
know that an expression X of
language L is true if and only if there are expressions Γ of
language L that connect X to known
facts. By extending the notion of a Well Formed Formula to include
syntactically formalized rules
for rejecting semantically incorrect expressions we recognize and
reject expressions that evaluate to
neither True nor False.
https://www.researchgate.net/publication/323866366_The_Notion_of_Truth_in_Natural_and_Formal_Languages
The Notion of Truth in Natural and Formal Languages
https://philpapers.org/archive/OLCTNO.pdf
Copyright 2016, 2017 2018 (and other years since 1997) Pete Olcott
There is nothing there that you haven't posted to sci.logic before.
You have not taken into account the criticisms you got in sci.logic.
You say that you require Mendelson premises to be axioms.  That
shows that you have not understood the passage from Mendelson even
though you have quoted it forty two million times.  (It may be that
you mean that you require the set of premises to be empty, but who
cares?)
I am taking Mendelson's specification, adding a new feature and from this
Had you understood Mendelson. you'd know that your "new feature" is no such thing.
So there is no such thing as the hypothesis that premises are axioms?
Wait a minute that was a hypothesis that premises are axioms, therefore
unequivocally proving that there is such a thing.
Read Mendelson. You quote it often enough, so why not read it?
According to Mendelson, a wff C is a consequence of a set of premises
Gamma if there is a sequence of wff B_1,..., B_k such that B_k is C and
each wff in the sequence B_1,..., B_k is either
a) an axiom, or
b) a member of Gamma, or
c) deduced from earlier wff in the sequence by a rule of inference.
What do you gain by requiring premises to be axioms? The axioms are
already there, so you are saying that you want no premises, i.e. that
Gamma be empty.

You really are unutterably vile, aren't you?
Post by peteolcott
Post by peteolcott
creating a new idea using Mendelson as the starting point of this new idea.
All new ideas are necessarily comprised entirely of new combinations of old ideas.
I have written two published patents. The requirement for a patent is a new
(and useful) combination of old ideas.
Provable(X, Y) merely shows that Y is logically entailed from Y
Provable(X, Y) and True(X) proves True(Y)
Copyright 2016, 2017, 2018 Pete Olcott
peteolcott
2018-10-18 05:16:46 UTC
Reply
Permalink
Post by peteolcott
Post by peteolcott
Post by peteolcott
The purpose of this paper is to complete the RHS of Tarski's famous formula: ∀x True(x) ↔ φ(x)
For any natural (human) or formal (mathematical) language L we know that an expression X of
language L is true if and only if there are expressions Γ of language L that connect X to known
facts. By extending the notion of a Well Formed Formula to include syntactically formalized rules
for rejecting semantically incorrect expressions we recognize and reject expressions that evaluate to
neither True nor False.
https://www.researchgate.net/publication/323866366_The_Notion_of_Truth_in_Natural_and_Formal_Languages
The Notion of Truth in Natural and Formal Languages
https://philpapers.org/archive/OLCTNO.pdf
Copyright 2016, 2017 2018 (and other years since 1997) Pete Olcott
There is nothing there that you haven't posted to sci.logic before. You have not taken into account the criticisms you got in sci.logic.
You say that you require Mendelson premises to be axioms.  That shows that you have not understood the passage from Mendelson even though you have quoted it forty two million times.  (It may be that you mean that you require the set of premises to be
empty, but who cares?)
I am taking Mendelson's specification, adding a new feature and from this
Had you understood Mendelson. you'd know that your "new feature" is no such thing.
So there is no such thing as the hypothesis that premises are axioms?
Wait a minute that was a hypothesis that premises are axioms, therefore
unequivocally proving that there is such a thing.
Read Mendelson.  You quote it often enough, so why not read it? According to Mendelson, a wff C is a consequence of a set of premises Gamma if there is a sequence of wff B_1,..., B_k such that B_k is C and each wff in the sequence B_1,..., B_k is either
a) an axiom, or
b) a member of Gamma, or
c) deduced from earlier wff in the sequence by a rule of inference.
What do you gain by requiring premises to be axioms?
I already said the answer to that question on the sub-title of my paper:
The purpose of this paper is to complete the RHS of Tarski's famous formula: ∀x True(x) ↔ φ(x)

When the RHS of the above formula is defined this refutes Tarski Undefinabity
because it defines what was "proven" to be undefinable.

The mistake made in Tarski Undefinability, the Liar Paradox, and the simplification
of the 1931 GIT is that all three of these conflated the assertion of an expression
of language with the satisfaction of an expression of language into a single Boolean
value when these are actually to distinct properties of expressions of language.

This sentence is not true.
(a) Assertion: ~True
(b) Satisfaction: Empty

bool LiarParadox = ~LiarParadox; // in C++

What time is it?
(1) Assertion: Empty
(2) Satisfaction: Empty

Five is greater than three:
(a) Assertion: True
(b) Satisfaction: True

This is a somewhat earlier version of these same ideas:
https://www.researchgate.net/publication/307442489_Formalizing_the_logical_self-reference_error_of_the_Liar_Paradox

Copyright 2016, 2017, 20187 Pete Olcott
The axioms are already there, so you are saying that you want no premises, i.e. that Gamma be empty.
That would be a much simpler way to say it.
peteolcott
2018-10-19 16:51:43 UTC
Reply
Permalink
Post by peteolcott
Post by peteolcott
Post by peteolcott
The purpose of this paper is to complete the RHS of Tarski's famous formula: ∀x True(x) ↔ φ(x)
For any natural (human) or formal (mathematical) language L we know that an expression X of
language L is true if and only if there are expressions Γ of language L that connect X to known
facts. By extending the notion of a Well Formed Formula to include syntactically formalized rules
for rejecting semantically incorrect expressions we recognize and reject expressions that evaluate to
neither True nor False.
https://www.researchgate.net/publication/323866366_The_Notion_of_Truth_in_Natural_and_Formal_Languages
The Notion of Truth in Natural and Formal Languages
https://philpapers.org/archive/OLCTNO.pdf
Copyright 2016, 2017 2018 (and other years since 1997) Pete Olcott
There is nothing there that you haven't posted to sci.logic before. You have not taken into account the criticisms you got in sci.logic.
You say that you require Mendelson premises to be axioms.  That shows that you have not understood the passage from Mendelson even though you have quoted it forty two million times.  (It may be that you mean that you require the set of premises to be
empty, but who cares?)
I am taking Mendelson's specification, adding a new feature and from this
Had you understood Mendelson. you'd know that your "new feature" is no such thing.
So there is no such thing as the hypothesis that premises are axioms?
Wait a minute that was a hypothesis that premises are axioms, therefore
unequivocally proving that there is such a thing.
Read Mendelson.  You quote it often enough, so why not read it? According to Mendelson, a wff C is a consequence of a set of premises Gamma if there is a sequence of wff B_1,..., B_k such that B_k is C and each wff in the sequence B_1,..., B_k is either
a) an axiom, or
b) a member of Gamma, or
c) deduced from earlier wff in the sequence by a rule of inference.
What do you gain by requiring premises to be axioms?  The axioms are already there, so you are saying that you want no premises, i.e. that Gamma be empty.
If Γ is the empty set ∅, then ∅ ⊢ C if and only if C is a theorem. It is customary
to omit the sign “∅” and simply write ⊢ C. Thus, ⊢ C is another way of asserting that
C is a theorem.

Because of the above breakdown Mendelson would encode sound deductive interfere
as ⊢ C. Because this is sound deductive inference that has no possibly false
premises and only has axioms in their place ⊢ C means True(C).

My formula for True(X)
∀L ∈ Formal_Systems True(L, C) ↔ ∃Γ ⊆ Axioms(L) (Γ ⊢ C)

Would be encoded in Mendelson as
∀L ∈ Formal_Systems True(L, C) ↔ ⊢L CL // The last two L are subscripts

This completes the RHS of Tarski's famous formula: ∀x True(x) ↔ φ(x)
and thus refutes Tarski Undefinability because it defines what Tarski "proved":
could not be defined.

My paper shows exactly how the mistake of {true but not provable} was made.

Expressions of language are only true when their assertion is satisfied.
Expressions of language are only false when the negation of their assertion is satisfied.

Some expressions of language make assertions that cannot be satisfied. This was
previously understood as a fundamental limitation of logic.

This mistake was made because no one ever broke propositions down to the granularity
of their (a) Assertion (b) Satisfaction of Assertion. These two distinct semantic
properties were always conflated together as Satisfiability.

That an expression of language could not be satisfied was previously understood
as a fundamental limitation of logic, and not merely an erroneous expression of language.

When an expression of language makes an assertion that cannot be satisfied
and the negation of this assertion also cannot be satisfied then this expression
of language does not meet the requirement of a logical proposition because all
logical propositions must evaluated to exactly one of {True, False}.

Copyright 2016, 2017, 2018 Pete Olcott
peteolcott
2018-10-19 16:58:43 UTC
Reply
Permalink
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
</head>
<body text="#000000" bgcolor="#FFFFFF">
<div class="moz-cite-prefix">On 10/19/2018 11:51 AM, peteolcott
wrote:<br>
</div>
<blockquote type="cite"
cite="mid:moadndO8qckEllfGnZ2dnUU7-***@giganews.com">On
10/17/2018 10:23 AM, Peter Percival wrote:
<br>
<blockquote type="cite">peteolcott wrote:
<br>
<blockquote type="cite">On 10/16/2018 11:20 AM, Peter Percival
wrote:
<br>
<blockquote type="cite">peteolcott wrote:
<br>
<blockquote type="cite">On 10/15/2018 12:46 PM, Peter
Percival wrote:
<br>
<blockquote type="cite">Peter Percival wrote:
<br>
<blockquote type="cite">peteolcott wrote:
<br>
<blockquote type="cite">The purpose of this paper is
to complete the RHS of Tarski's famous formula: ∀x
True(x) ↔ φ(x)
<br>
For any natural (human) or formal (mathematical)
language L we know that an expression X of
<br>
language L is true if and only if there are
expressions Γ of language L that connect X to known
<br>
facts. By extending the notion of a Well Formed
Formula to include syntactically formalized rules
<br>
for rejecting semantically incorrect expressions we
recognize and reject expressions that evaluate to
<br>
neither True nor False.
<br>
<br>
<a class="moz-txt-link-freetext" href="https://www.researchgate.net/publication/323866366_The_Notion_of_Truth_in_Natural_and_Formal_Languages">https://www.researchgate.net/publication/323866366_The_Notion_of_Truth_in_Natural_and_Formal_Languages</a>
<br>
<br>
The Notion of Truth in Natural and Formal Languages
<br>
<a class="moz-txt-link-freetext" href="https://philpapers.org/archive/OLCTNO.pdf">https://philpapers.org/archive/OLCTNO.pdf</a>
<br>
Copyright 2016, 2017 2018 (and other years since
1997) Pete Olcott
<br>
</blockquote>
<br>
There is nothing there that you haven't posted to
sci.logic before. You have not taken into account the
criticisms you got in sci.logic.
<br>
<br>
<br>
</blockquote>
<br>
You say that you require Mendelson premises to be
axioms.  That shows that you have not understood the
passage from Mendelson even though you have quoted it
forty two million times.  (It may be that you mean that
you require the set of premises to be empty, but who
cares?)
<br>
<br>
</blockquote>
<br>
I am taking Mendelson's specification, adding a new
feature and from this
<br>
</blockquote>
<br>
Had you understood Mendelson. you'd know that your "new
feature" is no such thing.
<br>
</blockquote>
<br>
So there is no such thing as the hypothesis that premises are
axioms?
<br>
Wait a minute that was a hypothesis that premises are axioms,
therefore
<br>
unequivocally proving that there is such a thing.
<br>
</blockquote>
<br>
Read Mendelson.  You quote it often enough, so why not read it?
According to Mendelson, a wff C is a consequence of a set of
premises Gamma if there is a sequence of wff B_1,..., B_k such
that B_k is C and each wff in the sequence B_1,..., B_k is
either
<br>
a) an axiom, or
<br>
b) a member of Gamma, or
<br>
c) deduced from earlier wff in the sequence by a rule of
inference.
<br>
What do you gain by requiring premises to be axioms?  The axioms
are already there, so you are saying that you want no premises,
i.e. that Gamma be empty.
<br>
<br>
</blockquote>
    If Γ is the empty set ∅, then ∅ ⊢ C if and only if C is a
theorem. It is customary
<br>
    to omit the sign “∅” and simply write ⊢ C. Thus, ⊢ C is
another way of asserting that
<br>
    C is a theorem.
<br>
<br>
Because of the above breakdown Mendelson would encode sound
deductive interfere
<br>
as ⊢ C. Because this is sound deductive inference that has no
possibly false
<br>
premises and only has axioms in their place ⊢ C means True(C).
<br>
<br>
My formula for True(X)
<br>
∀L ∈ Formal_Systems True(L, C) ↔ ∃Γ ⊆ Axioms(L) (Γ ⊢ C)
<br>
<br>
Would be encoded in Mendelson as
<br>
∀L ∈ Formal_Systems True(L, C) ↔ ⊢L CL  // The last two L are
subscripts
<br>
</blockquote>
<br>
<font face="Segoe UI Symbol, sans-serif"><font style="font-size:
15pt" size="4"><b>Encoded in Mendelson as: <br>
∀L
∈ Formal_Systems <span style="background: #ffff00">True(L, C)

⊢</span><sub><font size="2"><span style="background:
#ffff00">L</span></font></sub><span style="background:
#ffff00">
C</span><sub><font size="2"><span style="background:
#ffff00">L</span></font></sub></b></font></font><br>
<br>
<blockquote type="cite"
cite="mid:moadndO8qckEllfGnZ2dnUU7-***@giganews.com">This
completes the RHS of Tarski's famous formula: ∀x True(x) ↔ φ(x)
<br>
and thus refutes Tarski Undefinability because it defines what
Tarski "proved":
<br>
could not be defined.
<br>
<br>
My paper shows exactly how the mistake of {true but not provable}
was made.
<br>
<br>
Expressions of language are only true when their assertion is
satisfied.
<br>
Expressions of language are only false when the negation of their
assertion is satisfied.
<br>
<br>
Some expressions of language make assertions that cannot be
satisfied. This was
<br>
previously understood as a fundamental limitation of logic.
<br>
<br>
This mistake was made because no one ever broke propositions down
to the granularity
<br>
of their (a) Assertion (b) Satisfaction of Assertion. These two
distinct semantic
<br>
properties were always conflated together as Satisfiability.
<br>
<br>
That an expression of language could not be satisfied was
previously understood
<br>
as a fundamental limitation of logic, and not merely an erroneous
expression of language.
<br>
<br>
When an expression of language makes an assertion that cannot be
satisfied
<br>
and the negation of this assertion also cannot be satisfied then
this expression
<br>
of language does not meet the requirement of a logical proposition
because all
<br>
logical propositions must evaluated to exactly one of {True,
False}.
<br>
<br>
Copyright 2016, 2017, 2018 Pete Olcott
<br>
</blockquote>
<p><br>
</p>
</body>
</html>
Peter Percival
2018-10-19 17:01:55 UTC
Reply
Permalink
Post by peteolcott
Post by peteolcott
Post by Peter Percival
Post by peteolcott
The purpose of this paper is to complete the RHS of Tarski's
famous formula: ∀x True(x) ↔ φ(x)
For any natural (human) or formal (mathematical) language L we
know that an expression X of
language L is true if and only if there are expressions Γ of
language L that connect X to known
facts. By extending the notion of a Well Formed Formula to
include syntactically formalized rules
for rejecting semantically incorrect expressions we recognize
and reject expressions that evaluate to
neither True nor False.
https://www.researchgate.net/publication/323866366_The_Notion_of_Truth_in_Natural_and_Formal_Languages
The Notion of Truth in Natural and Formal Languages
https://philpapers.org/archive/OLCTNO.pdf
Copyright 2016, 2017 2018 (and other years since 1997) Pete Olcott
There is nothing there that you haven't posted to sci.logic
before. You have not taken into account the criticisms you got in
sci.logic.
You say that you require Mendelson premises to be axioms.  That
shows that you have not understood the passage from Mendelson even
though you have quoted it forty two million times.  (It may be
that you mean that you require the set of premises to be empty,
but who cares?)
I am taking Mendelson's specification, adding a new feature and from this
Had you understood Mendelson. you'd know that your "new feature" is no such thing.
So there is no such thing as the hypothesis that premises are axioms?
Wait a minute that was a hypothesis that premises are axioms, therefore
unequivocally proving that there is such a thing.
Read Mendelson.  You quote it often enough, so why not read it?
According to Mendelson, a wff C is a consequence of a set of premises
Gamma if there is a sequence of wff B_1,..., B_k such that B_k is C
and each wff in the sequence B_1,..., B_k is either
a) an axiom, or
b) a member of Gamma, or
c) deduced from earlier wff in the sequence by a rule of inference.
What do you gain by requiring premises to be axioms?  The axioms are
already there, so you are saying that you want no premises, i.e. that
Gamma be empty.
    If Γ is the empty set ∅, then ∅ ⊢ C if and only if C is a theorem.
It is customary
    to omit the sign “∅” and simply write ⊢ C. Thus, ⊢ C is another way
of asserting that
    C is a theorem.
Because of the above breakdown Mendelson would encode sound deductive interfere
as ⊢ C. Because this is sound deductive inference that has no possibly false
premises and only has axioms in their place ⊢ C means True(C).
No, ⊢ C means that C is provable (in some theory T or other, which one
possibly being identified by a subscript on ⊢). Sometimes provable and
true coincide, sometimes they don't. It depends on T and has to be
demonstrated in each case. All you ever do is make dogmatic
pronouncements. Nor does ⊢ C necessarily signal a sound inference. T
may be inconsistent. Again, demonstration, not dogmatic assertion, is
needed.
peteolcott
2018-10-19 17:19:22 UTC
Reply
Permalink
Post by peteolcott
Post by peteolcott
Post by peteolcott
The purpose of this paper is to complete the RHS of Tarski's famous formula: ∀x True(x) ↔ φ(x)
For any natural (human) or formal (mathematical) language L we know that an expression X of
language L is true if and only if there are expressions Γ of language L that connect X to known
facts. By extending the notion of a Well Formed Formula to include syntactically formalized rules
for rejecting semantically incorrect expressions we recognize and reject expressions that evaluate to
neither True nor False.
https://www.researchgate.net/publication/323866366_The_Notion_of_Truth_in_Natural_and_Formal_Languages
The Notion of Truth in Natural and Formal Languages
https://philpapers.org/archive/OLCTNO.pdf
Copyright 2016, 2017 2018 (and other years since 1997) Pete Olcott
There is nothing there that you haven't posted to sci.logic before. You have not taken into account the criticisms you got in sci.logic.
You say that you require Mendelson premises to be axioms.  That shows that you have not understood the passage from Mendelson even though you have quoted it forty two million times.  (It may be that you mean that you require the set of premises to
be empty, but who cares?)
I am taking Mendelson's specification, adding a new feature and from this
Had you understood Mendelson. you'd know that your "new feature" is no such thing.
So there is no such thing as the hypothesis that premises are axioms?
Wait a minute that was a hypothesis that premises are axioms, therefore
unequivocally proving that there is such a thing.
Read Mendelson.  You quote it often enough, so why not read it? According to Mendelson, a wff C is a consequence of a set of premises Gamma if there is a sequence of wff B_1,..., B_k such that B_k is C and each wff in the sequence B_1,..., B_k is either
a) an axiom, or
b) a member of Gamma, or
c) deduced from earlier wff in the sequence by a rule of inference.
What do you gain by requiring premises to be axioms?  The axioms are already there, so you are saying that you want no premises, i.e. that Gamma be empty.
     If Γ is the empty set ∅, then ∅ ⊢ C if and only if C is a theorem. It is customary
     to omit the sign “∅” and simply write ⊢ C. Thus, ⊢ C is another way of asserting that
     C is a theorem.
Because of the above breakdown Mendelson would encode sound deductive interfere
as ⊢ C. Because this is sound deductive inference that has no possibly false
premises and only has axioms in their place ⊢ C means True(C).
No, ⊢ C means that C is provable (in some theory T or other, which one possibly being identified by a subscript on ⊢).  Sometimes provable and true coincide, sometimes they don't.  It depends on T and has to be demonstrated in each case.  All you ever do
is make dogmatic pronouncements.  Nor does ⊢ C necessarily signal a sound inference.  T may be inconsistent.  Again, demonstration, not dogmatic assertion, is needed.
Validity and Soundness https://www.iep.utm.edu/val-snd/
A deductive argument is said to be valid if and only if it takes a form that makes it
impossible for the premises to be true and the conclusion nevertheless to be false.
Otherwise, a deductive argument is said to be invalid.

A deductive argument is sound if and only if it is both valid, and all of its premises
are actually true. Otherwise, a deductive argument is unsound.

When-so-ever a deductive argument is valid the Truth of the conclusion flows from the truth of the Premises.

When-so-ever a deductive argument is sound the Truth of the conclusion flows from the truth of the True Premises.

When-so-ever the premises are axioms the premises are True. I will stop here so that you don't get overwhelmed.

As soon as we get agreement on the above points we can proceed.

Copyright 2018 Pete Olcott
Peter Percival
2018-10-19 18:14:07 UTC
Reply
Permalink
Post by Peter Percival
Post by peteolcott
Post by Peter Percival
Post by peteolcott
Post by Peter Percival
Post by peteolcott
The purpose of this paper is to complete the RHS of Tarski's
famous formula: ∀x True(x) ↔ φ(x)
For any natural (human) or formal (mathematical) language L we
know that an expression X of
language L is true if and only if there are expressions Γ of
language L that connect X to known
facts. By extending the notion of a Well Formed Formula to
include syntactically formalized rules
for rejecting semantically incorrect expressions we recognize
and reject expressions that evaluate to
neither True nor False.
https://www.researchgate.net/publication/323866366_The_Notion_of_Truth_in_Natural_and_Formal_Languages
The Notion of Truth in Natural and Formal Languages
https://philpapers.org/archive/OLCTNO.pdf
Copyright 2016, 2017 2018 (and other years since 1997) Pete Olcott
There is nothing there that you haven't posted to sci.logic
before. You have not taken into account the criticisms you got
in sci.logic.
You say that you require Mendelson premises to be axioms.  That
shows that you have not understood the passage from Mendelson
even though you have quoted it forty two million times.  (It may
be that you mean that you require the set of premises to be
empty, but who cares?)
I am taking Mendelson's specification, adding a new feature and from this
Had you understood Mendelson. you'd know that your "new feature"
is no such thing.
So there is no such thing as the hypothesis that premises are axioms?
Wait a minute that was a hypothesis that premises are axioms, therefore
unequivocally proving that there is such a thing.
Read Mendelson.  You quote it often enough, so why not read it?
According to Mendelson, a wff C is a consequence of a set of
premises Gamma if there is a sequence of wff B_1,..., B_k such that
B_k is C and each wff in the sequence B_1,..., B_k is either
a) an axiom, or
b) a member of Gamma, or
c) deduced from earlier wff in the sequence by a rule of inference.
What do you gain by requiring premises to be axioms?  The axioms are
already there, so you are saying that you want no premises, i.e.
that Gamma be empty.
     If Γ is the empty set ∅, then ∅ ⊢ C if and only if C is a
theorem. It is customary
     to omit the sign “∅” and simply write ⊢ C. Thus, ⊢ C is another
way of asserting that
     C is a theorem.
Because of the above breakdown Mendelson would encode sound deductive interfere
as ⊢ C. Because this is sound deductive inference that has no possibly false
premises and only has axioms in their place ⊢ C means True(C).
No, ⊢ C means that C is provable (in some theory T or other, which one
possibly being identified by a subscript on ⊢).  Sometimes provable
and true coincide, sometimes they don't.  It depends on T and has to
be demonstrated in each case.  All you ever do is make dogmatic
pronouncements.  Nor does ⊢ C necessarily signal a sound inference.  T
may be inconsistent.  Again, demonstration, not dogmatic assertion, is
needed.
    Validity and Soundness https://www.iep.utm.edu/val-snd/
    A deductive argument is said to be valid if and only if it takes a
form that makes it
    impossible for the premises to be true and the conclusion
nevertheless to be false.
    Otherwise, a deductive argument is said to be invalid.
    A deductive argument is sound if and only if it is both valid, and
all of its premises
    are actually true. Otherwise, a deductive argument is unsound.
When-so-ever a deductive argument is valid
How do you test for validity?
the Truth of the conclusion
flows from the truth of the Premises.
When-so-ever a deductive argument is sound the Truth of the conclusion
flows from the truth of the True Premises.
When-so-ever the premises are axioms the premises are True. I will stop
here so that you don't get overwhelmed.
As soon as we get agreement on the above points we can proceed.
Copyright 2018 Pete Olcott
peteolcott
2018-10-19 18:18:17 UTC
Reply
Permalink
Post by Peter Percival
Post by peteolcott
Post by peteolcott
Post by peteolcott
The purpose of this paper is to complete the RHS of Tarski's famous formula: ∀x True(x) ↔ φ(x)
For any natural (human) or formal (mathematical) language L we know that an expression X of
language L is true if and only if there are expressions Γ of language L that connect X to known
facts. By extending the notion of a Well Formed Formula to include syntactically formalized rules
for rejecting semantically incorrect expressions we recognize and reject expressions that evaluate to
neither True nor False.
https://www.researchgate.net/publication/323866366_The_Notion_of_Truth_in_Natural_and_Formal_Languages
The Notion of Truth in Natural and Formal Languages
https://philpapers.org/archive/OLCTNO.pdf
Copyright 2016, 2017 2018 (and other years since 1997) Pete Olcott
There is nothing there that you haven't posted to sci.logic before. You have not taken into account the criticisms you got in sci.logic.
You say that you require Mendelson premises to be axioms.  That shows that you have not understood the passage from Mendelson even though you have quoted it forty two million times.  (It may be that you mean that you require the set of premises to
be empty, but who cares?)
I am taking Mendelson's specification, adding a new feature and from this
Had you understood Mendelson. you'd know that your "new feature" is no such thing.
So there is no such thing as the hypothesis that premises are axioms?
Wait a minute that was a hypothesis that premises are axioms, therefore
unequivocally proving that there is such a thing.
Read Mendelson.  You quote it often enough, so why not read it? According to Mendelson, a wff C is a consequence of a set of premises Gamma if there is a sequence of wff B_1,..., B_k such that B_k is C and each wff in the sequence B_1,..., B_k is either
a) an axiom, or
b) a member of Gamma, or
c) deduced from earlier wff in the sequence by a rule of inference.
What do you gain by requiring premises to be axioms?  The axioms are already there, so you are saying that you want no premises, i.e. that Gamma be empty.
     If Γ is the empty set ∅, then ∅ ⊢ C if and only if C is a theorem. It is customary
     to omit the sign “∅” and simply write ⊢ C. Thus, ⊢ C is another way of asserting that
     C is a theorem.
Because of the above breakdown Mendelson would encode sound deductive interfere
as ⊢ C. Because this is sound deductive inference that has no possibly false
premises and only has axioms in their place ⊢ C means True(C).
No, ⊢ C means that C is provable (in some theory T or other, which one possibly being identified by a subscript on ⊢).  Sometimes provable and true coincide, sometimes they don't.  It depends on T and has to be demonstrated in each case.  All you ever
do is make dogmatic pronouncements.  Nor does ⊢ C necessarily signal a sound inference.  T may be inconsistent.  Again, demonstration, not dogmatic assertion, is needed.
     Validity and Soundness https://www.iep.utm.edu/val-snd/
     A deductive argument is said to be valid if and only if it takes a form that makes it
     impossible for the premises to be true and the conclusion nevertheless to be false.
     Otherwise, a deductive argument is said to be invalid.
     A deductive argument is sound if and only if it is both valid, and all of its premises
     are actually true. Otherwise, a deductive argument is unsound.
When-so-ever a deductive argument is valid
How do you test for validity?
https://en.wikipedia.org/wiki/Logical_consequence#Syntactic_consequence
Post by Peter Percival
the Truth of the conclusion flows from the truth of the Premises.
When-so-ever a deductive argument is sound the Truth of the conclusion flows from the truth of the True Premises.
When-so-ever the premises are axioms the premises are True. I will stop here so that you don't get overwhelmed.
As soon as we get agreement on the above points we can proceed.
Copyright 2018 Pete Olcott
Peter Percival
2018-10-19 18:36:04 UTC
Reply
Permalink
Post by peteolcott
Post by Peter Percival
Post by Peter Percival
Post by peteolcott
Post by Peter Percival
Post by peteolcott
Post by Peter Percival
Post by Peter Percival
Post by peteolcott
The purpose of this paper is to complete the RHS of Tarski's
famous formula: ∀x True(x) ↔ φ(x)
For any natural (human) or formal (mathematical) language L
we know that an expression X of
language L is true if and only if there are expressions Γ of
language L that connect X to known
facts. By extending the notion of a Well Formed Formula to
include syntactically formalized rules
for rejecting semantically incorrect expressions we
recognize and reject expressions that evaluate to
neither True nor False.
https://www.researchgate.net/publication/323866366_The_Notion_of_Truth_in_Natural_and_Formal_Languages
The Notion of Truth in Natural and Formal Languages
https://philpapers.org/archive/OLCTNO.pdf
Copyright 2016, 2017 2018 (and other years since 1997) Pete Olcott
There is nothing there that you haven't posted to sci.logic
before. You have not taken into account the criticisms you
got in sci.logic.
You say that you require Mendelson premises to be axioms.
That shows that you have not understood the passage from
Mendelson even though you have quoted it forty two million
times.  (It may be that you mean that you require the set of
premises to be empty, but who cares?)
I am taking Mendelson's specification, adding a new feature and from this
Had you understood Mendelson. you'd know that your "new feature"
is no such thing.
So there is no such thing as the hypothesis that premises are axioms?
Wait a minute that was a hypothesis that premises are axioms, therefore
unequivocally proving that there is such a thing.
Read Mendelson.  You quote it often enough, so why not read it?
According to Mendelson, a wff C is a consequence of a set of
premises Gamma if there is a sequence of wff B_1,..., B_k such
that B_k is C and each wff in the sequence B_1,..., B_k is either
a) an axiom, or
b) a member of Gamma, or
c) deduced from earlier wff in the sequence by a rule of inference.
What do you gain by requiring premises to be axioms?  The axioms
are already there, so you are saying that you want no premises,
i.e. that Gamma be empty.
     If Γ is the empty set ∅, then ∅ ⊢ C if and only if C is a
theorem. It is customary
     to omit the sign “∅” and simply write ⊢ C. Thus, ⊢ C is
another way of asserting that
     C is a theorem.
Because of the above breakdown Mendelson would encode sound deductive interfere
as ⊢ C. Because this is sound deductive inference that has no possibly false
premises and only has axioms in their place ⊢ C means True(C).
No, ⊢ C means that C is provable (in some theory T or other, which
one possibly being identified by a subscript on ⊢).  Sometimes
provable and true coincide, sometimes they don't.  It depends on T
and has to be demonstrated in each case.  All you ever do is make
dogmatic pronouncements.  Nor does ⊢ C necessarily signal a sound
inference.  T may be inconsistent.  Again, demonstration, not
dogmatic assertion, is needed.
     Validity and Soundness https://www.iep.utm.edu/val-snd/
     A deductive argument is said to be valid if and only if it takes
a form that makes it
     impossible for the premises to be true and the conclusion
nevertheless to be false.
     Otherwise, a deductive argument is said to be invalid.
     A deductive argument is sound if and only if it is both valid,
and all of its premises
     are actually true. Otherwise, a deductive argument is unsound.
When-so-ever a deductive argument is valid
How do you test for validity?
https://en.wikipedia.org/wiki/Logical_consequence#Syntactic_consequence
That doesn't answer the question. Imagine that you are presented with a
logical formula, what will you do with it to demonstrate that it is
valid or invalid, as the case may be?
Post by peteolcott
Post by Peter Percival
the Truth of the conclusion flows from the truth of the Premises.
When-so-ever a deductive argument is sound the Truth of the
conclusion flows from the truth of the True Premises.
When-so-ever the premises are axioms the premises are True. I will
stop here so that you don't get overwhelmed.
As soon as we get agreement on the above points we can proceed.
Copyright 2018 Pete Olcott
peteolcott
2018-10-19 19:07:48 UTC
Reply
Permalink
Post by peteolcott
Post by Peter Percival
Post by peteolcott
Post by peteolcott
Post by peteolcott
The purpose of this paper is to complete the RHS of Tarski's famous formula: ∀x True(x) ↔ φ(x)
For any natural (human) or formal (mathematical) language L we know that an expression X of
language L is true if and only if there are expressions Γ of language L that connect X to known
facts. By extending the notion of a Well Formed Formula to include syntactically formalized rules
for rejecting semantically incorrect expressions we recognize and reject expressions that evaluate to
neither True nor False.
https://www.researchgate.net/publication/323866366_The_Notion_of_Truth_in_Natural_and_Formal_Languages
The Notion of Truth in Natural and Formal Languages
https://philpapers.org/archive/OLCTNO.pdf
Copyright 2016, 2017 2018 (and other years since 1997) Pete Olcott
There is nothing there that you haven't posted to sci.logic before. You have not taken into account the criticisms you got in sci.logic.
You say that you require Mendelson premises to be axioms. That shows that you have not understood the passage from Mendelson even though you have quoted it forty two million times.  (It may be that you mean that you require the set of premises
to be empty, but who cares?)
I am taking Mendelson's specification, adding a new feature and from this
Had you understood Mendelson. you'd know that your "new feature" is no such thing.
So there is no such thing as the hypothesis that premises are axioms?
Wait a minute that was a hypothesis that premises are axioms, therefore
unequivocally proving that there is such a thing.
Read Mendelson.  You quote it often enough, so why not read it? According to Mendelson, a wff C is a consequence of a set of premises Gamma if there is a sequence of wff B_1,..., B_k such that B_k is C and each wff in the sequence B_1,..., B_k is
either
a) an axiom, or
b) a member of Gamma, or
c) deduced from earlier wff in the sequence by a rule of inference.
What do you gain by requiring premises to be axioms?  The axioms are already there, so you are saying that you want no premises, i.e. that Gamma be empty.
     If Γ is the empty set ∅, then ∅ ⊢ C if and only if C is a theorem. It is customary
     to omit the sign “∅” and simply write ⊢ C. Thus, ⊢ C is another way of asserting that
     C is a theorem.
Because of the above breakdown Mendelson would encode sound deductive interfere
as ⊢ C. Because this is sound deductive inference that has no possibly false
premises and only has axioms in their place ⊢ C means True(C).
No, ⊢ C means that C is provable (in some theory T or other, which one possibly being identified by a subscript on ⊢).  Sometimes provable and true coincide, sometimes they don't.  It depends on T and has to be demonstrated in each case.  All you ever
do is make dogmatic pronouncements.  Nor does ⊢ C necessarily signal a sound inference.  T may be inconsistent.  Again, demonstration, not dogmatic assertion, is needed.
     Validity and Soundness https://www.iep.utm.edu/val-snd/
     A deductive argument is said to be valid if and only if it takes a form that makes it
     impossible for the premises to be true and the conclusion nevertheless to be false.
     Otherwise, a deductive argument is said to be invalid.
     A deductive argument is sound if and only if it is both valid, and all of its premises
     are actually true. Otherwise, a deductive argument is unsound.
When-so-ever a deductive argument is valid
How do you test for validity?
https://en.wikipedia.org/wiki/Logical_consequence#Syntactic_consequence
That doesn't answer the question.  Imagine that you are presented with a logical formula, what will you do with it to demonstrate that it is valid or invalid, as the case may be?
The syntactic rules of the language.
Peter Percival
2018-10-19 19:17:11 UTC
Reply
Permalink
Post by peteolcott
Post by peteolcott
Post by Peter Percival
Post by Peter Percival
Post by peteolcott
Post by Peter Percival
Post by peteolcott
Post by Peter Percival
Post by Peter Percival
Post by peteolcott
The purpose of this paper is to complete the RHS of
Tarski's famous formula: ∀x True(x) ↔ φ(x)
For any natural (human) or formal (mathematical) language
L we know that an expression X of
language L is true if and only if there are expressions Γ
of language L that connect X to known
facts. By extending the notion of a Well Formed Formula to
include syntactically formalized rules
for rejecting semantically incorrect expressions we
recognize and reject expressions that evaluate to
neither True nor False.
https://www.researchgate.net/publication/323866366_The_Notion_of_Truth_in_Natural_and_Formal_Languages
The Notion of Truth in Natural and Formal Languages
https://philpapers.org/archive/OLCTNO.pdf
Copyright 2016, 2017 2018 (and other years since 1997)
Pete Olcott
There is nothing there that you haven't posted to sci.logic
before. You have not taken into account the criticisms you
got in sci.logic.
You say that you require Mendelson premises to be axioms.
That shows that you have not understood the passage from
Mendelson even though you have quoted it forty two million
times.  (It may be that you mean that you require the set of
premises to be empty, but who cares?)
I am taking Mendelson's specification, adding a new feature
and from this
Had you understood Mendelson. you'd know that your "new
feature" is no such thing.
So there is no such thing as the hypothesis that premises are axioms?
Wait a minute that was a hypothesis that premises are axioms, therefore
unequivocally proving that there is such a thing.
Read Mendelson.  You quote it often enough, so why not read it?
According to Mendelson, a wff C is a consequence of a set of
premises Gamma if there is a sequence of wff B_1,..., B_k such
that B_k is C and each wff in the sequence B_1,..., B_k is either
a) an axiom, or
b) a member of Gamma, or
c) deduced from earlier wff in the sequence by a rule of inference.
What do you gain by requiring premises to be axioms?  The axioms
are already there, so you are saying that you want no premises,
i.e. that Gamma be empty.
     If Γ is the empty set ∅, then ∅ ⊢ C if and only if C is a
theorem. It is customary
     to omit the sign “∅” and simply write ⊢ C. Thus, ⊢ C is
another way of asserting that
     C is a theorem.
Because of the above breakdown Mendelson would encode sound deductive interfere
as ⊢ C. Because this is sound deductive inference that has no possibly false
premises and only has axioms in their place ⊢ C means True(C).
No, ⊢ C means that C is provable (in some theory T or other, which
one possibly being identified by a subscript on ⊢).  Sometimes
provable and true coincide, sometimes they don't.  It depends on T
and has to be demonstrated in each case.  All you ever do is make
dogmatic pronouncements.  Nor does ⊢ C necessarily signal a sound
inference.  T may be inconsistent.  Again, demonstration, not
dogmatic assertion, is needed.
     Validity and Soundness https://www.iep.utm.edu/val-snd/
     A deductive argument is said to be valid if and only if it
takes a form that makes it
     impossible for the premises to be true and the conclusion
nevertheless to be false.
     Otherwise, a deductive argument is said to be invalid.
     A deductive argument is sound if and only if it is both valid,
and all of its premises
     are actually true. Otherwise, a deductive argument is unsound.
When-so-ever a deductive argument is valid
How do you test for validity?
https://en.wikipedia.org/wiki/Logical_consequence#Syntactic_consequence
That doesn't answer the question.  Imagine that you are presented with
a logical formula, what will you do with it to demonstrate that it is
valid or invalid, as the case may be?
The syntactic rules of the language.
You are not answering the question. I am uncertain whether you know you
are not answering it.
peteolcott
2018-10-19 19:47:39 UTC
Reply
Permalink
Post by peteolcott
Post by peteolcott
Post by Peter Percival
Post by peteolcott
Post by peteolcott
Post by peteolcott
The purpose of this paper is to complete the RHS of Tarski's famous formula: ∀x True(x) ↔ φ(x)
For any natural (human) or formal (mathematical) language L we know that an expression X of
language L is true if and only if there are expressions Γ of language L that connect X to known
facts. By extending the notion of a Well Formed Formula to include syntactically formalized rules
for rejecting semantically incorrect expressions we recognize and reject expressions that evaluate to
neither True nor False.
https://www.researchgate.net/publication/323866366_The_Notion_of_Truth_in_Natural_and_Formal_Languages
The Notion of Truth in Natural and Formal Languages
https://philpapers.org/archive/OLCTNO.pdf
Copyright 2016, 2017 2018 (and other years since 1997) Pete Olcott
There is nothing there that you haven't posted to sci.logic before. You have not taken into account the criticisms you got in sci.logic.
You say that you require Mendelson premises to be axioms. That shows that you have not understood the passage from Mendelson even though you have quoted it forty two million times.  (It may be that you mean that you require the set of premises
to be empty, but who cares?)
I am taking Mendelson's specification, adding a new feature and from this
Had you understood Mendelson. you'd know that your "new feature" is no such thing.
So there is no such thing as the hypothesis that premises are axioms?
Wait a minute that was a hypothesis that premises are axioms, therefore
unequivocally proving that there is such a thing.
Read Mendelson.  You quote it often enough, so why not read it? According to Mendelson, a wff C is a consequence of a set of premises Gamma if there is a sequence of wff B_1,..., B_k such that B_k is C and each wff in the sequence B_1,..., B_k is
either
a) an axiom, or
b) a member of Gamma, or
c) deduced from earlier wff in the sequence by a rule of inference.
What do you gain by requiring premises to be axioms?  The axioms are already there, so you are saying that you want no premises, i.e. that Gamma be empty.
     If Γ is the empty set ∅, then ∅ ⊢ C if and only if C is a theorem. It is customary
     to omit the sign “∅” and simply write ⊢ C. Thus, ⊢ C is another way of asserting that
     C is a theorem.
Because of the above breakdown Mendelson would encode sound deductive interfere
as ⊢ C. Because this is sound deductive inference that has no possibly false
premises and only has axioms in their place ⊢ C means True(C).
No, ⊢ C means that C is provable (in some theory T or other, which one possibly being identified by a subscript on ⊢).  Sometimes provable and true coincide, sometimes they don't.  It depends on T and has to be demonstrated in each case.  All you
ever do is make dogmatic pronouncements.  Nor does ⊢ C necessarily signal a sound inference.  T may be inconsistent.  Again, demonstration, not dogmatic assertion, is needed.
     Validity and Soundness https://www.iep.utm.edu/val-snd/
     A deductive argument is said to be valid if and only if it takes a form that makes it
     impossible for the premises to be true and the conclusion nevertheless to be false.
     Otherwise, a deductive argument is said to be invalid.
     A deductive argument is sound if and only if it is both valid, and all of its premises
     are actually true. Otherwise, a deductive argument is unsound.
When-so-ever a deductive argument is valid
How do you test for validity?
https://en.wikipedia.org/wiki/Logical_consequence#Syntactic_consequence
That doesn't answer the question.  Imagine that you are presented with a logical formula, what will you do with it to demonstrate that it is valid or invalid, as the case may be?
The syntactic rules of the language.
You are not answering the question.  I am uncertain whether you know you are not answering it.
https://en.wikipedia.org/wiki/Modus_tollens
How do we know that Modus Tollens is not correctly expressed as:
(A & B) -> Z
Peter Percival
2018-10-19 19:57:38 UTC
Reply
Permalink
Post by peteolcott
Post by peteolcott
Post by peteolcott
Post by Peter Percival
Post by Peter Percival
Post by peteolcott
Post by Peter Percival
Post by peteolcott
Post by Peter Percival
Post by Peter Percival
Post by peteolcott
The purpose of this paper is to complete the RHS of
Tarski's famous formula: ∀x True(x) ↔ φ(x)
For any natural (human) or formal (mathematical)
language L we know that an expression X of
language L is true if and only if there are expressions
Γ of language L that connect X to known
facts. By extending the notion of a Well Formed Formula
to include syntactically formalized rules
for rejecting semantically incorrect expressions we
recognize and reject expressions that evaluate to
neither True nor False.
https://www.researchgate.net/publication/323866366_The_Notion_of_Truth_in_Natural_and_Formal_Languages
The Notion of Truth in Natural and Formal Languages
https://philpapers.org/archive/OLCTNO.pdf
Copyright 2016, 2017 2018 (and other years since 1997)
Pete Olcott
There is nothing there that you haven't posted to
sci.logic before. You have not taken into account the
criticisms you got in sci.logic.
You say that you require Mendelson premises to be axioms.
That shows that you have not understood the passage from
Mendelson even though you have quoted it forty two million
times.  (It may be that you mean that you require the set
of premises to be empty, but who cares?)
I am taking Mendelson's specification, adding a new feature
and from this
Had you understood Mendelson. you'd know that your "new
feature" is no such thing.
So there is no such thing as the hypothesis that premises are axioms?
Wait a minute that was a hypothesis that premises are axioms, therefore
unequivocally proving that there is such a thing.
Read Mendelson.  You quote it often enough, so why not read
it? According to Mendelson, a wff C is a consequence of a set
of premises Gamma if there is a sequence of wff B_1,..., B_k
such that B_k is C and each wff in the sequence B_1,..., B_k
is either
a) an axiom, or
b) a member of Gamma, or
c) deduced from earlier wff in the sequence by a rule of inference.
What do you gain by requiring premises to be axioms?  The
axioms are already there, so you are saying that you want no
premises, i.e. that Gamma be empty.
     If Γ is the empty set ∅, then ∅ ⊢ C if and only if C is a
theorem. It is customary
     to omit the sign “∅” and simply write ⊢ C. Thus, ⊢ C is
another way of asserting that
     C is a theorem.
Because of the above breakdown Mendelson would encode sound
deductive interfere
as ⊢ C. Because this is sound deductive inference that has no
possibly false
premises and only has axioms in their place ⊢ C means True(C).
No, ⊢ C means that C is provable (in some theory T or other,
which one possibly being identified by a subscript on ⊢).
Sometimes provable and true coincide, sometimes they don't.  It
depends on T and has to be demonstrated in each case.  All you
ever do is make dogmatic pronouncements.  Nor does ⊢ C
necessarily signal a sound inference.  T may be inconsistent.
Again, demonstration, not dogmatic assertion, is needed.
     Validity and Soundness https://www.iep.utm.edu/val-snd/
     A deductive argument is said to be valid if and only if it
takes a form that makes it
     impossible for the premises to be true and the conclusion
nevertheless to be false.
     Otherwise, a deductive argument is said to be invalid.
     A deductive argument is sound if and only if it is both
valid, and all of its premises
     are actually true. Otherwise, a deductive argument is unsound.
When-so-ever a deductive argument is valid
How do you test for validity?
https://en.wikipedia.org/wiki/Logical_consequence#Syntactic_consequence
That doesn't answer the question.  Imagine that you are presented
with a logical formula, what will you do with it to demonstrate that
it is valid or invalid, as the case may be?
The syntactic rules of the language.
You are not answering the question.  I am uncertain whether you know
you are not answering it.
https://en.wikipedia.org/wiki/Modus_tollens
(A & B) -> Z
We know that (A & B) -> Z is not valid (if that's what you mean) by
drawing a truth-table, or enough rows of a truth-table to find that it
can be given the value false.

Incidentally, if you had answered "by using truth tables" to my question
"How do you test for validity?", I would have pointed out that truth
tables have very limited applicability. But at least your answer would
have been relevant.
Peter Percival
2018-10-19 20:30:36 UTC
Reply
Permalink
Post by Peter Percival
Post by peteolcott
Post by peteolcott
Post by peteolcott
Post by Peter Percival
Post by Peter Percival
Post by peteolcott
Post by Peter Percival
Post by peteolcott
Post by Peter Percival
Post by Peter Percival
Post by peteolcott
The purpose of this paper is to complete the RHS of
Tarski's famous formula: ∀x True(x) ↔ φ(x)
For any natural (human) or formal (mathematical)
language L we know that an expression X of
language L is true if and only if there are expressions
Γ of language L that connect X to known
facts. By extending the notion of a Well Formed Formula
to include syntactically formalized rules
for rejecting semantically incorrect expressions we
recognize and reject expressions that evaluate to
neither True nor False.
https://www.researchgate.net/publication/323866366_The_Notion_of_Truth_in_Natural_and_Formal_Languages
The Notion of Truth in Natural and Formal Languages
https://philpapers.org/archive/OLCTNO.pdf
Copyright 2016, 2017 2018 (and other years since 1997)
Pete Olcott
There is nothing there that you haven't posted to
sci.logic before. You have not taken into account the
criticisms you got in sci.logic.
You say that you require Mendelson premises to be axioms.
That shows that you have not understood the passage from
Mendelson even though you have quoted it forty two
million times.  (It may be that you mean that you require
the set of premises to be empty, but who cares?)
I am taking Mendelson's specification, adding a new
feature and from this
Had you understood Mendelson. you'd know that your "new
feature" is no such thing.
So there is no such thing as the hypothesis that premises are axioms?
Wait a minute that was a hypothesis that premises are
axioms, therefore
unequivocally proving that there is such a thing.
Read Mendelson.  You quote it often enough, so why not read
it? According to Mendelson, a wff C is a consequence of a set
of premises Gamma if there is a sequence of wff B_1,..., B_k
such that B_k is C and each wff in the sequence B_1,..., B_k
is either
a) an axiom, or
b) a member of Gamma, or
c) deduced from earlier wff in the sequence by a rule of inference.
What do you gain by requiring premises to be axioms?  The
axioms are already there, so you are saying that you want no
premises, i.e. that Gamma be empty.
     If Γ is the empty set ∅, then ∅ ⊢ C if and only if C is a
theorem. It is customary
     to omit the sign “∅” and simply write ⊢ C. Thus, ⊢ C is
another way of asserting that
     C is a theorem.
Because of the above breakdown Mendelson would encode sound
deductive interfere
as ⊢ C. Because this is sound deductive inference that has no
possibly false
premises and only has axioms in their place ⊢ C means True(C).
No, ⊢ C means that C is provable (in some theory T or other,
which one possibly being identified by a subscript on ⊢).
Sometimes provable and true coincide, sometimes they don't.  It
depends on T and has to be demonstrated in each case.  All you
ever do is make dogmatic pronouncements.  Nor does ⊢ C
necessarily signal a sound inference.  T may be inconsistent.
Again, demonstration, not dogmatic assertion, is needed.
     Validity and Soundness https://www.iep.utm.edu/val-snd/
     A deductive argument is said to be valid if and only if it
takes a form that makes it
     impossible for the premises to be true and the conclusion
nevertheless to be false.
     Otherwise, a deductive argument is said to be invalid.
     A deductive argument is sound if and only if it is both
valid, and all of its premises
     are actually true. Otherwise, a deductive argument is unsound.
When-so-ever a deductive argument is valid
How do you test for validity?
https://en.wikipedia.org/wiki/Logical_consequence#Syntactic_consequence
That doesn't answer the question.  Imagine that you are presented
with a logical formula, what will you do with it to demonstrate
that it is valid or invalid, as the case may be?
The syntactic rules of the language.
You are not answering the question.  I am uncertain whether you know
you are not answering it.
https://en.wikipedia.org/wiki/Modus_tollens
(A & B) -> Z
We know that (A & B) -> Z is not valid (if that's what you mean) by
drawing a truth-table, or enough rows of a truth-table to find that it
can be given the value false.
Incidentally, if you had answered "by using truth tables" to my question
"How do you test for validity?", I would have pointed out that truth
tables have very limited applicability.  But at least your answer would
have been relevant.
Do you know any logic at all?
peteolcott
2018-10-20 03:16:11 UTC
Reply
Permalink
Post by Peter Percival
Post by Peter Percival
Post by peteolcott
https://en.wikipedia.org/wiki/Modus_tollens
How do we know that Modus Tollens is not correctly
expressed as: (A & B) -> Z
We know that (A & B) -> Z is not valid (if that's what
you mean) by drawing a truth-table, or enough rows of a
truth-table to find that it can be given the value false.
Incidentally, if you had answered "by using truth tables"
to my question "How do you test for validity?", I would
have pointed out that truth tables have very limited
applicability.  But at least your answer would have been
relevant.
Do you know any logic at all?
The problem with asking that of Pete Olcott is that he will
answer according to what _he_ has decided "logic" means.
I strongly suspect that Pete Olcott thinks that some
argument becomes logical by stuffing it with logical-sounding
buzzwords such as "categorical".
This is what is meant by a categorical proof:

If no physical or conceptual thing can possibly totally contain itself,
then the whole category of a thing totally containing itself is
impossible therefore the sub-category of a set totally containing itself
is necessarily also impossible.

This kind of reasoning is the key aspect of my system of infallible reasoning.
It is infallible only in the sense that it totally eliminates
gaps in reasoning. It eliminates gaps in reasoning by exhaustively
examining the complete set of all categories of specific ideas.

To maximize efficiency its starts at the broadest possible
categories pertaining to the area of investigation.

The element of the broadest possible category in the collection of
all things is {thing}.

There are only two most basic categories of thing:
(1) Physically existing
(2) Not(Physically existing) thus Conceptually existing.

{Total Containment} is one of many possible relations between things.
{Total Containment} between {things} forms the BASE TYPE pinnacle
of the inheritance hierarchy of the concept of {total containment}.

In the natural order of the collection of all knowledge every derived class
of the concept of {total containment} inherits its base meaning from the BASE CLASS.

Copyright 1993, 2016, 2017, 2018 Pete Olcott
----
What would be an effective way to address Pete Olcott's
misconceptions? If we point out where he is wrong, he
takes his disagreement with everyone else as proof that
everyone else is wrong.
The only method I can think of is Darwin's Algorithm.
When PO has gone splat on his face enough times, either he
will have auto-Darwinated or (conceivably) he will
ask himself whether his infallible reasoning is as
infallible as he thinks it is.
You still don't get it that I am looking at these things at a higher
levels of abstraction thus could derive greater insights without even
knowing most of the conventional details.

Of course it would seem to be enormously more likely a case of the
Dunning–Kruger effect, especially from what seems to be the dismissive
way that I address conventional terminology.

None-the-less it remains a hypothetical possibility that I really
am examining these things at a much higher level of abstraction
that lacks its own conventional terminology.

I must misuse conventional terminology as the best approximation
until my meanings can be progressively refined over time.
peteolcott
2018-10-22 20:14:51 UTC
Reply
Permalink
What would be an effective way to address Pete Olcott's
misconceptions? If we point out where he is wrong, he
takes his disagreement with everyone else as proof that
everyone else is wrong.
The only method I can think of is Darwin's Algorithm.
When PO has gone splat on his face enough times, either he
will have auto-Darwinated or (conceivably) he will
ask himself whether his infallible reasoning is as
infallible as he thinks it is.
I don't get the auto-Darwinated idea, but I think history shows that
the idea that PO being wrong enough times will result in PO "seeing
sense" can't be right - if it were, PO would have seen sense 25 years
ago.
- that he is an unrecognised Genius.
   [Reality:  PO is rather slow-witted, not following
   even basic reasoning that is understood by
   beginning students]
- that he has "powers beyond those of nearly every other
   human being" e.g. ability to "focus on the essence of
   a problem".
- that he can spot errors in the work of experts, without
   understanding the details or even the intended meanings
   of the terms they use.
- that his initial naive intuitions are the last word on
   a subject, and outweigh the considered conclusions of
   subject experts.
- that by posting on sci.math (or elsewhere) and refuting
   various established theorems, he can "achieve
   credibility" in the AI field that will compel Doug Lenat
   to put him in charge of Cyc project development.  (WHAAAT???!)
- that Truth is the same as Provability.
- that if a circle has a point removed, no PD-style manipulation of
the shape can result in a full circle.
- that a computer program is the same as a proof.
- that by changing the meaning of the terms used in a proof, so that
the theorem is false with the new meaning, he has somehow "refuted"
the theorem.
- any claim by PO starting with the word "Whensoever"
The problem for you is that while he is deluded, it is always going to
be VERY VERY VERY HARD to address even the simplest misconceptions,
because his delusions disincline him from listening seriously to what
you are saying.  Worse, he is inclined to simply reject anything that
contradicts his initial intuitions, because he is a superiour thinker
to you, and cannot conceive of his own thought processes being
flawed.  OK, history shows that occasionally some minor PO
misconception /can/ be addressed, but at what cost?
Regarding his delusions - the thing about delusions is that you can't
expel them just by pointing them out, however ridiculous they may seem
to everybody else!  Delusions by nature form a robust framework and
reinforce each other when challenged, if necessary becoming more and
more elaborate - basically, whatever it takes to maintain the
delusions, because the delusions are typically serving some higher
purpose for the patient.
So we're stuck with his delusions, and so I can't conceive of any
"efficient way" of addressing his misconceptions!
My question for you (JB and others) would be why do you feel the
/need/ to achieve this?
Do you feel this would somehow be "helping" PO?  I suggest that is a
mistake, and it really would not.  PO is not a student learning a
subject, and simply correcting some minor misconception does not in
reality help him AT ALL.  Perhaps if your aim is really to "help" him,
you should acknowledge his genius and write a letter to Doug Lenat
recommending PO as the perfect person to manage Cyc development,
except of course that would not help either, that's just going deeper
into PO's delusional framework.  (But you see what I'm getting at...)
If after A LOT of effort, you correct a PO misconception, SO WHAT?
There will just be another misconception around the corner, then
another and another and so on.  What is genuinely being achieved by
this? Nobody is getting any closer to achieving their goals!
[I should say that personally I like helping students with problems,
and don't mind investing my own time doing that, but that's simply not
what's going on with PO (or NN, AP, WM, PV, etc.).  Of course, I do
accept there are many other reasons for posting: getting your own
ideas properly sorted, entertainment, boredom, social contact and so on.]
OTOH, NOT addressing PO's misconceptions has no disadvantages that I
can see.  :)  Years of futile effort saved, and the overall outcome is
substantially unchanged!
1)  Still PO will fail to gain his required credibility through
     discrediting famous theorems (or otherwise)
2)  Still PO will not be put in charge of Cyc development,
     or create a human mind in a computer, or teach mankind
     the ultimate meaning of Truth/Love/Peace or whatever
3)  Still PO will believe he is an unrecognised genius, and
     will from time to time make outrageous claims of
     refuting this theorem or that.
4)  Still all his claims will have absolutely no effect on other
     peoples' lives.  (He will not be put in charge
     of your kid's education, or be extracting taxes from you to
     fund his research.)
Regards,
Mike.
You say all this stuff yet bottom line you cannot point to any actual
mistake in my reasoning.
It is all along the line of: Oh but it is not conventional to think of
these things that way.
On the contrary, I and others have pointed out many faults in your reasoning, but you are not capable of following those explanations. There is no point in repeating the arguments here.
No one ever directly addressed any of my actual reasoning:
https://philpapers.org/archive/OLCTNO.pdf

Introduction to Mathematical logic Sixth edition Elliott Mendelson
1.4 An Axiom System for the Propositional Calculus
A wf C is said to be a consequence in S of a set Γ of wfs if and only if there is a
sequence B1, …, Bk of wfs such that C is Bk and, for each i, either Bi is an axiom
or Bi is in Γ, or Bi is a direct consequence by some rule of inference of some of
the preceding wfs in the sequence. Such a sequence is called a proof (or deduction)
of C from Γ. The members of Γ are called the hypotheses or premisses of the proof.
We use Γ ⊢ C as an abbreviation for “C is a consequence of Γ”...

If Γ is the empty set ∅, then ∅ ⊢ C if and only if C is a theorem. It is customary
to omit the sign “∅” and simply write ⊢ C. Thus, ⊢ C is another way of asserting that
C is a theorem.

My actual reasoning now finally translated into conventional terminology says that Tarski Undefinability is refuted by:
∀x ∈ L True(L, x) ↔ Theorem(L, x)

Copyright 2018 Pete Olcott
Peter Percival
2018-10-22 20:29:14 UTC
Reply
Permalink
Post by peteolcott
What would be an effective way to address Pete Olcott's
misconceptions? If we point out where he is wrong, he
takes his disagreement with everyone else as proof that
everyone else is wrong.
The only method I can think of is Darwin's Algorithm.
When PO has gone splat on his face enough times, either he
will have auto-Darwinated or (conceivably) he will
ask himself whether his infallible reasoning is as
infallible as he thinks it is.
I don't get the auto-Darwinated idea, but I think history shows that
the idea that PO being wrong enough times will result in PO "seeing
sense" can't be right - if it were, PO would have seen sense 25 years
ago.
- that he is an unrecognised Genius.
   [Reality:  PO is rather slow-witted, not following
   even basic reasoning that is understood by
   beginning students]
- that he has "powers beyond those of nearly every other
   human being" e.g. ability to "focus on the essence of
   a problem".
- that he can spot errors in the work of experts, without
   understanding the details or even the intended meanings
   of the terms they use.
- that his initial naive intuitions are the last word on
   a subject, and outweigh the considered conclusions of
   subject experts.
- that by posting on sci.math (or elsewhere) and refuting
   various established theorems, he can "achieve
   credibility" in the AI field that will compel Doug Lenat
   to put him in charge of Cyc project development.  (WHAAAT???!)
- that Truth is the same as Provability.
- that if a circle has a point removed, no PD-style manipulation of
the shape can result in a full circle.
- that a computer program is the same as a proof.
- that by changing the meaning of the terms used in a proof, so that
the theorem is false with the new meaning, he has somehow "refuted"
the theorem.
- any claim by PO starting with the word "Whensoever"
The problem for you is that while he is deluded, it is always going to
be VERY VERY VERY HARD to address even the simplest misconceptions,
because his delusions disincline him from listening seriously to what
you are saying.  Worse, he is inclined to simply reject anything that
contradicts his initial intuitions, because he is a superiour thinker
to you, and cannot conceive of his own thought processes being
flawed.  OK, history shows that occasionally some minor PO
misconception /can/ be addressed, but at what cost?
Regarding his delusions - the thing about delusions is that you can't
expel them just by pointing them out, however ridiculous they may seem
to everybody else!  Delusions by nature form a robust framework and
reinforce each other when challenged, if necessary becoming more and
more elaborate - basically, whatever it takes to maintain the
delusions, because the delusions are typically serving some higher
purpose for the patient.
So we're stuck with his delusions, and so I can't conceive of any
"efficient way" of addressing his misconceptions!
My question for you (JB and others) would be why do you feel the
/need/ to achieve this?
Do you feel this would somehow be "helping" PO?  I suggest that is a
mistake, and it really would not.  PO is not a student learning a
subject, and simply correcting some minor misconception does not in
reality help him AT ALL.  Perhaps if your aim is really to "help" him,
you should acknowledge his genius and write a letter to Doug Lenat
recommending PO as the perfect person to manage Cyc development,
except of course that would not help either, that's just going deeper
into PO's delusional framework.  (But you see what I'm getting at...)
If after A LOT of effort, you correct a PO misconception, SO WHAT?
There will just be another misconception around the corner, then
another and another and so on.  What is genuinely being achieved by
this? Nobody is getting any closer to achieving their goals!
[I should say that personally I like helping students with problems,
and don't mind investing my own time doing that, but that's simply not
what's going on with PO (or NN, AP, WM, PV, etc.).  Of course, I do
accept there are many other reasons for posting: getting your own
ideas properly sorted, entertainment, boredom, social contact and so on.]
OTOH, NOT addressing PO's misconceptions has no disadvantages that I
can see.  :)  Years of futile effort saved, and the overall outcome is
substantially unchanged!
1)  Still PO will fail to gain his required credibility through
     discrediting famous theorems (or otherwise)
2)  Still PO will not be put in charge of Cyc development,
     or create a human mind in a computer, or teach mankind
     the ultimate meaning of Truth/Love/Peace or whatever
3)  Still PO will believe he is an unrecognised genius, and
     will from time to time make outrageous claims of
     refuting this theorem or that.
4)  Still all his claims will have absolutely no effect on other
     peoples' lives.  (He will not be put in charge
     of your kid's education, or be extracting taxes from you to
     fund his research.)
Regards,
Mike.
You say all this stuff yet bottom line you cannot point to any actual
mistake in my reasoning.
It is all along the line of: Oh but it is not conventional to think of
these things that way.
On the contrary, I and others have pointed out many faults in your
reasoning, but you are not capable of following those explanations.
There is no point in repeating the arguments here.
https://philpapers.org/archive/OLCTNO.pdf
    Introduction to Mathematical logic Sixth edition Elliott Mendelson
    1.4 An Axiom System for the Propositional Calculus
    A wf C is said to be a consequence in S of a set Γ of wfs if and
only if there is a
    sequence B1, …, Bk of wfs such that C is Bk and, for each i, either
Bi is an axiom
    or Bi is in Γ, or Bi is a direct consequence by some rule of
inference of some of
    the preceding wfs in the sequence. Such a sequence is called a
proof (or deduction)
    of C from Γ. The members of Γ are called the hypotheses or
premisses of the proof.
    We use Γ ⊢ C as an abbreviation for “C is a consequence of Γ”...
    If Γ is the empty set ∅, then ∅ ⊢ C if and only if C is a theorem.
It is customary
    to omit the sign “∅” and simply write ⊢ C. Thus, ⊢ C is another way
of asserting that
    C is a theorem.
You don't know what reasoning is, do you? The above isn't any of your
reasoning , or any of your anything. It's a quotation from Mendelson
which, just a few days ago you did not understand. Also...
Post by peteolcott
My actual reasoning now finally translated into conventional terminology
∀x ∈ L True(L, x) ↔ Theorem(L, x)
... the above is not reasoning, it is just a formula. It is not even a
very meaningful formula, you could at least give informal readings of
True(L, x) and Theorem(L, x).
Post by peteolcott
Copyright 2018 Pete Olcott
peteolcott
2018-10-22 20:59:26 UTC
Reply
Permalink
Post by peteolcott
What would be an effective way to address Pete Olcott's
misconceptions? If we point out where he is wrong, he
takes his disagreement with everyone else as proof that
everyone else is wrong.
The only method I can think of is Darwin's Algorithm.
When PO has gone splat on his face enough times, either he
will have auto-Darwinated or (conceivably) he will
ask himself whether his infallible reasoning is as
infallible as he thinks it is.
I don't get the auto-Darwinated idea, but I think history shows that
the idea that PO being wrong enough times will result in PO "seeing
sense" can't be right - if it were, PO would have seen sense 25 years
ago.
- that he is an unrecognised Genius.
   [Reality:  PO is rather slow-witted, not following
   even basic reasoning that is understood by
   beginning students]
- that he has "powers beyond those of nearly every other
   human being" e.g. ability to "focus on the essence of
   a problem".
- that he can spot errors in the work of experts, without
   understanding the details or even the intended meanings
   of the terms they use.
- that his initial naive intuitions are the last word on
   a subject, and outweigh the considered conclusions of
   subject experts.
- that by posting on sci.math (or elsewhere) and refuting
   various established theorems, he can "achieve
   credibility" in the AI field that will compel Doug Lenat
   to put him in charge of Cyc project development.  (WHAAAT???!)
- that Truth is the same as Provability.
- that if a circle has a point removed, no PD-style manipulation of
the shape can result in a full circle.
- that a computer program is the same as a proof.
- that by changing the meaning of the terms used in a proof, so that
the theorem is false with the new meaning, he has somehow "refuted"
the theorem.
- any claim by PO starting with the word "Whensoever"
The problem for you is that while he is deluded, it is always going to
be VERY VERY VERY HARD to address even the simplest misconceptions,
because his delusions disincline him from listening seriously to what
you are saying.  Worse, he is inclined to simply reject anything that
contradicts his initial intuitions, because he is a superiour thinker
to you, and cannot conceive of his own thought processes being
flawed.  OK, history shows that occasionally some minor PO
misconception /can/ be addressed, but at what cost?
Regarding his delusions - the thing about delusions is that you can't
expel them just by pointing them out, however ridiculous they may seem
to everybody else!  Delusions by nature form a robust framework and
reinforce each other when challenged, if necessary becoming more and
more elaborate - basically, whatever it takes to maintain the
delusions, because the delusions are typically serving some higher
purpose for the patient.
So we're stuck with his delusions, and so I can't conceive of any
"efficient way" of addressing his misconceptions!
My question for you (JB and others) would be why do you feel the
/need/ to achieve this?
Do you feel this would somehow be "helping" PO?  I suggest that is a
mistake, and it really would not.  PO is not a student learning a
subject, and simply correcting some minor misconception does not in
reality help him AT ALL.  Perhaps if your aim is really to "help" him,
you should acknowledge his genius and write a letter to Doug Lenat
recommending PO as the perfect person to manage Cyc development,
except of course that would not help either, that's just going deeper
into PO's delusional framework.  (But you see what I'm getting at...)
If after A LOT of effort, you correct a PO misconception, SO WHAT?
There will just be another misconception around the corner, then
another and another and so on.  What is genuinely being achieved by
this? Nobody is getting any closer to achieving their goals!
[I should say that personally I like helping students with problems,
and don't mind investing my own time doing that, but that's simply not
what's going on with PO (or NN, AP, WM, PV, etc.).  Of course, I do
accept there are many other reasons for posting: getting your own
ideas properly sorted, entertainment, boredom, social contact and so on.]
OTOH, NOT addressing PO's misconceptions has no disadvantages that I
can see.  :)  Years of futile effort saved, and the overall outcome is
substantially unchanged!
1)  Still PO will fail to gain his required credibility through
     discrediting famous theorems (or otherwise)
2)  Still PO will not be put in charge of Cyc development,
     or create a human mind in a computer, or teach mankind
     the ultimate meaning of Truth/Love/Peace or whatever
3)  Still PO will believe he is an unrecognised genius, and
     will from time to time make outrageous claims of
     refuting this theorem or that.
4)  Still all his claims will have absolutely no effect on other
     peoples' lives.  (He will not be put in charge
     of your kid's education, or be extracting taxes from you to
     fund his research.)
Regards,
Mike.
You say all this stuff yet bottom line you cannot point to any actual
mistake in my reasoning.
It is all along the line of: Oh but it is not conventional to think of
these things that way.
On the contrary, I and others have pointed out many faults in your reasoning, but you are not capable of following those explanations. There is no point in repeating the arguments here.
https://philpapers.org/archive/OLCTNO.pdf
     Introduction to Mathematical logic Sixth edition Elliott Mendelson
     1.4 An Axiom System for the Propositional Calculus
     A wf C is said to be a consequence in S of a set Γ of wfs if and only if there is a
     sequence B1, …, Bk of wfs such that C is Bk and, for each i, either Bi is an axiom
     or Bi is in Γ, or Bi is a direct consequence by some rule of inference of some of
     the preceding wfs in the sequence. Such a sequence is called a proof (or deduction)
     of C from Γ. The members of Γ are called the hypotheses or premisses of the proof.
     We use Γ ⊢ C as an abbreviation for “C is a consequence of Γ”...
     If Γ is the empty set ∅, then ∅ ⊢ C if and only if C is a theorem. It is customary
     to omit the sign “∅” and simply write ⊢ C. Thus, ⊢ C is another way of asserting that
     C is a theorem.
You don't know what reasoning is, do you?  The above isn't any of your reasoning , or any of your anything.  It's a quotation from Mendelson which, just a few days ago you did not understand.  Also...
Post by peteolcott
∀x ∈ L True(L, x) ↔ Theorem(L, x)
... the above is not reasoning, it is just a formula.  It is not even a very meaningful formula, you could at least give informal readings of True(L, x) and Theorem(L, x).
Post by peteolcott
Copyright 2018 Pete Olcott
Now finally for the first time my whole point is made using the
conventional meanings of conventional terms.

How do we know that a {cat} is not a type of {dog} ?
There is a natural language theorem that specifies this.

How do we know that: "This sentence is not true"
is a not a semantically correct declarative sentence?

Natural_Language_Theorem("This sentence is not true" ) = False
Natural_Language_Theorem(~"This sentence is not true" ) = False

Copyright 2018 Pete Olcott
Peter Percival
2018-10-22 21:20:37 UTC
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Post by peteolcott
Now finally for the first time my whole point is made using the
conventional meanings of conventional terms.
How do we know that a {cat} is not a type of {dog} ?
There is a natural language theorem that specifies this.
Cats can distinguish cats from dogs, as can dogs. Do they need natural
language theorems (whatever they are) to do so?
Post by peteolcott
How do we know that: "This sentence is not true"
is a not a semantically correct declarative sentence?
Natural_Language_Theorem("This sentence is not true" ) = False
Natural_Language_Theorem(~"This sentence is not true" ) = False
You are merely asserting that it is so.
peteolcott
2018-10-22 23:14:19 UTC
Reply
Permalink
Post by peteolcott
Now finally for the first time my whole point is made using the
conventional meanings of conventional terms.
How do we know that a {cat} is not a type of {dog} ?
There is a natural language theorem that specifies this.
Cats can distinguish cats from dogs, as can dogs.  Do they need natural language theorems (whatever they are) to do so?
The only way that the finite string "cat" can be distinguished from the
finite string "dog" is the mutually exclusive properties that have been
assigned to these finite strings such that ~IsTypeOf("cat", "dog") is
a theorem.
Post by peteolcott
How do we know that: "This sentence is not true"
is a not a semantically correct declarative sentence?
Natural_Language_Theorem("This sentence is not true" ) = False
Natural_Language_Theorem(~"This sentence is not true" ) = False
You are merely asserting that it is so.
It is an axiom that declarative sentences have a non-empty Boolean property.
Peter Percival
2018-10-22 23:42:37 UTC
Reply
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Post by peteolcott
Post by peteolcott
Now finally for the first time my whole point is made using the
conventional meanings of conventional terms.
How do we know that a {cat} is not a type of {dog} ?
There is a natural language theorem that specifies this.
Cats can distinguish cats from dogs, as can dogs.  Do they need
natural language theorems (whatever they are) to do so?
The only way that the finite string "cat" can be distinguished from the
finite string "dog"
My apologies. I had assumed you were talking about cats and dogs, not
the strings "cat" and "dog". I distinguish between "cat" and "dog" by
observing (for example) that the letter c is not the letter d. That
does indeed look like a language matter. But a computer might recognize
that 0110011 isn't 01100100, which doesn't look like a _natural_
language matter.
Post by peteolcott
is the mutually exclusive properties that have been
assigned to these finite strings such that ~IsTypeOf("cat", "dog") is
a theorem.
I've no idea what that means.
Post by peteolcott
Post by peteolcott
How do we know that: "This sentence is not true"
is a not a semantically correct declarative sentence?
Natural_Language_Theorem("This sentence is not true" ) = False
Natural_Language_Theorem(~"This sentence is not true" ) = False
You are merely asserting that it is so.
It is an axiom that declarative sentences have a non-empty Boolean property.
Axioms are just what people choose to be axioms. Pete Olcott has chosen

declarative sentences have a non-empty Boolean property

to be an axiom. So what? It isn't a truth handed down by God. Axioms
in general aren't truth handed down by God. Nor do I know what a
non-empty Boolean property is. Is 5 Grenville Place, Cork, occupied?
peteolcott
2018-10-25 05:03:15 UTC
Reply
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Post by peteolcott
Post by peteolcott
Now finally for the first time my whole point is made using the
conventional meanings of conventional terms.
How do we know that a {cat} is not a type of {dog} ?
There is a natural language theorem that specifies this.
Cats can distinguish cats from dogs, as can dogs.  Do they need natural language theorems (whatever they are) to do so?
The only way that the finite string "cat" can be distinguished from the
finite string "dog"
My apologies. I had assumed you were talking about cats and dogs, not the strings "cat" and "dog".  I distinguish between "cat" and "dog" by observing (for example) that the letter c is not the letter d.  That does indeed look like a language matter.  But
a computer might recognize that 0110011 isn't 01100100, which doesn't look like a _natural_ language matter.
Post by peteolcott
is the mutually exclusive properties that have been
assigned to these finite strings such that ~IsTypeOf("cat", "dog") is
a theorem.
I've no idea what that means.
Post by peteolcott
Post by peteolcott
How do we know that: "This sentence is not true"
is a not a semantically correct declarative sentence?
Natural_Language_Theorem("This sentence is not true" ) = False
Natural_Language_Theorem(~"This sentence is not true" ) = False
You are merely asserting that it is so.
It is an axiom that declarative sentences have a non-empty Boolean property.
Axioms are just what people choose to be axioms.  Pete Olcott has chosen
    declarative sentences have a non-empty Boolean property
to be an axiom.  So what?  It isn't a truth handed down by God.  Axioms in general aren't truth handed down by God.  Nor do I know what a non-empty Boolean property is.  Is 5 Grenville Place, Cork, occupied?
The value of my new Truth predicate is that it rejects incorrect
expressions of language that were previously used to prove
Undefinability and Incompleteness.

It finally does this using conventional terminology with exactly
conventional meanings.

∀x ∈ L True(L, x) ↔ Theorem(L, x)

“This sentence cannot be proven”
G ≡ ~Provable(G)
If G is neither true nor false then G is not a Boolean proposition.

If G was a theorem (thus true) then G would be provable
contradicting its assertion that G is not provable making G not a
theorem thus not true.

If ~G was a theorem (thus true) then ~G would be provable
~G asserts that G is provable contradicting ~G making ~G not a
theorem, thus not true.

~G is True is the same thing as saying that G is False.

Since G is neither True nor False, G is not a correct
Boolean proposition and is thus rejected.

Copyright 2018 Pete Olcott
peteolcott
2018-10-22 20:29:50 UTC
Reply
Permalink
You say all this stuff yet bottom line you cannot point to any actual mistake in my reasoning.
Two points.  First, your posts are often devoid of reasoning: there is nothing there to harbour any mistakes.  Second, when you do write something substantive, mistakes are pointed out but you don't bother to try to understand what is said.
It is difficult to tell you what the problem is without it sounding impolite.  You are ignorant of the subject matter (be it limitative theorems in logic, Banach-Tarski, or anything else).  For some people their ignorance doesn't matter, or at least it
doesn't continue mattering: they learn what they need to learn, or they recognize that it's too difficult for them and they direct their attention elsewhere. But you are too thick to know that you are ignorant, and even if you somehow come to it, you are
too thick to learn.
Sorry, but there it is.
There are plenty of things that a person of your limited intellect could do.  For example, buy a tabloid newspaper each day and fill in the a's, b's, d's, e's, g's, o's, p's and q's.  After you've done that, draw moustaches on the women depicted in it.
My actual reasoning now finally translated into conventional
terminology says that Tarski Undefinability is refuted by:
∀x ∈ L True(L, x) ↔ Theorem(L, x)
∀x ∈ L False(L, x) ↔ Theorem(L, ~x)

Copyright 2018 Pete Olcott
Peter Percival
2018-10-22 20:47:35 UTC
Reply
Permalink
Post by peteolcott
You say all this stuff yet bottom line you cannot point to any actual
mistake in my reasoning.
Two points.  First, your posts are often devoid of reasoning: there is
nothing there to harbour any mistakes.  Second, when you do write
something substantive, mistakes are pointed out but you don't bother
to try to understand what is said.
It is difficult to tell you what the problem is without it sounding
impolite.  You are ignorant of the subject matter (be it limitative
theorems in logic, Banach-Tarski, or anything else).  For some people
their ignorance doesn't matter, or at least it doesn't continue
mattering: they learn what they need to learn, or they recognize that
it's too difficult for them and they direct their attention elsewhere.
But you are too thick to know that you are ignorant, and even if you
somehow come to it, you are too thick to learn.
Sorry, but there it is.
There are plenty of things that a person of your limited intellect
could do.  For example, buy a tabloid newspaper each day and fill in
the a's, b's, d's, e's, g's, o's, p's and q's.  After you've done
that, draw moustaches on the women depicted in it.
My actual reasoning now finally translated into conventional
∀x ∈ L  True(L, x) ↔ Theorem(L, x)
∀x ∈ L False(L, x) ↔ Theorem(L, ~x)
There is no reasoning, there are just two formulae with no explanation
of what they mean.

My guess is that the first says

Something is said to be true (by you, that is) in
x iff it is a theorem of x.

Since Tarski didn't define true to mean that, it has no bearing on what
Tarski did.

My guess is that the second says

Something is said to be false (by you, that is) in
x iff its logical negation is a theorem of x.

Still further explanation is needed in both cases. E.g., what kind of
thing is L?
peteolcott
2018-10-22 23:56:30 UTC
Reply
Permalink
Post by peteolcott
You say all this stuff yet bottom line you cannot point to any actual mistake in my reasoning.
Two points.  First, your posts are often devoid of reasoning: there is nothing there to harbour any mistakes.  Second, when you do write something substantive, mistakes are pointed out but you don't bother to try to understand what is said.
It is difficult to tell you what the problem is without it sounding impolite.  You are ignorant of the subject matter (be it limitative theorems in logic, Banach-Tarski, or anything else).  For some people their ignorance doesn't matter, or at least it
doesn't continue mattering: they learn what they need to learn, or they recognize that it's too difficult for them and they direct their attention elsewhere. But you are too thick to know that you are ignorant, and even if you somehow come to it, you
are too thick to learn.
Sorry, but there it is.
There are plenty of things that a person of your limited intellect could do.  For example, buy a tabloid newspaper each day and fill in the a's, b's, d's, e's, g's, o's, p's and q's.  After you've done that, draw moustaches on the women depicted in it.
My actual reasoning now finally translated into conventional
∀x ∈ L  True(L, x) ↔ Theorem(L, x)
∀x ∈ L False(L, x) ↔ Theorem(L, ~x)
There is no reasoning, there are just two formulae with no explanation of what they mean.
My guess is that the first says
    Something is said to be true (by you, that is) in
    x iff it is a theorem of x.
An expression of language x is true if and only if it is a theorem.
Since Tarski didn't define true to mean that, it has no bearing on what Tarski did.
Tarski "proved" that no one could ever correctly define a Truth predicate.
He was under the misconception that he found an expression of language that
was simultaneously undecidable and true.

The concept of truth in formalized languages 1936 (Pages 275-276)
My guess is that the second says
    Something is said to be false (by you, that is) in
    x iff its logical negation is a theorem of x.
Still further explanation is needed in both cases.  E.g., what kind of thing is L?
Peter Percival
2018-10-23 00:29:40 UTC
Reply
Permalink
Post by peteolcott
Post by peteolcott
You say all this stuff yet bottom line you cannot point to any
actual mistake in my reasoning.
Two points.  First, your posts are often devoid of reasoning: there
is nothing there to harbour any mistakes.  Second, when you do write
something substantive, mistakes are pointed out but you don't bother
to try to understand what is said.
It is difficult to tell you what the problem is without it sounding
impolite.  You are ignorant of the subject matter (be it limitative
theorems in logic, Banach-Tarski, or anything else).  For some
people their ignorance doesn't matter, or at least it doesn't
continue mattering: they learn what they need to learn, or they
recognize that it's too difficult for them and they direct their
attention elsewhere. But you are too thick to know that you are
ignorant, and even if you somehow come to it, you are too thick to
learn.
Sorry, but there it is.
There are plenty of things that a person of your limited intellect
could do.  For example, buy a tabloid newspaper each day and fill in
the a's, b's, d's, e's, g's, o's, p's and q's.  After you've done
that, draw moustaches on the women depicted in it.
My actual reasoning now finally translated into conventional
∀x ∈ L  True(L, x) ↔ Theorem(L, x)
∀x ∈ L False(L, x) ↔ Theorem(L, ~x)
There is no reasoning, there are just two formulae with no explanation of what they mean.
My guess is that the first says
     Something is said to be true (by you, that is) in
     x iff it is a theorem of x.
An expression of language x is true if and only if it is a theorem.
A theorem of what? Languages don't have theorems, theories have theorems.
Post by peteolcott
Since Tarski didn't define true to mean that, it has no bearing on what Tarski did.
Tarski "proved" that no one could ever correctly define a Truth predicate.
He was under the misconception that he found an expression of language that
was simultaneously undecidable and true.
The concept of truth in formalized languages 1936 (Pages 275-276)
My guess is that the second says
     Something is said to be false (by you, that is) in
     x iff its logical negation is a theorem of x.
Still further explanation is needed in both cases.  E.g., what kind of thing is L?
peteolcott
2018-10-25 05:05:44 UTC
Reply
Permalink
Post by peteolcott
Post by peteolcott
You say all this stuff yet bottom line you cannot point to any actual mistake in my reasoning.
Two points.  First, your posts are often devoid of reasoning: there is nothing there to harbour any mistakes.  Second, when you do write something substantive, mistakes are pointed out but you don't bother to try to understand what is said.
It is difficult to tell you what the problem is without it sounding impolite.  You are ignorant of the subject matter (be it limitative theorems in logic, Banach-Tarski, or anything else).  For some people their ignorance doesn't matter, or at least
it doesn't continue mattering: they learn what they need to learn, or they recognize that it's too difficult for them and they direct their attention elsewhere. But you are too thick to know that you are ignorant, and even if you somehow come to it,
you are too thick to learn.
Sorry, but there it is.
There are plenty of things that a person of your limited intellect could do.  For example, buy a tabloid newspaper each day and fill in the a's, b's, d's, e's, g's, o's, p's and q's.  After you've done that, draw moustaches on the women depicted in it.
My actual reasoning now finally translated into conventional
∀x ∈ L  True(L, x) ↔ Theorem(L, x)
∀x ∈ L False(L, x) ↔ Theorem(L, ~x)
There is no reasoning, there are just two formulae with no explanation of what they mean.
My guess is that the first says
     Something is said to be true (by you, that is) in
     x iff it is a theorem of x.
An expression of language x is true if and only if it is a theorem.
A theorem of what?  Languages don't have theorems, theories have theorems.
Even the fact that a cat is not a type of dog is a theorem of English
evaluated based on the axioms of the mutually exclusive properties
assigned to cat and dog.
Peter Percival
2018-11-01 15:49:15 UTC
Reply
Permalink
Post by peteolcott
Post by peteolcott
Post by Peter Percival
Post by peteolcott
You say all this stuff yet bottom line you cannot point to any
actual mistake in my reasoning.
there is nothing there to harbour any mistakes.  Second, when you
do write something substantive, mistakes are pointed out but you
don't bother to try to understand what is said.
It is difficult to tell you what the problem is without it
sounding impolite.  You are ignorant of the subject matter (be it
limitative theorems in logic, Banach-Tarski, or anything else).
For some people their ignorance doesn't matter, or at least it
doesn't continue mattering: they learn what they need to learn, or
they recognize that it's too difficult for them and they direct
their attention elsewhere. But you are too thick to know that you
are ignorant, and even if you somehow come to it, you are too
thick to learn.
Sorry, but there it is.
There are plenty of things that a person of your limited intellect
could do.  For example, buy a tabloid newspaper each day and fill
in the a's, b's, d's, e's, g's, o's, p's and q's.  After you've
done that, draw moustaches on the women depicted in it.
My actual reasoning now finally translated into conventional
∀x ∈ L  True(L, x) ↔ Theorem(L, x)
∀x ∈ L False(L, x) ↔ Theorem(L, ~x)
There is no reasoning, there are just two formulae with no
explanation of what they mean.
My guess is that the first says
     Something is said to be true (by you, that is) in
     x iff it is a theorem of x.
An expression of language x is true if and only if it is a theorem.
A theorem of what?  Languages don't have theorems, theories have theorems.
Even the fact that a cat is not a type of dog is a theorem of English
evaluated based on the axioms of the mutually exclusive properties
assigned to cat and dog.
Your talking nonsense. English doesn't have axioms. I don't doubt that
someone may take some statement of interest and declare that it's an
axiom. But since someone else may take a contrary statement and declare
that it is an axiom, that gets us nowhere.
peteolcott
2018-11-01 18:59:55 UTC
Reply
Permalink
Post by peteolcott
Post by peteolcott
Post by peteolcott
You say all this stuff yet bottom line you cannot point to any actual mistake in my reasoning.
Two points.  First, your posts are often devoid of reasoning: there is nothing there to harbour any mistakes.  Second, when you do write something substantive, mistakes are pointed out but you don't bother to try to understand what is said.
It is difficult to tell you what the problem is without it sounding impolite.  You are ignorant of the subject matter (be it limitative theorems in logic, Banach-Tarski, or anything else). For some people their ignorance doesn't matter, or at least
it doesn't continue mattering: they learn what they need to learn, or they recognize that it's too difficult for them and they direct their attention elsewhere. But you are too thick to know that you are ignorant, and even if you somehow come to it,
you are too thick to learn.
Sorry, but there it is.
There are plenty of things that a person of your limited intellect could do.  For example, buy a tabloid newspaper each day and fill in the a's, b's, d's, e's, g's, o's, p's and q's.  After you've done that, draw moustaches on the women depicted in it.
My actual reasoning now finally translated into conventional
∀x ∈ L  True(L, x) ↔ Theorem(L, x)
∀x ∈ L False(L, x) ↔ Theorem(L, ~x)
There is no reasoning, there are just two formulae with no explanation of what they mean.
My guess is that the first says
     Something is said to be true (by you, that is) in
     x iff it is a theorem of x.
An expression of language x is true if and only if it is a theorem.
A theorem of what?  Languages don't have theorems, theories have theorems.
Even the fact that a cat is not a type of dog is a theorem of English
evaluated based on the axioms of the mutually exclusive properties
assigned to cat and dog.
Your talking nonsense.  English doesn't have axioms.  I don't doubt that someone may take some statement of interest and declare that it's an axiom.  But since someone else may take a contrary statement and declare that it is an axiom, that gets us nowhere.
We can think of English axioms as the set of properties assigned to words when defining the meaning of these words.

This gives us what I previously referred to as Base_Facts in English.

We can think of Theorems of English as Facts that are derived through correct reasoning from other Facts including Base_Facts.

Copyright 2018 Pete Olcott
peteolcott
2018-11-01 20:03:24 UTC
Reply
Permalink
Post by peteolcott
We can think of English axioms as the set of properties assigned to words when defining the meaning of these words.
Definitions are not axioms.
Post by peteolcott
We can think of Theorems of English as Facts that are derived through correct reasoning from other Facts including Base_Facts.
English is not a deductive system.
EFQ
When developing a mathematical model of the formalization of natural language semantics a lingua franca is required.

A Theorem is essentially nothing more than an expression of language that can be proven True entirely on the basis of facts, thus the conclusion of sound deductive inference.

Axioms can be thought of as (facts) expressions of language that have been expressly defined to have the semantic property of Boolean True.

Rules-of-inference show how to correctly transform some expressions of language into other expressions of language.
peteolcott
2018-11-01 21:46:25 UTC
Reply
Permalink
Post by peteolcott
Post by peteolcott
We can think of English axioms as the set of properties assigned to words when defining the meaning of these words.
Definitions are not axioms.
Post by peteolcott
We can think of Theorems of English as Facts that are derived through correct reasoning from other Facts including Base_Facts.
English is not a deductive system.
When developing a mathematical model of the formalization of natural language semantics a lingua franca is required.
A Theorem is essentially nothing more than an expression of language that can be proven True entirely on the basis of facts, thus the conclusion of sound deductive inference.
No, that is not what a theorem is.
A theorem in a formal language L is a WFF that has a deductive proof requiring nothing but the axioms and rules of inference in L.
It has no inherent (intensional) connection to truth.
There is nothing stopping anyone from building a model of L in which some or all theorems are false.
Post by peteolcott
Axioms can be thought of as (facts) expressions of language that have been expressly defined to have the semantic property of Boolean True.
No, that is not what an axiom is.
An axiom in a formal language L is a WFF that can be introduced on any line of a deductive proof without needing a rule of inference to justify it.
It has no inherent (intensional) connection to truth.
There is nothing stopping anyone from building a model of L in which some or all axioms are false.
You STILL don't understand the difference between a language and a model of a language, between syntax and semantics. This is why you keep trying to translate statements and concepts from the metalanguage into the formal language.
I understand that this only adds purely extraneous complexity.
You could understand this too if you assumed the hypothetical
possibility of this and carefully examined my much simpler
connection between syntax and semantics.

If Axioms (English facts) are considered to be no more and
no less than expressions of formal / natural language that
have been defined to have the semantic property of Boolean
true, much extraneous complexity is stripped away.

When the ultimate ground of being of truth is directly anchored
in the language itself, there is no need for any separate
metalanguage.

Copyright 2018 Pete Olcott
Peter Percival
2018-11-01 22:14:49 UTC
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Post by peteolcott
If Axioms (English facts) are considered to be no more and
no less than expressions of formal / natural language that
have been defined to have the semantic property of Boolean
true, much extraneous complexity is stripped away.
What is this process of defining?

It's a fact that my car is red. (I mean it's a fact in the sense that
normal people use the word 'fact'.) Does it become an Olcottian fact if
someone declares

I define 'Peter's car is red' to have the
semantic property of Boolean true.

What's to stop some impish fellow declaring

I define 'Peter's car is blue' to have the
semantic property of Boolean true.

What do you think you're achieving?

Also, if you want no 'extraneous complexity' why won't just the declarations

Peter's car is red.

or

Peter's car is blue.

do?

peteolcott
2018-10-20 00:45:00 UTC
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The purpose of this paper is to complete the RHS of Tarski's famous formula: ∀x True(x) ↔ φ(x)
For any natural (human) or formal (mathematical) language L we know that an expression X of
language L is true if and only if there are expressions Γ of language L that connect X to known
facts. By extending the notion of a Well Formed Formula to include syntactically formalized rules
for rejecting semantically incorrect expressions we recognize and reject expressions that evaluate to
neither True nor False.
https://www.researchgate.net/publication/323866366_The_Notion_of_Truth_in_Natural_and_Formal_Languages
The Notion of Truth in Natural and Formal Languages
https://philpapers.org/archive/OLCTNO.pdf
Copyright 2016, 2017 2018 (and other years since 1997) Pete Olcott
There is nothing there that you haven't posted to sci.logic before. You have not taken into account the criticisms you got in sci.logic.
You say that you require Mendelson premises to be axioms. That shows that you have not understood the passage from Mendelson even though you have quoted it forty two million times.  (It may be that you mean that you require the set of
premises to be empty, but who cares?)
I am taking Mendelson's specification, adding a new feature and from this
Had you understood Mendelson. you'd know that your "new feature" is no such thing.
So there is no such thing as the hypothesis that premises are axioms?
Wait a minute that was a hypothesis that premises are axioms, therefore
unequivocally proving that there is such a thing.
Read Mendelson.  You quote it often enough, so why not read it? According to Mendelson, a wff C is a consequence of a set of premises Gamma if there is a sequence of wff B_1,..., B_k such that B_k is C and each wff in the sequence B_1,..., B_k
is either
a) an axiom, or
b) a member of Gamma, or
c) deduced from earlier wff in the sequence by a rule of inference.
What do you gain by requiring premises to be axioms?  The axioms are already there, so you are saying that you want no premises, i.e. that Gamma be empty.
     If Γ is the empty set ∅, then ∅ ⊢ C if and only if C is a theorem. It is customary
     to omit the sign “∅” and simply write ⊢ C. Thus, ⊢ C is another way of asserting that
     C is a theorem.
Because of the above breakdown Mendelson would encode sound deductive interfere
as ⊢ C. Because this is sound deductive inference that has no possibly false
premises and only has axioms in their place ⊢ C means True(C).
No, ⊢ C means that C is provable (in some theory T or other, which one possibly being identified by a subscript on ⊢). Sometimes provable and true coincide, sometimes they don't.  It depends on T and has to be demonstrated in each case.  All you
ever do is make dogmatic pronouncements.  Nor does ⊢ C necessarily signal a sound inference.  T may be inconsistent. Again, demonstration, not dogmatic assertion, is needed.
     Validity and Soundness https://www.iep.utm.edu/val-snd/
     A deductive argument is said to be valid if and only if it takes a form that makes it
     impossible for the premises to be true and the conclusion nevertheless to be false.
     Otherwise, a deductive argument is said to be invalid.
     A deductive argument is sound if and only if it is both valid, and all of its premises
     are actually true. Otherwise, a deductive argument is unsound.
When-so-ever a deductive argument is valid
How do you test for validity?
https://en.wikipedia.org/wiki/Logical_consequence#Syntactic_consequence
That doesn't answer the question.  Imagine that you are presented with a logical formula, what will you do with it to demonstrate that it is valid or invalid, as the case may be?
The syntactic rules of the language.
You are not answering the question.  I am uncertain whether you know you are not answering it.
https://en.wikipedia.org/wiki/Modus_tollens
(A & B) -> Z
We know that (A & B) -> Z is not valid (if that's what you mean) by drawing a truth-table, or enough rows of a truth-table to find that it can be given the value false.
Gödel's completeness theorem states that the theorems (provable statements)
are exactly the logically valid well-formed formulas, so identifying valid
formulas is recursively enumerable: given unbounded resources, any valid
formula can eventually be proven.

https://en.wikipedia.org/wiki/G%C3%B6del%27s_completeness_theorem
peteolcott
2018-10-16 15:47:18 UTC
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Post by peteolcott
The purpose of this paper is to complete the RHS of Tarski's famous formula: ∀x True(x) ↔ φ(x)
For any natural (human) or formal (mathematical) language L we know that an expression X of
language L is true if and only if there are expressions Γ of language L that connect X to known
facts. By extending the notion of a Well Formed Formula to include syntactically formalized rules
for rejecting semantically incorrect expressions we recognize and reject expressions that evaluate to
neither True nor False.
https://www.researchgate.net/publication/323866366_The_Notion_of_Truth_in_Natural_and_Formal_Languages
The Notion of Truth in Natural and Formal Languages
https://philpapers.org/archive/OLCTNO.pdf
Copyright 2016, 2017 2018 (and other years since 1997) Pete Olcott
There is nothing there that you haven't posted to sci.logic before.  You have not taken into account the criticisms you got in sci.logic.
None of the criticisms ever pointed out any actual error.
All of the criticisms pertained to differences in communication conventions.

For example I use the term tautology in a way that is different than conventional
usage and define exactly how I am using it, and people say that I am wrong because
I did not use the term in its conventional way.
Jeff Barnett
2018-10-15 18:27:21 UTC
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Post by peteolcott
The purpose of this paper is to complete the RHS of Tarski's famous
formula: ∀x True(x) ↔ φ(x)
For any natural (human) or formal (mathematical) language L we know that an expression X of
language L is true if and only if there are expressions Γ of language L
that connect X to known
facts. By extending the notion of a Well Formed Formula to include
syntactically formalized rules
for rejecting semantically incorrect expressions we recognize and reject
expressions that evaluate to
neither True nor False.
https://www.researchgate.net/publication/323866366_The_Notion_of_Truth_in_Natural_and_Formal_Languages
The Notion of Truth in Natural and Formal Languages
https://philpapers.org/archive/OLCTNO.pdf
Copyright 2016, 2017 2018 (and other years since 1997) Pete Olcott
I see you are reopening a topic after soiling yourself discussing the
BTP for so long. Try to listen to your betters and learn from them here
so you might redeem yourself a little in their eyes. Remember the jury
is still out as to whether you are an over-proud ignoramus or a
successful troll. Think how much better it would be if you could elevate
to status of successful student.
--
Jeff Barnett
António Marques
2018-10-15 21:29:33 UTC
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Post by Jeff Barnett
Post by peteolcott
The purpose of this paper is to complete the RHS of Tarski's famous
formula: ∀x True(x) ↔ φ(x)
For any natural (human) or formal (mathematical) language L we know that
an expression X of
language L is true if and only if there are expressions Γ of language L
that connect X to known
facts. By extending the notion of a Well Formed Formula to include
syntactically formalized rules
for rejecting semantically incorrect expressions we recognize and reject
expressions that evaluate to
neither True nor False.
https://www.researchgate.net/publication/323866366_The_Notion_of_Truth_in_Natural_and_Formal_Languages
The Notion of Truth in Natural and Formal Languages
https://philpapers.org/archive/OLCTNO.pdf
Copyright 2016, 2017 2018 (and other years since 1997) Pete Olcott
I see you are reopening a topic after soiling yourself discussing the
BTP for so long. Try to listen to your betters and learn from them here
so you might redeem yourself a little in their eyes. Remember the jury
is still out as to whether you are an over-proud ignoramus or a
successful troll. Think how much better it would be if you could elevate
to status of successful student.
He’s an immensely successful ignoramus. He’s got all you honchos tied up
doing nothing but catering to his ignorance, and you can’t even spare
sci.lang from it.
DKleinecke
2018-10-16 01:35:57 UTC
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Post by António Marques
Post by Jeff Barnett
Post by peteolcott
The purpose of this paper is to complete the RHS of Tarski's famous
formula: ∀x True(x) ↔ φ(x)
For any natural (human) or formal (mathematical) language L we know that
an expression X of
language L is true if and only if there are expressions Γ of language L
that connect X to known
facts. By extending the notion of a Well Formed Formula to include
syntactically formalized rules
for rejecting semantically incorrect expressions we recognize and reject
expressions that evaluate to
neither True nor False.
https://www.researchgate.net/publication/323866366_The_Notion_of_Truth_in_Natural_and_Formal_Languages
The Notion of Truth in Natural and Formal Languages
https://philpapers.org/archive/OLCTNO.pdf
Copyright 2016, 2017 2018 (and other years since 1997) Pete Olcott
I see you are reopening a topic after soiling yourself discussing the
BTP for so long. Try to listen to your betters and learn from them here
so you might redeem yourself a little in their eyes. Remember the jury
is still out as to whether you are an over-proud ignoramus or a
successful troll. Think how much better it would be if you could elevate
to status of successful student.
He’s an immensely successful ignoramus. He’s got all you honchos tied up
doing nothing but catering to his ignorance, and you can’t even spare
sci.lang from it.
PO imagines he has something to say about human speech and
keeps cross-posting to sci.lang.

Personally I plan to ignore him and his until he actually
says some nontrivial about human language.
Jeff Barnett
2018-10-16 05:46:42 UTC
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Post by DKleinecke
Post by António Marques
Post by Jeff Barnett
Post by peteolcott
The purpose of this paper is to complete the RHS of Tarski's famous
formula: ∀x True(x) ↔ φ(x)
For any natural (human) or formal (mathematical) language L we know that
an expression X of
language L is true if and only if there are expressions Γ of language L
that connect X to known
facts. By extending the notion of a Well Formed Formula to include
syntactically formalized rules
for rejecting semantically incorrect expressions we recognize and reject
expressions that evaluate to
neither True nor False.
https://www.researchgate.net/publication/323866366_The_Notion_of_Truth_in_Natural_and_Formal_Languages
The Notion of Truth in Natural and Formal Languages
https://philpapers.org/archive/OLCTNO.pdf
Copyright 2016, 2017 2018 (and other years since 1997) Pete Olcott
I see you are reopening a topic after soiling yourself discussing the
BTP for so long. Try to listen to your betters and learn from them here
so you might redeem yourself a little in their eyes. Remember the jury
is still out as to whether you are an over-proud ignoramus or a
successful troll. Think how much better it would be if you could elevate
to status of successful student.
He’s an immensely successful ignoramus. He’s got all you honchos tied up
doing nothing but catering to his ignorance, and you can’t even spare
sci.lang from it.
PO imagines he has something to say about human speech and
keeps cross-posting to sci.lang.
Personally I plan to ignore him and his until he actually
says some nontrivial about human language.
That's reasonable. However, I'd add to "nontrivial" the requirement that
it must also be "close to correct". In other words you will probably
never need to not-ignore PO.
--
Jeff Barnett
peteolcott
2018-10-16 15:43:20 UTC
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Post by António Marques
Post by Jeff Barnett
Post by peteolcott
The purpose of this paper is to complete the RHS of Tarski's famous
formula: ∀x True(x) ↔ φ(x)
For any natural (human) or formal (mathematical) language L we know that
an expression X of
language L is true if and only if there are expressions Γ of language L
that connect X to known
facts. By extending the notion of a Well Formed Formula to include
syntactically formalized rules
for rejecting semantically incorrect expressions we recognize and reject
expressions that evaluate to
neither True nor False.
https://www.researchgate.net/publication/323866366_The_Notion_of_Truth_in_Natural_and_Formal_Languages
The Notion of Truth in Natural and Formal Languages
https://philpapers.org/archive/OLCTNO.pdf
Copyright 2016, 2017 2018 (and other years since 1997) Pete Olcott
I see you are reopening a topic after soiling yourself discussing the
BTP for so long. Try to listen to your betters and learn from them here
so you might redeem yourself a little in their eyes. Remember the jury
is still out as to whether you are an over-proud ignoramus or a
successful troll. Think how much better it would be if you could elevate
to status of successful student.
He’s an immensely successful ignoramus. He’s got all you honchos tied up
doing nothing but catering to his ignorance, and you can’t even spare
sci.lang from it.
If it is true that the ignorance is on my side then explain in complete
detail exactly why no mistake in the above has ever been found.
peteolcott
2018-10-16 15:41:03 UTC
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Post by peteolcott
The purpose of this paper is to complete the RHS of Tarski's famous formula: ∀x True(x) ↔ φ(x)
For any natural (human) or formal (mathematical) language L we know that an expression X of
language L is true if and only if there are expressions Γ of language L that connect X to known
facts. By extending the notion of a Well Formed Formula to include syntactically formalized rules
for rejecting semantically incorrect expressions we recognize and reject expressions that evaluate to
neither True nor False.
https://www.researchgate.net/publication/323866366_The_Notion_of_Truth_in_Natural_and_Formal_Languages
The Notion of Truth in Natural and Formal Languages
https://philpapers.org/archive/OLCTNO.pdf
Copyright 2016, 2017 2018 (and other years since 1997) Pete Olcott
I see you are reopening a topic after soiling yourself discussing the BTP for so long. Try to listen to your betters and learn from them here so you might redeem yourself a little in their eyes. Remember the jury is still out as to whether you are an
over-proud ignoramus or a successful troll. Think how much better it would be if you could elevate to status of successful student.
When the rebuttals are only of the form of the ad ignorantiam
fallacy it is unequivocally clear that I have been correct all long.

In one possible world all those that that intentionally lie for
the purpose of causing any harm to others reserve for themselves
a spot with the currently metaphorical father of all lies.
Franz Gnaedinger
2018-10-16 07:18:19 UTC
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Post by peteolcott
Copyright 2016, 2017 2018 (and other years since 1997) Pete Olcott
Peter Olcott knows the absolute and complete and total truth, he is the author
of life and creator of life, he has hundred reasons to assume that he is God,
he creates our future minds in order that we can go on existing, he is a human
being and God in personal union, he is the one Creator of the Universe (claims
he made in schi.lang). The self-declared author of life imposes a lifeless
language on us. He argues in the name of mathematical logic which he deprives
of its power by dismissing proven theorems - Goedel was wrong, Turing was wrong,
Allogd is right. He eliminates paradoxa by becoming a paradox himself.
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