Discussion:
The error of the Liar Paradox and Gödel's 1931 Incompleteness Theorem.
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pete olcott
2020-02-24 18:38:16 UTC
Permalink
The error of the Liar Paradox and Gödel's 1931 Incompleteness Theorem.

Here is the kind of self reference that creates the liar "paradox".

void main()
{
bool LP = !(LP == true);
}

Before LP is defined to have any value, this non-existent value is tested to see if it is equal to true.

This is like asking a person that does not own a car: How many feet long is your car?

Or asking someone that has never been married: Have you stopped beating your spouse yet?

The problem with the Liar Paradox is that its value is only defined on the basis of testing this value before it has been defined.

We can see that this same reasoning also applies to Gödel's 1931 Incompleteness Theorem.

void main()
{
bool G = !(G == Provable(G));
}

Copyright 2016 and 2020 Pete Olcott
pete olcott
2020-02-24 19:55:50 UTC
Permalink
Post by pete olcott
The error of the Liar Paradox and Gödel's 1931 Incompleteness Theorem.
Here is the kind of self reference that creates the liar "paradox".
void main()
{
bool LP = !(LP == true);
}
Before LP is defined to have any value, this non-existent value is tested to see if it is equal to true.
This is like asking a person that does not own a car: How many feet long is your car?
Or asking someone that has never been married: Have you stopped beating your spouse yet?
The problem with the Liar Paradox is that its value is only defined on the basis of testing this value before it has been defined.
We can see that this same reasoning also applies to Gödel's 1931 Incompleteness Theorem.
void main()
{
bool G = !(G == Provable(G));
}
Copyright 2016 and 2020 Pete Olcott
Before LP is defined to have any value, this non-existent value is tested to see if it is equal to true. It is easy to see this through the "C" program because "C" has precisely defined and fully elaborated semantics.

When we understand that the above "C" program accurately captures the essence of the Liar Paradox we see that the problem with the Liar Paradox is that its value is only defined on the basis of testing this value before it has been defined.

"This sentence is not true". It not a truth bearer because it does not specify a relation between things that can be tested that resolves to a single Boolean value.

"This sentence is a bag of green onions". Is a truth bearer because it specifies a relation between things that can be tested that resolves to a single Boolean value.

https://plato.stanford.edu/entries/truthmakers/ This much is agreed: “x makes it true that p” is a construction that signifies, if it signifies anything at all, a relation borne to a truth-bearer by something else, a truth-maker.

"This sentence is not true". Has no object of truth, there is only a relation between the negation of the Boolean value of TRUE and an undefined Boolean value.

"This sentence is a bag of green onions". Has an object of truth, when we test the assertion that the abstraction of the sentence (having no physical existence) is a member of the set of a specific set of physically existing things we find that the answer is Boolean false.
Ruud Harmsen
2020-02-25 12:24:11 UTC
Permalink
Mon, 24 Feb 2020 10:38:16 -0800 (PST): pete olcott
Post by pete olcott
Here is the kind of self reference that creates the liar "paradox".
void main()
{
bool LP = !(LP == true);
}
Did you try recursion yet? It's fun!
https://rudhar.com/sfreview/slshexpd/
Post by pete olcott
bool LP = !(LP == true);
In C, C90 that is, this is equivalent to simply:
int LP = !LP;
A statement which will at least cause a compiler warning, because you
are using an unitialised automatic variable.
When making the variable static, it is probably valid, and results in
LP being 1, because the initialisation is done only once, by the
compiler, after the implicit initialisation to all zero bits.

Trying it out: I am wrong. With a automatic variable: no warning,
value printed is 1:
#include <stdio.h>
void main()
{
int LP = !LP;

printf("LP = %d\n", LP);
}

With a static variable, you do get an error message:
#include <stdio.h>
void main()
{
static int LP = !LP;

printf("LP = %d\n", LP);
}

$cc c.c
c.c: In function ‘main’:
c.c:4:20: error: initializer element is not constant
static int LP = !LP;
^

So there you are. Not a paradox, but an error.
--
Ruud Harmsen, http://rudhar.com
pete olcott
2020-02-25 18:38:27 UTC
Permalink
Post by Ruud Harmsen
Mon, 24 Feb 2020 10:38:16 -0800 (PST): pete olcott
Post by pete olcott
Here is the kind of self reference that creates the liar "paradox".
void main()
{
bool LP = !(LP == true);
}
Did you try recursion yet? It's fun!
https://rudhar.com/sfreview/slshexpd/
Post by pete olcott
bool LP = !(LP == true);
int LP = !LP;
A statement which will at least cause a compiler warning, because you
are using an unitialised automatic variable.
When making the variable static, it is probably valid, and results in
LP being 1, because the initialisation is done only once, by the
compiler, after the implicit initialisation to all zero bits.
Trying it out: I am wrong. With a automatic variable: no warning,
#include <stdio.h>
void main()
{
int LP = !LP;
printf("LP = %d\n", LP);
}
#include <stdio.h>
void main()
{
static int LP = !LP;
printf("LP = %d\n", LP);
}
$cc c.c
c.c:4:20: error: initializer element is not constant
static int LP = !LP;
^
So there you are. Not a paradox, but an error.
--
Ruud Harmsen, http://rudhar.com
That is my point. When we redefine formal systems as my updated paper specifies we can create an automated systems that read the online news and point out all of the lies. A single bot with online access can automatically correctly refute all of the Fake News.

Without proving that Tarski undefinability is incorrect (as my paper has done) this would not be possible.

https://www.researchgate.net/publication/333907915_Proof_that_Wittgenstein_is_correct_about_Godel
peteolcott
2020-02-28 00:36:18 UTC
Permalink
(a) Some expressions of language are stipulated to be true and (b) some relations between expressions of language are stipulated to be truth preserving.

This is all there is to the whole body of truth that can be expressed using language.

When you try and find a counter-example and find this is impossible, my point is proven.

(a) Axioms + (b) rules-of-inference ⊢ (c) Theorems
(a) True Premises + (b) Valid Deduction ⊨ (c) True conclusion.

https://en.wikipedia.org/wiki/Logical_consequence#Proofs_and_models

Copyright 2020 Pete Olcott
DKleinecke
2020-02-28 01:11:48 UTC
Permalink
Post by peteolcott
(a) Some expressions of language are stipulated to be true and (b) some relations between expressions of language are stipulated to be truth preserving.
This is all there is to the whole body of truth that can be expressed using language.
When you try and find a counter-example and find this is impossible, my point is proven.
(a) Axioms + (b) rules-of-inference ⊢ (c) Theorems
(a) True Premises + (b) Valid Deduction ⊨ (c) True conclusion.
https://en.wikipedia.org/wiki/Logical_consequence#Proofs_and_models
IMO language (specifically English) cannot be reduced to a
non-trivial formal system. The trivial method of making everything
an axiom is, of course, always possible.
peteolcott
2020-02-28 01:23:12 UTC
Permalink
Post by DKleinecke
Post by peteolcott
(a) Some expressions of language are stipulated to be true and (b) some relations between expressions of language are stipulated to be truth preserving.
This is all there is to the whole body of truth that can be expressed using language.
When you try and find a counter-example and find this is impossible, my point is proven.
(a) Axioms + (b) rules-of-inference ⊢ (c) Theorems
(a) True Premises + (b) Valid Deduction ⊨ (c) True conclusion.
https://en.wikipedia.org/wiki/Logical_consequence#Proofs_and_models
IMO language (specifically English) cannot be reduced to a
non-trivial formal system.
(a) Some expressions of language are stipulated to be true and
(b) Some relations between expressions of language are stipulated to be truth preserving

Try and find any truth expressed in English that does not fit into some combination of (a) and (b).
DKleinecke
2020-02-28 05:27:54 UTC
Permalink
Post by peteolcott
Post by DKleinecke
Post by peteolcott
(a) Some expressions of language are stipulated to be true and (b) some relations between expressions of language are stipulated to be truth preserving.
This is all there is to the whole body of truth that can be expressed using language.
When you try and find a counter-example and find this is impossible, my point is proven.
(a) Axioms + (b) rules-of-inference ⊢ (c) Theorems
(a) True Premises + (b) Valid Deduction ⊨ (c) True conclusion.
https://en.wikipedia.org/wiki/Logical_consequence#Proofs_and_models
IMO language (specifically English) cannot be reduced to a
non-trivial formal system.
(a) Some expressions of language are stipulated to be true and
(b) Some relations between expressions of language are stipulated to be truth preserving
Try and find any truth expressed in English that does not fit into some combination of (a) and (b).
You just stipulate everything you call true and QED.

The problem is that what you call true is not what the rest of us
call true.

There is a type of implication using words that holds:
"He lives in a red house" -> "He lives in a house"
You might call it "adjective removal". So far I have
discovered no truth preserving relations that are purely
linguistic rather than linguistic expressions for non-
linguistic facts except adjective removal.
Ymir
2020-02-28 07:20:58 UTC
Permalink
Post by DKleinecke
Post by peteolcott
Post by DKleinecke
Post by peteolcott
(a) Some expressions of language are stipulated to be true and (b) some relations between expressions of language are stipulated to be truth preserving.
This is all there is to the whole body of truth that can be expressed using language.
When you try and find a counter-example and find this is impossible, my point is proven.
(a) Axioms + (b) rules-of-inference ⊢ (c) Theorems
(a) True Premises + (b) Valid Deduction ⊨ (c) True conclusion.
https://en.wikipedia.org/wiki/Logical_consequence#Proofs_and_models
IMO language (specifically English) cannot be reduced to a
non-trivial formal system.
(a) Some expressions of language are stipulated to be true and
(b) Some relations between expressions of language are stipulated to be truth preserving
Try and find any truth expressed in English that does not fit into some combination of (a) and (b).
You just stipulate everything you call true and QED.
The problem is that what you call true is not what the rest of us
call true.
"He lives in a red house" -> "He lives in a house"
You might call it "adjective removal". So far I have
discovered no truth preserving relations that are purely
linguistic rather than linguistic expressions for non-
linguistic facts except adjective removal.
'He owned a counterfeit Monet' -/-> 'He owned a Monet'.

Or, more apropos of any thread involving Olcott, 'He constructed a
faulty proof' arguably does not imply 'He constructed a proof'.

André
--
To email remove 'invalid' & replace 'gm' with well known Google mail
service.
peteolcott
2020-02-28 14:54:06 UTC
Permalink
Post by Ymir
Post by DKleinecke
Post by peteolcott
Post by DKleinecke
Post by peteolcott
(a) Some expressions of language are stipulated to be true and (b) some relations between expressions of language are stipulated to be truth preserving.
This is all there is to the whole body of truth that can be expressed using language.
When you try and find a counter-example and find this is impossible, my point is proven.
(a) Axioms + (b) rules-of-inference ⊢ (c) Theorems
(a) True Premises + (b) Valid Deduction ⊨ (c) True conclusion.
https://en.wikipedia.org/wiki/Logical_consequence#Proofs_and_models
IMO language (specifically English) cannot be reduced to a
non-trivial formal system.
(a) Some expressions of language are stipulated to be true and
(b) Some relations between expressions of language are stipulated to be truth preserving
Try and find any truth expressed in English that does not fit into some combination of (a) and (b).
You just stipulate everything you call true and QED.
The problem is that what you call true is not what the rest of us
call true.
"He lives in a red house" -> "He lives in a house"
You might call it "adjective removal". So far I have
discovered no truth preserving relations that are purely
linguistic rather than linguistic expressions for non-
linguistic facts except adjective removal.
'He owned a counterfeit Monet' -/-> 'He owned a Monet'.
Or, more apropos of any thread involving Olcott, 'He constructed a
faulty proof' arguably does not imply 'He constructed a proof'.
André
--
To email remove 'invalid' & replace 'gm' with well known Google mail
service.
Unique_Individual X ∈ Male_Humans
Unique_Individual Y ∈ Work-of-Art
Owned(X, Y) & Not_Authentic(Y, Monet)
peteolcott
2020-02-28 15:02:38 UTC
Permalink
Post by Ymir
Post by DKleinecke
Post by peteolcott
Post by DKleinecke
Post by peteolcott
(a) Some expressions of language are stipulated to be true and (b) some relations between expressions of language are stipulated to be truth preserving.
This is all there is to the whole body of truth that can be expressed using language.
When you try and find a counter-example and find this is impossible, my point is proven.
(a) Axioms + (b) rules-of-inference ⊢ (c) Theorems
(a) True Premises + (b) Valid Deduction ⊨ (c) True conclusion.
https://en.wikipedia.org/wiki/Logical_consequence#Proofs_and_models
IMO language (specifically English) cannot be reduced to a
non-trivial formal system.
(a) Some expressions of language are stipulated to be true and
(b) Some relations between expressions of language are stipulated to be truth preserving
Try and find any truth expressed in English that does not fit into some combination of (a) and (b).
You just stipulate everything you call true and QED.
The problem is that what you call true is not what the rest of us
call true.
"He lives in a red house" -> "He lives in a house"
You might call it "adjective removal". So far I have
discovered no truth preserving relations that are purely
linguistic rather than linguistic expressions for non-
linguistic facts except adjective removal.
'He owned a counterfeit Monet' -/-> 'He owned a Monet'.
Or, more apropos of any thread involving Olcott, 'He constructed a
faulty proof' arguably does not imply 'He constructed a proof'.
André
--
To email remove 'invalid' & replace 'gm' with well known Google mail
service.
∃!x ∈ Male_Humans
∃!y ∈ Work-of-Art
(Owned(x, y) & Not_Authentic(y, Monet))
Ymir
2020-02-28 16:21:57 UTC
Permalink
Post by peteolcott
Post by Ymir
Post by DKleinecke
Post by peteolcott
Post by DKleinecke
Post by peteolcott
(a) Some expressions of language are stipulated to be true and (b) some relations between expressions of language are stipulated to be truth preserving.
This is all there is to the whole body of truth that can be expressed using language.
When you try and find a counter-example and find this is impossible, my point is proven.
(a) Axioms + (b) rules-of-inference ⊢ (c) Theorems
(a) True Premises + (b) Valid Deduction ⊨ (c) True conclusion.
https://en.wikipedia.org/wiki/Logical_consequence#Proofs_and_models
IMO language (specifically English) cannot be reduced to a
non-trivial formal system.
(a) Some expressions of language are stipulated to be true and
(b) Some relations between expressions of language are stipulated to be truth preserving
Try and find any truth expressed in English that does not fit into some combination of (a) and (b).
You just stipulate everything you call true and QED.
The problem is that what you call true is not what the rest of us
call true.
"He lives in a red house" -> "He lives in a house"
You might call it "adjective removal". So far I have
discovered no truth preserving relations that are purely
linguistic rather than linguistic expressions for non-
linguistic facts except adjective removal.
'He owned a counterfeit Monet' -/-> 'He owned a Monet'.
Or, more apropos of any thread involving Olcott, 'He constructed a
faulty proof' arguably does not imply 'He constructed a proof'.
André
--
To email remove 'invalid' & replace 'gm' with well known Google mail
service.
Unique_Individual X ∈ Male_Humans
Unique_Individual Y ∈ Work-of-Art
Owned(X, Y) & Not_Authentic(Y, Monet)
Did you have an actual point?

André
--
To email remove 'invalid' & replace 'gm' with well known Google mail
service.
peteolcott
2020-02-28 17:23:25 UTC
Permalink
Post by Ymir
Post by peteolcott
Post by Ymir
Post by DKleinecke
Post by peteolcott
Post by DKleinecke
Post by peteolcott
(a) Some expressions of language are stipulated to be true and (b) some relations between expressions of language are stipulated to be truth preserving.
This is all there is to the whole body of truth that can be expressed using language.
When you try and find a counter-example and find this is impossible, my point is proven.
(a) Axioms + (b) rules-of-inference ⊢ (c) Theorems
(a) True Premises + (b) Valid Deduction ⊨ (c) True conclusion.
https://en.wikipedia.org/wiki/Logical_consequence#Proofs_and_models
IMO language (specifically English) cannot be reduced to a
non-trivial formal system.
(a) Some expressions of language are stipulated to be true and
(b) Some relations between expressions of language are stipulated to be truth preserving
Try and find any truth expressed in English that does not fit into some combination of (a) and (b).
You just stipulate everything you call true and QED.
The problem is that what you call true is not what the rest of us
call true.
"He lives in a red house" -> "He lives in a house"
You might call it "adjective removal". So far I have
discovered no truth preserving relations that are purely
linguistic rather than linguistic expressions for non-
linguistic facts except adjective removal.
'He owned a counterfeit Monet' -/-> 'He owned a Monet'.
Or, more apropos of any thread involving Olcott, 'He constructed a
faulty proof' arguably does not imply 'He constructed a proof'.
André
--
To email remove 'invalid' & replace 'gm' with well known Google mail
service.
Unique_Individual X ∈ Male_Humans
Unique_Individual Y ∈ Work-of-Art
Owned(X, Y) & Not_Authentic(Y, Monet)
Did you have an actual point?
André
I asked for counter-examples to the following statement:

The entire body of knowledge that can be expressed using language is entirely comprised of: expressions of language stipulated to be true and relations between expressions of language that are stipulated to be truth preserving.

You provided one, and I showed how it is not a counter-example.
DKleinecke
2020-02-28 18:41:48 UTC
Permalink
Post by peteolcott
Post by Ymir
Post by peteolcott
Post by Ymir
Post by DKleinecke
Post by peteolcott
Post by DKleinecke
Post by peteolcott
(a) Some expressions of language are stipulated to be true and (b) some relations between expressions of language are stipulated to be truth preserving.
This is all there is to the whole body of truth that can be expressed using language.
When you try and find a counter-example and find this is impossible, my point is proven.
(a) Axioms + (b) rules-of-inference ⊢ (c) Theorems
(a) True Premises + (b) Valid Deduction ⊨ (c) True conclusion.
https://en.wikipedia.org/wiki/Logical_consequence#Proofs_and_models
IMO language (specifically English) cannot be reduced to a
non-trivial formal system.
(a) Some expressions of language are stipulated to be true and
(b) Some relations between expressions of language are stipulated to be truth preserving
Try and find any truth expressed in English that does not fit into some combination of (a) and (b).
You just stipulate everything you call true and QED.
The problem is that what you call true is not what the rest of us
call true.
"He lives in a red house" -> "He lives in a house"
You might call it "adjective removal". So far I have
discovered no truth preserving relations that are purely
linguistic rather than linguistic expressions for non-
linguistic facts except adjective removal.
'He owned a counterfeit Monet' -/-> 'He owned a Monet'.
Or, more apropos of any thread involving Olcott, 'He constructed a
faulty proof' arguably does not imply 'He constructed a proof'.
André
--
To email remove 'invalid' & replace 'gm' with well known Google mail
service.
Unique_Individual X ∈ Male_Humans
Unique_Individual Y ∈ Work-of-Art
Owned(X, Y) & Not_Authentic(Y, Monet)
Did you have an actual point?
André
The entire body of knowledge that can be expressed using language is entirely comprised of: expressions of language stipulated to be true and relations between expressions of language that are stipulated to be truth preserving.
You provided one, and I showed how it is not a counter-example.
You misunderstood me. I was partially agreeing with you and I provided
an example of where your notions are accurate. Mine was an example of
where there was a valid deduction of one true statement from another
true statement.
Ymir
2020-02-28 19:20:56 UTC
Permalink
Post by peteolcott
Post by Ymir
Post by peteolcott
Post by Ymir
Post by DKleinecke
Post by peteolcott
Post by DKleinecke
Post by peteolcott
(a) Some expressions of language are stipulated to be true and (b) some relations between expressions of language are stipulated to be truth preserving.
This is all there is to the whole body of truth that can be expressed using language.
When you try and find a counter-example and find this is impossible, my point is proven.
(a) Axioms + (b) rules-of-inference ⊢ (c) Theorems
(a) True Premises + (b) Valid Deduction ⊨ (c) True conclusion.
https://en.wikipedia.org/wiki/Logical_consequence#Proofs_and_models
IMO language (specifically English) cannot be reduced to a
non-trivial formal system.
(a) Some expressions of language are stipulated to be true and
(b) Some relations between expressions of language are stipulated to be truth preserving
Try and find any truth expressed in English that does not fit into some combination of (a) and (b).
You just stipulate everything you call true and QED.
The problem is that what you call true is not what the rest of us
call true.
"He lives in a red house" -> "He lives in a house"
You might call it "adjective removal". So far I have
discovered no truth preserving relations that are purely
linguistic rather than linguistic expressions for non-
linguistic facts except adjective removal.
'He owned a counterfeit Monet' -/-> 'He owned a Monet'.
Or, more apropos of any thread involving Olcott, 'He constructed a
faulty proof' arguably does not imply 'He constructed a proof'.
André
--
To email remove 'invalid' & replace 'gm' with well known Google mail
service.
Unique_Individual X ∈ Male_Humans
Unique_Individual Y ∈ Work-of-Art
Owned(X, Y) & Not_Authentic(Y, Monet)
Did you have an actual point?
André
The entire body of knowledge that can be expressed using language is entirely comprised of: expressions of language stipulated to be true and relations between expressions of language that are stipulated to be truth preserving.
You provided one, and I showed how it is not a counter-example.
I provided a counterexample to DKleinecke's claim.

Translating the statement into some sort of pseudoformalism doesn't show
anything about whether it is a counterexample or not.

André
--
To email remove 'invalid' & replace 'gm' with well known Google mail
service.
s***@gmail.com
2020-02-29 15:37:34 UTC
Permalink
Post by peteolcott
Post by Ymir
Post by peteolcott
Post by Ymir
Post by DKleinecke
Post by peteolcott
Post by DKleinecke
Post by peteolcott
(a) Some expressions of language are stipulated to be true and (b) some relations between expressions of language are stipulated to be truth preserving.
This is all there is to the whole body of truth that can be expressed using language.
When you try and find a counter-example and find this is impossible, my point is proven.
(a) Axioms + (b) rules-of-inference ⊢ (c) Theorems
(a) True Premises + (b) Valid Deduction ⊨ (c) True conclusion.
https://en.wikipedia.org/wiki/Logical_consequence#Proofs_and_models
IMO language (specifically English) cannot be reduced to a
non-trivial formal system.
(a) Some expressions of language are stipulated to be true and
(b) Some relations between expressions of language are stipulated to be truth preserving
Try and find any truth expressed in English that does not fit into some combination of (a) and (b).
You just stipulate everything you call true and QED.
The problem is that what you call true is not what the rest of us
call true.
"He lives in a red house" -> "He lives in a house"
You might call it "adjective removal". So far I have
discovered no truth preserving relations that are purely
linguistic rather than linguistic expressions for non-
linguistic facts except adjective removal.
'He owned a counterfeit Monet' -/-> 'He owned a Monet'.
Or, more apropos of any thread involving Olcott, 'He constructed a
faulty proof' arguably does not imply 'He constructed a proof'.
André
--
To email remove 'invalid' & replace 'gm' with well known Google mail
service.
Unique_Individual X ∈ Male_Humans
Unique_Individual Y ∈ Work-of-Art
Owned(X, Y) & Not_Authentic(Y, Monet)
Did you have an actual point?
André
The entire body of knowledge that can be expressed using language is entirely comprised of: expressions of language stipulated to be true and relations between expressions of language that are stipulated to be truth preserving.
You provided one, and I showed how it is not a counter-example.
your writings seem to be the ravings of a mentally ill person. If you are sane and like to be well-paid, talk to google or microsoft. If your ideas can help reducing existence to bits and bytes they would be interested.
DKleinecke
2020-02-28 18:36:40 UTC
Permalink
Post by Ymir
Post by DKleinecke
Post by peteolcott
Post by DKleinecke
Post by peteolcott
(a) Some expressions of language are stipulated to be true and (b) some relations between expressions of language are stipulated to be truth preserving.
This is all there is to the whole body of truth that can be expressed using language.
When you try and find a counter-example and find this is impossible, my point is proven.
(a) Axioms + (b) rules-of-inference ⊢ (c) Theorems
(a) True Premises + (b) Valid Deduction ⊨ (c) True conclusion.
https://en.wikipedia.org/wiki/Logical_consequence#Proofs_and_models
IMO language (specifically English) cannot be reduced to a
non-trivial formal system.
(a) Some expressions of language are stipulated to be true and
(b) Some relations between expressions of language are stipulated to be truth preserving
Try and find any truth expressed in English that does not fit into some combination of (a) and (b).
You just stipulate everything you call true and QED.
The problem is that what you call true is not what the rest of us
call true.
"He lives in a red house" -> "He lives in a house"
You might call it "adjective removal". So far I have
discovered no truth preserving relations that are purely
linguistic rather than linguistic expressions for non-
linguistic facts except adjective removal.
'He owned a counterfeit Monet' -/-> 'He owned a Monet'.
Or, more apropos of any thread involving Olcott, 'He constructed a
faulty proof' arguably does not imply 'He constructed a proof'.
You got me.

Adjective dropping doesn't work with negative adjectives.
Approximately I have to preserve the negativity:
'He owned a counterfeit Monet' > 'He did not own a Monet'.
puts the NOT at the wrong place
'He owned a counterfeit Monet' > 'He owned a NOT Monet'.
which I think does not ever reach utterance status.

But my intuition is that
'He constructed a faulty proof' does imply
'He constructed a proof'.
and something appears to be going on that I cannot explain.
a faulty proof
Ymir
2020-02-28 19:25:07 UTC
Permalink
Post by DKleinecke
Post by Ymir
Post by DKleinecke
Post by peteolcott
Post by DKleinecke
Post by peteolcott
(a) Some expressions of language are stipulated to be true and (b) some relations between expressions of language are stipulated to be truth preserving.
This is all there is to the whole body of truth that can be expressed using language.
When you try and find a counter-example and find this is impossible, my point is proven.
(a) Axioms + (b) rules-of-inference ⊢ (c) Theorems
(a) True Premises + (b) Valid Deduction ⊨ (c) True conclusion.
https://en.wikipedia.org/wiki/Logical_consequence#Proofs_and_models
IMO language (specifically English) cannot be reduced to a
non-trivial formal system.
(a) Some expressions of language are stipulated to be true and
(b) Some relations between expressions of language are stipulated to be truth preserving
Try and find any truth expressed in English that does not fit into some combination of (a) and (b).
You just stipulate everything you call true and QED.
The problem is that what you call true is not what the rest of us
call true.
"He lives in a red house" -> "He lives in a house"
You might call it "adjective removal". So far I have
discovered no truth preserving relations that are purely
linguistic rather than linguistic expressions for non-
linguistic facts except adjective removal.
'He owned a counterfeit Monet' -/-> 'He owned a Monet'.
Or, more apropos of any thread involving Olcott, 'He constructed a
faulty proof' arguably does not imply 'He constructed a proof'.
You got me.
Adjective dropping doesn't work with negative adjectives.
'He owned a counterfeit Monet' > 'He did not own a Monet'.
puts the NOT at the wrong place
'He owned a counterfeit Monet' > 'He owned a NOT Monet'.
which I think does not ever reach utterance status.
But my intuition is that
'He constructed a faulty proof' does imply
'He constructed a proof'.
I agree that this example is much less clear-cut, which is why I put the
word 'arguably' in there. It really depends on how 'proof' is defined.
If it includes the notion of validity, then a faulty proof isn't a
proof, but it also means the word is being abused in the expression 'a
faulty proof'. I suspect you'd find people willing to argue both
positions on this one.

André
Post by DKleinecke
and something appears to be going on that I cannot explain.
a faulty proof
--
To email remove 'invalid' & replace 'gm' with well known Google mail
service.
peteolcott
2020-02-28 21:04:09 UTC
Permalink
Post by Ymir
Post by DKleinecke
Post by Ymir
Post by DKleinecke
Post by peteolcott
Post by DKleinecke
Post by peteolcott
(a) Some expressions of language are stipulated to be true and (b) some relations between expressions of language are stipulated to be truth preserving.
This is all there is to the whole body of truth that can be expressed using language.
When you try and find a counter-example and find this is impossible, my point is proven.
(a) Axioms + (b) rules-of-inference ⊢ (c) Theorems
(a) True Premises + (b) Valid Deduction ⊨ (c) True conclusion.
https://en.wikipedia.org/wiki/Logical_consequence#Proofs_and_models
IMO language (specifically English) cannot be reduced to a
non-trivial formal system.
(a) Some expressions of language are stipulated to be true and
(b) Some relations between expressions of language are stipulated to be truth preserving
Try and find any truth expressed in English that does not fit into some combination of (a) and (b).
You just stipulate everything you call true and QED.
The problem is that what you call true is not what the rest of us
call true.
"He lives in a red house" -> "He lives in a house"
You might call it "adjective removal". So far I have
discovered no truth preserving relations that are purely
linguistic rather than linguistic expressions for non-
linguistic facts except adjective removal.
'He owned a counterfeit Monet' -/-> 'He owned a Monet'.
Or, more apropos of any thread involving Olcott, 'He constructed a
faulty proof' arguably does not imply 'He constructed a proof'.
You got me.
Adjective dropping doesn't work with negative adjectives.
'He owned a counterfeit Monet' > 'He did not own a Monet'.
puts the NOT at the wrong place
'He owned a counterfeit Monet' > 'He owned a NOT Monet'.
which I think does not ever reach utterance status.
But my intuition is that
'He constructed a faulty proof' does imply
'He constructed a proof'.
I agree that this example is much less clear-cut, which is why I put the
word 'arguably' in there. It really depends on how 'proof' is defined.
If it includes the notion of validity, then a faulty proof isn't a
proof, but it also means the word is being abused in the expression 'a
faulty proof'. I suspect you'd find people willing to argue both
positions on this one.
André
Post by DKleinecke
and something appears to be going on that I cannot explain.
a faulty proof
--
To email remove 'invalid' & replace 'gm' with well known Google mail
service.
Sound deduction is merely valid inference on the basis of known facts.
DKleinecke
2020-02-29 01:39:33 UTC
Permalink
Post by Ymir
Post by DKleinecke
Post by Ymir
Post by DKleinecke
Post by peteolcott
Post by DKleinecke
Post by peteolcott
(a) Some expressions of language are stipulated to be true and (b) some relations between expressions of language are stipulated to be truth preserving.
This is all there is to the whole body of truth that can be expressed using language.
When you try and find a counter-example and find this is impossible, my point is proven.
(a) Axioms + (b) rules-of-inference ⊢ (c) Theorems
(a) True Premises + (b) Valid Deduction ⊨ (c) True conclusion.
https://en.wikipedia.org/wiki/Logical_consequence#Proofs_and_models
IMO language (specifically English) cannot be reduced to a
non-trivial formal system.
(a) Some expressions of language are stipulated to be true and
(b) Some relations between expressions of language are stipulated to be truth preserving
Try and find any truth expressed in English that does not fit into some combination of (a) and (b).
You just stipulate everything you call true and QED.
The problem is that what you call true is not what the rest of us
call true.
"He lives in a red house" -> "He lives in a house"
You might call it "adjective removal". So far I have
discovered no truth preserving relations that are purely
linguistic rather than linguistic expressions for non-
linguistic facts except adjective removal.
'He owned a counterfeit Monet' -/-> 'He owned a Monet'.
Or, more apropos of any thread involving Olcott, 'He constructed a
faulty proof' arguably does not imply 'He constructed a proof'.
You got me.
Adjective dropping doesn't work with negative adjectives.
'He owned a counterfeit Monet' > 'He did not own a Monet'.
puts the NOT at the wrong place
'He owned a counterfeit Monet' > 'He owned a NOT Monet'.
which I think does not ever reach utterance status.
But my intuition is that
'He constructed a faulty proof' does imply
'He constructed a proof'.
I agree that this example is much less clear-cut, which is why I put the
word 'arguably' in there. It really depends on how 'proof' is defined.
If it includes the notion of validity, then a faulty proof isn't a
proof, but it also means the word is being abused in the expression 'a
faulty proof'. I suspect you'd find people willing to argue both
positions on this one.
I see, at this moment:
(NOT non-counterfeit) Monet
faulty proof

So far as I know there is no other evidence for such a proposal

This is new to me - I am still thinking
peteolcott
2020-02-28 14:49:24 UTC
Permalink
Post by DKleinecke
Post by peteolcott
Post by DKleinecke
Post by peteolcott
(a) Some expressions of language are stipulated to be true and (b) some relations between expressions of language are stipulated to be truth preserving.
This is all there is to the whole body of truth that can be expressed using language.
When you try and find a counter-example and find this is impossible, my point is proven.
(a) Axioms + (b) rules-of-inference ⊢ (c) Theorems
(a) True Premises + (b) Valid Deduction ⊨ (c) True conclusion.
https://en.wikipedia.org/wiki/Logical_consequence#Proofs_and_models
IMO language (specifically English) cannot be reduced to a
non-trivial formal system.
(a) Some expressions of language are stipulated to be true and
(b) Some relations between expressions of language are stipulated to be truth preserving
Try and find any truth expressed in English that does not fit into some combination of (a) and (b).
You just stipulate everything you call true and QED.
The problem is that what you call true is not what the rest of us
call true.
When we simply encode the entire set of knowledge that can be expressed in language we have what the rest of the world calls true.

The rest of the world does not call the following sentence either true or false: "This sentence is not true." because it is neither true nor false, thus it is not a truth bearer and rejected as ill-formed on that basis.
Post by DKleinecke
"He lives in a red house" -> "He lives in a house"
You might call it "adjective removal". So far I have
discovered no truth preserving relations that are purely
linguistic rather than linguistic expressions for non-
linguistic facts except adjective removal.
Unique-Individual X ∈ Male_Humans
Unique-Individual Y ∈ Houses
(Lives-In(X, Y) & Has_Color(Y, RED))
peteolcott
2020-02-29 15:51:24 UTC
Permalink
(a) John owns a brick house
(b) John owns a house
(c) John owns a counterfeit Monet
(d) John owns a Monet

∃!JOHN ∈ Male_Humans
∃!y ∈ Houses
(Owns(JOHN, y) & Construction_Material(y, BRICK))

∃!JOHN ∈ Male_Humans
∃!y ∈ Houses
(Owns(JOHN, y)

∃!JOHN ∈ Male_Humans
∃!y ∈ Work-of-Art
∃!MONET ∈ Famous_Artists
∃!MONET_ART ∈ Artwork(MONET)
(Owns(JOHN, y) & ~Authentic(y, MONET_ART))

∃!JOHN ∈ Male_Humans
∃!y ∈ Work-of-Art
∃!MONET ∈ Famous_Artists
∃!MONET_ART ∈ Artwork(MONET)
(Owns(JOHN, y) & Authentic(y, MONET_ART))

Copyright 2020 Pete Olcott

https://www.researchgate.net/publication/331859461_Minimal_Type_Theory_YACC_BNF
DKleinecke
2020-02-29 16:47:38 UTC
Permalink
Post by peteolcott
(a) John owns a brick house
(b) John owns a house
(c) John owns a counterfeit Monet
(d) John owns a Monet
∃!JOHN ∈ Male_Humans
∃!y ∈ Houses
(Owns(JOHN, y) & Construction_Material(y, BRICK))
∃!JOHN ∈ Male_Humans
∃!y ∈ Houses
(Owns(JOHN, y)
∃!JOHN ∈ Male_Humans
∃!y ∈ Work-of-Art
∃!MONET ∈ Famous_Artists
∃!MONET_ART ∈ Artwork(MONET)
(Owns(JOHN, y) & ~Authentic(y, MONET_ART))
∃!JOHN ∈ Male_Humans
∃!y ∈ Work-of-Art
∃!MONET ∈ Famous_Artists
∃!MONET_ART ∈ Artwork(MONET)
(Owns(JOHN, y) & Authentic(y, MONET_ART))
Copyright 2020 Pete Olcott
https://www.researchgate.net/publication/331859461_Minimal_Type_Theory_YACC_BNF
Today I have decided I was almost right originally and
John owns a counterfeit Monet
does entail
John owns a Monet
The confusion arises because of the semantics of "a Monet".

However it is not just adjectives that can be dropped.
I often visited Paris
entails
I visited Paris
Apparently any adjunct can be dropped to get a true entailment.

Adjunct dropping is an example of a true entailment that
arises within English syntax without reference to semantics.
peteolcott
2020-02-29 17:15:54 UTC
Permalink
Post by DKleinecke
Post by peteolcott
(a) John owns a brick house
(b) John owns a house
(c) John owns a counterfeit Monet
(d) John owns a Monet
∃!JOHN ∈ Male_Humans
∃!y ∈ Houses
(Owns(JOHN, y) & Construction_Material(y, BRICK))
∃!JOHN ∈ Male_Humans
∃!y ∈ Houses
(Owns(JOHN, y)
∃!JOHN ∈ Male_Humans
∃!y ∈ Work-of-Art
∃!MONET ∈ Famous_Artists
∃!MONET_ART ∈ Artwork(MONET)
(Owns(JOHN, y) & ~Authentic(y, MONET_ART))
∃!JOHN ∈ Male_Humans
∃!y ∈ Work-of-Art
∃!MONET ∈ Famous_Artists
∃!MONET_ART ∈ Artwork(MONET)
(Owns(JOHN, y) & Authentic(y, MONET_ART))
Copyright 2020 Pete Olcott
https://www.researchgate.net/publication/331859461_Minimal_Type_Theory_YACC_BNF
Today I have decided I was almost right originally and
John owns a counterfeit Monet
does entail
John owns a Monet
The confusion arises because of the semantics of "a Monet".
However it is not just adjectives that can be dropped.
I often visited Paris
entails
I visited Paris
Apparently any adjunct can be dropped to get a true entailment.
Adjunct dropping is an example of a true entailment that
arises within English syntax without reference to semantics.
https://en.wikipedia.org/wiki/Colorless_green_ideas_sleep_furiously
Yet the only way that we can know that the above sentence is a truth bearer with the semantic value of false is a type mismatch error between its tokens.
Peter T. Daniels
2020-02-29 19:16:33 UTC
Permalink
Post by DKleinecke
Today I have decided I was almost right originally and
John owns a counterfeit Monet
does entail
John owns a Monet
The confusion arises because of the semantics of "a Monet".
However it is not just adjectives that can be dropped.
I often visited Paris
entails
I visited Paris
Apparently any adjunct can be dropped to get a true entailment.
Adjunct dropping is an example of a true entailment that
arises within English syntax without reference to semantics.
Could DK and Ymir start a new thread, so that their discussion can be
followed without having to dodge the messages from someone else?
DKleinecke
2020-02-29 20:15:57 UTC
Permalink
Post by Peter T. Daniels
Post by DKleinecke
Today I have decided I was almost right originally and
John owns a counterfeit Monet
does entail
John owns a Monet
The confusion arises because of the semantics of "a Monet".
However it is not just adjectives that can be dropped.
I often visited Paris
entails
I visited Paris
Apparently any adjunct can be dropped to get a true entailment.
Adjunct dropping is an example of a true entailment that
arises within English syntax without reference to semantics.
Could DK and Ymir start a new thread, so that their discussion can be
followed without having to dodge the messages from someone else?
We could but we probably wont. I, at least, have nothing more to say.
peteolcott
2020-02-29 20:31:30 UTC
Permalink
Post by Peter T. Daniels
Post by DKleinecke
Today I have decided I was almost right originally and
John owns a counterfeit Monet
does entail
John owns a Monet
The confusion arises because of the semantics of "a Monet".
However it is not just adjectives that can be dropped.
I often visited Paris
entails
I visited Paris
Apparently any adjunct can be dropped to get a true entailment.
Adjunct dropping is an example of a true entailment that
arises within English syntax without reference to semantics.
Could DK and Ymir start a new thread, so that their discussion can be
followed without having to dodge the messages from someone else?
DK is talking to me.
peteolcott
2020-02-29 21:56:36 UTC
Permalink
Post by DKleinecke
Post by peteolcott
(a) John owns a brick house
(b) John owns a house
(c) John owns a counterfeit Monet
(d) John owns a Monet
∃!JOHN ∈ Male_Humans
∃!y ∈ Houses
(Owns(JOHN, y) & Construction_Material(y, BRICK))
∃!JOHN ∈ Male_Humans
∃!y ∈ Houses
(Owns(JOHN, y)
∃!JOHN ∈ Male_Humans
∃!y ∈ Work-of-Art
∃!MONET ∈ Famous_Artists
∃!MONET_ART ∈ Artwork(MONET)
(Owns(JOHN, y) & ~Authentic(y, MONET_ART))
∃!JOHN ∈ Male_Humans
∃!y ∈ Work-of-Art
∃!MONET ∈ Famous_Artists
∃!MONET_ART ∈ Artwork(MONET)
(Owns(JOHN, y) & Authentic(y, MONET_ART))
Copyright 2020 Pete Olcott
https://www.researchgate.net/publication/331859461_Minimal_Type_Theory_YACC_BNF
Today I have decided I was almost right originally and
John owns a counterfeit Monet
does entail
John owns a Monet
The confusion arises because of the semantics of "a Monet".
The semantic meaning of {counterfeit} has an effect similar to Boolean negation.
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