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Oct 10, 2015, 4:49:53 PM10/10/15

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P.F. Strawson proposed to translate “No F is G” as ~(∃x)(Fx & Gx) &

(∃x)Fx & (∃x)Gx. (Strawson, 1952, Introduction to Logical Theory,

London, Methuen, pp. 163-179.) Furthermore he proposed to take the term

(∃x)Fx & (∃x)Gx as a PRESUPPOSITION. That is if (∃x)Fx & (∃x)Gx is not

true then ~(∃x)(Fx & Gx) is neither true nor false. So for example the

sentence “All John's children are asleep” is ~(T v F) if John has no

children. How does this help with the Liar paradox? Consider

This sentence is not true (Y)

The argument usually goes as follows.

(1) Assume that Y is true

(2) Then what it says is the case

(3) It says it is not true

(4) Then it is not true

Result: (4) contradicts (1).

Let us now modify the argument and make the assumption (1) part of the

sentence itself:

This true sentence is not true (Y')

If we go through the steps (1)-(4) again we find that the sentence is

not true, and therefore there is no such thing as “this true sentence”.

A presupposition of Y' is that its subject term “this true sentence” has

a referent. But it does not! Hence Y' is ~(T v F).

But then the sentence is not true, and what it says is the case!! Well,

in order to resolve the paradox being ~(T v F) is not sufficient - in

addition the sentence must be meaningless. But we in fact do know that Y

(and Y') is meaningless.

https://groups.google.com/forum/#!topic/sci.logic/FOEZFcy0ZR4

But Strawson developed his theory precisely because he thought that the

sentence “All John's children” are asleep” was perfectly meaningful. (We

agree.) He rejected the trichotomy T, F, meaningless. (We agree.)

What follows is my addition. The meaningless sentences are a proper

subset of the sentences that are ~(T v F). In particular when the

non-existence of the subject is necessary [e.g. ~(Ex)(x # x)] then the

sentence is meaningless, when the non-existence of the subject is

merely contingent [e.g. John has no children] then the sentence is

merely ~(T v F).

Gödel's sentence behaves the same way as Y':

~(Ex)(Ey)(Prf(x,y) & This(y)) (G)

where This() is satisfied only by the Gödel number of G. Let us substitute

~(Ex)(Prf(x,<#G#>) & This(<#G#>)) (J)

We observe that (Ex)(Prf(x,<#G#>) is a presupposition of (J), and it is

not true. But then J is not true [it is ~(T v F).] No sound system

should derive either it or G, although there is no reason why it could

not derive

~(Ex)(Prf(x,<#G#>) (K)

Note that (J) and (K) are not the same sentences. The latter talks about

numbers, the former about unicorns. It says that no unicorn is the Gödel

sentence.

It is possible to specify a semantics such that the latter is true, but

the former is ~(T v F).

http://arxiv.org/abs/1509.06837

--

X.Y. Newberry

If Jack says ‘What I am saying at this very moment is not true’, we can

successfully and truly assert that he did not utter a truth: ‘What Jack

said is not true’. But it is hardly conceivable that Jack’s utterance is

true by virtue of its success in attributing non-truth to itself.

Haim Gaifman

---

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(∃x)Fx & (∃x)Gx. (Strawson, 1952, Introduction to Logical Theory,

London, Methuen, pp. 163-179.) Furthermore he proposed to take the term

(∃x)Fx & (∃x)Gx as a PRESUPPOSITION. That is if (∃x)Fx & (∃x)Gx is not

true then ~(∃x)(Fx & Gx) is neither true nor false. So for example the

sentence “All John's children are asleep” is ~(T v F) if John has no

children. How does this help with the Liar paradox? Consider

This sentence is not true (Y)

The argument usually goes as follows.

(1) Assume that Y is true

(2) Then what it says is the case

(3) It says it is not true

(4) Then it is not true

Result: (4) contradicts (1).

Let us now modify the argument and make the assumption (1) part of the

sentence itself:

This true sentence is not true (Y')

If we go through the steps (1)-(4) again we find that the sentence is

not true, and therefore there is no such thing as “this true sentence”.

A presupposition of Y' is that its subject term “this true sentence” has

a referent. But it does not! Hence Y' is ~(T v F).

But then the sentence is not true, and what it says is the case!! Well,

in order to resolve the paradox being ~(T v F) is not sufficient - in

addition the sentence must be meaningless. But we in fact do know that Y

(and Y') is meaningless.

https://groups.google.com/forum/#!topic/sci.logic/FOEZFcy0ZR4

But Strawson developed his theory precisely because he thought that the

sentence “All John's children” are asleep” was perfectly meaningful. (We

agree.) He rejected the trichotomy T, F, meaningless. (We agree.)

What follows is my addition. The meaningless sentences are a proper

subset of the sentences that are ~(T v F). In particular when the

non-existence of the subject is necessary [e.g. ~(Ex)(x # x)] then the

sentence is meaningless, when the non-existence of the subject is

merely contingent [e.g. John has no children] then the sentence is

merely ~(T v F).

Gödel's sentence behaves the same way as Y':

~(Ex)(Ey)(Prf(x,y) & This(y)) (G)

where This() is satisfied only by the Gödel number of G. Let us substitute

~(Ex)(Prf(x,<#G#>) & This(<#G#>)) (J)

We observe that (Ex)(Prf(x,<#G#>) is a presupposition of (J), and it is

not true. But then J is not true [it is ~(T v F).] No sound system

should derive either it or G, although there is no reason why it could

not derive

~(Ex)(Prf(x,<#G#>) (K)

Note that (J) and (K) are not the same sentences. The latter talks about

numbers, the former about unicorns. It says that no unicorn is the Gödel

sentence.

It is possible to specify a semantics such that the latter is true, but

the former is ~(T v F).

http://arxiv.org/abs/1509.06837

--

X.Y. Newberry

If Jack says ‘What I am saying at this very moment is not true’, we can

successfully and truly assert that he did not utter a truth: ‘What Jack

said is not true’. But it is hardly conceivable that Jack’s utterance is

true by virtue of its success in attributing non-truth to itself.

Haim Gaifman

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Oct 10, 2015, 8:30:31 PM10/10/15

to

On Saturday, October 10, 2015 at 4:49:53 PM UTC-4, Newberry wrote:

> P.F. Strawson proposed to translate “No F is G” as ~(∃x)(Fx & Gx) &

> (∃x)Fx & (∃x)Gx. (Strawson, 1952, Introduction to Logical Theory,

> London, Methuen, pp. 163-179.) Furthermore he proposed to take the term

> (∃x)Fx & (∃x)Gx as a PRESUPPOSITION. That is if (∃x)Fx & (∃x)Gx is not

> true then ~(∃x)(Fx & Gx) is neither true nor false. So for example the

> sentence “All John's children are asleep” is ~(T v F) if John has no

> children. How does this help with the Liar paradox? Consider

>

> This sentence is not true (Y)

>

> The argument usually goes as follows.

>

> (1) Assume that Y is true

> (2) Then what it says is the case

> (3) It says it is not true

> (4) Then it is not true

> Result: (4) contradicts (1).

Every sentence is both true and false because you are allowing a syntax with the semantics of expressing truth, which is inconsistent. It's like having a programming language with a function that solves the halting problem.
> P.F. Strawson proposed to translate “No F is G” as ~(∃x)(Fx & Gx) &

> (∃x)Fx & (∃x)Gx. (Strawson, 1952, Introduction to Logical Theory,

> London, Methuen, pp. 163-179.) Furthermore he proposed to take the term

> (∃x)Fx & (∃x)Gx as a PRESUPPOSITION. That is if (∃x)Fx & (∃x)Gx is not

> true then ~(∃x)(Fx & Gx) is neither true nor false. So for example the

> sentence “All John's children are asleep” is ~(T v F) if John has no

> children. How does this help with the Liar paradox? Consider

>

> This sentence is not true (Y)

>

> The argument usually goes as follows.

>

> (1) Assume that Y is true

> (2) Then what it says is the case

> (3) It says it is not true

> (4) Then it is not true

> Result: (4) contradicts (1).

C-B

Oct 11, 2015, 11:05:44 AM10/11/15

to

theory is inconsistent, in which case every sentence is meaningless.

> Gödel's sentence behaves the same way as Y':

>

> ~(Ex)(Ey)(Prf(x,y) & This(y)) (G)

>

> where This() is satisfied only by the Gödel number of G. Let us substitute

>

> ~(Ex)(Prf(x,<#G#>) & This(<#G#>)) (J)

>

> We observe that (Ex)(Prf(x,<#G#>) is a presupposition of (J), and it is

> not true.

that ~(Ex)(Prf(x,<#G#>)).

> But then J is not true [it is ~(T v F).] No sound system

> should derive either it or G, although there is no reason why it could

> not derive

>

> ~(Ex)(Prf(x,<#G#>) (K)

>

> Note that (J) and (K) are not the same sentences. The latter talks about

> numbers, the former about unicorns. It says that no unicorn is the Gödel

> sentence.

Martin Shobe

Oct 11, 2015, 9:12:13 PM10/11/15

to

> unless the

> theory is inconsistent, in which case every sentence is meaningless.

>

>> Gödel's sentence behaves the same way as Y':

>>

>> ~(Ex)(Ey)(Prf(x,y) & This(y)) (G)

>>

>> where This() is satisfied only by the Gödel number of G. Let us

>> substitute

>>

>> ~(Ex)(Prf(x,<#G#>) & This(<#G#>)) (J)

>>

>> We observe that (Ex)(Prf(x,<#G#>) is a presupposition of (J), and it is

>> not true.

>

> According to the Strawson definition, it is not as it follows from (J)

> that ~(Ex)(Prf(x,<#G#>)).

Strawson's logic, if ~(Ex)(Prf(x,<#G#>)) is true then (J) is neither

true nor false.

>

>> But then J is not true [it is ~(T v F).] No sound system

>> should derive either it or G, although there is no reason why it could

>> not derive

>>

>> ~(Ex)(Prf(x,<#G#>) (K)

>>

>> Note that (J) and (K) are not the same sentences. The latter talks about

>> numbers, the former about unicorns. It says that no unicorn is the Gödel

>> sentence.

>

> Both (J) and (K) are about numbers.

Is the following sentence true?
>> should derive either it or G, although there is no reason why it could

>> not derive

>>

>> ~(Ex)(Prf(x,<#G#>) (K)

>>

>> Note that (J) and (K) are not the same sentences. The latter talks about

>> numbers, the former about unicorns. It says that no unicorn is the Gödel

>> sentence.

>

> Both (J) and (K) are about numbers.

No unicorn is the code of Gödel's sentence.

>

> Martin Shobe

Oct 12, 2015, 10:37:37 AM10/12/15

to

>> unless the

>> theory is inconsistent, in which case every sentence is meaningless.

>>

>>> Gödel's sentence behaves the same way as Y':

>>>

>>> ~(Ex)(Ey)(Prf(x,y) & This(y)) (G)

>>>

>>> where This() is satisfied only by the Gödel number of G. Let us

>>> substitute

>>>

>>> ~(Ex)(Prf(x,<#G#>) & This(<#G#>)) (J)

>>>

>>> We observe that (Ex)(Prf(x,<#G#>) is a presupposition of (J), and it is

>>> not true.

>>

>> According to the Strawson definition, it is not as it follows from (J)

>> that ~(Ex)(Prf(x,<#G#>)).

>

> In classical logic ~(Ex)(Prf(x,<#G#>)) follows from (J). But in

> Strawson's logic, if ~(Ex)(Prf(x,<#G#>)) is true then (J) is neither

> true nor false.

rules for handling existential quantifiers in his system?

>>> But then J is not true [it is ~(T v F).] No sound system

>>> should derive either it or G, although there is no reason why it could

>>> not derive

>>>

>>> ~(Ex)(Prf(x,<#G#>) (K)

>>>

>>> Note that (J) and (K) are not the same sentences. The latter talks about

>>> numbers, the former about unicorns. It says that no unicorn is the Gödel

>>> sentence.

>>

>> Both (J) and (K) are about numbers.

>

> Is the following sentence true?

>

> No unicorn is the code of Gödel's sentence.

Martin Shobe

Oct 12, 2015, 10:14:14 PM10/12/15

to

does not model them correctly.

>

>>> unless the

>>> theory is inconsistent, in which case every sentence is meaningless.

>>>

>>>> Gödel's sentence behaves the same way as Y':

>>>>

>>>> ~(Ex)(Ey)(Prf(x,y) & This(y)) (G)

>>>>

>>>> where This() is satisfied only by the Gödel number of G. Let us

>>>> substitute

>>>>

>>>> ~(Ex)(Prf(x,<#G#>) & This(<#G#>)) (J)

>>>>

>>>> We observe that (Ex)(Prf(x,<#G#>) is a presupposition of (J), and it is

>>>> not true.

>>>

>>> According to the Strawson definition, it is not as it follows from (J)

>>> that ~(Ex)(Prf(x,<#G#>)).

>>

>> In classical logic ~(Ex)(Prf(x,<#G#>)) follows from (J). But in

>> Strawson's logic, if ~(Ex)(Prf(x,<#G#>)) is true then (J) is neither

>> true nor false.

>

> But does ~(Ex)(Prf(x,<#G#>)) follow from (J)? Could you give us the

> rules for handling existential quantifiers in his system?

so nothing follows from it. Please refer to P. F. Strawson, 1952,

Introduction to Logical Theory, London, Methuen, pp. 173. He showed that

given the interpretation below

A: ~(∃x)(Fx & ~Gx) & (∃x)Fx & (∃x)~Gx

E: ~(∃x)(Fx & Gx) & (∃x)Fx & (∃x)Gx

I: (∃x)(Fx & Gx) v ~(∃x)Fx v ~(∃x)Gx

O: (∃x)(Fx & Gx) v ~(∃x)Fx v ~(∃x~)Gx

all the laws of the traditional syllogism will hold. Furthermore he

proposed to take the terms (∃x)Fx & (∃x)Gx etc. as PRESUPPOSITIONS. But

Strawson considered only simple sentences with two terms. His semantics

has to be generalized to arbitrary monadic and polyadic sentences. I

have done so here http://arxiv.org/ftp/arxiv/papers/1509/1509.06837.pdf

utilizing truth-relevant logic.

>

>>>> But then J is not true [it is ~(T v F).] No sound system

>>>> should derive either it or G, although there is no reason why it could

>>>> not derive

>>>>

>>>> ~(Ex)(Prf(x,<#G#>) (K)

>>>>

>>>> Note that (J) and (K) are not the same sentences. The latter talks

>>>> about

>>>> numbers, the former about unicorns. It says that no unicorn is the

>>>> Gödel

>>>> sentence.

>>>

>>> Both (J) and (K) are about numbers.

>>

>> Is the following sentence true?

>>

>> No unicorn is the code of Gödel's sentence.

>

> Yes, but both (J) and (K) are still about numbers.

Oct 13, 2015, 11:05:51 AM10/13/15

to

does it need them?

neither does the rest of your response. So, once again, what are the

rules for handling existential quantifiers in his system?

(BTW, You still haven't fixed the issues I mentioned last time you
pointed me to this paper. For example, either your first example is

wrong, or you are using a non-standard valuation which you neither warn

the reader of nor explain.)

>>>>> But then J is not true [it is ~(T v F).] No sound system

>>>>> should derive either it or G, although there is no reason why it could

>>>>> not derive

>>>>>

>>>>> ~(Ex)(Prf(x,<#G#>) (K)

>>>>>

>>>>> Note that (J) and (K) are not the same sentences. The latter talks

>>>>> about

>>>>> numbers, the former about unicorns. It says that no unicorn is the

>>>>> Gödel

>>>>> sentence.

>>>>

>>>> Both (J) and (K) are about numbers.

>>>

>>> Is the following sentence true?

>>>

>>> No unicorn is the code of Gödel's sentence.

>>

>> Yes, but both (J) and (K) are still about numbers.

>

> But (J) is also about unicorns and (K) is not.

about exactly the same things. If you are using a many sorted logic, you

should say so and indicate which sort is being used by which statement.

In the usual treatment of these things, there is only one sort, and its

domain is N. From this it follows that (J) and (K) are both about

numbers and neither is about unicorns.

Martin Shobe

Oct 13, 2015, 9:20:42 PM10/13/15

to

because classical logic is not able to model them.

no sensible derivation system will derive truth from non-truth.

>

> (BTW, You still haven't fixed the issues I mentioned last time you

> pointed me to this paper.

have not come anywhere close to finding any.

> For example, either your first example is

> wrong, or you are using a non-standard valuation which you neither warn

> the reader of nor explain.)

valuation when the whole purpose of the paper is to explain the

non-standard validation?

>

>>>>>> But then J is not true [it is ~(T v F).] No sound system

>>>>>> should derive either it or G, although there is no reason why it

>>>>>> could

>>>>>> not derive

>>>>>>

>>>>>> ~(Ex)(Prf(x,<#G#>)

>>>>>> (K)

>>>>>>

>>>>>> Note that (J) and (K) are not the same sentences. The latter talks

>>>>>> about

>>>>>> numbers, the former about unicorns. It says that no unicorn is the

>>>>>> Gödel

>>>>>> sentence.

>>>>>

>>>>> Both (J) and (K) are about numbers.

>>>>

>>>> Is the following sentence true?

>>>>

>>>> No unicorn is the code of Gödel's sentence.

>>>

>>> Yes, but both (J) and (K) are still about numbers.

>>

>> But (J) is also about unicorns and (K) is not.

>

> Unless you've decided to use a many-sorted logic, (J) and (K) have to be

> about exactly the same things. If you are using a many sorted logic, you

> should say so and indicate which sort is being used by which statement.

> In the usual treatment of these things, there is only one sort, and its

> domain is N. From this it follows that (J) and (K) are both about

> numbers and neither is about unicorns.

Oct 13, 2015, 9:37:08 PM10/13/15

to

a. If it is the code of Godel's sentence, then halt.

2. Go back to 1.

The question is logically equivalent to "Does the above not halt?".

>

> >

> > Martin Shobe

> >

>

>

> --

> X.Y. Newberry

>

> If Jack says ‘What I am saying at this very moment is not true’, we can

> successfully and truly assert that he did not utter a truth: ‘What Jack

> said is not true’. But it is hardly conceivable that Jack’s utterance is

> true by virtue of its success in attributing non-truth to itself.

C-B

Oct 13, 2015, 9:41:06 PM10/13/15

to

On Sunday, October 11, 2015 at 9:12:13 PM UTC-4, Newberry wrote:

C-B

Oct 14, 2015, 10:56:19 AM10/14/15

to

them? What's wrong with leaving such statements outside the scope of logic?

traditional syllogism from it. How did he do that?

>> (BTW, You still haven't fixed the issues I mentioned last time you

>> pointed me to this paper.

> It is entirely possible that the paper is swarming with errors, but you

> have not come anywhere close to finding any.

>> For example, either your first example is

>> wrong, or you are using a non-standard valuation which you neither warn

>> the reader of nor explain.)

> Do you think I have to warn the reader that I am using non-standard

> valuation when the whole purpose of the paper is to explain the

> non-standard validation?

(It's not even clear that you are explaining a non-standard valuation.

The only reason I know that you are using a non-standard valuation is

that you told me you were when I pointed out this error previously.)

>>>>>>> But then J is not true [it is ~(T v F).] No sound system

>>>>>>> should derive either it or G, although there is no reason why it

>>>>>>> could

>>>>>>> not derive

>>>>>>>

>>>>>>> ~(Ex)(Prf(x,<#G#>)

>>>>>>> (K)

>>>>>>>

>>>>>>> Note that (J) and (K) are not the same sentences. The latter talks

>>>>>>> about

>>>>>>> numbers, the former about unicorns. It says that no unicorn is the

>>>>>>> Gödel

>>>>>>> sentence.

>>>>>>

>>>>>> Both (J) and (K) are about numbers.

>>>>>

>>>>> Is the following sentence true?

>>>>>

>>>>> No unicorn is the code of Gödel's sentence.

>>>>

>>>> Yes, but both (J) and (K) are still about numbers.

>>>

>>> But (J) is also about unicorns and (K) is not.

>>

>> Unless you've decided to use a many-sorted logic, (J) and (K) have to be

>> about exactly the same things. If you are using a many sorted logic, you

>> should say so and indicate which sort is being used by which statement.

>

> I am not using many-sorted logic, never have, and never shall.

the same things.

>> In the usual treatment of these things, there is only one sort, and its

>> domain is N. From this it follows that (J) and (K) are both about

>> numbers and neither is about unicorns.

>

> Does not (J) say that the empty set is a subset of the empty set?

(G) and satisfies this(<#G#>). If you want to say that the empty set is

a subset of the empty set, you say something like

∅⊂∅

Martin Shobe

Oct 15, 2015, 12:15:44 AM10/15/15

to

> but why do we logic to model

> them? What's wrong with leaving such statements outside the scope of logic?

are outright meaningless. It is wrong to pretend that they are true.

Secondly, treating vacuous propositions as ~(T v F) gets rid of semantic

incompleteness.

valuation that it is an "error" because it does not conform to the

standard valuation. It is even more strange to say about a paper whose

only purpose is to explain a non-standard validation that it is not

present. I guess I am not explaining it too well if you did not even

realize that is what I was doing. BTW, what did you think the paper was

about?

Oct 15, 2015, 8:48:20 AM10/15/15

to

>> but why do we logic to model

>> them? What's wrong with leaving such statements outside the scope of

>> logic?

> Because vacuous propositions ARE ~(T v F). In fact in mathematics they

> are outright meaningless. It is wrong to pretend that they are true.

> Secondly, treating vacuous propositions as ~(T v F) gets rid of semantic

> incompleteness.

semantics, so there's no pretending that they are true. They *are* true.

>>>> (BTW, You still haven't fixed the issues I mentioned last time you

>>>> pointed me to this paper.

>>

>>> It is entirely possible that the paper is swarming with errors, but you

>>> have not come anywhere close to finding any.

>>

>> You wish.

>>

>>>> For example, either your first example is

>>>> wrong, or you are using a non-standard valuation which you neither warn

>>>> the reader of nor explain.)

>>

>>> Do you think I have to warn the reader that I am using non-standard

>>> valuation when the whole purpose of the paper is to explain the

>>> non-standard validation?

>>

>> Everything else in the paper relies on it and it's simply not present.

>> (It's not even clear that you are explaining a non-standard valuation.

>> The only reason I know that you are using a non-standard valuation is

>> that you told me you were when I pointed out this error previously.)

>

> It is strange to say about a paper that describes a non-standard

> valuation that it is an "error" because it does not conform to the

> standard valuation.

> It is even more strange to say about a paper whose

> only purpose is to explain a non-standard validation that it is not

> present.

explains why you claim that something can't be derived yet you can't

state the derivation rules. See above.)

> I guess I am not explaining it too well if you did not even

> realize that is what I was doing. BTW, what did you think the paper was

> about?

Prf(x,<#G#>)} doesn't appear in (J).

Martin Shobe

Oct 15, 2015, 11:04:50 AM10/15/15

to

There were some parts of your post that I had a bit of a hard time following. I don't think it is reasonable to take "This sentence is not true" as equivalent with "This true sentence is not true". As far as Gödel's sentence goes the point is it is a sentence in the first-order language of arithmetic and so for that reason surely has a truth-value.

Oct 15, 2015, 9:30:40 PM10/15/15

to

(x)(x = x+1 -> x = x+2)

does not have any interpretation in the domain of the natural numbers.

>

>>>>> (BTW, You still haven't fixed the issues I mentioned last time you

>>>>> pointed me to this paper.

>>>

>>>> It is entirely possible that the paper is swarming with errors, but you

>>>> have not come anywhere close to finding any.

>>>

>>> You wish.

>>>

>>>>> For example, either your first example is

>>>>> wrong, or you are using a non-standard valuation which you neither

>>>>> warn

>>>>> the reader of nor explain.)

>>>

>>>> Do you think I have to warn the reader that I am using non-standard

>>>> valuation when the whole purpose of the paper is to explain the

>>>> non-standard validation?

>>>

>>> Everything else in the paper relies on it and it's simply not present.

>>> (It's not even clear that you are explaining a non-standard valuation.

>>> The only reason I know that you are using a non-standard valuation is

>>> that you told me you were when I pointed out this error previously.)

>>

>> It is strange to say about a paper that describes a non-standard

>> valuation that it is an "error" because it does not conform to the

>> standard valuation.

>

> What's strange here is that you think I said that. That's not what I said.

>

>> It is even more strange to say about a paper whose

>> only purpose is to explain a non-standard validation that it is not

>> present.

>

> That's easy to explain. You don't know what you're doing. (This also

> explains why you claim that something can't be derived yet you can't

> state the derivation rules. See above.)

stated. Do you understand that no sound derivation system will derive

truth from non-truth?

>

>> I guess I am not explaining it too well if you did not even

>> realize that is what I was doing. BTW, what did you think the paper was

>> about?

>

> From the contents, you appear to be classifying statements.

Are you suggesting that any logic that does not conform to classical

logic merely classifies statements?

the same set as

S = {x| Prf(x,<#G#>)}

> Of course, {x|

> Prf(x,<#G#>)} doesn't appear in (J).

Oct 15, 2015, 9:41:48 PM10/15/15

to

Rupert wrote:

> There were some parts of your post that I had a bit of a hard time

> following. I don't think it is reasonable to take "This sentence is

> not true" as equivalent with "This true sentence is not true".

The proof of contradiction of the Liar typically starts with the
> There were some parts of your post that I had a bit of a hard time

> following. I don't think it is reasonable to take "This sentence is

> not true" as equivalent with "This true sentence is not true".

assumption that the sentence is true. Liar + this assumption make "This

true sentence is not true." So it seems to me that at the very least you

cannot walk through the proof without stepping through "This true

sentence is not true."

> As far

> as Gödel's sentence goes the point is it is a sentence in the

> first-order language of arithmetic and so for that reason surely has

> a truth-value.

"first-order language of arithmetic" usually implies classical logic. In
> As far

> as Gödel's sentence goes the point is it is a sentence in the

> first-order language of arithmetic and so for that reason surely has

> a truth-value.

the present context I am suggesting that there is an alternative

logic/interpretation such that it does NOT have a truth value. Are you

claiming that no such logic/interpretation is possible, or are you just

injecting an orthogonal statement for fun?

Oct 15, 2015, 10:37:43 PM10/15/15

to

On 10/15/2015 8:30 PM, X.Y. Newberry wrote:

> Martin Shobe wrote:

>> On 10/14/2015 11:15 PM, X.Y. Newberry wrote:

>>> Martin Shobe wrote:

>>>> On 10/13/2015 8:20 PM, X.Y. Newberry wrote:

>>>>> Martin Shobe wrote:

>>>>>> On 10/12/2015 9:13 PM, X.Y. Newberry wrote:

>>>>>>> Martin Shobe wrote:

>>>>>>>> On 10/11/2015 8:11 PM, X.Y. Newberry wrote:

>>>>>>>>> Martin Shobe wrote:

>>>>>>>>>> On 10/10/2015 3:49 PM, X.Y. Newberry wrote:

>>>> but why do we logic to model

>>>> them? What's wrong with leaving such statements outside the scope of

>>>> logic?

>>

>>> Because vacuous propositions ARE ~(T v F). In fact in mathematics they

>>> are outright meaningless. It is wrong to pretend that they are true.

>>> Secondly, treating vacuous propositions as ~(T v F) gets rid of semantic

>>> incompleteness.

>>

>> No they aren't outright meaningless. Formally, the have a well defined

>> semantics, so there's no pretending that they are true. They *are* true.

>

> They don't. For example the sentence

>

> (x)(x = x+1 -> x = x+2)

>

> does not have any interpretation in the domain of the natural numbers.

Yes it does. Furthermore, the statement is true.
> Martin Shobe wrote:

>> On 10/14/2015 11:15 PM, X.Y. Newberry wrote:

>>> Martin Shobe wrote:

>>>> On 10/13/2015 8:20 PM, X.Y. Newberry wrote:

>>>>> Martin Shobe wrote:

>>>>>> On 10/12/2015 9:13 PM, X.Y. Newberry wrote:

>>>>>>> Martin Shobe wrote:

>>>>>>>> On 10/11/2015 8:11 PM, X.Y. Newberry wrote:

>>>>>>>>> Martin Shobe wrote:

>>>>>>>>>> On 10/10/2015 3:49 PM, X.Y. Newberry wrote:

>>>> but why do we logic to model

>>>> them? What's wrong with leaving such statements outside the scope of

>>>> logic?

>>

>>> Because vacuous propositions ARE ~(T v F). In fact in mathematics they

>>> are outright meaningless. It is wrong to pretend that they are true.

>>> Secondly, treating vacuous propositions as ~(T v F) gets rid of semantic

>>> incompleteness.

>>

>> No they aren't outright meaningless. Formally, the have a well defined

>> semantics, so there's no pretending that they are true. They *are* true.

>

> They don't. For example the sentence

>

> (x)(x = x+1 -> x = x+2)

>

> does not have any interpretation in the domain of the natural numbers.

>>>>>> (BTW, You still haven't fixed the issues I mentioned last time you

>>>>>> pointed me to this paper.

>>>>

>>>>> It is entirely possible that the paper is swarming with errors, but

>>>>> you

>>>>> have not come anywhere close to finding any.

>>>>

>>>> You wish.

>>>>

>>>>>> For example, either your first example is

>>>>>> wrong, or you are using a non-standard valuation which you neither

>>>>>> warn

>>>>>> the reader of nor explain.)

>>>>

>>>>> Do you think I have to warn the reader that I am using non-standard

>>>>> valuation when the whole purpose of the paper is to explain the

>>>>> non-standard validation?

>>>>

>>>> Everything else in the paper relies on it and it's simply not present.

>>>> (It's not even clear that you are explaining a non-standard valuation.

>>>> The only reason I know that you are using a non-standard valuation is

>>>> that you told me you were when I pointed out this error previously.)

>>>

>>> It is strange to say about a paper that describes a non-standard

>>> valuation that it is an "error" because it does not conform to the

>>> standard valuation.

>>

>> What's strange here is that you think I said that. That's not what I

>> said.

>

> What did you say?

idea where you go wrong.

>>> It is even more strange to say about a paper whose

>>> only purpose is to explain a non-standard validation that it is not

>>> present.

>>

>> That's easy to explain. You don't know what you're doing. (This also

>> explains why you claim that something can't be derived yet you can't

>> state the derivation rules. See above.)

>

> That I have not stated the rules yet does not mean that they cannot be

> stated. Do you understand that no sound derivation system will derive

> truth from non-truth?

do is derive a non-truth from a truth. (That is, after all, what it

means to be sound.)

>>> I guess I am not explaining it too well if you did not even

>>> realize that is what I was doing. BTW, what did you think the paper was

>>> about?

>>

>> From the contents, you appear to be classifying statements.

>

> Suppose this is true. How is it an error?

> Are you suggesting that any logic that does not conform to classical

> logic merely classifies statements?

describe any semantics and only defines categories of statements.

must refer to something. As such, S' is a singleton and not empty.

Therefore, S is not the same set as S'.

>> Of course, {x|

>> Prf(x,<#G#>)} doesn't appear in (J).

>

> But 'Prf(x,<#G#>)' does.

the empty set. In fact, (J) doesn't say anything about sets at all.

(Unless they are part of the domain, but that would be a bit unusual for

something like this. Usually, the domain is restricted to just natural

numbers.)

Martin Shobe

Oct 16, 2015, 12:23:39 AM10/16/15

to

> Furthermore, the statement is true.

>

>>>> It is even more strange to say about a paper whose

>>>> only purpose is to explain a non-standard validation that it is not

>>>> present.

>>>

>>> That's easy to explain. You don't know what you're doing. (This also

>>> explains why you claim that something can't be derived yet you can't

>>> state the derivation rules. See above.)

>>

>> That I have not stated the rules yet does not mean that they cannot be

>> stated. Do you understand that no sound derivation system will derive

>> truth from non-truth?

>

> Uh no. I don't understand that as it's false. What a sound system won't

> do is derive a non-truth from a truth. (That is, after all, what it

> means to be sound.)

did not even cross anybody's mind.

>

>>>> I guess I am not explaining it too well if you did not even

>>>> realize that is what I was doing. BTW, what did you think the paper was

>>>> about?

>>>

>>> From the contents, you appear to be classifying statements.

>>

>> Suppose this is true. How is it an error?

>

> I didn't say that was an error?

non-standard valuation which you neither warn the reader of nor

explain." So your position is that that my description is not semantics
but rather statement categorization therefore it does not "explain" the

non-standard valuation?

the same set as

S = {x| Prf(x,<#G#>)} ?

>

>>> Of course, {x|

>>> Prf(x,<#G#>)} doesn't appear in (J).

>>

>> But 'Prf(x,<#G#>)' does.

>

> So? That doesn't mean that (J) says that the empty set is a subset of

> the empty set. In fact, (J) doesn't say anything about sets at all.

> (Unless they are part of the domain, but that would be a bit unusual for

> something like this. Usually, the domain is restricted to just natural

> numbers.)

>

> Martin Shobe

>

Oct 16, 2015, 12:35:39 AM10/16/15

to

On Sunday, October 11, 2015 at 6:12:13 PM UTC-7, Newberry wrote:

>

> That is why we need new logic.

>

We need "new" consistent, complete, and "concrete"
>

> That is why we need new logic.

>

logic as possible, that is still only extra-classical,

extra-standard, and extra-regular, with "all that".

Mathematics could use this, and physics could use that.

Oct 16, 2015, 9:35:27 AM10/16/15

to

>> Furthermore, the statement is true.

> How does it manage to do that?

it follows that x=x+1 -> x=x+2 is true regardless of which value of x is

used. Therefore, (x)(x=x+1 -> x=x+2) is true.

interpretation from.

>>>>> It is even more strange to say about a paper whose

>>>>> only purpose is to explain a non-standard validation that it is not

>>>>> present.

>>>>

>>>> That's easy to explain. You don't know what you're doing. (This also

>>>> explains why you claim that something can't be derived yet you can't

>>>> state the derivation rules. See above.)

>>>

>>> That I have not stated the rules yet does not mean that they cannot be

>>> stated. Do you understand that no sound derivation system will derive

>>> truth from non-truth?

>>

>> Uh no. I don't understand that as it's false. What a sound system won't

>> do is derive a non-truth from a truth. (That is, after all, what it

>> means to be sound.)

>

> That is because the idea that a system would derive truth from non-truth

> did not even cross anybody's mind.

>>>>> I guess I am not explaining it too well if you did not even

>>>>> realize that is what I was doing. BTW, what did you think the paper

>>>>> was

>>>>> about?

>>>>

>>>> From the contents, you appear to be classifying statements.

>>>

>>> Suppose this is true. How is it an error?

>>

>> I didn't say that was an error?

> You said "either your first example is wrong, or you are using a

> non-standard valuation which you neither warn the reader of nor

> explain." So your position is that that my description is not semantics

> but rather statement categorization therefore it does not "explain" the

> non-standard valuation?

things I've said.) Now, how are you getting to me saying that

classifying statements is an error?

(x)(~Unicorn(x)), then yes S' = S. But, to put it into the larger

picture, if that is sufficient to claim that (J) is about Unicorns, then

it should also be sufficient to claim that (K) is about Unicorns. Once

again, both (J) and (K) have to be about exactly the same things unless

you are using different sorts (and you've said that you aren't).

Martin Shobe

Oct 17, 2015, 2:29:42 AM10/17/15

to

>>> Furthermore, the statement is true.

>

>> How does it manage to do that?

>

> There's no x such that x = x + 1.

> By the semantics of the ->

> operator,

natural numbers per se.

> it follows that x=x+1 -> x=x+2 is true regardless of which

> value of x is used. Therefore, (x)(x=x+1 -> x=x+2) is true.

is no error.

~(Ey)(Unicorn(y) & This(y)).

> But, to put it into the larger

> picture, if that is sufficient to claim that (J) is about Unicorns,

> then it should also be sufficient to claim that (K) is about

> Unicorns.

> Once again, both (J) and (K) have to be about exactly the

> same things

> unless you are using different sorts (and you've said

> that you aren't).

> Martin Shobe

>

I am not sure what exactly you are asking about Strawson pp. 173, 174.

Oct 17, 2015, 2:38:27 AM10/17/15

to

On Friday, October 16, 2015 at 3:41:48 AM UTC+2, Newberry wrote:

> Rupert wrote:

> > There were some parts of your post that I had a bit of a hard time

> > following. I don't think it is reasonable to take "This sentence is

> > not true" as equivalent with "This true sentence is not true".

>

> The proof of contradiction of the Liar typically starts with the

> assumption that the sentence is true. Liar + this assumption make "This

> true sentence is not true." So it seems to me that at the very least you

> cannot walk through the proof without stepping through "This true

> sentence is not true."

But it is not equivalent to the original sentence.
> Rupert wrote:

> > There were some parts of your post that I had a bit of a hard time

> > following. I don't think it is reasonable to take "This sentence is

> > not true" as equivalent with "This true sentence is not true".

>

> The proof of contradiction of the Liar typically starts with the

> assumption that the sentence is true. Liar + this assumption make "This

> true sentence is not true." So it seems to me that at the very least you

> cannot walk through the proof without stepping through "This true

> sentence is not true."

> > As far

> > as Gödel's sentence goes the point is it is a sentence in the

> > first-order language of arithmetic and so for that reason surely has

> > a truth-value.

>

> "first-order language of arithmetic" usually implies classical logic. In

> the present context I am suggesting that there is an alternative

> logic/interpretation such that it does NOT have a truth value. Are you

> claiming that no such logic/interpretation is possible, or are you just

> injecting an orthogonal statement for fun?

Oct 17, 2015, 3:47:53 AM10/17/15

to

On 17/10/2015 12:38 AM, Rupert wrote:

> On Friday, October 16, 2015 at 3:41:48 AM UTC+2, Newberry wrote:

>> Rupert wrote:

>>> There were some parts of your post that I had a bit of a hard time

>>> following. I don't think it is reasonable to take "This sentence is

>>> not true" as equivalent with "This true sentence is not true".

>>

>> The proof of contradiction of the Liar typically starts with the

>> assumption that the sentence is true. Liar + this assumption make "This

>> true sentence is not true." So it seems to me that at the very least you

>> cannot walk through the proof without stepping through "This true

>> sentence is not true."

>

> But it is not equivalent to the original sentence.

>

>>> As far

>>> as Gödel's sentence goes the point is it is a sentence in the

>>> first-order language of arithmetic and so for that reason surely has

>>> a truth-value.

Except surely nobody knows the truth value of G(PA + cGC),
> On Friday, October 16, 2015 at 3:41:48 AM UTC+2, Newberry wrote:

>> Rupert wrote:

>>> There were some parts of your post that I had a bit of a hard time

>>> following. I don't think it is reasonable to take "This sentence is

>>> not true" as equivalent with "This true sentence is not true".

>>

>> The proof of contradiction of the Liar typically starts with the

>> assumption that the sentence is true. Liar + this assumption make "This

>> true sentence is not true." So it seems to me that at the very least you

>> cannot walk through the proof without stepping through "This true

>> sentence is not true."

>

> But it is not equivalent to the original sentence.

>

>>> As far

>>> as Gödel's sentence goes the point is it is a sentence in the

>>> first-order language of arithmetic and so for that reason surely has

>>> a truth-value.

G(PA + ~cGC), ... and infinitely many Gödel's sentences.

>> "first-order language of arithmetic" usually implies classical logic. In

>> the present context I am suggesting that there is an alternative

>> logic/interpretation such that it does NOT have a truth value. Are you

>> claiming that no such logic/interpretation is possible, or are you just

>> injecting an orthogonal statement for fun?

>

> Of course you can always come up with some nonstandard semantics with respect to which some given sentence does not have a truth-value, but why is that supposed to be interesting? When we are talking about the first-order language of arithmetic then surely we usually have the standard semantics in mind.

--

Is there something in your cultural background that

makes it impossible for you to admit to your errors?

Justin Thyme (being racist) -- in sci.logic

Oct 17, 2015, 8:55:34 AM10/17/15

to

On 10/17/2015 3:47 AM, Nam Nguyen wrote:

> On 17/10/2015 12:38 AM, Rupert wrote:

>> On Friday, October 16, 2015 at 3:41:48 AM UTC+2, Newberry wrote:

>>> Rupert wrote:

>>>> There were some parts of your post that I had a bit of a hard time

>>>> following. I don't think it is reasonable to take "This sentence is

>>>> not true" as equivalent with "This true sentence is not true".

>>>

>>> The proof of contradiction of the Liar typically starts with the

>>> assumption that the sentence is true. Liar + this assumption make "This

>>> true sentence is not true." So it seems to me that at the very least you

>>> cannot walk through the proof without stepping through "This true

>>> sentence is not true."

>>

>> But it is not equivalent to the original sentence.

>>

>>>> As far

>>>> as Gödel's sentence goes the point is it is a sentence in the

>>>> first-order language of arithmetic and so for that reason surely has

>>>> a truth-value.

>

> Except surely nobody knows the truth value of G(PA + cGC),

> G(PA + ~cGC), ... and infinitely many Gödel's sentences.

You seem to think that this is relevant at this point.
> On 17/10/2015 12:38 AM, Rupert wrote:

>> On Friday, October 16, 2015 at 3:41:48 AM UTC+2, Newberry wrote:

>>> Rupert wrote:

>>>> There were some parts of your post that I had a bit of a hard time

>>>> following. I don't think it is reasonable to take "This sentence is

>>>> not true" as equivalent with "This true sentence is not true".

>>>

>>> The proof of contradiction of the Liar typically starts with the

>>> assumption that the sentence is true. Liar + this assumption make "This

>>> true sentence is not true." So it seems to me that at the very least you

>>> cannot walk through the proof without stepping through "This true

>>> sentence is not true."

>>

>> But it is not equivalent to the original sentence.

>>

>>>> As far

>>>> as Gödel's sentence goes the point is it is a sentence in the

>>>> first-order language of arithmetic and so for that reason surely has

>>>> a truth-value.

>

> Except surely nobody knows the truth value of G(PA + cGC),

> G(PA + ~cGC), ... and infinitely many Gödel's sentences.

And that would seem to indicate you think "nobody knows the

truth value of" opposes "has a truth value" somehow.

Is it true that you think that, Nam?

If you think it does, you should say it loud and clear,

so that everyone knows what you're saying.

>>> "first-order language of arithmetic" usually implies classical logic. In

>>> the present context I am suggesting that there is an alternative

>>> logic/interpretation such that it does NOT have a truth value. Are you

>>> claiming that no such logic/interpretation is possible, or are you just

>>> injecting an orthogonal statement for fun?

>>

>> Of course you can always come up with some nonstandard semantics with

>> respect to which some given sentence does not have a truth-value, but

>> why is that supposed to be interesting? When we are talking about the

>> first-order language of arithmetic then surely we usually have the

>> standard semantics in mind.

>

> "Standard semantics" is very much philosophical here.

(Ax)P(x) as "There _exists_ an x such that P(x)".

If the standard semantics is not mathematical/logical, then there is

no mathematics/logic.

Is that your point, Nam? That there is no mathematics/logic?

If you think there isn't, you should say it loud and clear,

so that everyone knows what you're saying.

Oct 17, 2015, 5:58:56 PM10/17/15

to

would be the standard ones.

> Please name the standard integer.

>>>> Furthermore, the statement is true.

>>

>>> How does it manage to do that?

>>

>> There's no x such that x = x + 1.

>

> So the sentence does not talk about anything.

>> By the semantics of the ->

>> operator,

>

> So it is all about the semantics of -> and has nothing to do with the

> natural numbers per se.

is a natural number.

>> it follows that x=x+1 -> x=x+2 is true regardless of which

>> value of x is used. Therefore, (x)(x=x+1 -> x=x+2) is true.

> How is not talking about anything true? You got me on this one.

>>>>>>> I guess I am not explaining it too well if you did not

>>>>>>> even realize that is what I was doing. BTW, what did you

>>>>>>> think the paper was about?

>>>>>>

>>>>>> From the contents, you appear to be classifying statements.

>>>>>

>>>>> Suppose this is true. How is it an error?

>>>>

>>>> I didn't say that was an error?

>>

>>> You said "either your first example is wrong, or you are using a

>>> non-standard valuation which you neither warn the reader of nor

>>> explain." So your position is that that my description is not

>>> semantics but rather statement categorization therefore it does not

>>> "explain" the non-standard valuation?

>>

>> Your so doesn't follow from the statement (it does follow from other

>> things I've said.) Now, how are you getting to me saying that

>> classifying statements is an error?

>

> The error is that I thought you said there was an error. In fact there

> is no error.

not the fact that you are classifying statements. The error is your

failure to state which non-standard semantics you are using.

~(Ex)(Ey)(Prf(x,y) & This(y)). Of course, this is because

~(Ex)(Unicorn(x) is equivalent to ~(Ex)(Prf(x,<#G#>). So once again, we

see that (J) is about unicorns if and only if (k) is about unicorns.

>> But, to put it into the larger

>> picture, if that is sufficient to claim that (J) is about Unicorns,

>> then it should also be sufficient to claim that (K) is about

>> Unicorns.

>

> I do not see any unicorns in K. It says that there is no proof of G.

encodes a proof of G."

Likewise, I do not see any unicorns in (J). It says that there is no

natural number that both encodes a proof of G and satisfies the

statement This(<#G#>).

>> Once again, both (J) and (K) have to be about exactly the

>> same things

>

> No, they don't.

(unless you are using multiple sorts).

>> unless you are using different sorts (and you've said

>> that you aren't).

>

> Never have and never shall.

>

>> Martin Shobe

>>

>

> I am not sure what exactly you are asking about Strawson pp. 173, 174.

>

for the existential quantifiers in Strawson's system. They are not

present on those pages.

Martin Shobe

Oct 18, 2015, 12:03:34 AM10/18/15

to

Rupert wrote:

> On Friday, October 16, 2015 at 3:41:48 AM UTC+2, Newberry wrote:

>> Rupert wrote:

>>> There were some parts of your post that I had a bit of a hard

>>> time following. I don't think it is reasonable to take "This

>>> sentence is not true" as equivalent with "This true sentence is

>>> not true".

>>

>> The proof of contradiction of the Liar typically starts with the

>> assumption that the sentence is true. Liar + this assumption make

>> "This true sentence is not true." So it seems to me that at the

>> very least you cannot walk through the proof without stepping

>> through "This true sentence is not true."

>

> But it is not equivalent to the original sentence.

This is true [no pun intended], they are not equivalent. "This sentence"
> On Friday, October 16, 2015 at 3:41:48 AM UTC+2, Newberry wrote:

>> Rupert wrote:

>>> There were some parts of your post that I had a bit of a hard

>>> time following. I don't think it is reasonable to take "This

>>> sentence is not true" as equivalent with "This true sentence is

>>> not true".

>>

>> The proof of contradiction of the Liar typically starts with the

>> assumption that the sentence is true. Liar + this assumption make

>> "This true sentence is not true." So it seems to me that at the

>> very least you cannot walk through the proof without stepping

>> through "This true sentence is not true."

>

> But it is not equivalent to the original sentence.

has a referent, "This true sentence" does not. Another interesting

observation is that "This true sentence is not true" is unable to refer

to itself. In Strawson's logic "This true sentence is not true" is ~(T v

F) because the subject term does not have a referent. I think this much

is clear.

I am also suggesting that given

"This sentence is not true" (Y)

then

Y & Y is not true

is equivalent to "This true sentence is not true". Is it an unreasonable

conclusion?

>

>>> As far as Gödel's sentence goes the point is it is a sentence in

>>> the first-order language of arithmetic and so for that reason

>>> surely has a truth-value.

>>

>> "first-order language of arithmetic" usually implies classical

>> logic. In the present context I am suggesting that there is an

>> alternative logic/interpretation such that it does NOT have a truth

>> value. Are you claiming that no such logic/interpretation is

>> possible, or are you just injecting an orthogonal statement for

>> fun?

>

> Of course you can always come up with some nonstandard semantics with

> respect to which some given sentence does not have a truth-value, but

> why is that supposed to be interesting?

a) The idea that empty sentences are true is implausible - it does not

correspond to the intuitive notion of truth

b) The semantics I am proposing formalizes the notion of

meaninglessness. I.e. sentences that do not have interpretation are

meaningless.

c) Truth and derivability can be equated. It gets rid of the paradoxical

situation that there are true but unprovable sentences.

d) Since a sound derivation system (i.e. system that does not derive

non-truth) will not derive G even if it did derive ~(Ex)Prf(x,<#G#>)

more axiom(s) can be added to Peano Arithmetic without causing a

contradiction.

> When we are talking about the

> first-order language of arithmetic then surely we usually have the

> standard semantics in mind.

Sounds like you want us back in the box.

Oct 18, 2015, 12:55:41 AM10/18/15

to

1+1=1, 2+1=2, 3+1=3, 4+1=4?

>>>>> Furthermore, the statement is true.

>>>

>>>> How does it manage to do that?

>>>

>>> There's no x such that x = x + 1.

>>

>> So the sentence does not talk about anything.

>

> No. It talks about natural numbers.

>>> By the semantics of the -> operator,

>>

>> So it is all about the semantics of -> and has nothing to do with

>> the natural numbers per se.

>

> It has something to do with the natural numbers, every x in the

> domain is a natural number.

includes unicorns]. I am asking what natural numbers is (x)(x=x+1 ->

x=x+2) talking about.

>

>>> it follows that x=x+1 -> x=x+2 is true regardless of which value

>>> of x is used. Therefore, (x)(x=x+1 -> x=x+2) is true.

>

>> How is not talking about anything true? You got me on this one.

>

> Your presupposition is incorrect.

>

>>>>>>>> I guess I am not explaining it too well if you did not

>>>>>>>> even realize that is what I was doing. BTW, what did

>>>>>>>> you think the paper was about?

>>>>>>>

>>>>>>> From the contents, you appear to be classifying

>>>>>>> statements.

>>>>>>

>>>>>> Suppose this is true. How is it an error?

>>>>>

>>>>> I didn't say that was an error?

>>>

>>>> You said "either your first example is wrong, or you are using

>>>> a non-standard valuation which you neither warn the reader of

>>>> nor explain." So your position is that that my description is

>>>> not semantics but rather statement categorization therefore it

>>>> does not "explain" the non-standard valuation?

>>>

>>> Your so doesn't follow from the statement (it does follow from

>>> other things I've said.) Now, how are you getting to me saying

>>> that classifying statements is an error?

>>

>> The error is that I thought you said there was an error. In fact

>> there is no error.

>

> There is no error is pointing out the error in your paper. The error

> is not the fact that you are classifying statements. The error is

> your failure to state which non-standard semantics you are using.

a) classification of statements does not amount to a definition of semantics

or

b) I failed to state which non standard semantics I am using?

>>> But, to put it into the larger picture, if that is sufficient to

>>> claim that (J) is about Unicorns, then it should also be

>>> sufficient to claim that (K) is about Unicorns.

>>

>> I do not see any unicorns in K. It says that there is no proof of

>> G.

>

> A more accurate translation would be, "There is no natural number

> that encodes a proof of G."

>

> Likewise, I do not see any unicorns in (J). It says that there is no

> natural number that both encodes a proof of G and satisfies the

> statement This(<#G#>).

attribute anything to it. You cannot attribute something to nothing.

>

>>> Once again, both (J) and (K) have to be about exactly the same

>>> things

>>

>> No, they don't.

>

> Yes they do. The semantics of FOL

FOL. Hasn't this been abundantly clear from the beginning? We are

talking about the logic of presuppositions. And (K) is a presupposition

of (J).

> don't allow for any for anything

> else (unless you are using multiple sorts).

>

>>> unless you are using different sorts (and you've said that you

>>> aren't).

>>

>> Never have and never shall.

>>

>>> Martin Shobe

>>>

>>

>> I am not sure what exactly you are asking about Strawson pp. 173,

>> 174.

>>

>

> I'm not asking about Stawson pp. 173, 174. I'm asking about the rules

> for the existential quantifiers in Strawson's system. They are not

> present on those pages.

that logic was not formalizable. I am using him only as a source of

inspiration. He nevertheless did show that if Aristotelian logic is

interpreted as below

A: ~(∃x)(Fx & ~Gx) & (∃x)Fx & (∃x)~Gx

E: ~(∃x)(Fx & Gx) & (∃x)Fx & (∃x)Gx

I: (∃x)(Fx & Gx) v ~(∃x)Fx v ~(∃x)Gx

O: (∃x)(Fx & Gx) v ~(∃x)Fx v ~(∃x~)Gx

proposed to take the last two terms, such as '(∃x)Fx & (∃x)Gx', as

PRESUPPOSITIONS. Now in order to formalize this, the concept has to be

extended to arbitrary monadic first order sentences. This is what I have

done in my paper, and it turns out it is just a mirror image of the

truth-relevant logic. Derivation rules are a small technical detail that

will be added in due course.

>

> Martin Shobe

Oct 18, 2015, 11:58:23 AM10/18/15

to

discussion here certainly doesn't say they do.

>>>>>> Furthermore, the statement is true.

>>>>

>>>>> How does it manage to do that?

>>>>

>>>> There's no x such that x = x + 1.

>>>

>>> So the sentence does not talk about anything.

>>

>> No. It talks about natural numbers.

>

> Which natural numbers is the sentence talking about?

>>>> By the semantics of the -> operator,

>>>

>>> So it is all about the semantics of -> and has nothing to do with

>>> the natural numbers per se.

>>

>> It has something to do with the natural numbers, every x in the

>> domain is a natural number.

>

> I know that A(x) denotes the domain of the natural numbers [which also

> includes unicorns]. I am asking what natural numbers is (x)(x=x+1 ->

> x=x+2) talking about.

not include any unicorns.)

>>>> it follows that x=x+1 -> x=x+2 is true regardless of which value

>>>> of x is used. Therefore, (x)(x=x+1 -> x=x+2) is true.

>>

>>> How is not talking about anything true? You got me on this one.

>>

>> Your presupposition is incorrect.

>

> What is the sentence talking about then?

is also equal to x + 2.

semantics.)

>>>> But, to put it into the larger picture, if that is sufficient to

>>>> claim that (J) is about Unicorns, then it should also be

>>>> sufficient to claim that (K) is about Unicorns.

>>>

>>> I do not see any unicorns in K. It says that there is no proof of

>>> G.

>>

>> A more accurate translation would be, "There is no natural number

>> that encodes a proof of G."

>>

>> Likewise, I do not see any unicorns in (J). It says that there is no

>> natural number that both encodes a proof of G and satisfies the

>> statement This(<#G#>).

>

> If there is no natural number that encodes a proof of G then you cannot

> attribute anything to it. You cannot attribute something to nothing.

>>>> Once again, both (J) and (K) have to be about exactly the same

>>>> things

>>>

>>> No, they don't.

>>

>> Yes they do. The semantics of FOL

>

> But in this thread we are NOT talking about the [standard] semantics of

> FOL. Hasn't this been abundantly clear from the beginning?

you have only mentioned using something else (though you never give

details on that something else) when it leads to a result you don't

like. (So much for your claim of not being able to attribute something

to nothing, you've managed to do that repeatedly in this thread.)

> We are

> talking about the logic of presuppositions. And (K) is a presupposition

> of (J).

Strawson's).

>> don't allow for any for anything

>> else (unless you are using multiple sorts).

>>

>>>> unless you are using different sorts (and you've said that you

>>>> aren't).

>>>

>>> Never have and never shall.

>>> I am not sure what exactly you are asking about Strawson pp. 173,

>>> 174.

>>>

>>

>> I'm not asking about Stawson pp. 173, 174. I'm asking about the rules

>> for the existential quantifiers in Strawson's system. They are not

>> present on those pages.

>

> Of course they are not present. If I am not mistaken Strawson believed

> that logic was not formalizable.

That is incorrect. What he said was that natural language doesn't have a
>>> 174.

>>>

>>

>> I'm not asking about Stawson pp. 173, 174. I'm asking about the rules

>> for the existential quantifiers in Strawson's system. They are not

>> present on those pages.

>

> Of course they are not present. If I am not mistaken Strawson believed

> that logic was not formalizable.

precise logic. That's almost, but not quite, totally unlike saying that

logic is not formalizable.

> I am using him only as a source of

> inspiration. He nevertheless did show that if Aristotelian logic is

> interpreted as below

>

> A: ~(∃x)(Fx & ~Gx) & (∃x)Fx & (∃x)~Gx

> E: ~(∃x)(Fx & Gx) & (∃x)Fx & (∃x)Gx

> I: (∃x)(Fx & Gx) v ~(∃x)Fx v ~(∃x)Gx

> O: (∃x)(Fx & Gx) v ~(∃x)Fx v ~(∃x~)Gx

>

> then all the laws of the traditional syllogism hold together. But he

> proposed to take the last two terms, such as '(∃x)Fx & (∃x)Gx', as

> PRESUPPOSITIONS.

context of logic? Repeatedly asserting that Strawson was able to do

something with it indicates that you don't.

> Now in order to formalize this, the concept has to be

> extended to arbitrary monadic first order sentences. This is what I have

> done in my paper, and it turns out it is just a mirror image of the

> truth-relevant logic. Derivation rules are a small technical detail that

> will be added in due course.

Martin Shobe

Oct 18, 2015, 9:17:18 PM10/18/15

to

>>>>>>> Furthermore, the statement is true.

>>>>>

>>>>>> How does it manage to do that?

>>>>>

>>>>> There's no x such that x = x + 1.

>>>>

>>>> So the sentence does not talk about anything.

>>>

>>> No. It talks about natural numbers.

>>

>> Which natural numbers is the sentence talking about?

>

> Every last one of them.

>

>>>>> By the semantics of the -> operator,

>>>>

>>>> So it is all about the semantics of -> and has nothing to do

>>>> with the natural numbers per se.

>>>

>>> It has something to do with the natural numbers, every x in the

>>> domain is a natural number.

>>

>> I know that A(x) denotes the domain of the natural numbers [which

>> also includes unicorns]. I am asking what natural numbers is

>> (x)(x=x+1 -> x=x+2) talking about.

>

> It's talking about all of them. (And the domain of natural numbers

> does not include any unicorns.)

John's children or about all the objects in the domain?

If you have a discussion about John's children, another person joins the

conversation, and asks "what are you talking about?" do you answer "we

are talking about all the objects in the domain"?

>>>>> it follows that x=x+1 -> x=x+2 is true regardless of which

>>>>> value of x is used. Therefore, (x)(x=x+1 -> x=x+2) is true.

>>>

>>>> How is not talking about anything true? You got me on this

>>>> one.

>>>

>>> Your presupposition is incorrect.

>>

>> What is the sentence talking about then?

>

> It says that for every natural number, x, if x is equal to x + 1

> then x is also equal to x + 2.

"classical" one. Even when you are confronted with one you claim that it

is not semantics but "sentence classification". All you can see is that

it does not conform to the standard one, and you are not able to square

it your head. The thrust of all your arguments in essence is that if it

does not conform to ZFC/classical logic/standard semantics then it must

be wrong.

>>>>> But, to put it into the larger picture, if that is

>>>>> sufficient to claim that (J) is about Unicorns, then it

>>>>> should also be sufficient to claim that (K) is about

>>>>> Unicorns.

>>>>

>>>> I do not see any unicorns in K. It says that there is no proof

>>>> of G.

>>>

>>> A more accurate translation would be, "There is no natural number

>>> that encodes a proof of G."

>>>

>>> Likewise, I do not see any unicorns in (J). It says that there

>>> is no natural number that both encodes a proof of G and

>>> satisfies the statement This(<#G#>).

>>

>> If there is no natural number that encodes a proof of G then you

>> cannot attribute anything to it. You cannot attribute something to

>> nothing.

>

> Who is doing such a thing? I certainly haven't in this discussion.

that both encodes a proof of G and satisfies the statement This(<#G#>)"

If John has no children you do not get around it by saying "there is no
such object that it is both a John's child and it is asleep." If there

are no John's children there is nothing to say about them no matter how

you twist or turn.

>>>>> Once again, both (J) and (K) have to be about exactly the

>>>>> same things

>>>>

>>>> No, they don't.

>>>

>>> Yes they do. The semantics of FOL

>>

>> But in this thread we are NOT talking about the [standard]

>> semantics of FOL. Hasn't this been abundantly clear from the

>> beginning?

>

> Furthermore, you have only mentioned using something else

OK, so I have "only mentioned" something else. You injected an
orthogonal statement, which trumps it because it was "explicitly

mentioned." This is the best I can make of your logic.

you want to hear. Obviously I am missing something.

>> Now in order to formalize this, the concept has to be extended to

>> arbitrary monadic first order sentences. This is what I have done

>> in my paper, and it turns out it is just a mirror image of the

>> truth-relevant logic. Derivation rules are a small technical

>> detail that will be added in due course.

>

> You've done nothing of the sort in your paper.

Oct 18, 2015, 10:54:40 PM10/18/15

to

>>>>>> By the semantics of the -> operator,

>>>>>

>>>>> So it is all about the semantics of -> and has nothing to do

>>>>> with the natural numbers per se.

>>>>

>>>> It has something to do with the natural numbers, every x in the

>>>> domain is a natural number.

>>>

>>> I know that A(x) denotes the domain of the natural numbers [which

>>> also includes unicorns]. I am asking what natural numbers is

>>> (x)(x=x+1 -> x=x+2) talking about.

>>

>> It's talking about all of them. (And the domain of natural numbers

>> does not include any unicorns.)

>

> So if you say "All John's children are asleep", are you talking about

> John's children or about all the objects in the domain?

a matter of course in natural languages.

> If you have a discussion about John's children, another person joins the

> conversation, and asks "what are you talking about?" do you answer "we

> are talking about all the objects in the domain"?

Strawson saying that natural languages don't have a precise logic.

>>>>>> it follows that x=x+1 -> x=x+2 is true regardless of which

>>>>>> value of x is used. Therefore, (x)(x=x+1 -> x=x+2) is true.

>>>>

>>>>> How is not talking about anything true? You got me on this

>>>>> one.

>>>>

>>>> Your presupposition is incorrect.

>>>

>>> What is the sentence talking about then?

>>

>> It says that for every natural number, x, if x is equal to x + 1

>> then x is also equal to x + 2.

>

> Which numbers have the property x=x+1?

> Even when you are confronted with one you claim that it

> is not semantics but "sentence classification". All you can see is that

> it does not conform to the standard one, and you are not able to square

> it your head. The thrust of all your arguments in essence is that if it

> does not conform to ZFC/classical logic/standard semantics then it must

> be wrong.

>>>>>> But, to put it into the larger picture, if that is

>>>>>> sufficient to claim that (J) is about Unicorns, then it

>>>>>> should also be sufficient to claim that (K) is about

>>>>>> Unicorns.

>>>>>

>>>>> I do not see any unicorns in K. It says that there is no proof

>>>>> of G.

>>>>

>>>> A more accurate translation would be, "There is no natural number

>>>> that encodes a proof of G."

>>>>

>>>> Likewise, I do not see any unicorns in (J). It says that there

>>>> is no natural number that both encodes a proof of G and

>>>> satisfies the statement This(<#G#>).

>>>

>>> If there is no natural number that encodes a proof of G then you

>>> cannot attribute anything to it. You cannot attribute something to

>>> nothing.

>>

>> Who is doing such a thing? I certainly haven't in this discussion.

>

> You have just done it: "(J). It says that there is no natural number

> that both encodes a proof of G and satisfies the statement This(<#G#>)"

> If John has no children you do not get around it by saying "there is no

> such object that it is both a John's child and it is asleep." If there

> are no John's children there is nothing to say about them no matter how

> you twist or turn.

>>>>>> Once again, both (J) and (K) have to be about exactly the

>>>>>> same things

>>>>>

>>>>> No, they don't.

>>>>

>>>> Yes they do. The semantics of FOL

>>>

>>> But in this thread we are NOT talking about the [standard]

>>> semantics of FOL. Hasn't this been abundantly clear from the

>>> beginning?

>>

>> Of course not. I've even explicitly mentioned using FOL.ic.

>> Furthermore, you have only mentioned using something else

>

> OK, so I have "only mentioned" something else. You injected an

> orthogonal statement, which trumps it because it was "explicitly

> mentioned." This is the best I can make of your logic.

It's not even close.

>>> Now in order to formalize this, the concept has to be extended to

>>> arbitrary monadic first order sentences. This is what I have done

>>> in my paper, and it turns out it is just a mirror image of the

>>> truth-relevant logic. Derivation rules are a small technical

>>> detail that will be added in due course.

>>

>> You've done nothing of the sort in your paper.

>

> You mean I have not specified semantics, I have merely classified

> sentences?

Martin Shobe

Oct 19, 2015, 12:05:05 AM10/19/15

to

On Sunday, October 18, 2015 at 7:54:40 PM UTC-7, Martin Shobe wrote:

> On 10/18/2015 8:16 PM, X.Y. Newberry wrote:

> >>

> >> It's talking about all of them. (And the domain of natural numbers

> >> does not include any unicorns.)

> >

> > So if you say "All John's children are asleep", are you talking about

> > John's children or about all the objects in the domain?

>

> I would say John's children, but that's because we use multiple sorts as

> a matter of course in natural languages.

>

> > If you have a discussion about John's children, another person joins the

> > conversation, and asks "what are you talking about?" do you answer "we

> > are talking about all the objects in the domain"?

>

> No, since it's a natural language. It's issues like this that lead to

> Strawson saying that natural languages don't have a precise logic.

>

"Natural languages" have as precise a logic
> On 10/18/2015 8:16 PM, X.Y. Newberry wrote:

> >>

> >> It's talking about all of them. (And the domain of natural numbers

> >> does not include any unicorns.)

> >

> > So if you say "All John's children are asleep", are you talking about

> > John's children or about all the objects in the domain?

>

> I would say John's children, but that's because we use multiple sorts as

> a matter of course in natural languages.

>

> > If you have a discussion about John's children, another person joins the

> > conversation, and asks "what are you talking about?" do you answer "we

> > are talking about all the objects in the domain"?

>

> No, since it's a natural language. It's issues like this that lead to

> Strawson saying that natural languages don't have a precise logic.

>

within them as any "symbolic language", it

is just usually that the "elements" include

the imprecise. Symbolic language is contained

within natural language.

If there's no ambiguity in definition there's

no ambiguity in terms.

Some natural words as match quantifiers and

other primitives in the symbolic, can establish

the quantifier separations but only as maintained,

where the quantifiers themselves may reflect

structural properties of the domain(s), whether

it's the impredicative or the collective, for examples.

So, a "precise logic" is yet _within_ natural language,

then for the disambiguation via definition and convention

of the imprecise.

Thank you for reviewing my opinion.

Oct 20, 2015, 4:54:20 AM10/20/15

to

On Saturday, October 17, 2015 at 9:47:53 AM UTC+2, Nam Nguyen wrote:

> On 17/10/2015 12:38 AM, Rupert wrote:

> > On Friday, October 16, 2015 at 3:41:48 AM UTC+2, Newberry wrote:

> >> Rupert wrote:

> >>> There were some parts of your post that I had a bit of a hard time

> >>> following. I don't think it is reasonable to take "This sentence is

> >>> not true" as equivalent with "This true sentence is not true".

> >>

> >> The proof of contradiction of the Liar typically starts with the

> >> assumption that the sentence is true. Liar + this assumption make "This

> >> true sentence is not true." So it seems to me that at the very least you

> >> cannot walk through the proof without stepping through "This true

> >> sentence is not true."

> >

> > But it is not equivalent to the original sentence.

> >

> >>> As far

> >>> as Gödel's sentence goes the point is it is a sentence in the

> >>> first-order language of arithmetic and so for that reason surely has

> >>> a truth-value.

>

> Except surely nobody knows the truth value of G(PA + cGC),

> G(PA + ~cGC), ... and infinitely many Gödel's sentences.

Those two examples of Gödel sentences you just gave are examples where nobody *currently* knows the truth-value, although you haven't offered any good reason for thinking that there is any deep obstacle to us knowing the truth-value one day.
> On 17/10/2015 12:38 AM, Rupert wrote:

> > On Friday, October 16, 2015 at 3:41:48 AM UTC+2, Newberry wrote:

> >> Rupert wrote:

> >>> There were some parts of your post that I had a bit of a hard time

> >>> following. I don't think it is reasonable to take "This sentence is

> >>> not true" as equivalent with "This true sentence is not true".

> >>

> >> The proof of contradiction of the Liar typically starts with the

> >> assumption that the sentence is true. Liar + this assumption make "This

> >> true sentence is not true." So it seems to me that at the very least you

> >> cannot walk through the proof without stepping through "This true

> >> sentence is not true."

> >

> > But it is not equivalent to the original sentence.

> >

> >>> As far

> >>> as Gödel's sentence goes the point is it is a sentence in the

> >>> first-order language of arithmetic and so for that reason surely has

> >>> a truth-value.

>

> Except surely nobody knows the truth value of G(PA + cGC),

> G(PA + ~cGC), ... and infinitely many Gödel's sentences.

> >> "first-order language of arithmetic" usually implies classical logic. In

> >> the present context I am suggesting that there is an alternative

> >> logic/interpretation such that it does NOT have a truth value. Are you

> >> claiming that no such logic/interpretation is possible, or are you just

> >> injecting an orthogonal statement for fun?

> >

> > Of course you can always come up with some nonstandard semantics with respect to which some given sentence does not have a truth-value, but why is that supposed to be interesting? When we are talking about the first-order language of arithmetic then surely we usually have the standard semantics in mind.

>

> "Standard semantics" is very much philosophical here.

Oct 20, 2015, 5:04:04 AM10/20/15

to

> >>> As far as Gödel's sentence goes the point is it is a sentence in

> >>> the first-order language of arithmetic and so for that reason

> >>> surely has a truth-value.

> >>

> >> "first-order language of arithmetic" usually implies classical

> >> logic. In the present context I am suggesting that there is an

> >> alternative logic/interpretation such that it does NOT have a truth

> >> value. Are you claiming that no such logic/interpretation is

> >> possible, or are you just injecting an orthogonal statement for

> >> fun?

> >

> > Of course you can always come up with some nonstandard semantics with

> > respect to which some given sentence does not have a truth-value, but

> > why is that supposed to be interesting?

>

> It is interesting for a number of reasons

>

> a) The idea that empty sentences are true is implausible - it does not

> correspond to the intuitive notion of truth

>

> b) The semantics I am proposing formalizes the notion of

> meaninglessness. I.e. sentences that do not have interpretation are

> meaningless.

>

> c) Truth and derivability can be equated. It gets rid of the paradoxical

> situation that there are true but unprovable sentences.

>

> d) Since a sound derivation system (i.e. system that does not derive

> non-truth) will not derive G even if it did derive ~(Ex)Prf(x,<#G#>)

> more axiom(s) can be added to Peano Arithmetic without causing a

> contradiction.

The point is, you are introducing a non-standard truth for the first-order language of arithmetic, so you need to say something about why it should be thought better than the standard notion of truth that we have. It needs to be a bit more than that it enables us to do the things you listed IMHO.

> > When we are talking about the

> > first-order language of arithmetic then surely we usually have the

> > standard semantics in mind.

>

> Yes, but in this thread we are NOT talking about the standard semantics.

> Sounds like you want us back in the box.

Oct 20, 2015, 9:53:22 AM10/20/15

to

On 20/10/2015 2:54 AM, Rupert wrote:

> On Saturday, October 17, 2015 at 9:47:53 AM UTC+2, Nam Nguyen wrote:

>> On 17/10/2015 12:38 AM, Rupert wrote:

>>> On Friday, October 16, 2015 at 3:41:48 AM UTC+2, Newberry wrote:

>>>> Rupert wrote:

>>>>> There were some parts of your post that I had a bit of a hard time

>>>>> following. I don't think it is reasonable to take "This sentence is

>>>>> not true" as equivalent with "This true sentence is not true".

>>>>

>>>> The proof of contradiction of the Liar typically starts with the

>>>> assumption that the sentence is true. Liar + this assumption make "This

>>>> true sentence is not true." So it seems to me that at the very least you

>>>> cannot walk through the proof without stepping through "This true

>>>> sentence is not true."

>>>

>>> But it is not equivalent to the original sentence.

>>>

>>>>> As far

>>>>> as Gödel's sentence goes the point is it is a sentence in the

>>>>> first-order language of arithmetic and so for that reason surely has

>>>>> a truth-value.

>>

>> Except surely nobody knows the truth value of G(PA + cGC),

>> G(PA + ~cGC), ... and infinitely many Gödel's sentences.

>

> Those two examples of Gödel sentences you just gave are examples where nobody *currently* knows the truth-value, although you haven't offered any good reason for thinking that there is any deep obstacle to us knowing the truth-value one day.

I did, through undecide(cGC). You're just unable to understand basic
> On Saturday, October 17, 2015 at 9:47:53 AM UTC+2, Nam Nguyen wrote:

>> On 17/10/2015 12:38 AM, Rupert wrote:

>>> On Friday, October 16, 2015 at 3:41:48 AM UTC+2, Newberry wrote:

>>>> Rupert wrote:

>>>>> There were some parts of your post that I had a bit of a hard time

>>>>> following. I don't think it is reasonable to take "This sentence is

>>>>> not true" as equivalent with "This true sentence is not true".

>>>>

>>>> The proof of contradiction of the Liar typically starts with the

>>>> assumption that the sentence is true. Liar + this assumption make "This

>>>> true sentence is not true." So it seems to me that at the very least you

>>>> cannot walk through the proof without stepping through "This true

>>>> sentence is not true."

>>>

>>> But it is not equivalent to the original sentence.

>>>

>>>>> As far

>>>>> as Gödel's sentence goes the point is it is a sentence in the

>>>>> first-order language of arithmetic and so for that reason surely has

>>>>> a truth-value.

>>

>> Except surely nobody knows the truth value of G(PA + cGC),

>> G(PA + ~cGC), ... and infinitely many Gödel's sentences.

>

> Those two examples of Gödel sentences you just gave are examples where nobody *currently* knows the truth-value, although you haven't offered any good reason for thinking that there is any deep obstacle to us knowing the truth-value one day.

notions used in the offer, such as "meta proof". In fact you weren't

telling sci.logic the truth I had never explained what I'd mean by

"meta proof"!

>>>> "first-order language of arithmetic" usually implies classical logic. In

>>>> the present context I am suggesting that there is an alternative

>>>> logic/interpretation such that it does NOT have a truth value. Are you

>>>> claiming that no such logic/interpretation is possible, or are you just

>>>> injecting an orthogonal statement for fun?

>>>

>>> Of course you can always come up with some nonstandard semantics with respect to which some given sentence does not have a truth-value, but why is that supposed to be interesting? When we are talking about the first-order language of arithmetic then surely we usually have the standard semantics in mind.

>>

>> "Standard semantics" is very much philosophical here.

>

> Well, it has a precise mathematical definition.

though.

There are those who would precisely defined any number greater than

10^500 to be an infinite number. So what?

Oct 20, 2015, 9:58:23 AM10/20/15

to

> telling sci.logic the truth in claiming, in a recent post, that I had never explained what I'd mean by

> "meta proof"!

[The above has been edited for clarity].

Oct 20, 2015, 10:02:45 AM10/20/15

to

Nam Nguyen wrote:

> On 20/10/2015 2:54 AM, Rupert wrote:

>> On Saturday, October 17, 2015 at 9:47:53 AM UTC+2, Nam Nguyen wrote:

>>> Except surely nobody knows the truth value of G(PA + cGC),

>>> G(PA + ~cGC), ... and infinitely many Gödel's sentences.

>>

>> Those two examples of Gödel sentences you just gave are examples where

>> nobody *currently* knows the truth-value, although you haven't offered

>> any good reason for thinking that there is any deep obstacle to us

>> knowing the truth-value one day.

>

> I did, through undecide(cGC).

You've never proved that undecide(cGC).
> On 20/10/2015 2:54 AM, Rupert wrote:

>> On Saturday, October 17, 2015 at 9:47:53 AM UTC+2, Nam Nguyen wrote:

>>> Except surely nobody knows the truth value of G(PA + cGC),

>>> G(PA + ~cGC), ... and infinitely many Gödel's sentences.

>>

>> Those two examples of Gödel sentences you just gave are examples where

>> nobody *currently* knows the truth-value, although you haven't offered

>> any good reason for thinking that there is any deep obstacle to us

>> knowing the truth-value one day.

>

> I did, through undecide(cGC).

--

It simply means that kind of empty set isn't the kind of empty

set admissible in reasoning in meta level in the context of FOL

reasoning framework.

Nam Nguyen in sci.logic

Oct 20, 2015, 10:05:59 AM10/20/15

to

On 20/10/2015 8:02 AM, Justin Thyme wrote:

> Nam Nguyen wrote:

>> On 20/10/2015 2:54 AM, Rupert wrote:

>>> On Saturday, October 17, 2015 at 9:47:53 AM UTC+2, Nam Nguyen wrote:

>

>>>> Except surely nobody knows the truth value of G(PA + cGC),

>>>> G(PA + ~cGC), ... and infinitely many Gödel's sentences.

>>>

>>> Those two examples of Gödel sentences you just gave are examples where

>>> nobody *currently* knows the truth-value, although you haven't offered

>>> any good reason for thinking that there is any deep obstacle to us

>>> knowing the truth-value one day.

>>

>> I did, through undecide(cGC).

>

> You've never proved that undecide(cGC).

That's a lie and trolling.
> Nam Nguyen wrote:

>> On 20/10/2015 2:54 AM, Rupert wrote:

>>> On Saturday, October 17, 2015 at 9:47:53 AM UTC+2, Nam Nguyen wrote:

>

>>>> Except surely nobody knows the truth value of G(PA + cGC),

>>>> G(PA + ~cGC), ... and infinitely many Gödel's sentences.

>>>

>>> Those two examples of Gödel sentences you just gave are examples where

>>> nobody *currently* knows the truth-value, although you haven't offered

>>> any good reason for thinking that there is any deep obstacle to us

>>> knowing the truth-value one day.

>>

>> I did, through undecide(cGC).

>

> You've never proved that undecide(cGC).

Oct 20, 2015, 10:35:07 AM10/20/15

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On Tuesday, October 20, 2015 at 3:53:22 PM UTC+2, Nam Nguyen wrote:

> On 20/10/2015 2:54 AM, Rupert wrote:

> > On Saturday, October 17, 2015 at 9:47:53 AM UTC+2, Nam Nguyen wrote:

> >> On 17/10/2015 12:38 AM, Rupert wrote:

> >>> On Friday, October 16, 2015 at 3:41:48 AM UTC+2, Newberry wrote:

> >>>> Rupert wrote:

> >>>>> There were some parts of your post that I had a bit of a hard time

> >>>>> following. I don't think it is reasonable to take "This sentence is

> >>>>> not true" as equivalent with "This true sentence is not true".

> >>>>

> >>>> The proof of contradiction of the Liar typically starts with the

> >>>> assumption that the sentence is true. Liar + this assumption make "This

> >>>> true sentence is not true." So it seems to me that at the very least you

> >>>> cannot walk through the proof without stepping through "This true

> >>>> sentence is not true."

> >>>

> >>> But it is not equivalent to the original sentence.

> >>>

> >>>>> As far

> >>>>> as Gödel's sentence goes the point is it is a sentence in the

> >>>>> first-order language of arithmetic and so for that reason surely has

> >>>>> a truth-value.

> >>

> >> Except surely nobody knows the truth value of G(PA + cGC),

> >> G(PA + ~cGC), ... and infinitely many Gödel's sentences.

> >

> > Those two examples of Gödel sentences you just gave are examples where nobody *currently* knows the truth-value, although you haven't offered any good reason for thinking that there is any deep obstacle to us knowing the truth-value one day.

>

> I did, through undecide(cGC). You're just unable to understand basic

> notions used in the offer, such as "meta proof".

You *think* that's where the problem lies, as opposed to the problem being in the fact that the notions used in your proof are not particularly precise or coherent.
> On 20/10/2015 2:54 AM, Rupert wrote:

> > On Saturday, October 17, 2015 at 9:47:53 AM UTC+2, Nam Nguyen wrote:

> >> On 17/10/2015 12:38 AM, Rupert wrote:

> >>> On Friday, October 16, 2015 at 3:41:48 AM UTC+2, Newberry wrote:

> >>>> Rupert wrote:

> >>>>> There were some parts of your post that I had a bit of a hard time

> >>>>> following. I don't think it is reasonable to take "This sentence is

> >>>>> not true" as equivalent with "This true sentence is not true".

> >>>>

> >>>> The proof of contradiction of the Liar typically starts with the

> >>>> assumption that the sentence is true. Liar + this assumption make "This

> >>>> true sentence is not true." So it seems to me that at the very least you

> >>>> cannot walk through the proof without stepping through "This true

> >>>> sentence is not true."

> >>>

> >>> But it is not equivalent to the original sentence.

> >>>

> >>>>> As far

> >>>>> as Gödel's sentence goes the point is it is a sentence in the

> >>>>> first-order language of arithmetic and so for that reason surely has

> >>>>> a truth-value.

> >>

> >> Except surely nobody knows the truth value of G(PA + cGC),

> >> G(PA + ~cGC), ... and infinitely many Gödel's sentences.

> >

> > Those two examples of Gödel sentences you just gave are examples where nobody *currently* knows the truth-value, although you haven't offered any good reason for thinking that there is any deep obstacle to us knowing the truth-value one day.

>

> I did, through undecide(cGC). You're just unable to understand basic

> notions used in the offer, such as "meta proof".

> In fact you weren't

> telling sci.logic the truth I had never explained what I'd mean by

> "meta proof"!

> >>>> "first-order language of arithmetic" usually implies classical logic. In

> >>>> the present context I am suggesting that there is an alternative

> >>>> logic/interpretation such that it does NOT have a truth value. Are you

> >>>> claiming that no such logic/interpretation is possible, or are you just

> >>>> injecting an orthogonal statement for fun?

> >>>

> >>> Of course you can always come up with some nonstandard semantics with respect to which some given sentence does not have a truth-value, but why is that supposed to be interesting? When we are talking about the first-order language of arithmetic then surely we usually have the standard semantics in mind.

> >>

> >> "Standard semantics" is very much philosophical here.

> >

> > Well, it has a precise mathematical definition.

>

> Yeah sure, very precisely conveniently so. It's a buzzword-definition

> though.

>

> There are those who would precisely defined any number greater than

> 10^500 to be an infinite number. So what?

Oct 20, 2015, 12:00:45 PM10/20/15

to

> as opposed to the problem being in the fact that the notions used in your proof are not particularly precise or coherent.

to muster a disproof or counter example to these basic notions? I mean

the cranks, the trolls, the inquisitors, etc... can always whine,

creating smoke-screens like "the notions used in your proof are not

particularly precise or coherent" against their opponent's argument!

>

>> In fact you weren't

>> telling sci.logic the truth I had never explained what I'd mean by

>> "meta proof"!

>

> If I recall correctly what I said was that I'd never read any explanation from you that I'd found particular enlightening.

But again, that you not being able to understand my _simple_

definition of "meta proof" isn't my problem and is a clear indication

you're unable to comprehend my meta proof of undecide(cGC), and

everything else related to such as MR, etc..., whatever you wish to

say as a smokescreen.

>>>>>> "first-order language of arithmetic" usually implies classical logic. In

>>>>>> the present context I am suggesting that there is an alternative

>>>>>> logic/interpretation such that it does NOT have a truth value. Are you

>>>>>> claiming that no such logic/interpretation is possible, or are you just

>>>>>> injecting an orthogonal statement for fun?

>>>>>

>>>>> Of course you can always come up with some nonstandard semantics with respect to which some given sentence does not have a truth-value, but why is that supposed to be interesting? When we are talking about the first-order language of arithmetic then surely we usually have the standard semantics in mind.

>>>>

>>>> "Standard semantics" is very much philosophical here.

>>>

>>> Well, it has a precise mathematical definition.

>>

>> Yeah sure, very precisely conveniently so. It's a buzzword-definition

>> though.

>>

>> There are those who would precisely defined any number greater than

>> 10^500 to be an infinite number. So what?

>

> So, actually, these people of whom you speak have not shown how to make that a part of a consistent mathematical theory, so the case is completely different.

No logical differences: both (your side and those people) would ignore

standard definitions and permissible rules of reasoning in meta level,

and both _believe_ they are right, while actually being wrong.

The insignificant difference is non-technical: one of them of higher

social or certificate ranking so the ignorance (or even idiocy) is not

supposed to be visible.

Oct 20, 2015, 12:12:55 PM10/20/15

to

Nam Nguyen wrote:

> But again, that you not being able to understand my _simple_

> definition of "meta proof" isn't my problem and is a clear indication

> you're unable to comprehend my meta proof of undecide(cGC), and

> everything else related to such as MR, etc..., whatever you wish to

> say as a smokescreen.

You have never defined "meta proof". At best you say that there are
> But again, that you not being able to understand my _simple_

> definition of "meta proof" isn't my problem and is a clear indication

> you're unable to comprehend my meta proof of undecide(cGC), and

> everything else related to such as MR, etc..., whatever you wish to

> say as a smokescreen.

certain statements such a proof begins with and certain rules for

deriving statements from other statements. But you have never listed

all the initial statements nor all the rules. How, then, can anyone

tell if a purported meta proof is valid or not?

Oct 20, 2015, 12:17:27 PM10/20/15

to

> > as opposed to the problem being in the fact that the notions used in your proof are not particularly precise or coherent.

>

> "Precise or coherent" in precisely what way?

> Do you even have ability

> to muster a disproof or counter example to these basic notions?

> I mean

> the cranks, the trolls, the inquisitors, etc... can always whine,

> creating smoke-screens like "the notions used in your proof are not

> particularly precise or coherent" against their opponent's argument!

> >

> >> In fact you weren't

> >> telling sci.logic the truth I had never explained what I'd mean by

> >> "meta proof"!

> >

> > If I recall correctly what I said was that I'd never read any explanation from you that I'd found particular enlightening.

>

> I took it back: you did have "which I found enlightening" then.

> But again, that you not being able to understand my _simple_

> definition of "meta proof" isn't my problem and is a clear indication

> you're unable to comprehend my meta proof of undecide(cGC), and

> everything else related to such as MR, etc..., whatever you wish to

> say as a smokescreen.

> >>>>>> "first-order language of arithmetic" usually implies classical logic. In

> >>>>>> the present context I am suggesting that there is an alternative

> >>>>>> logic/interpretation such that it does NOT have a truth value. Are you

> >>>>>> claiming that no such logic/interpretation is possible, or are you just

> >>>>>> injecting an orthogonal statement for fun?

> >>>>>

> >>>>> Of course you can always come up with some nonstandard semantics with respect to which some given sentence does not have a truth-value, but why is that supposed to be interesting? When we are talking about the first-order language of arithmetic then surely we usually have the standard semantics in mind.

> >>>>

> >>>> "Standard semantics" is very much philosophical here.

> >>>

> >>> Well, it has a precise mathematical definition.

> >>

> >> Yeah sure, very precisely conveniently so. It's a buzzword-definition

> >> though.

> >>

> >> There are those who would precisely defined any number greater than

> >> 10^500 to be an infinite number. So what?

> >

> > So, actually, these people of whom you speak have not shown how to make that a part of a consistent mathematical theory, so the case is completely different.

>

> (In sci.logic, I don't speak to them, any more than you do!)

>

> No logical differences: both (your side and those people) would ignore

> standard definitions and permissible rules of reasoning in meta level,

> and both _believe_ they are right, while actually being wrong.

Oct 20, 2015, 12:22:07 PM10/20/15

to

>>>> There are those who would precisely defined any number greater than

>>>> 10^500 to be an infinite number. So what?

>>>

>>> So, actually, these people of whom you speak have not shown how to make that a part of a consistent mathematical theory, so the case is completely different.

>>

>> (In sci.logic, I don't speak to them, any more than you do!)

>>

>> No logical differences: both (your side and those people) would ignore

>> standard definitions and permissible rules of reasoning in meta level,

>> and both _believe_ they are right, while actually being wrong.

>

> No, I'm afraid you're mistaken about that.

Oct 20, 2015, 12:27:36 PM10/20/15

to

On 20/10/2015 10:12 AM, Justin Thyme wrote:

> Nam Nguyen wrote:

>

>> But again, that you not being able to understand my _simple_

>> definition of "meta proof" isn't my problem and is a clear indication

>> you're unable to comprehend my meta proof of undecide(cGC), and

>> everything else related to such as MR, etc..., whatever you wish to

>> say as a smokescreen.

>

> You have never defined "meta proof".

Liar.
> Nam Nguyen wrote:

>

>> But again, that you not being able to understand my _simple_

>> definition of "meta proof" isn't my problem and is a clear indication

>> you're unable to comprehend my meta proof of undecide(cGC), and

>> everything else related to such as MR, etc..., whatever you wish to

>> say as a smokescreen.

>

> You have never defined "meta proof".

> At best you say that there are

> certain statements such a proof begins with and certain rules for

> deriving statements from other statements. But you have never listed

> all the initial statements nor all the rules. How, then, can anyone

> tell if a purported meta proof is valid or not?

rules *required* (and if any one of them is in doubt it can be

addressed individually).

Presenting a meta proof isn't the same as writing an education book

teaching about Meta-mathematical logic!

Oct 20, 2015, 12:31:28 PM10/20/15

to

On Tuesday, October 20, 2015 at 9:00:45 AM UTC-7, Nam Nguyen wrote:

>

> I know, not just think.

>

You're hallucinating!
>

> I know, not just think.

>

Oct 20, 2015, 12:33:15 PM10/20/15

to

> >>>> There are those who would precisely defined any number greater than

> >>>> 10^500 to be an infinite number. So what?

> >>>

> >>> So, actually, these people of whom you speak have not shown how to make that a part of a consistent mathematical theory, so the case is completely different.

> >>

> >> (In sci.logic, I don't speak to them, any more than you do!)

> >>

> >> No logical differences: both (your side and those people) would ignore

> >> standard definitions and permissible rules of reasoning in meta level,

> >> and both _believe_ they are right, while actually being wrong.

> >

> > No, I'm afraid you're mistaken about that.

>

> I'm afraid you're mistaken about that, Rupert.

Oct 20, 2015, 12:46:56 PM10/20/15

to

understanding that my presentation isn't FOL formal system theorem/proof

work: I've informed you this is meta reasoning about the FOL

reasoning framework _in meta level_ .

How many more time do you need to be reminded of these premisses into

the presentation?

> Do you just think I'm mathematically incompetent, do you?

comes to making arguments about foundation/logic of mathematics.

>>>>>> There are those who would precisely defined any number greater than

>>>>>> 10^500 to be an infinite number. So what?

>>>>>

>>>>> So, actually, these people of whom you speak have not shown how to make that a part of a consistent mathematical theory, so the case is completely different.

>>>>

>>>> (In sci.logic, I don't speak to them, any more than you do!)

>>>>

>>>> No logical differences: both (your side and those people) would ignore

>>>> standard definitions and permissible rules of reasoning in meta level,

>>>> and both _believe_ they are right, while actually being wrong.

>>>

>>> No, I'm afraid you're mistaken about that.

>>

>> I'm afraid you're mistaken about that, Rupert.

>

> So which standard definitions are we ignoring, then?

undecide(cGC), etc...

For sure you're unable to understand that.

Oct 20, 2015, 12:47:33 PM10/20/15

to

Oct 20, 2015, 12:50:04 PM10/20/15

to

Nam Nguyen wrote:

> On 20/10/2015 10:12 AM, Justin Thyme wrote:

>> Nam Nguyen wrote:

>>

>>> But again, that you not being able to understand my _simple_

>>> definition of "meta proof" isn't my problem and is a clear indication

>>> you're unable to comprehend my meta proof of undecide(cGC), and

>>> everything else related to such as MR, etc..., whatever you wish to

>>> say as a smokescreen.

>>

>> You have never defined "meta proof".

>

> Liar.

>

>> At best you say that there are

>> certain statements such a proof begins with and certain rules for

>> deriving statements from other statements. But you have never listed

>> all the initial statements nor all the rules. How, then, can anyone

>> tell if a purported meta proof is valid or not?

>

> Easy: just listing enough finitely many initial statements and all the

> rules *required* (and if any one of them is in doubt it can be

> addressed individually).

Ok, so why not get back to the logic/mathematics by proving nK(cGC) and
> On 20/10/2015 10:12 AM, Justin Thyme wrote:

>> Nam Nguyen wrote:

>>

>>> But again, that you not being able to understand my _simple_

>>> definition of "meta proof" isn't my problem and is a clear indication

>>> you're unable to comprehend my meta proof of undecide(cGC), and

>>> everything else related to such as MR, etc..., whatever you wish to

>>> say as a smokescreen.

>>

>> You have never defined "meta proof".

>

> Liar.

>

>> At best you say that there are

>> certain statements such a proof begins with and certain rules for

>> deriving statements from other statements. But you have never listed

>> all the initial statements nor all the rules. How, then, can anyone

>> tell if a purported meta proof is valid or not?

>

> Easy: just listing enough finitely many initial statements and all the

> rules *required* (and if any one of them is in doubt it can be

> addressed individually).

then following the proof by a list of the initial statements and

required rules used in that proof? And then if anyone has doubts about

any statement or rule you can address it.

Writing down the proof might be best done off-line and then you could

start a new thread by posting the finished whole. Take a few days over

it, get it nice and clear before you post it. How about that?

> Presenting a meta proof isn't the same as writing an education book

> teaching about Meta-mathematical logic!

>

>

--

Oct 20, 2015, 12:54:50 PM10/20/15

to

comprehending what a meta proof is - *despite clear cut examples*?

Nah.

>

>> Presenting a meta proof isn't the same as writing an education book

>> teaching about Meta-mathematical logic!

--

Oct 20, 2015, 12:58:37 PM10/20/15

to

Nam Nguyen wrote:

logic.

> work: I've informed you this is meta reasoning about the FOL

> reasoning framework _in meta level_ .

Any text on first order logic and first order theories (like

Shoenfield's /Mathematical logic/, for example) is almost all on the

meta level: such books prove things *about* theories rather more than

the prove things *in* theories.

So you seem to be saying that Rupert hasn't read (or, at least, hasn't

read with understanding) a single maths book or logic book. Is that

what you think?

> On 20/10/2015 10:33 AM, Rupert wrote:

>> Do you have any thoughts on why I would fail to understand if you were

>> giving me a satisfactory presentation of a cogent mathematical argument?

>

> Yes I do, and I said that many times already. You're incapable of

> understanding that my presentation isn't FOL formal system theorem/proof

That can't be it. Almost all of mathematics isn't proofs in first order
>> Do you have any thoughts on why I would fail to understand if you were

>> giving me a satisfactory presentation of a cogent mathematical argument?

>

> Yes I do, and I said that many times already. You're incapable of

> understanding that my presentation isn't FOL formal system theorem/proof

logic.

> work: I've informed you this is meta reasoning about the FOL

> reasoning framework _in meta level_ .

Shoenfield's /Mathematical logic/, for example) is almost all on the

meta level: such books prove things *about* theories rather more than

the prove things *in* theories.

So you seem to be saying that Rupert hasn't read (or, at least, hasn't

read with understanding) a single maths book or logic book. Is that

what you think?