On 5/18/22 7:54 PM, olcott wrote:
> On 5/18/2022 6:30 PM, Richard Damon wrote:
>> On 5/18/22 11:06 AM, olcott wrote:
>>> On 5/18/2022 6:32 AM, Richard Damon wrote:
>>>> On 5/17/22 11:17 PM, olcott wrote:
>>>>> On 5/15/2022 6:31 AM, Richard Damon wrote:
>>>>>> On 5/15/22 12:13 AM, olcott wrote:
>>>>>>> On 5/14/2022 11:06 PM, André G. Isaak wrote:
>>>>>>>> On 2022-05-14 21:02, olcott wrote:
>>>>>>>>> On 5/14/2022 6:32 PM, André G. Isaak wrote:
>>>>>>>>>> On 2022-05-14 17:27, olcott wrote:
>>>>>>>>>>> On 5/14/2022 6:21 PM, André G. Isaak wrote:
>>>>>>>>>>>> On 2022-05-14 17:00, Richard Damon wrote:
>>>>>>>>>>>>> On 5/14/22 6:21 PM, olcott wrote:
>>>>>>>>>>>>
>>>>>>>>>>>>>> Wittgenstein, Ludwig 1983. Remarks on the Foundations of
>>>>>>>>>>>>>> Mathematics (Appendix III), 118-119.Cambridge,
>>>>>>>>>>>>>> Massachusetts and London, England: The MIT Press
>>>>>>>>>>>>>>
>>>>>>>>>>>>> And, my understanding is that Wittgestein hadn't read
>>>>>>>>>>>>> Godel's paper at this point either, so he makes the same
>>>>>>>>>>>>> error you do of know knowing what he is talking about.
>>>>>>>>>>>>
>>>>>>>>>>>> There is one crucial difference -- Wittgenstein recorded his
>>>>>>>>>>>> initial reactions to first hearing of Gödel's proof in a
>>>>>>>>>>>> private journal which was never intended for publication
>>>>>>>>>>>> (which explains why he never bothered to retract this remark
>>>>>>>>>>>> once the error became clear to him).
>>>>>>>>>>>>
>>>>>>>>>>>> Olcott, on the other hand, is intent on broadcasting his
>>>>>>>>>>>> misunderstanding to the world even after his errors have
>>>>>>>>>>>> been pointed out to him repeatedly.
>>>>>>>>>>>>
>>>>>>>>>>>> André
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Unprovable(F, G) merely means Untrue(F, G) and not
>>>>>>>>>>> Incomplete(F).
>>>>>>>>>>
>>>>>>>>>> That's an assertion, not an argument.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Some of these terms are from standard analytic philosophy.
>>>>>>>>>
>>>>>>>>> Proofs over infinite sets can be tricky.
>>>>>>>>
>>>>>>>> Yet people make proofs over infinite sets all the time.
>>>>>>>>
>>>>>>>>> KEY_INSIGHT:
>>>>>>>>> (a) The proof is that the entire body of analytic knowledge
>>>>>>>>> (including all math, logic, et cetera) is structured as
>>>>>>>>> semantic connections between elements of this same body.
>>>>>>>>
>>>>>>>> Again, this is simply a baseless assertion, not an argument.
>>>>>>>>
>>>>>>>>> (b) All analytic expressions of language only obtain their
>>>>>>>>> meaning through semantic connections.
>>>>>>>>
>>>>>>>> Again, this is simply a baseless assertion, not an argument. And
>>>>>>>> your use of the term 'analytic' doesn't seem to correspond to
>>>>>>>> the standard usage. The analytic/synthetic distinction is one
>>>>>>>> that normally arises when talking about the philosophy of
>>>>>>>> language, not logic.
>>>>>>>>
>>>>>>>>> *The proof of these two is that no counter-examples can be found*
>>>>>>>>
>>>>>>>> That is not how proofs work. You're the one making a claim. The
>>>>>>>> burden of proof lies with you.
>>>>>>>>
>>>>>>>> And your specific claims are far too vaguely defined for anyone
>>>>>>>> to track down counterexamples. For example, I have absolutely no
>>>>>>>> idea what you mean by 'semantic connection'.
>>>>>>>
>>>>>>> I will make that one concrete.
>>>>>>> Try to provide a sentence that is true that is not connected to
>>>>>>> anything else that shows that it is true.
>>>>>>>
>>>>>>
>>>>>>
>>>>>> One of:
>>>>>>
>>>>>> The Collbatz conjecture is True.
>>>>>>
>>>>>> The Collbatz conjecture is False.
>>>>>>
>>>>>
>>>>> That is connected to tautology.
>>>>>
>>>>
>>>> Nope. We know that one of the sentences is true.
>>>>
>>>> THAT sentence is not establisned by "Tautology"
>>>>
>>>> That sentence being true disproves your statement.
>>>>
>>>
>>> You did not provide an example of a sentence that is true that is not
>>> connected to anything else that shows that it is true.
>>
>> One of these sentences is such an example, I don't know which one:
>>
>> The Collbatz conjecture is True.
>>
>> The Collbatz conjecture is False.
>
> Then you did not meet my challenge.
>
>>
>>
>> The fact that I don't know which one doesn't make the arguement
>> invalid, it points out that there is a limit to knowledge.
>>
>> A second example.
>>
>> Godel sentence G is True.
>>
>> You may not accept that it is True, but it is. To quote from one of
>> your favorite sources:
>>
>
> G is not true in F the same way and for the same reason that the Liar
> Paradox is not true.
>
> When we move outside of self-contradiction into Tarski's meta-theory it
> is true that the liar paradox is not true in Tarski's theory.
>
>> https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems
>>
>> The Gödel sentence is designed to refer, indirectly, to itself. The
>> sentence states that, when a particular sequence of steps is used to
>> construct another sentence, that constructed sentence will not be
>> provable in F. However, the sequence of steps is such that the
>> constructed sentence turns out to be GF itself. In this way, the Gödel
>> sentence GF indirectly states its own unprovability within F (Smith
>> 2007, p. 135).
>>
>
> Exactly the same as Tarski.

Sort of, and just as True.

>
>> To prove the first incompleteness theorem, Gödel demonstrated that the
>> notion of provability within a system could be expressed purely in
>> terms of arithmetical functions that operate on Gödel numbers of
>> sentences of the system. Therefore, the system, which can prove
>> certain facts about numbers, can also indirectly prove facts about its
>> own statements, provided that it is effectively generated. Questions
>> about the provability of statements within the system are represented
>> as questions about the arithmetical properties of numbers themselves,
>> which would be decidable by the system if it were complete.
>>
>> Thus, although the Gödel sentence refers indirectly to sentences of
>> the system F, when read as an arithmetical statement the Gödel
>> sentence directly refers only to natural numbers. It asserts that no
>> natural number has a particular property, where that property is given
>> by a primitive recursive relation (Smith 2007, p. 141). As such, the
>> Gödel sentence can be written in the language of arithmetic with a
>> simple syntactic form. In particular, it can be expressed as a formula
>> in the language of arithmetic consisting of a number of leading
>> universal quantifiers followed by a quantifier-free body (these
>> formulas are at level Π 1 0 {\displaystyle \Pi _{1}^{0}} \Pi _{1}^{0}
>> of the arithmetical hierarchy). Via the MRDP theorem, the Gödel
>> sentence can be re-written as a statement that a particular polynomial
>> in many variables with integer coefficients never takes the value zero
>> when integers are substituted for its variables (Franzén 2005, p. 71).
>>
>>
>> So the Godel sentence, being "Just" a mathematical sentence, if
>> definitionally a Truth Bearer, and either needs to be True, or it is
>> False.
>>
>>
>
> It is NOT a truth bearer.

But it IS, that or Mathematics isn't Analytical, since the actual Godel
Sentence is merely about the existence of some finite set of natural
numbers, which, by definition, either exists or it doesn't.

>
>>
>>>
>>> We know that logic sentences are true or false on the basis of the
>>> definition of logic sentence.
>>
>> Right, so G needs to be either True of False, and if it is False, then
>> we can prove it, making it True.
>>
>
> That is exact the same as saying that the liar paradox is true or false,
> it is actually neither.

Nope, just shows you don't know what the actual Godel G statement is.

>
>>>
>>>
>>>> Unless you are defining that "untrue or untrue" is True, you have a
>>>> problem (and if yoy do, you still have a proble).
>>>
>>>
>>
>
>