On 1/23/2023 10:51 AM, Richard Damon wrote:
> On 1/23/23 10:18 AM, olcott wrote:
>> On 1/20/2023 4:54 PM, Richard Damon wrote:
>>> On 1/20/23 5:16 PM, olcott wrote:
>>>> On 1/20/2023 4:09 PM, Richard Damon wrote:
>>>>> On 1/20/23 5:02 PM, olcott wrote:
>>>>>> On 1/20/2023 2:46 PM, Richard Damon wrote:
>>>>>>> On 1/20/23 2:31 PM, olcott wrote:
>>>>>>>> On 1/19/2023 8:34 PM, Richard Damon wrote:
>>>>>>>>> On 1/19/23 2:12 PM, olcott wrote:
>>>>>>>>>> On 1/17/2023 5:44 PM, Richard Damon wrote:
>>>>>>>>>>> On 1/17/23 11:39 AM, olcott wrote:
>>>>>>>>>>>> On 1/16/2023 7:51 PM, Richard Damon wrote:
>>>>>>>>>>>>> No, because I am showing that G is TRUE, not PROVABLE.
>>>>>>>>>>>>> Truth can use infinte sets oc connections, proofs can't.
>>>>>>>>>>>>> Only YOU have perposed that we think about infinite proofs.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Formal systems cannot ever use infinite connections from their
>>>>>>>>>>>> expressions of language to their truth maker axioms thus
>>>>>>>>>>>> eliminating
>>>>>>>>>>>> these from consideration as any measure of true "in the
>>>>>>>>>>>> system".
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Source? or is this just another of your made up "Facts"
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> You can't even remember that you said this?
>>>>>>>>>
>>>>>>>>> No, I said they can't have infinite PROOFS, not infinite
>>>>>>>>> connections to Truth.
>>>>>>>>>>
>>>>>>>>>>> WHERE in the definition of a "Formal System" does it say that
>>>>>>>>>>> the connecti0on must be finite.
>>>>>>>>>>
>>>>>>>>>> You said that formal system cannot have infinite proofs.
>>>>>>>>>> Did you change your mind?
>>>>>>>>>
>>>>>>>>> Right ***PROOF*** not ***TRUTH***
>>>>>>>>>
>>>>>>>>> Truth can be based on an infinite chain of connections, proofs
>>>>>>>>> can not.
>>>>>>>>
>>>>>>>> Truth *in a formal system* cannot be based on infinite
>>>>>>>> connections because formal systems are not allowed to have
>>>>>>>> infinite connections.
>>>>>>>
>>>>>>> Says Who ***FOR TRUTH***
>>>>>>>
>>>>>>> You reference does not provide that data, so I guess you are just
>>>>>>> making it up, and thus showing you to be a LIAR.
>>>>>>>
>>>>>>>>
>>>>>>>> Haskell Curry establishes that truth in a theory (AKA formal
>>>>>>>> system) is anchored in the elementary theorems (AKA axioms) of
>>>>>>>> this formal system.
>>>>>>>
>>>>>>> Right, ANCHORED TO, not limited to. Statments other than the
>>>>>>> elementary theorems are True, and they are true if they have a
>>>>>>> connection (not limited to finite) to these Truths.
>>>>>>>
>>>>>>> Where does he say True statements must have a FINITE connection
>>>>>>> to the elementary theorems.
>>>>>>>
>>>>>>>>
>>>>>>>> A theory (over (f) is defined as a conceptual class of these
>>>>>>>> elementary
>>>>>>>> statements. Let::t be such a theory. Then the elementary statements
>>>>>>>> which belong to ::t we shall call the elementary theorems of::t;
>>>>>>>> we also
>>>>>>>> say that these elementary statements are true for::t. Thus,
>>>>>>>> given ::t,
>>>>>>>> an elementary theorem is an elementary statement which is true.
>>>>>>>> A theory
>>>>>>>> is thus a way of picking out from the statements of (f a certain
>>>>>>>> subclass of true statements.
>>>>>>>> https://www.liarparadox.org/Haskell_Curry_45.pdf
>>>>>>>>
>>>>>>>> Perhaps you believe that you are enormously much brighter than
>>>>>>>> Haskell Curry ?
>>>>>>>>
>>>>>>>
>>>>>>> You don't understand what he is saying,
>>>>>>>
>>>>>>> He is saying these statements are True in F, as a given.
>>>>>>
>>>>>> Wrongo !!!
>>>>>>
>>>>>>     The terminology which has just been used implies that the
>>>>>>     elementary statements are not such that their truth and
>>>>>>     falsity are known to us without reference to::t.
>>>>>>
>>>>>>
>>>>>
>>>>> Right, they aren't just true in the Statement class, but are only
>>>>> considerdd true because we are in the Theory F.
>>>>>
>>>>
>>>> F is not the theory T is the theory.
>>>>
>>>>
>>>
>>>
>>> Red Herring.
>>>
>>> F is the Theory in Godels descussion.
>>>
>>
>> https://en.wikipedia.org/wiki/Metamathematics
>> LP := ~True(LP) is untrue yet that does not make it true.
>>
>> When we examine this at the meta level we escape the self-contradiction
>> and can say that it is true that LP is untrue.
>
>
> Excpet that untrue is not ~True() in classical logic, which makes
> statements either True or False, or makes them Not a Truth Bearer, which
> makes them not in the domain of the True predicate.
>
> You need to move to tri-value logic to do this, at which point you loose
> the relationship that ~True(x) -> False(x)
>

True / false and not a truth bearer.

> Note, most of mathematics is based on the two-value logic system.
>
>

Thus forcing it to classify "not a truth bearer" incorrectly.
If all you have is a hammer the unscrewing a screw becomes quite
destructive.

>>
>> https://plato.stanford.edu/entries/tarski-truth/#195DefOff
>>
>> It looks like model theory is required to determine the truth of
>> some mathematical expressions, this had it origins in Tarski's
>> definition of truth.
>>
>> ∃n ∈ ℕ (N > 3)       // does not seem to need model theory
>> ∃G ∈ F (G ↔ (F ⊬ G)) // does not seem to need model theory
>>
>
> ∃ is a symbol out of model theory, so hard to not need model theory.
>
> Quoting from your reference:
>
> Model theory by contrast works with three levels of symbol. There are
> the logical constants ( = , ¬ , & for example), the variables (as
> before), and between these a middle group of symbols which have no fixed
> meaning but get a meaning through being applied to a particular
> structure. The symbols of this middle group include the nonlogical
> constants of the language, such as relation symbols, function symbols
> and constant individual symbols. They also include the quantifier
> symbols  ∀ and ∃, since we need to refer to the structure to see what
> set they range over.

I just showed how to explicitly specify what they range over: ∃n ∈ ℕ

>> G is true in F iff it cannot be shown that G is true in F
>>
>
> Nope, you don't understand what G is. The Definition of G in F does NOT
> refer in any way determinable in F to the statement G.
>

∃n ∈ ℕ (n > 3) // Is this true or false?
How do you know?

Generically how does ascertain that that any logic expression is true or
false?

Most generically an analytical expression of formal or natural language
is only true if it has a semantic connection to its truth maker axioms.

The "truth maker axioms" of natural language are the definition of the
meaning of its words.

The truth maker axioms for the above expression is the definition of the
ordered set of natural numbers:

https://www.britannica.com/science/Peano-axioms

--
Copyright 2023 Olcott

"Talent hits a target no one else can hit;
Genius hits a target no one else can see."
Arthur Schopenhauer