> On 10 Dec 2018, at 20:26, Brent Meeker <[email protected]> wrote:
>
>
>
> On 12/9/2018 11:38 PM, Philip Thrift wrote:
>>
>>
>> On Sunday, December 9, 2018 at 8:43:59 PM UTC-6, Jason wrote:
>>
>>
>> On Sun, Dec 9, 2018 at 2:02 PM Philip Thrift <[email protected]
>> <javascript:>> wrote:
>>
>>
>> On Sunday, December 9, 2018 at 9:36:39 AM UTC-6, Jason wrote:
>>
>>
>> On Sun, Dec 9, 2018 at 2:53 AM Philip Thrift <[email protected] <>> wrote:
>>
>>
>> On Saturday, December 8, 2018 at 2:27:45 PM UTC-6, Jason wrote:
>>
>> I think truth is primitive.
>>
>> Jason
>>
>>
>> As a matter of linguistics (and philosophy), truth and matter are linked:
>>
>> "As a matter of fact, ..."
>> "The truth of the matter is ..."
>> "It matters that ..."
>> ...
>> [ https://www.etymonline.com/word/matter
>> <https://www.etymonline.com/word/matter> ]
>>
>> I agree they are linked. Though matter may be a few steps removed from
>> truth. Perhaps one way to interpret the link more directly is thusly:
>>
>> There is an equation whose every solution (where the equation happens to be
>> true, e.g. is satisfied when it has certain values assigned to its
>> variables) maps its variables to states of the time evolution of the wave
>> function of our universe. You might say that we (literally not
>> figuratively) live within such an equation. That its truth reifies what we
>> call matter.
>>
>> But I think truth plays an even more fundamental roll than this. e.g.
>> because the following statement is true "two has a successor" then there
>> exists a successor to 2 distinct from any previous number. Similarly, the
>> truth of "9 is not prime" implies the existence of a factor of 9 besides 1
>> and 9.
>>
>> Jason
>>
>>
>>
>>
>> Schopenhauer 's view: "A judgment has material truth if its concepts are
>> based on intuitive perceptions that are generated from sensations. If a
>> judgment has its reason (ground) in another judgment, its truth is called
>> logical or formal. If a judgment, of, for example, pure mathematics or pure
>> science, is based on the forms (space, time, causality) of intuitive,
>> empirical knowledge, then the judgment has transcendental truth."
>> [ https://en.wikipedia.org/wiki/Truth <https://en.wikipedia.org/wiki/Truth> ]
>>
>>
>> I guess I am referring to transcend truth here. Truth concerning the
>> integers is sufficient to yield the universe, matter, and all that we see
>> around us.
>>
>> Jason
>>
>>
>>
>> In my view there is basically just material (from matter) truth and
>> linguistic (from language) truth.
>>
>> [ https://codicalist.wordpress.com/2018/06/18/to-tell-the-truth/
>> <https://codicalist.wordpress.com/2018/06/18/to-tell-the-truth/> ]
>>
>> Relations and functions are linguistic: relational type theory (RTT) ,
>> functional type theory (FTT) languages.
>>
>> Numbers are also linguistic beings, the (fictional) semantic objects of
>> Peano arithmetic (PA).
>>
>> Numbers can be "materialized" via nominalization (cf. Hartry Field, refs. in
>> [ https://en.wikipedia.org/wiki/Hartry_Field
>> <https://en.wikipedia.org/wiki/Hartry_Field> ]).
>>
>>
>> Assuming the primacy of matter assumes more and explains less, than assuming
>> the primacy of arithmetical truth.
>>
>> Jason
>>
>>
>>
>> In today's era of mathematics, Joel David Hamkins (@JDHamkins
>> <https://twitter.com/JDHamkins>) has shown there is a "multiverse" of truths:
>>
>> The set-theoretic multiverse
>> [ https://arxiv.org/abs/1108.4223 <https://arxiv.org/abs/1108.4223> ]
>>
>> The multiverse view in set theory, introduced and argued for in this
>> article, is the view that there are many distinct concepts of set, each
>> instantiated in a corresponding set-theoretic universe. The universe view,
>> in contrast, asserts that there is an absolute background set concept, with
>> a corresponding absolute set-theoretic universe in which every set-theoretic
>> question has a definite answer. The multiverse position, I argue, explains
>> our experience with the enormous diversity of set-theoretic possibilities, a
>> phenomenon that challenges the universe view. In particular, I argue that
>> the continuum hypothesis is settled on the multiverse view by our extensive
>> knowledge about how it behaves in the multiverse, and as a result it can no
>> longer be settled in the manner formerly hoped for.
>>
>>
>> What this means is that for mathematics (a language category), truth depends
>> on the language.
>
> I think Hamkins could say the same thing in French. His example of the
> continuum hypothesis just says that by adding as axioms different undecidable
> propositions we get different sets of theorems. He doesn't use the word
> "truth" and I think with good reason. Theorems in mathematics aren't "true"
> in any normal sense of the word. What is true is that the axioms imply the
> theorem...given the rules of inference.
By incompleteness truth is bigger than what *any* consistent can prove. Of
course you can say that the meaning of
[Exyz(x^3 + y^3 + z^3 = 33) v ~ (Exyz(x^3 + y^3 + z^3 = 33))
Is true because it is an substitution instance of the tautology A v ~A. But you
can also reflect on this, and believe it is true, because either such numbers
do exist, or they don’t. But "Exyz(x^3 + y^3 + z^3 = 33) “ is an open problem.
Such open problem would not make sense if you define truth by proof.
Recently I have proven that TOT (the set of Gödel numbers of the codes of the
total computable function is not recursively enumerable. That proofs would have
no meaning if truth = proof. Intuitionism is recovered in Mechanism as the
particular first person solipsistic view ([]p & p, S4Grz1).
In mathematical logic, we study since long the difference between proof and
truth (satisfied by a reality).
Bruno
PS I will use the word “reality" instead of “model", as most physicisst
continue to use “model” for theories.
>
> Brent
>
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