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]> 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.
