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 ]
/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.
Brent
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