On 21 Aug 2017, at 14:43, Philip Benjamin wrote:
[Philip Benjamin]
There is a difference between mathematical proposition and
mathematical operation.
OK. "2+2 = 2 * 2" is a mathematical proposition. "+" and "*" denotes
operations.
For example, quantum theory is a mathematical proposition,
Hmm... OK. It is a theory. It is a list of assumptions, or their
conjunction, about a reality, itself assumed (at the metalevel in
physics, and at the base level in some physicalist metaphysics).
but Quantum interpretation such as "Collapse", "Many Worlds" etc.
The collapse is one more assumption.
"many-worlds" is when we don't do that collapse assumption.
In fact "many-world", with the logician's weak sense of "world" is a
mathematical consequence of QM without collapse, and assuming a
collapse makes the SWE false, or not applicable to the observer in QM
+collapse theory (a good reason to be suspicious about the collapse).
is philosophy/religion deserving no mathematical operation.
? (this does not make sense to me).
Genetics can be subjected to mathematical operation,
? (I guess we are not using "operation" in the same sense. What do
you mean by "operation"? You mean perhaps "analysis". Then OK here,
but I do not see why philosophy/religion would not be subjected to
mathematical analysis. That is possible in some theory, but not in
another theory---and indeed, I illustrate that once we assume the
mechanist hypothesis in the cognitive sciences, then we do have the
mean to use mathematics in metaphysics/religion.
but Common Descent is a philosophical speculation beyond mathematics.
I prefer to not separate philosophy from science. That separation is
too much often used to allow absence of rigor in philosophy, and that
is a very bad habit. Same for theology, metaphysics. I limit myself to
hypothesis making a mathematical treatment operational, leading to
testable conclusions.
I don't really believe in something called "science", but I do believe
in scientific attitude, and this is independent of the domain of
investigation.
So is the evidential Natural Selection. It can be subjected to
mathematical analysis, but the un-evidential trans-speciation is
philosophy beyond mathematics.
It will depend on your fundamental theory/assumption, I would say.
Bruno Marchal
Philip Benjamin
From: [email protected] <[email protected]
> on behalf of Bruno Marchal <[email protected]>
Sent: Sunday, August 20, 2017 4:50 PM
To: [email protected]
Subject: Re: Is math real?
On 20 Aug 2017, at 17:31, Philip Benjamin wrote:
[Philip Benjamin]
This is the wrong question, "not even wrong"!! The right question
is "are the THINGS/SUBJECTS which mathematics deal with real?
OK, we agree I think, but fundamentally, it is not even that, at
least when we apply mathematics (in the natural science, or in
metaphysics; theology, ...).
It is "do you agree with this or that mathematical proposition".
(followed by "agreement" on definitions).
Now some mathematical proposition does not ask much, like most
theorem in first order arithmetic (when the proof are not too long).
Some propositions ask us more, like when using set theory, or set
theory + the choice axiom.
Some proposition asks for so much that we will never stop searching
a proof, like Riemann hypothesis, which we know refutable in very
elementary arithmetic in case it would be false.
But the question "is math real" is often answered in the negative by
the conventionalist (like Goethe, Perhaps Bergson, and the early
positivist in math). In my opinion, this is not defensible, from a
mathematical logical viewpoint, even before Gödel's theorem, and
still much more non-defensible after.
See my other post to David for some precision. The mathematical real
is very vast, and it is normal some part are more doubtful than
other parts. Some part are real, but only phenomenologically so,
like with physics when we assume computationalism, as I explained
often here.
Bruno
Best regards
Philip Benjamin
From: [email protected] <[email protected]
> on behalf of David Nyman <[email protected]>
Sent: Sunday, August 20, 2017 3:24 PM
To: everything-list
Subject: Re: Is math real?
On 20 Aug 2017 2:46 p.m., "Bruno Marchal" <[email protected]> wrote:
On 19 Aug 2017, at 01:21, David Nyman wrote:
On 18 August 2017 at 18:13, Bruno Marchal <[email protected]> wrote:
On 18 Aug 2017, at 15:39, David Nyman wrote:
He points at a mug and says that 'representations' (meaning
numbers) aren't to be confused with things themselves.
He confuses a number and a possible representation of a number.
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