On 08 Sep 2012, at 06:19, meekerdb wrote:
On 9/7/2012 8:43 PM, Jason Resch wrote:
Platonism (or mathematical realism) is the majority viewpoint of
modern mathematicians.
In a survey of mathematicians I know it is an even division. Of
course they are all methodological Platonists, but not necessarily
philosophical ones.
Computationalism (or functionalism) is the majority viewpoint of
cognitive scientists and philosophers of mind. Thus the scientific
consensus is that infinite (mathematical) truth
Except mathematical truth is just a marker, T, whose value is
preserved by the rules of logic. Whether a proposition that has T
corresponds with any fact is another question.
Be careful to distinguish a true sentence (like T) with the notion of
truth or of arithmetical true sentence, which is not even definable in
arithmetic, and can be meta-defined in some set theory or second order
arithmetic, at the meta-level. God can be arithmetical truth, but God
can't be just T.
is the self-existent cause and reason for our existence.
That is very far from a scientific consensus. I'd say majority the
opinion among scientists who are philosophically inclined is that
mathematics and logic are languages in which we create models that
represent what we think about reality. This explains why there can
be contradictory mathematical models and even mutually inconsistent
sets of axioms and rules of inference.
Yes, but this makes sense only for people agreeing on elementary
arithmetical truth. If not, the notion of axioms and rules of
inference don't make sense.
Nobody serious disagree on elementary arithmetic. I have never seen
someone doubting the meaning of (N, +, *), except philosophers. Bad
philosophers, I would say, when they are in desperate needs to
demolish some argument, or to look original or something. We need
assess arithmetic to make sense of doubting arithmetic, and so,
doubting arithmetic does not make sense, in fact.
Bruno
Few people today have realized that this is inevitable conclusion
of these two commonly held beliefs.
Not only that a few people have rejected it.
Brent
--
You received this message because you are subscribed to the Google
Groups "Everything List" group.
To post to this group, send email to [email protected].
To unsubscribe from this group, send email to [email protected]
.
For more options, visit this group at http://groups.google.com/group/everything-list?hl=en
.
http://iridia.ulb.ac.be/~marchal/
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To post to this group, send email to [email protected].
To unsubscribe from this group, send email to
[email protected].
For more options, visit this group at
http://groups.google.com/group/everything-list?hl=en.
