On 14 Jun 2015, at 21:48, meekerdb wrote:
On 6/14/2015 9:23 AM, Bruno Marchal wrote:
Arithmetic is full of life, ... and taxes and death.
But it needs interpretation to be full of death and taxes.
Otherwise it is just abstract relations.
Yes. But the one doing the interpretation are the universal (Löbian)
entity.
They build model satisfying their beliefs.
Now, with computationalism, there indeed a truncation made for our own
self-description (if not, the doctor can't do its job), and that
entails that many notions cannot be entirely translated into text,
except if based on some intuition that the machine can develop through
examples. Numbers are already of that kind.
That's exactly why it is so useful; the same relations hold under
many different interpretations.
In algebra, yes. That is why they got the "universal problem" (not in
the Turing sense), and the adjointness which occurs everywhere in math.
But in arithmetic and computer science, we have also sort of token-
like ultra-concrete objects, like we thought of the (standard) natural
numbers, and machines.
I recently asked on a mathematicians forum for a definition of
mathematics. The common ones were the study of relations and the
study of patterns.
No problem with this. Except that this is very general, and even
without comp, might still encompass human and alien psychology,
biology, conditional theologies, etc.
The term mathematics has no mathematical definition, and what it
encompass will depend on the philosophical, metaphysical or
theological hypotheses.
Bruno
Brent
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