Re: Current Issues in the Philosophy of Practice of Mathematics & Informatics

[Patrik Eklund <peklund@cs.umu.se>]

Philosophy of mathematics is still philosophy and has nothing to do with
mathematics, since philosophy does not adhere to any mathematical
principles.

Philosophy of logic is the same, since philosophy does not adhere to any
logical principles.

However, the logic of mathematics and the mathematics of logic is more
interesting in particular as a major part of informatics can learn from
logic.

It is somehow interesting that the philosophy of set theory is never on
any agenda, even if set theory, logic and mathematics is very much
intertwined. Early 20th century work and development in G??ttingen,
Vienna and Warsaw, and other places, of course, is often said to be very
well known, but surprisingly few actually still read work from that era.

Why, for instance, is it so clear that G??del's Incompleteness Theorem is
a "theorem" and not a "paradox"? After all, it is nothing but a bit more
subtle version of the Liar paradox. I paradox means Fix it!, whereas a
theorem means Don't touch!.

In logic, why do we make a giant leap from Aristotle (who was a
philosopher, not a logician) to Boole/Peano/Frege, ignoring whatever
happened logically in between? In math we don't do that.

Category theory can play a role in all this, in particular in more
strict definitions of the notion of logic. Type theory is good example,
where type constructors are still allowed to dangle around any formalism
adopted, and then something magic comes in from the outside and provides
a "solution". HoTT and its predecessors are doing that all the time.

The phrase "Philosophy of Practice of Mathematics & Informatics", I
guess, is as good as any variation  of it. WE could also debate about
the "Mathematical Practice of the Informatics of Philosophy", or the
"Informatics if Mathematics of Philosophy & Practice", or even the
"Mathematical Practice of Informatics without any interference
whatsoever of Philosophy".

Best,

Patrik

www.glioc.com



On 2015-07-25 16:57, Graham White wrote:
> And (continuing "why on the categories mailing list?") it seems
> to some people (such as me) that what category theory actually is, is
> a formal description of the practice of mathematics, rather than a
> foundation for mathematics. It may do the latter as well (though I
> don't
> really believe so), but an account of the practice of mathematics
> would be far more philosophically interesting than a foundation. It
> would, for example, allow a dialogue between the philosophy of
> mathematics and the rest of philosophy, which has, for 30 or 40 years
> now, been much less foundational than it used to be. And it may even
> make category theory an important tool in philosophy generally.
>
> Graham
>
> On 24/07/15 05:12, Ralph Matthes wrote:
>> [why on the categories mailing list? some of the courses are strongly
>> based on category theory, and it seems that quite some subscribers to
>> this list are interested in connections between mathematics and
>> philosophy]
>>
>>
>> Dear colleagues,
>>
>> The thematic trimester CIPPMI "Current Issues in the Philosophy of
>> Practice of Mathematics & Informatics" will be held from 4th April to
>> 1st July 2016 at the Centre International de Math??matiques et
>> d'Informatique de Toulouse (CIMI).
>>
>> This thematic trimester is organised by an interdisciplinary team of
>> researchers in Mathematics, Philosophy, and Computer Science from the
>> Institut de Math??matiques de Toulouse (IMT) & the Institut de
>> Recherche en Informatique de Toulouse (IRIT).
>>
>> It will feature course sessions, workshops, and a thematic school on
>> themes at the interface of Philosophy, Mathematics and Computer
>> Science.
>>
>> You will find all relevant information on the website of the thematic
>> trimester that will be regularly updated:
>> http://www.cimi.univ-toulouse.fr/cippmi/en
>>
>> A mailing list allows you to receive the different announcements from
>> CIPPMI: https://sympa.math.ups-tlse.fr/wws/info/cippmi
>>
>> You can register at
>> http://www.cimi.univ-toulouse.fr/cippmi/fr/inscriptionregistration
>>
>> A funding for accommodation is available in priority for junior
>> researchers and for some senior researchers without funding from their
>> laboratory. For further information, please consult the page:
>> http://www.cimi.univ-toulouse.fr/cippmi/fr/boursesgrants
>>
>> With apologies for cross-posting, best regards, the CIPPMI scientific
>> organisation committee.
>>
>> ---
>>
>> Ralph Matthes
>>
>> IRIT (CNRS & Univ. Toulouse)
>> http://www.irit.fr/~Ralph.Matthes/
>>

-- 
Prof. Patrik Eklund
Ume?? University
Department of Computing Science
SE-90187 Ume??
Sweden

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