[FOM] mathematics as formal

praatika@mappi.helsinki.fi praatika at mappi.helsinki.fi
Fri Mar 7 06:48:40 EST 2008

The emergence of non-euclidian geometry certainly was an important
inspiration for the idea that mathematics is formal: it did not make sense
any more to consider the parallel axioms as definitely true (or false). And
surely Hilbert's work on axiomatizing geometry was very important in this

But already earlier Frege, in his Grundlagen (1884), criticized formalists
of his time, so there must have been such ideas in the air before Hilbert.

Hilbert, on the other hand, was not a pure formalist: he thought that
finitary mathematics is contentful; his "formalism" was limited to
infinistic mathematics. 

Best, Panu   

Panu Raatikainen

Ph.D., Academy Research Fellow,
Docent in Theoretical Philosophy

Department of Philosophy
University of Helsinki

E-mail: panu.raatikainen at helsinki.fi


Quoting catarina dutilh <cdutilhnovaes at yahoo.com>:

> Many thanks for the several informative and insightful replies to my
> query. At this point, my impression is that the attribution of formality
> to mathematics is a phenomenon much more recent than I had thought at
> first, apparently it only started with Hilbert and the formalist program.

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