[FOM] ] Incentives for the development of philosophical views in
Adriano Palma
Palma at ukzn.ac.za
Fri Dec 23 06:29:09 EST 2011
** Low Priority **
** Reply Requested by 12/23/2011 (Friday) **
One thing that you want to consider is the epistemological incentive:
for a number of reasons (non progress/non revisionary status)
mathematical knowledge is never refuted (calling F undecidable is
knowing something interesting about F, if not its truth value, by the
standards of proof theory)
hence you may well see the formalist approach as an outgrowth of an
empiricist strand (dead after Goedel for self evident reasons), in which
finitary procedures are "effective" in the sense of being controllable
up to epsilon degrees of precision
you may as well see intuitionism as a quasi"kantian" view in which the
uncertain status fo the mathematical ontology is fixed by its nature
(being mental products of the creative mathematical mind) and to be sure
you may see Frege as reducing mathematical knowledge to logical truths,
though again failed by its own failures...
all the best for the new year
>>> "Denyer, Callum" <cad214 at exeter.ac.uk> 12/21/2011 6:36 PM >>>
Hello,
I am interested to understand some viewpoints regarding the incentives
for different philosophical views held about the nature of mathematics,
for example logicism ( 鬀攀᷍攀᷍ ) (Russell and Whitehead/Frege),
intuitionism (Brouwer) and formalism (Hilbert). Specifically, in what
ways were these different views responses to the foundational questions
that had arisen in 19th Century mathematics (i.e. discovery of
consistent non-euclidean geometries and development of set theory)?
Any arguments/suggested readings would greatly help in my research.
Callum
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