[FOM] The observational standpoint for numbers

[Eray Ozkural]

On 1/25/06, Giovanni Lagnese <lagnese at ngi.it> wrote:
> The observational standpoint for space was definitively proved untenable
> thanks principally to Albert Einstein.

It is arguable whether Einstein proved it untenable. Non-euclidian
geometry is a slightly simpler axiomatic system, and is a proper generalization
of Euclidian geometry. Einstein derived his theory of gravity not out
of thin air but again scientific observations similar to the sensory
observations,
the idealization of which resulted in the Euclidian theory. Thus, in a sense
he changed the observational standpoint but did not demolish it.

On the other hand, it is worth noting that studies of the cosmic microwave
background radiation have shown the space to be Euclidian at the
cosmic scale:
http://solarsystem.nasa.gov/scitech/display.cfm?ST_ID=253

I am however intrigued by your implications that mathematical knowledge
comes from neither sensory input nor self-reflection. Where does it
come from according to your opinion?

Regards,

--
Eray Ozkural (exa), PhD candidate.  Comp. Sci. Dept., Bilkent University, Ankara
http://www.cs.bilkent.edu.tr/~erayo  Malfunct: http://www.malfunct.com
ai-philosophy group: http://groups.yahoo.com/group/ai-philosophy
Pardus: www.uludag.org.tr   KDE Project: http://www.kde.org