kp@uts.amdahl.com (Ken Presting) (01/17/90)
In article <1839@aipna.ed.ac.uk> cam@aipna.ed.ac.uk (Chris Malcolm) writes: >In article <GILHAM.90Jan9100839@cassius.csl.sri.com> gilham@csl.sri.com (Fred Gilham) writes: > >>The consensus seems to be that some ``pattern'' is doing the understanding. This is a very fragile consensus, if it exists at all. >>The alternatives seem to be that either a pattern has some independent >>existence of its own (concrete reality) or a mind is necessary to >>perceive it. On the one hand, I say we have dualism; on the other >>hand, I say we have the ``hermeneutical hall of mirrors'', where we >>project our own thought processes onto something in the outside world. > >Ok. So how do you explain mathematics, or even humble numbers, without >recourse to dualism or the hermeneutic hall of mirrors? The traditional solution to this problem goes all the way back to Aristotle. Patterns are explained as properties, which exist only as attributes of objects. Thus squareness exists only in square objects. If no objects in the world are perfectly square, then perfect squareness does not exist, at least not in this world. The existence of other worlds is up for grabs. Numbers get a similar treatment. Mathematics as a whole is treated as a language for describing patterns. Followups to sci.philosophy.tech, please.