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Go figure, philosophy gets real

July 13, 2005

AT last, someone to put that upstart Plato in his place.

Jim Franklin has opened for business his new Sydney School of philosophy. He did this with a flourish and an impudent seeming claim.

"For the first time in 2400 years philosophers and mathematicians will take a new approach to mathematics," his press release said last week.

Franklin, an associate professor at the University of NSW, laughs when asked about this. "My marketing manager went a bit overboard," he says.

Still, he has set up a new school of the philosophy of mathematics - complete with manifesto, website, four colleagues and an ambition to win research grants, popularise its credo and take Plato down a notch.


For Plato, numbers were otherworldly things. But for Aristotle, or at least for his champions in the Sydney School, mathematics is here and now. It describes the way the real world is structured; its patterns (weather, for example), symmetries and ratios.

"Our approach is innovative in that it starts with applied mathematics rather than detouring via pure mathematics and wondering how pure mathematics can apply to something so removed from it as the physical world," Franklin says.

He'd like this philosophical realism to "percolate down" into school and university curriculums, where some of the formulas beloved of pure mathematicians could make way for more work in modelling and simulation.

Joining Franklin in the new school are UNSW colleague Anne Newstead, Adrian Heathcote (University of Sydney), Andrew Irvine and Lisa Dive (both of whom share connections with the University of British Columbia and the University of Sydney).

Franklin joked that Dive was not quite ready yet for full duties at the school since she was, "busy teaching her baby to count".

Dive wasn't so sure newborns could count. But she does believe that children learn their numbers by detecting real-world patterns: strings of words or play blocks.

Stringing together the words "realism" and "Sydney" suggests the influence of John Anderson, a dominant figure in Australian philosophy.

This is an influence Franklin happily acknowledges.

Indeed, he hopes the Sydney School can teach overseas scholars the underappreciated virtues of an Andersonian approach to thinking about mathematics.

He'd also like to collaborate with his school chums on a book to popularise philosophy that takes applied mathematics as its departure point.

Franklin does not expect miracles, however, and it seems philosophy of mathematics is calculated to alienate both philosophers and mathematicians.

"Philosophers hate complexity," Franklin says. "What they want is to see complexity explained away in terms of a few simple principles."

Unfortunately, mathematics is nothing less than the science of complexity.

As for mathematicians, they are "blind to philosophy," Franklin says.

He quotes his New Zealand colleague Alan Musgrave: "Fish are good at swimming but poor at hydrodynamics, meaning they can do it but there's no point in asking them why."

In this proposition, substitute mathematicians for fish.

web.maths.unsw.edu.au/~jim/structmath.html




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