A Dialogue on Infinity

Save The London Mathematical Society October 20, 2008

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New Directions in the Philosophy of Mathematics October 8, 2008

To celebrate the founding of MIMS, the mathematics department of the recently unified Manchester University, it was proposed that various workshops named ‘New Directions in…’ be run. They kindly agreed to allow Alexandre Borovik and me to organise one of these workshops on the Philosophy of Mathematics.

So, on Saturday 4 October, we began with Mary Leng, a philosopher at Liverpool, talking about whether the creation of mathematical theories, e.g., Hamilton’s quaternions, gives us any more reason to think mathematical entities exist than does the discovery of new consequences within existing theories. She concluded that it does not — both concern the drawing of consequences from suppositions, e.g., “Were there to be a 3 or 4-dimensional number system sharing specified properties with the complex numbers, then…”.

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