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Logic&Meta: Daniel Hoek
March 21, 2016 @ 4:15 pm - 6:15 pm
Logic and Metaphysics Workshop Spring 2016
Mondays, 4.15-6.15. Room 6421, Graduate Center
The workshop is organized by Graham Priest
Monday 21 March, 4.15-6.15
Daniel Hoek, NYU
Mathematics as a Metaphor
Room 6421, CUNY Graduate Center. [This is on the 6th floor, but it’s tucked away in a cul-de-sac, so be prepared for a bit of a wander til you find it.]
Abstract: Scientists and the folk constantly use mathematics in describing the world. How can it be that reference to mathematical entities facilitates the description of concrete reality? The puzzle is especially vexing to the nominalist, who denies that mathematical objects even exist. But even mad-dog Platonists ought to ask themselves from time to time how it can be that investigations of remote and causally inert abstracta can serve a practical purpose.
In an attempt to address the question, Stephen Yablo proposed that our use of mathematics to describe the concrete world around us is just like our use of metaphors to do the same. While that’s an intriguing suggestion, it’s not all that illuminating unless we have an account of how, precisely, the relevant class of metaphors work. In this talk, I try to supply such an account. I’ll outline, in formal terms, a transformation on propositions that, at the same time, explains how relevant information is extracted from the metaphors we wrap them in, and how purely concrete information is extracted from the partly mathematical statements we use to present it. I will also prove a conservativity result, stating (roughly) that derivations involving reference to mathematical objects retain their classical validity after they’ve been transformed in this way into a sequence of propositions about the concrete world.
Full schedule with announced titles & abstracts here.