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Thursday, April 08, 2021

Klarman fellow bridges divide between math and philosophy | Arts & Humanities - Cornell Chronicle

James Walsh will spend three years tapping into Cornell’s robust resources in the field of logic, combining the precision and methods of math with the interests of philosophy by Kate Blackwood, writer for the College of Arts and Sciences.

In mathematics, axioms are statements that don’t need to be proved; they are truths one can assume, such as the axioms “for any number x, x + 0 = x” or “Between any two points is a line.”

Working in the field of logic, James Walsh, a Klarman Postdoctoral Fellow in philosophy, studies the axiomatic method, a central methodology in mathematics whereby claims are proven from axioms.

Based in the Sage School of Philosophy in the College of Arts and Sciences, Walsh is tapping into Cornell’s robust logic resources in philosophy, mathematics and linguistics to accomplish three years of study under the Klarman Postdoctoral Fellowship, working closely with Alexander (Arc) Kocurek, assistant professor of philosophy.

Walsh is trying to get to the heart of a discrepancy between the natural theories, which arise in mathematical practice, and unnatural ones that do not...

Walsh stands out for his ability to bridge the divide between mathematics and philosophy, Kocurek said. “Often, researchers in logic are either really just mathematicians or really just philosophers. But James is really both: He publishes serious mathematical work while also being able to isolate the philosophically important aspects of that work.”...

Logic appeals to Walsh because the field combines the precision and methods of math with the interests of philosophy. “You prove things that say something important about the scope of what we can know and what we can prove,” he said. “But you do so with mathematical techniques and a lot of precision.”

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Source: Cornell Chronicle