Dr Shay Allen Logan

Picture of Dr Shay Allen Logan

Postdoctoral Teaching Scholar

Biography

I gew up in Western Montana. So I didn't have to parallel park until college, which was at Gonzaga University. My wife, who I met there, taught me how. Eventually we both went to graduate school at the University of Minnesota. Since then I've had jobs here at NCSU, at Smith College, and at the University of Connecticut. I still spend my summers in Minnesota, where the Minnesota Center for Philosophy of Science kindly hosts me. 

Teaching and Research Interests

I'm a philosopher of mathematical practice. This means I explain why mathematics is done the way it's done. I do this in two ways. First, I describe the logical structure of mathematics. If that sounds cool, you can learn more about this in any of my LOG classes! Second, I describe the origin and structure of norms in mathematics. This involves me in work in cognitive linguistics and philosophy of language.

 

Projects

As I said, I'm a philosopher of mathematical practice. I explain why mathematics is done the way it's done. I do this in two ways.

First, I examine the logical structure of mathematics. Of course, this means I have to say something about what 'logical structure' is. There are options on the table here. For a variety of reasons, I use relevance logics. But, in contrast to the tameness of classical logic, relevance logics are relatively wild. So much of my research involves simply getting these logics to behave.

Second, I examine the role of conceptual metaphors in mathematical practice. Right now I'm examining how conceptual metaphors ground normative claims in algebraic geometry. A bit more detail: algebraic geometers (and mathematicians more generally) frequently say things like 'the right way to do this is...' or `what we should do is...'. More famously, Alexander Grothendieck was angry when his student Pierre Dilgne proved the last Weil Conjecture -- earning him a Fields Medal -- but did it `the wrong way'. What I do is apply tools from contemporary work in philosophy of language and cognitive linguistics to explain the structure and origin of these norms. I'm in particular interested in explaining why we should take them seriously. (Although Grothendieck was, as it turns out, just being a curmudgeon.)

Education

  • PhD in Philosophy from University of Minnesota, 2015
  • MS in Mathematics from University of Minnesota, 2013
  • MA in Philosophy from University of Minnesota, 2013
  • BS in Mathematics from Gonzaga University, 2008
  • BA in Philosophy from Gonzaga University, 2008