On Logic, Language and Numbers: Sanford Shieh Discusses Gottlob Frege’s Enduring Mathematical Legacy

Sanford Shieh

Friedrich Ludwig Gottlob Frege (1848-1925) was a German philosopher, logician, and mathematician responsible for the development of modern logic. He made important contributions to the foundations of mathematics and the philosophy of language.

Sanford Shieh teaches in the philosophy department of Wesleyan University. He specializes in the philosophies of logic and mathematics, and in the history of analytic philosophy. He has written on intuitionism and anti-realism about mathematics,  co-edited, with Juliet Floyd, Future Pasts (2001), one of the first collections of essays on the history of analytic philosophy, and has just completed the first of a two-volume work on the concepts of necessity and possibility in early analytic philosophy, Necessity Lost.

Q: What initially sparked your interest in exploring the work of Gottlob Frege, a little-known German mathematician and logician?

A: The first thing I read by Frege was The Foundations of Arithmetic (Die Grundlagen der Arithmetik). At that time, I had studied a lot of math, but no philosophy whatsoever. Frege began the book with a question that had never occurred to me: what is the number 1? For me, it was a striking question. What was more striking was the fact that, not only had I never thought of that question, but I also had no idea what I would say in answer.

Now perhaps it would seem to some that this is the kind of question that would only grip mathematicians and other people interested in math. For most of us, who are interested in concrete things, or who have to worry about the realities of making a living, of what use are the airy-fairy abstractions of math?

But in fact, math is perhaps the most concrete thing there is in the world. Recently, for example, several news headlines are about a number, 20,000, that the Dow had reached. The relation of this number to the stock offerings of 30 companies is the subject of excitement, and maybe also fear. Numbers also permeate the realities of making a living; what do we worry about if not a bunch of numbers: the number related to your wages, the number related to the sum of your mortgage or your rent, your car or property taxes, your food bill, etc. And, the numbers that with which engineers and scientists work are, ultimately, responsible for, among other things, our ability to travel from New York to Paris in three and a half hours, the existence of machines that can defeat the best human chess players, and, alas, the traffic congestion of mid-town Manhattan. Of course, numbers are not the only objects of math that concern us. We are often preoccupied with the shapes of things: we worry about the shape and size of a table relative to the shape and size of our dining room, baseball teams worry about the shape of Fenway Park, and some of us, sometimes, spend quite a bit of money and time to alter the shapes of parts of our bodies.

But what exactly are these things, numbers, and shapes, that we bump into all the time, and obsess over sometimes? That’s Frege’s question, and his attempts to answer it got me interested in philosophy in general, and Frege’s philosophy in particular.

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