On the Work of Howard Stein: Philosophy, Math, and Physics

On the Work of Howard Stein: Philosophy, Math, and Physics 

9:00 AM to 9:30 AM - Introductory Remarks by Lydia Goehr, Jonathan Levi, and David Malament

9:30 AM to 12:30 PM - Session One - Jenann Ismael, Chair

André W. Carus

“Howard Stein’s Dialectical Conception of Metaphysics”

It has plausibly been argued—and Stein himself agreed—that his philosophy can be placed in the logical empiricist tradition of his teacher Carnap. But then why the frequent references to metaphysics? What does he mean by it? One clue is provided by his equally frequent references to “dialectic” (in the Platonic sense). It turns out there are (at least) two fundamentally different possible paths from Carnap—the “ontological” path followed by Quine and the “dialectical” one followed by Stein. This is illustrated by one of Stein’s own favorite contrasts, between Descartes and Galileo. In keeping with the dialectical spirit of Stein’s writings, no firm conclusion is reached. 

Erich Reck

“Howard Stein, the Second Birth of Mathematics, and Understanding in Mathematics”

Besides his influential writings in the philosophy of physics, Howard Stein contributed several important papers to the philosophy of mathematics as well, although they are less widely known.  In them he formulated and substantiated, among others, the striking suggestion that the nineteenth century witnesses a “second birth” of mathematics, based on the shift from a more computational to a more conceptual way of practicing it, and with “modern mathematics” as the result.  In this talk I will reconsider, further defend, and then extend this suggestion in a number of ways, including the following two: by tracing the trajectory of this conceptual transformation of mathematics forward into the twentieth and twenty-first centuries; and by connecting its substantive core with current philosophical discussions about the notion of understanding in mathematics.

12:30 PM to 2:00 PM - Catered Lunch

2:00 PM to 5:00 PM - Session Two - David Albert, Chair

Robert DiSalle

“Newton’s Revolution in Metaphysics”

Howard Stein’s 1967 paper, “Newtonian Space-Time,” had profound implications regarding not only Newton’s views, but also broader questions about space-time structure, its role in the conceptual structure of physics, and its connection with experience. Previously, philosophers had generally regarded Newton as a brilliant mathematician who was, philosophically, naive and even retrograde; he postulated “absolute” theoretical objects just as physics was emerging from such metaphysical prejudices, and as contemporaries such as Huygens and Leibniz supposedly foreshadowed the “relativistic” ideas of the 20th century. From Stein’s work, philosophers learned that Newton’s arguments for “absolute” space, time, and motion were far more subtle, and more firmly grounded in physics, than his critics had understood. Subsequent debates surrounding the philosophy of space and time had, at least, to take Newton’s arguments seriously.

            But Stein’s account of Newton went further than this: he showed that the traditional picture of Newton was not only too dismissive, but, in an important respect, backwards. It was Newton who was remarkably forward-looking, in that he saw the nature of space and time as inextricably bound to the laws of physics: space and time must be understood, not through traditional philosophical conceptions of them, but through the structural connections between the two that are implicit in the principles of dynamics. Newton’s freedom from contemporary metaphysical boundaries, and his focus on mathematical representations of phenomena, led him to insights into the nature of space, time, and gravity—and of physical interaction in general—that remain central to theoretical physics.

JB Manchak

“Howard Stein on Gödel Spacetime”

In his 1970 paper “On the Paradoxical Time-Structures of Gödel,” Howard Stein helps us better understand the strange geometry of Gödel spacetime which allows for “time travel” of a certain kind. He also considers (variations of) a central question: “Consider either an arbitrary given cosmological model, or a model having the structure of one of the sorts assumed to hold in the real world. Then…is it ((a) ever, (b) always) possible to introduce into such a model a continuous deformation of the structure, leading through intermediate states, all compatible with Einstein’s theory, to a state in which Gödel-type relationships occur?” In this talk, I will first give a short primer on the geometry of Gödel spacetime and Stein's own contributions to our understanding of it. I will then explore several ways of making precise the central question mentioned above. Finally, I will catalogue what is presently known concerning these precise questions and what is still left unsettled some fifty-odd years on.

5:00 PM to 6:15PM - Reception