David J. Stump

In april 1872, with the caisson at a depth of seventy-odd feet and still no bedrock, two men died. The strain for Roebling was nearly unbearable, as his wife later said. On May 18, a third man died, and that same day Roebling made the most difficult and courageous decision of the project. Staking everything — the success of the bridge, his reputation, his career - he ordered a halt. The New York tower, he had concluded, could stand where it was, at a depth of 78 feet 6 inches, not on bedrock, but on “hardpack” sand. From examinations of the strata he had determined to his own satisfaction that no movement had occured at the level since the time of deposit millions of years in the geologic past; so, he said, it was “good enough to found upon”

I trace the development of arguments for the consistency of non-Euclidean geometries and for the independence of the parallel postulate, showing how the arguments become more rigorous as a formal conception of geometry is introduced. I analyze the kinds of arguments offered by Jules Hoüel in 1860-1870 for the unprovability of the parallel postulate and for the existence of non-Euclidean geometries, especially his reaction to the publication of Beltrami’s seminal papers, showing that Beltrami was much more concerned with the existence of non-Euclidean objects than he was with the formal consistency of non-Euclidean geometries. The final step towards rigorous consistency proofs is taken in the 1880s by Henri Poincaré. It is the formal conception of geometry, stripping the geometric primitive terms of their usual meanings, that allows the introduction of a modern fully rigorous consistency proof.

Poincare’s arguments for his thesis of the conventionality of metric depend on a relationalist program for dynamics, not on any general philosophical interpretation of science. I will sketch Poincare’s development of the relationalist program and show that his arguments for the conventionality of metric do not depend on any global strategies such as a general empiricism or Duhemian underdetermination arguments. Poincare’s theory of space, while empirically false, is more philosophically sophisticated than his critics have claimed.

Poincaré's claim that Euclidean and non-Euclidean geometries are translatable has generally been thought to be based on his introduction of a model to prove the consistency of Lobachevskian geometry and to be equivalent to a claim that Euclidean and non-Euclidean geometries are logically isomorphic axiomatic systems. In contrast to the standard view, I argue that Poincaré's translation thesis has a mathematical, rather than a meta-mathematical basis. The mathematical basis of Poincaré's translation thesis is that the underlying manifolds of Euclidean and Lobachevskian geometries are homeomorphic. Assuming as Poincaré does that metric relations are not factual, it follows that we can rewrite a physical theory using Euclidean geometry as one using Lobachevskian geometry and express the same facts.

Members of the Vienna Circle played a pivotal role in defining the work that came to be known as the philosophy of science, yet the Vienna Circle itself is now known to have had much broader concerns and to have been more rooted in philosophical tradition than was once thought. Like current and past philosophers of science, members of the Vienna Circle took science as the object of philosophical reflection but they also endeavored to render philosophy in general compatible with contemporary science and to define and promote a scientific world view. This latter task seems to continue the work of so-called scientific philosophy, a label embraced by many philosophers in the late nineteenth and early twentieth century, such as Helmholtz, Mach, Avenarius, the neo-Kantians, Husserl, Carus, Peirce, and, of course, Russell during the period when he was applying modern logic to philosophical problems. Russell’s program influenced Carnap directly, though the idea of applying modem logic to philosophical problems became a defining feature of analytic philosophy and was applied to many areas of philosophy, not only to the philosophy of science. Scientific philosophy included the promotion of the cultural values of modernity, especially the values embodied in the scientific world conception. By exploring the various meanings ascribed to scientific philosophy in the late nineteenth and early twentieth centuries, I will investigate whether the promotion of scientific philosophy and of the values associated with a scientific world conception is merely part of a transitory social context within which Logical Positivism developed or if it is an enduring part of the philosophy of science. Moreover, the residue of values remaining in the philosophy of science can be brought to light by studying its history

In this book, David Stump traces alternative conceptions of the a priori in the philosophy of science and defends a unique position in the current debates over conceptual change and the constitutive elements in science. Stump emphasizes the unique epistemological status of the constitutive elements of scientific theories, constitutive elements being the necessary preconditions that must be assumed in order to conduct a particular scientific inquiry. These constitutive elements, such as logic, mathematics, and even some fundamental laws of nature, were once taken to be a priori knowledge but can change, thus leading to a dynamic or relative a priori. Stump critically examines developments in thinking about constitutive elements in science as a priori knowledge, from Kant’s fixed and absolute a priori to Quine’s holistic empiricism. By examining the relationship between conceptual change and the epistemological status of constitutive elements in science, Stump puts forward an argument that scientific revolutions can be explained and relativism can be avoided without resorting to universals or absolutes.

Arthur Pap was not quite a Logical Empiricist. He wrote his dissertation in philosophy of science under Ernest Nagel, and he published a textbook in the philosophy of science at the end of his tragically short career, but most of his work would be classified as analytic philosophy. More important, he took some stands that went against Logical Empiricist orthodoxy and was a persistent if friendly critic of the movement. Pap diverged most strongly from Logical Empiricism in his theory of a “functional a priori” in which fundamental principles of science are hardened into definitions and act as criteria for further inquiry. Pap was strongly influenced by the pragmatists C. I. Lewis and John Dewey in developing this alternative theory of a priori knowledge. Using Poincaré’s conventionalism as a springboard, Pap attempted to substantiate these views with examples from physics, and this was his largest foray into philosophy of science topics. Pap, as well as Lewis and Dewey, developed an alternative theory of the a priori in the 1950s that never quite took hold, despite the fact that their views are very intriguing and similar to Michael Friedman’s recent work on the constitutive a priori.