Hans Reichenbach's relativity of geometry

Hans Reichenbach's 1928 thesis of the relativity of geometry has been misunderstood as the statement that the geometrical structure of space can be described in different languages. In this interpretation the thesis becomes an instance of trivial semantical conventionalism, as Grünbaum calls it. To understand Reichenbach correctly, we have to interpret it in the light of the linguistic turn, the transition from thought oriented philosophy to language oriented philosophy, which mainly took place in the first decades of our century. Reichenbach — as Poincaré before him — is undermining the prejudice of thought oriented philosophy, that two propositions have different factual content, if they are associated with different ideas in our mind. Thus Reichenbach prepared the change to language oriented philosophy, which he also accepted later.     

Carnap and Achinstein on evidence

Two notions of evidence are focused on in this essay, Carnap's positive-relevance notion of evidence (1962, pp. 462 ff.), and Achinstein's notion of potential evidence (1978; and 1983, pp. 322–350). Achinstein creates several interesting examples in his attempt to find faults in Carnap's notion of evidence; his motive, ultimately, is to impel us towards potential evidence. The purpose of this essay is to show that positive relevance is significantly more promising than potential evidence with respect to capturing the scientific sense of the term evidence. This is accomplished by finding faults in the notion of potential evidence, and by defending positive relevance against Achinstein's examples.I am especially indebted to Peter Achinstein, Edwin Allaire and Bob Kane for many valuable suggestions. I would also like to thank my colleagues Donald Becker and Jean Kazez for their constructive criticisms and other useful suggestions. (The defense of the positive-relevance notion of evidence provided here fulfills an obligation made in an earlier essay (Kronz, 1988).)     

Intuitionist type theory and foundations

A version of intuitionistic type theory is presented here in which all logical symbols are defined in terms of equality. This language is used to construct the so-called free topos with natural number object. It is argued that the free topos may be regarded as the universe of mathematics from an intuitionist's point of view.     

Measurement and the interpretation of quantum mechanics and relativity theory

The axiomatic approaches of quantum mechanics and relativity theory are compared with approaches in which the theories are thought to describe readings of certain measurement operations. The usual axioms are shown to correspond with classes of ideal measurements. The necessity is discussed of generalizing the formalisms of both quantum mechanics and relativity theory so as to encompass more realistic nonideal measurements. It is argued that this generalization favours an empiricist interpretation of the mathematical formalisms over a realist one.     

Category theory and the foundations of mathematics: Philosophical excavations

The aim of this paper is to clarify the role of category theory in the foundations of mathematics. There is a good deal of confusion surrounding this issue. A standard philosophical strategy in the face of a situation of this kind is to draw various distinctions and in this way show that the confusion rests on divergent conceptions of what the foundations of mathematics ought to be. This is the strategy adopted in the present paper. It is divided into 5 sections. We first show that already in the set theoretical framework, there are different dimensions to the expression foundations of. We then explore these dimensions more thoroughly. After a very short discussion of the links between these dimensions, we move to some of the arguments presented for and against category theory in the foundational landscape. We end up on a more speculative note by examining the relationships between category theory and set theory.Various versions of this paper have been read by many people, many of whom have made crucial comments. Needless to say, I am entirely responsible for the claims made in this paper. I would particularly like to thank, in alphabetical order, Mario Bunge, Marta Bunge, Michael Hallett, Andrew Irvine, Saunders Mac Lane, Collin McLarty, Peneloppe Maddy and Mihaly Makkai. Part of the work was done while the author was a visiting fellow at REHSEIS in Paris and at the Center for Philosophy of Science in Pittsburgh. I would like to thank everyone for his or her help and support. I gratefully acknowledge the financial support received from the SSHRC of Canada while this work was done.     

Carnap, the Ramsey-Sentence and Realistic Empiricism

Based on archival material from the Carnap and FeiglArchives, this paper re-examines Carnap's approach tothe issue of scientific realism in the 1950s and theearly 1960s. It focuses on Carnap's re-invention ofthe Ramsey-sentence approach to scientific theoriesand argues that Carnap wanted to entertain a genuineneutral stance in the realism-instrumentalism debate.Following Grover Maxwell, it claims that Carnap'sposition may be best understood as a version of`structural realism'. However, thus understood,Carnap's position faces the challenge that Newmanraised against Russell's structuralism: the claim thatthe knowledge of the unobservable is limited to itspurely structural characteristics is eitheruninformative or unsustainable.     

Life experience and the value-free foundations of Blumer's collective behavior theory

Herbert Blumer stated throughout his long career that his ideas regarding collective behavior originated with his introduction to pragmatist philosophy under the auspices of G. H. Mead at the University of Chicago. Blumer's biography, however, presents a different picture. Firsthand experiences with mob behavior, collective outrage, and the fallout associated with Blumer's public utterances early in his career may have had significant impact on the eventual corpus of collective behavior.     

James and Carnap on philosophical systems and the role of temperaments

The relationship between American pragmatism and logical empiricism is complicated at best. The received view is that by around the late 1930s or early 1940s pragmatism had been replaced, supplanted, or eclipsed by the younger and more logic-oriented form of empiricism developed in interwar Vienna. Recently, however, this picture has been challenged, and this paper offers further reasons for thinking that the received view is inadequate. Through a critical examination of William James's Pragmatism and “The Sentiment of Rationality” and Rudolf Carnap's “Elimination of Metaphysics Through Logical Analysis of Language” and other works, the paper builds a case for the existence of a rather striking correspondence between the work of one of pragmatism's most vaunted figures and the thought of logical empiricism's most famous advocate. Not only were both philosophers interested in what might be called metaphilosophy or the psychology of philosophy, both held very similar deflationary views.     

Stimulus control topography coherence theory: foundations and extensions

Stimulus control topography refers to qualitative differences among members of a functional stimulus class. Stimulus control topography coherence refers to the degree of concordance between the stimulus properties specified as relevant by the individual arranging a reinforcement contingency (behavior analyst, experimenter, teacher, etc.) and the stimulus properties that come to control the behavior of the organism (experimental subject, student, etc.) that experiences those contingencies. This paper summarizes the rationale for analyses of discrimination learning outcomes in terms of stimulus control topography coherence and briefly reviews some of the foundational studies that led to this perspective. We also suggest directions for future research, including pursuit of conceptual and methodological challenges to a complete stimulus control topography coherence analysis of processes involved in discriminated and generalized operants.