The Marburg neo-Kantians argue that Hermann von Helmholtz's empiricist account of the a priori does not account for certain knowledge, since it is based on a psychological phenomenon, trust in the regularities of nature. They argue that Helmholtz's account raises the 'problem of validity' (Gueltigkeitsproblem): how to establish a warranted claim that observed regularities are based on actual relations. I reconstruct Heinrich Hertz's and Ludwig Wittgenstein's Bild theoretic answer to the problem of validity: that scientists and philosophers can depict the (...) necessary a priori constraints on states of affairs in a given system, and can establish whether these relations are actual relations in nature. The analysis of necessity within a system is a lasting contribution of the Bild theory. However, Hertz and Wittgenstein argue that the logical and mathematical sentences of a Bild are rules, tools for constructing relations, and the rules themselves are meaningless outside the theory. Carnap revises the argument for validity by attempting to give semantic rules for translation between frameworks. Russell and Quine object that pragmatics better accounts for the role of a priori reasoning in translating between frameworks. The conclusion of the tale, then, is a partial vindication of Helmholtz's original account. (shrink)

Moti Mizrahi has argued that Thomas Kuhn does not have a good argument for the incommensurability of successive scientific paradigms. With Rouse, Andersen, and others, I defend a view on which Kuhn primarily was trying to explain scientific practice in Structure. Kuhn, like Hilary Putnam, incorporated sociological and psychological methods into his history of science. On Kuhn’s account, the education and initiation of scientists into a research tradition is a key element in scientific training and in his explanation of incommensurability (...) between research paradigms. The first part of this paper will explain and defend my reading of Kuhn. The second part will probe the extent to which Kuhn’s account can be supported, and the extent to which it rests on shaky premises. That investigation will center on Moti Mizrahi’s project, which aims to transform the Kuhnian account of science and of its history. While I do defend a modified kind of incommensurability, I agree that the strongest version of Kuhn’s account is steadfastly local and focused on the practice of science. (shrink)

Hermann von Helmholtz allows for not only physiological facts and psychological inferences, but also perspectival reasoning, to influence perceptual experience and knowledge gained from perception. But Helmholtz also defends a version of the view according to which there can be a kind of “perspectival truth” revealed in scientific research and investigation. Helmholtz argues that the relationships between subjective and objective, real and actual, actual and illusory, must be analyzed scientifically, within experience. There is no standpoint outside experience from which we (...) can reason, no extra-sensory knowledge of the constitution of the “ideal subject” or of the properties of “real objects.” In the tradition of psychophysics inherited by Helmholtz, we can arrive at a kind of perspectival analysis of perceptual experience, which embeds an account of that experience within the context of the history and situation of the perceiving subject. That analysis is relative to the perceiving subject, but the perspectival explanations Helmholtz constructs are not thereby relativist: in fact, for Helmholtz, the more squarely the perceiving subject is placed in a scientific, perspectival context, the more facts we are able to learn about her experience and the objects with which she interacts. (shrink)

In my dissertation, I present Hermann Cohen's foundation for the history and philosophy of science. My investigation begins with Cohen's formulation of a neo-Kantian epistemology. I analyze Cohen's early work, especially his contributions to 19th century debates about the theory of knowledge. I conclude by examining Cohen's mature theory of science in two works, The Principle of the Infinitesimal Method and its History of 1883, and Cohen's extensive 1914 Introduction to Friedrich Lange's History of Materialism. In the former, Cohen gives (...) an historical and philosophical analysis of the foundations of the infinitesimal method in mathematics. In the latter, Cohen presents a detailed account of Heinrich Hertz's Principles of Mechanics of 1894. Hertz considers a series of possible foundations for mechanics, in the interest of finding a secure conceptual basis for mechanical theories. Cohen argues that Hertz's analysis can be completed, and his goal achieved, by means of a philosophical examination of the role of mathematical principles and fundamental concepts in scientific theories. (shrink)

In the growing Prussian university system of the early nineteenth century, "Wissenschaft" (science) was seen as an endeavor common to university faculties, characterized by a rigorous methodology. On this view, history and jurisprudence are sciences, as much as is physics. Nineteenth century trends challenged this view: the increasing influence of materialist and positivist philosophies, profound changes in the relationships between university faculties, and the defense of Kant's classification of the sciences by neo-Kantians. Wilhelm Dilthey's defense of the independence of the (...) methodology of the human sciences (Geisteswissenschaften) from those of the natural sciences (Naturwissenschaften) is as much a return to the ideal of Wissenschaft as a cooperative endeavor as it is a defense of the autonomy of interpretive or hermeneutic methods. The debate between Dilthey and the neo-Kantian Wilhelm Windelband at the close of the century illuminates the development of this dialogue over the nineteenth century. (shrink)

Ott (2009) identifies two kinds of philosophical theories about laws: top-down, and bottom-up. An influential top-down reading, exemplified by Ernst Cassirer, emphasized the ‘mere form of law’. Recent bottom-up accounts emphasize the mind-independent natures of objects as the basis of laws of nature. Stang and Pollok in turn focus on the transcendental idealist elements of Kant’s theory of matter, which leads to the question: is the essence of Kantian matter that it obeys the form of law? I argue that Kant (...) has an independent theory of matter in the Metaphysical Foundations of Natural Science, one that gives what Kant himself calls a ‘real definition’ of matter as a theory-independent (if not mind-independent) entity. I argue that this matter theory underpins physical arguments about inertia and impenetrability, which resemble Einstein’s arguments about the unification of fields in general relativity. (shrink)

Kant's account of space as an infinite given magnitude in the Critique of Pure Reason is paradoxical, since infinite magnitudes go beyond the limits of possible experience. Michael Friedman's and Charles Parsons's accounts make sense of geometrical construction, but I argue that they do not resolve the paradox. I argue that metaphysical space is based on the ability of the subject to generate distinctly oriented spatial magnitudes of invariant scalar quantity through translation or rotation. The set of determinately oriented, constructed (...) geometrical spaces is a proper subset of metaphysical space, thus, metaphysical space is infinite. Kant's paradoxical doctrine of metaphysical space is necessary to reconcile his empiricism with his transcendental idealism. (shrink)

Detlefsen (1986) reads Hilbert's program as a sophisticated defense of instrumentalism, but Feferman (1998) has it that Hilbert's program leaves significant ontological questions unanswered. One such question is of the reference of individual number terms. Hilbert's use of admittedly "meaningless" signs for numbers and formulae appears to impair his ability to establish the reference of mathematical terms and the content of mathematical propositions (Weyl (1949); Kitcher (1976)). The paper traces the history and context of Hilbert's reasoning about signs, which illuminates (...) Hilbert's account of mathematical objectivity, axiomatics, idealization, and consistency. (shrink)

I examine the role of inference from experiment in theory building. What are the options open to the scientific community when faced with an experimental result that appears to be in conflict with accepted theory? I distinguish, in Laudan's (1977), Nickels's (1981), and Franklin's (1993) sense, between the context of pursuit and the context of justification of a scientific theory. Making this distinction allows for a productive middle position between epistemic realism and constructivism. The decision to pursue a new or (...) a revised theory in response to the new evidence may not be fully rationally determined. Nonetheless, it is possible to distinguish the question of whether there is reason to pursue a theory from the question of whether that theory, once it has been pursued over time, solves a problem of interest to science. I argue that, in this context, there is a solid way to distinguish between the contexts of pursuit and of justification, on the basis of a theory's evidential support and problem-solving ability. (shrink)

Scientists working within a paradigm must play by the rules of the game of that paradigm in solving problems, and that is why incommensurability arises when the rules of the game change. If we deny the thesis of the priority of paradigms, then there is no good argument for the incommensurability of theories and thus for taxonomic incommensurability, because there is no invariant way to determine the set of results provable, puzzles solvable, and propositions cogently formulable under a given paradigm.

In the nineteenth century, the separation of naturalist or psychological accounts of validity from normative validity came into question. In his 1877 Logical Studies (Logische Studien), Friedrich Albert Lange argues that the basis for necessary inference is demonstration, which takes place by spatially delimiting the extension of concepts using imagined or physical diagrams. These diagrams are signs or indications of concepts' extension, but do not represent their content. Only the inference as a whole captures the objective content of the proof. (...) Thus, Lange argues, the necessity of an inference is independent of psychological accounts of how we grasp the content of a proposition. (shrink)

German supporters of the Kantian philosophy in the late 19th century took one of two forks in the road: the fork leading to Baden, and the Southwest School of neo-Kantian philosophy, and the fork leading to Marburg, and the Marburg School, founded by Hermann Cohen. Between 1876, when Cohen came to Marburg, and 1918, the year of Cohen's death, Cohen, with his Marburg School, had a profound influence on German academia.

Ernst Cassirer’s focus on the expressive function of language should be read, not in the context of Carnap’s debate with Heidegger, but in the context of the earlier work of Chajim (Heymann) Steinthal. Steinthal distinguishes the expressive form of language, when language is studied as a natural phenomenon, from language as a logical, inferential system. Steinthal argues that language always can be expressed in terms of logical inference. Thus, he would disagree with Heidegger, just as Carnap does. But, Steinthal insists, (...) that is not to say that language, as a natural phenomenon, is exhausted by logic or by the place of terms or relations in inferential structures. Steinthal’s “form” of linguistic “expression” is an early version of Cassirer’s “expressive function” for language. The expressive function, then, should not be seen to place a barrier between Carnap and Cassirer. Rather, Steinthal and Cassirer deal with a question that, as far as I know, Carnap does not address directly: how should philosophers analyze human language as a natural phenomenon, as a part of our expression as animals? And how does that expression determine the semantic categories, kind terms, and other structures that develop within, and characterize, human language itself? (shrink)

Francesca Biagioli’s Space, Number, and Geometry from Helmholtz to Cassirer is a substantial and pathbreaking contribution to the energetic and growing field of researchers delving into the physics, physiology, psychology, and mathematics of the nineteenth and twentieth centuries. The book provides a bracing and painstakingly researched re-appreciation of the work of Hermann von Helmholtz and Ernst Cassirer, and of their place in the tradition, and is worth study for that alone. The contributions of the book go far beyond that, however. (...) It is a clear, accurate, and deep account of fascinating and philosophically momentous implications of the move to relativity theory. (shrink)

Hermann von Helmholtz (1821-1894) established results both controversial and enduring: analysis of mixed colors and of combination tones, arguments against nativism, and the analysis of sensation and perception using the techniques of natural science. The paper focuses on Helmholtz’s account of sensation, perception, and representation via “physiological psychology”. Helmholtz emphasized that external stimuli of sensations are causes, and sensations are their effects, and he had a practical and naturalist orientation toward the analysis of phenomenal experience. However, he argued as well (...) that sensation must be interpreted to yield representation, and that representation is geared toward objective representation (the central thesis of contemporary intentionalism). The interpretation of sensation is based on “facts” revealed in experiment, but extends to the analysis of the quantitative, causal relationships between stimuli and responses. A key question for Helmholtz’s theory is the extent to which mental operations are to be ascribed a role in interpreting sensation. (shrink)

Two questions should be considered when assessing the Kantian dimensions of Kuhn’s thought. First, was Kuhn himself a Kantian? Second, did Kuhn have an influence on later Kantians and neo-Kantians? Kuhn mentioned Kant as an inspiration, and his focus on explanatory frameworks and on the conditions of knowledge appear Kantian. But Kuhn’s emphasis on learning; on activities of symbolization; on paradigms as practical, not just theoretical; and on the social and community aspects of scientific research as constitutive of scientific reasoning, (...) are all outside the Kantian perspective. Kuhn’s admiration for Kant is tempered by his desire to understand the processes of learning, of initiation into a scientific community, of experimentation using instruments, and of persuasion, drawing on the work of familiar influences, including Piaget, Koyré, and Wittgenstein, and less familiar ones, including Langer, Demos, and Frank. Both Kuhn and Kant were interested in the question: what is the status of science, and what is the role of the scientist in its development and justification? But Kuhn presents science in a much more messy, historically contingent, and socially charged way than Kant does. The paper’s conclusion evaluates Kuhn’s reception among researchers including Richardson and Friedman, assessing the prospects for future work. (shrink)

George Boole emerged from the British tradition of the “New Analytic”, known for the view that the laws of logic are laws of thought. Logicians in the New Analytic tradition were influenced by the work of Immanuel Kant, and by the German logicians Wilhelm Traugott Krug and Wilhelm Esser, among others. In his 1854 work An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities, Boole argues that the laws of thought acquire (...) normative force when constrained to mathematical reasoning. Boole’s motivation is, first, to address issues in the foundations of mathematics, including the relationship between arithmetic and algebra, and the study and application of differential equations (Durand-Richard, van Evra, Panteki). Second, Boole intended to derive the laws of logic from the laws of the operation of the human mind, and to show that these laws were valid of algebra and of logic both, when applied to a restricted domain. Boole’s thorough and flexible work in these areas influenced the development of model theory (see Hodges, forthcoming), and has much in common with contemporary inferentialist approaches to logic (found in, e.g., Peregrin and Resnik). (shrink)

Ernst Mach’s defense of relativist theories of motion in Die Mechanik involves a well-known criticism of Newton’s theory appealing to absolute space, and of Newton’s “bucket” experiment. Sympathetic readers (Norton 1995) and critics (Stein 1967, 1977) agree that there’s a tension in Mach’s view: he allows for some constructed scientific concepts, but not others, and some kinds of reasoning about unobserved phenomena, but not others. Following Banks (2003), I argue that this tension can be interpreted as a constructive one, springing (...) from Mach’s approach to scientific reasoning. Mach’s “economy of science” allows for a principled distinction to be made, between natural and artificial hypothetical reasoning, and Mach defends a division of labor between the sciences in a 1903 paper for The Monist, “Space and Geometry from the Point of View of Physical Inquiry”. That division supports counterfactual reasoning in Mach’s system, something that’s long been denied is possible for him. (shrink)

A volume dealing seriously with the influence of the major schools of Neo-Kantian thought on contemporary philosophy has been needed sorely for some time. But this volume of essays aims higher: it 'is published in the hopes that it will secure Neo-Kantianism a significant place in contemporary philosophical discussions' (Introduction, 1). The aim of the book, then, is partly to provide a history of major Neo-Kantian thinkers and their influence, and partly to argue for their importance in contemporary (continental) philosophy.

In the early 1900s, Russell began to recognize that he, and many other mathematicians, had been using assertions like the Axiom of Choice implicitly, and without explicitly proving them. In working with the Axioms of Choice, Infinity, and Reducibility, and his and Whitehead’s Multiplicative Axiom, Russell came to take the position that some axioms are necessary to recovering certain results of mathematics, but may not be proven to be true absolutely. The essay traces historical roots of, and motivations for, Russell’s (...) method of analysis, which are intended to shed light on his view about the status of mathematical axioms. I describe the position Russell develops in consequence as “immanent logicism,” in contrast to what Irving (1989) describes as “epistemic logicism.” Immanent logicism allows Russell to avoid the logocentric predicament, and to propose a method for discovering structural relationships of dependence within mathematical theories. (shrink)