Helmholtz’s Physiological Psychology

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

New Water in Old Buckets: Hypothetical and Counterfactual Reasoning in Mach’s Economy of Science

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

Laws of Thought and Laws of Logic after Kant

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)

Cassirer and Steinthal on Expression and the Science of Language

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

“Kuhn, Pedagogy, and Practice: A Local Reading of Structure”

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

Reconsidering Experiments

Experiments may not reveal their full import at the time that they are performed. The scientists who perform them usually are testing a specific hypothesis and quite often have specific expectations limiting the possible inferences that can be drawn from the experiment. Nonetheless, as Hacking has said, experiments have lives of their own. Those lives do not end with the initial report of the results and consequences of the experiment. Going back and rethinking the consequences of the experiment in a new context, theoretical or empirical, has great merit as a strategy for investigation and for scientific problem analysis. I apply this analysis to the interplay between Fizeau’s classic optical experiments and the building of special relativity. Einstein’s understanding of the problems facing classical electrodynamics and optics, in part, was informed by Fizeau’s 1851 experiments. However, between 1851 and 1905, Fizeau’s experiments were duplicated and reinterpreted by a succession of scientists, including Hertz, Lorentz, and Michelson. Einstein’s analysis of the consequences of the experiments is tied closely to this theoretical and experimental tradition. However, Einstein’s own inferences from the experiments differ greatly from the inferences drawn by others in that tradition

Russell’s method of analysis and the axioms of mathematics

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

The Paradox of Infinite Given Magnitude: Why Kantian Epistemology Needs Metaphysical Space

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

Experiment and theory building

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