David Hyder

Dieter Henrich ‘s “Notion of a Deduction” (1989), opened up approaches to both Deductions in terms of legal as opposed to syllogistic reasoning. Since the CpR is shot through with juridical metaphors and analogies, many points of connection suggest themselves. In this paper, I extend and modify Henrich’s approach, in order to extract a particular logic of evidence. I argue that the three syntheses of the A-Deduction correspond to parts of a deductive procedure, and that their names have been chosen to indicate this connection to the reader. Nonetheless, the principal aim of the paper is not to develop and defend these historiographical claims, but to explicate the structure of the logic of evidence in question and link it to Kant’s intended refutation of Hume. Since the procedures Kant describes are part of the law of evidence of many nations and are equally well at work in contemporary information-theory, a precise reconstruction can map directly onto contemporary problems in philosophy, physics, and informatics, without any loss of historical accuracy.

The theory of space-time developed in Kant’s Critique of Pure Reason and his Metaphysical Foundations of Natural Science is connected to Leonhard Euler’s proof of invariance under Galilean transformations in the “On Motion in General” of the latter’s 1736 Analytical Mechanics. It is argued that Kant, by using the Principle of Relativity that is the output of Euler’s proof as an input to his own proof of the kinematic parallelogram law, makes essential use of absolute simultaneity. This is why, in the Transcendental Aesthetic, he observes that “our theory of time explains as much a priori knowledge as the general theory of motion displays.” In conclusion, it is shown that the same proof-method, under a different definition of simultaneity, leads to the parallelogram law of the “Kinematic Part” of Einstein’s 1905 “On the Electrodynamics of Moving Bodies”.

Parmenides’ Poem on Nature contains a proof that the world could not have come into being in time, because no explanation could be given for why it would do so at a given time. This same proof reappears in the Leibniz-Clarke Correspondence, where it is directed against Newtonian absolute time. Newtonians, Leibniz explains, believe that time is homogeneous and absolute, but this makes it inexplicable how God could have chosen to create the world on a given day. Similarly, in his correspondence with Schrödinger in the 1930s, Einstein suggests that certain quantum mechanical occurrences, such as the spontaneous decay of a radioactive atom, are absurd, because they cannot be assigned a definite location in time. In Schrödinger’s version of Einstein’s argument, we must say that the cat dies twice: first, inside the box; yet, second, when we open the box. But both accounts cannot be true. Since each of the authors discussed was aware of the approach of his predecessors, they share a structure. In this article, I develop a unified account of all three.

This book offers a new interpretation of Hermann von Helmholtz's work on the epistemology of geometry. A detailed analysis of the philosophical arguments of Helmholtz's Erhaltung der Kraft shows that he took physical theories to be constrained by a regulative ideal. They must render nature "completely comprehensible", which implies that all physical magnitudes must be relations among empirically given phenomena. This conviction eventually forced Helmholtz to explain how geometry itself could be so construed. Hyder shows how Helmholtz answered this question by drawing on the theory of magnitudes developed in his research on the colour-space. He argues against the dominant interpretation of Helmholtz's work by suggesting that for the latter, it is less the inductive character of geometry that makes it empirical, and rather the regulative requirement that the system of natural science be empirically closed.

The dissertation analyzes the theory of "logical space" developed by Ludwig Wittgenstein in his Tractatus Logico-Philosophicus, I show how this idea represents a development of arguments first put forward by Hermann von Helmholtz, the physicist and physiologist. Helmholtz--instead of honouring Kant's distinction between on the one hand time and space, and, on the other, empirical qualia --stretched the Kantian spatial manifold to cover the other qualia as well: the qualia are also organized in manifolds; and this new, extended manifold is the "space" of all possible human experience. He explained this a priori mesh as being a consequence of the physiological constitution of our bodies, and the physical constitution of the world in which they are situated. The subject is enclosed in an inner world whose structure is the network of possible sensation; outside of her is a world of unknown complexity; and separating the two is what Heinrich Hertz called the "no-man's-land" of sense-physiology, a border zone regulating all traffic between the two realms, common to both, yet proper to neither. ;Wittgenstein, in his Tractatus, adapted the picture-theories of Helmholtz and Hertz to his analysis of logic. He too was confronted with the problem of defining a field of possible experience, of possible facts: his analysis of Russell's and Frege's logical theories had led him to the conclusion that the fundamental properties of logic could not be accounted for without assuming such an a priori space. Thus he assimilated Russell's types to the dimensions of a manifold, the elements of which were his Sachverhalte, or elementary facts. The truth-functions of our logic are defined on top of this space: it is the basis on which all symbolic systems, including those of the natural sciences, are erected

ArgumentHermann von Helmholtz’s distinction between “pure intuitive” and “physical” geometry must be counted as the most influential of his many contributions to the philosophy of science. In a series of papers from the 1860s and 70s, Helmholtz argued against Kant’s claim that our knowledge of Euclidean geometry was an a priori condition for empirical knowledge. He claimed that geometrical propositions could be meaningful only if they were taken to concern the behaviors of physical bodies used in measurement, from which it followed that it was posterior to our acquaintance with this behavior. This paper argues that Helmholtz’s understanding of geometry was fundamentally shaped by his work in sense-physiology, above all on the continuum of colors. For in the course of that research, Helmholtz was forced to realize that the color-space had no inherent metrical structure. The latter was a product of axiomatic definitions of color-addition and the empirical results of such additions. Helmholtz’s development of these views is explained with detailed reference to the competing work of the mathematician Hermann Grassmann and that of the young James Clerk Maxwell. It is this separation between 1) essential properties of a continuum, 2) supplementary axioms concerning distance-measurement, and 3) the behaviors of the physical apparatus used to realize the axioms, which is definitive of Helmholtz’s arguments concerning geometry.

: This paper discusses the origins of two key notions in Foucault's work up to and including The Archaeology of Knowledge. The first of these notions is the notion of "archaeology" itself, a form of historical investigation of knowledge that is distinguished from the mere history of ideas in part by its unearthing what Foucault calls "historical a prioris". Both notions, I argue, are derived from Husserlian phenomenology. But both are modified by Foucault in the light of Jean Cavaillès's critique of Husserl's theory of science. On Husserl's view, we demand that propositions holding of scientific objects be intersubjective and invariant, but this demand conflicts with our immediate experience, which is essentially bound to a subject's perspective. Thus the mathematical and physical sciences must utilise formal languages to fix these truths independently of the thoughts of a particular subject. This necessary procedure leads to the sedimentation of these formal systems: we forget their source in the concrete experiences of individuals, and use them as purely technical means. The technique of reactivating the intentional acts in which sedimented formal systems originated is thus, in Fink's terminology, an archaeological method. Foucault and Cavaillès retain the general outlines of this archaeology of the sciences, but they reject its appeal to conscious acts of meaning, to what Cavaillès calls "the philosophy of consciousness". I conclude by discussing the implicit difficulties in the "linguistic transcendentalism" proposed as an alternative by these French critics of Husserl

I analyze the two main theses of Helmholtz's "The Applicability of the Axioms to the Physical World," in which he argued that the axioms of Euclidean geometry are not, as his neo-Kantian opponents had argued, binding on any experience of the external world. This required two argumentative steps: 1) a new account of the structure of our representations which was consistent both with the experience of our (for him) Euclidean world and with experience of a non-Euclidean one, and 2) a demonstration of why geometric propositions are essentially connected to material and temporal aspects of experience. The effect of Helmholtz's discussion is to throw into relief an intermediate category of metrological objects--objects which are required for the properly theoretical activity of doing physical science (in this sense, a priori requirements for doing science), all while being recognizably contingent aspects of experience

This book is a collection of essays on Husserl's _Crisis of European Sciences_ by leading philosophers of science and scholars of Husserl. Published and ignored under the Nazi dictatorship, Husserl's last work has never received the attention its author's prominence demands. In the _Crisis_, Husserl considers the gap that has grown between the "life-world" of everyday human experience and the world of mathematical science. He argues that the two have become disconnected because we misunderstand our own scientific past—we confuse mathematical idealities with concrete reality and thereby undermine the validity of our immediate experience. The philosopher's foundational work in the theory of intentionality is relevant to contemporary discussions of _qualia_, naive science, and the fact-value distinction. The scholars included in this volume consider Husserl's diagnosis of this "crisis" and his proposed solution. Topics addressed include Husserl's late philosophy, the relation between scientific and everyday objects and "worlds," the history of Greek and Galilean science, the philosophy of history, and Husserl's influence on Foucault.