In 1870, Hermann von Helmholtz criticized the Kantian conception of geometrical axioms as a priori synthetic judgments grounded in spatial intuition. However, during his dispute with Albrecht Krause (Kant und Helmholtz über den Ursprung und die Bedeutung der Raumanschauung und der geometrischen Axiome. Lahr, Schauenburg, 1878), Helmholtz maintained that space can be transcendental without the axioms being so. In this paper, I will analyze Helmholtz’s claim in connection with his theory of measurement. Helmholtz uses a Kantian argument that can be (...) summarized as follows: mathematical structures that can be defined independently of the objects we experience are necessary for judgments about magnitudes to be generally valid. I suggest that space is conceived by Helmholtz as one such structure. I will analyze his argument in its most detailed version, which is found in Helmholtz (Zählen und Messen, erkenntnistheoretisch betrachtet 1887. In: Schriften zur Erkenntnistheorie. Springer, Berlin, 1921, 70–97). In support of my view, I will consider alternative formulations of the same argument by Ernst Cassirer and Otto Hölder. (shrink)

It is the purpose of this article to explicate the logical implications of a television analogy for perception, first suggested by John R. Smythies (1956). It aims to show not only that one cannot escape the postulation of qualia that have an evolutionary purpose not accounted for within a strong functionalist theory, but also that it undermines other anti-representationalist arguments as well as some representationalist ones.

Abstract This article examines the little-explored remarks on verification in Wittgenstein's notebooks during the period between 1930 and 1932. In these remarks, Wittgenstein connects a verificationist theory of meaning with the notion of logical multiplicity, understood as a space of possibilities: a proposition is verified by a fact if and only if the proposition and the fact have the same logical multiplicity. But while in his early philosophy logical multiplicities were analysed as an outcome of the formal properties of simple (...) objects and simple signs, Wittgenstein in the early 1930s connects the notion of logical multiplicity with the notion of ways of seeing. I will argue that the relevant ways of seeing are closely similar to seeing-as or aspect seeing. According to Wittgenstein's view in the early 1930s, logical multiplicities are part of our perceptual experience of propositions and facts. In this sense, the verification relation depends on how we experience propositions and facts as being surrounded by a logical space of possibilities. Strikingly, Wittgenstein's way of thinking about the verification relation offers solutions to a set of seemingly intractable problems connected with the versions of verificationism developed by members of the Vienna Circle. (shrink)

A formal theory of quantity T Q is presented which is realist, Platonist, and syntactically second-order (while logically elementary), in contrast with the existing formal theories of quantity developed within the theory of measurement, which are empiricist, nominalist, and syntactically first-order (while logically non-elementary). T Q is shown to be formally and empirically adequate as a theory of quantity, and is argued to be scientifically superior to the existing first-order theories of quantity in that it does not depend upon empirically (...) unsupported assumptions concerning existence of physical objects (e.g. that any two actual objects have an actual sum). The theory T Q supports and illustrates a form of naturalistic Platonism, for which claims concerning the existence and properties of universals form part of natural science, and the distinction between accidental generalizations and laws of nature has a basis in the second-order structure of the world. (shrink)

In early major works, Cassirer and Schlick differently recast traditional doctrines of the concept and of the relation of concept to intuitive content along the lines of recent epistemological discussions within the exact sciences. In this, they attempted to refashion epistemology by incorporating as its basic principle the notion of functional coordination, the theoretical sciences' own methodological tool for dispensing with the imprecise and unreliable guide of intuitive evidence. Examining their respective reconstructions of the theory of knowledge provides an axis (...) of comparison along which to locate Cassirer's Neo-Kantianism and Schlick's pre-positivist empiricism, and an immediate background of contrast to the subsequent rise of logical empiricism. For in the absence of intuition all our knowledge is without objects and therefore remains entirely empty. (Kant A62/B87) And how awkward is the human mind in diving the nature of things when forsaken by the analogy of what we see and touch directly? (Boltzmann 1895). (shrink)

Hermann von Helmholtz has been widely acknowledged as one of the forerunners of contemporary theories of measurement. However, his conception of measurement differs from later, representational conceptions in two main respects. Firstly, Helmholtz advocated an empiricist philosophy of arithmetic as grounded in some psychological facts concerning quantification. Secondly, his theory implies that mathematical structures are common to both subjective experiences and objective ones. My suggestion is that both of these differences depend on a classical approach to measurement, according to which (...) the arithmetic laws of addition define what is measurable as a particular domain for their application, and, at the same time, the extensibility of these laws to all known physical processes works as a heuristic principle for empirical research. Such an approach is worth reconsidering, not only because it lends plausibility to some of the controversial aspects of Helmholtz’s theory, but also because it offers a philosophical perspective on quantification problems that originated in the nineteenth-century.This paper draws insights on Helmholtz’s philosophical views from his engagement with the measurability of sensations via Fechner’s psychophysical law. This seems to be in contrast with the fact that the reception of Helmholtz’s theory culminated with the formulation of the theory of extensive measurement. I will contend that Helmholtz reached a no less important standpoint in the nineteenth-century debate on whether sensations are different (i.e., intensive) kinds of magnitudes and on how, if at all, they can be measured. (shrink)

According to Wittgenstein, internal relations are such that, once their terms are given, it is unthinkable that they do not hold. In his early philosophy, the concept of internal relation plays a central role in his views on meaning. The present paper addresses the question of how Wittgenstein's views about internal relations develop during his years of transition (1930-32). In particular, it investigates the connections between the concepts of internal relation, logical multiplicity, and aspect seeing in two thematic fields: (1) (...) Wittgenstein's discussion of the relation between an expectation and what fulfils it, and (2) his discussion of the relation between a sign and an action guided by it. (shrink)

© The Authors [2017]. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: [email protected] book Space, Number, and Geometry from Helmholtz to Cassirer is a reworked version of Francesca Biagioli’s PhD thesis. It aims ‘[to offer] a reconstruction of the debate on non-Euclidean geometry in neo-Kantianism between the second half of the nineteenth century and the first decades of the twentieth century’. More precisely, Biagioli concentrates on how the Marburg school of neo-Kantianism dealt with what may be (...) called ‘Helmholtz’s challenge’ to the classical Kantian thesis that the geometry of space is necessarily Euclidean. To be precise, besides the Marburg current, SNG also deals with some other neo-Kantians, among them the realist neo-Kantian Alois Riehl and the South-West German neo-Kantian Bruno Bauch.According to SNG, the Marburg revision of the Kantian theory of space opened the door to a new way... (shrink)

The Greeks had a ready answer for what happens when the mind suddenly finds the answer to a question for which it had been searching: insight was regarded as a gift of the Muses, its origins were divine. It served to highlight the Greeks'' belief that there are some things which are not meant to be scientifically explained. The essence of insight is that it comes from some supernatural source: unpredicted and unfettered. In other words, the origins of insight are (...) unconscious, and hence, unexplainable. Wittgenstein felt that, as long as there continues to be a noun expression like to have a moment of insight which functions in the same way as the expression to have a hunger pang, thereby inducing us to treat moment of insight as the name of an experience, then people will keep stumbling over the same puzzling difficulties and find themselves staring at something which no explanation seems capable of clearing up. To the founders of AI, this argument reeked of obscurantism. The moment of insight, they felt, is indeed a mystery, but it is one that begs to be explained in causal terms. Indeed, the problem of insight served as one of the leading problems in the evolution of AI. Hence anyone interested in the foundations of AI is compelled to examine the manner in which the early pioneers of the field sought to explain the eureka experience. In this paper I will look at some of the key conceptual developments which paved the way for Newell and Simon''s theory of GPS: the fundamental changes in the notion of the unconscious — the emergence of the cognitive unconscious — which took place in the nineteenth- and early twentieth-century. In so doing, I hope to clarify what Wittgenstein may have had in mind in his strictures against mechanist attempts to analyse the nature of insight. (shrink)

The formal methods of the representational theory of measurement (RTM) are applied to the extensive scales of physical science, with some modifications of interpretation and of formalism. The interpretative modification is in the direction of theoretical realism rather than the narrow empiricism which is characteristic of RTM. The formal issues concern the formal representational conditions which extensive scales should be assumed to satisfy; I argue in the physical case for conditions related to weak rather than strong extensive measurement, in the (...) sense of Holman 1969 and Colonius 1978. The problem of justifying representational conditions is addressed in more detail than is customary in the RTM literature; this continues the study of the foundations of RTM begun in an earlier paper. The most important formal consequence of the present interpretation of physical extensive scales is that the basic existence and uniqueness properties of scales (representation theorem) may be derived without appeal to an Archimedean axiom; this parallels a conclusion drawn by Narens for representations of qualitative probability. It is concluded that there is no physical basis for postulation of an Archimedean axiom. (shrink)

Ecological and sensorimotor theories of perception build on the notion of action-dependent invariants as the basic structures underlying perceptual capacities. In this paper we contrast the assumptions these theories make on the nature of perceptual information modulated by action. By focusing on the question, how movement specifies perceptual information, we show that ecological and sensorimotor theories endorse substantially different views about the role of action in perception. In particular we argue that ecological invariants are characterized with reference to transformations produced (...) in the sensory array by movement: such invariants are transformation-specific but do not imply motor-specificity. In contrast, sensorimotor theories assume that perceptual invariants are intrinsically tied to specific movements. We show that this difference leads to different empirical predictions and we submit that the distinction between motor equivalence and motor-specificity needs further clarification in order to provide a more constrained account of action/perception relations. (shrink)

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. (shrink)