What is the relationship between the world and logic, between intuition and language, between objects and their quantitative determinations? Rationalists, on the one hand, hold that the world is structured in a rational way. Representationalists, on the other hand, assume that language, logic, and mathematics are only the means to order and describe the intuitively given world. In World and Logic, Jens Lemanski takes up three surprising arguments from Arthur Schopenhauer’s hitherto undiscovered Berlin Lectures, which concern the philosophy of language, (...) logic, and mathematics. Based on these arguments, Lemanski develops a new position entitled ‘rational representationalism’: the world is always structured by human beings according to linguistic, logical, and mathematical principles, but the basic vocabulary of these structural descriptions already contains metaphors taken from the world around us. (shrink)

This paper attempts to show how the logical empiricists’ interpretation of the relation between geometry and reality emerges from a “collision” of mathematical traditions. Considering Riemann’s work as the initiator of a 19th century geometrical tradition, whose main protagonists were Helmholtz and Poincaré, the logical empiricists neglected the fact that Riemann’s revolutionary insight flourished instead in a non-geometrical tradition dominated by the works of Christoffel and Ricci-Curbastro roughly in the same years. I will argue that, in the attempt to interpret (...) general relativity as the last link of the chain Riemann–Helmholtz–Poincaré–Einstein, logical empiricists were led to argue that Einstein’s theory of gravitation mainly raised a problem of mathematical under-determination, i.e. the discovery that there are physical differences that cannot be expressed in the relevant mathematical structure of the theory. However, a historical reconstruction of the alternative Riemann–Christoffel–Ricci–Einstein line of evolution shows on the contrary that the main philosophical issue raised by Einstein’s theory was instead that of mathematical over-determination, i.e. the recognition of the presence of redundant mathematical differences that do not have any correspondence in physical reality. (shrink)

The present paper attempts to show that a 1915 article by Erich Kretschmann must be credited not only for being the source of Einstein’s point-coincidence remark, but also for having anticipated the main lines of the logical-empiricist interpretation of general relativity. Whereas Kretschmann was inspired by the work of Mach and Poincaré, Einstein inserted Kretschmann’s point-coincidence parlance into the context of Ricci and Levi-Civita’s absolute differential calculus. Kretschmann himself realized this and turned the point-coincidence argument against Einstein in his second (...) and more famous 1918 paper. While Einstein had taken nothing from Kretschmann but the expression “point-coincidences”, the logical empiricists, however, instinctively dragged along with it the entire apparatus of Kretschmann’s conventionalism. Disappointingly, in their interpretation of general relativity, the logical empiricists unwittingly replicated some epistemological remarks Kretschmann had written before General Relativity even existed. (shrink)

The important switch from the so-called old B-theory to the new tenseless theory of time (NTT), which had significant implications for the field of tense and indexicals, occurred after Carnap’s era. Against this new background, Carnap’s original inter-translatability thesis can no longer be upheld. The most natural way out would be to modify Carnap’s position according to the NTT; but this is not compatible with Carnap’s metaphysical neutrality thesis. Even worse, Carnap’s work on measurement theory can be used to develop (...) an argument in favour of the A-theory. I argue that there are tensed basic sentences which are needed in order to construct a tenseless system and thus cannot be translated without loss of meaning into tenseless ones (old B-theory) or made true by tenseless facts (NTT). (shrink)

ZusammenfassungAusgehend von einer operational vorgehenden Wissenschaftstheorie, die die kantische Ein‐teilung der erfahrungswissenschaftlichen Urteile auf den heutigen Stand dieser philosophischen Disziplin überträgt, wird eine Epistemologie entwickelt, welche sich sowohl an den Ergebnissen der Metalogik und philosophischen Semantik als auch an den empirischen Hypothesen der gegen‐wärtigen Wahrnehmungspsychologie orientiert. In bezug auf den Inhalt des zugrundegelegten Universums der zu interpretierenden Sprache wird hierbei eine Position des Suppositionismus vertreten, welche von einem sprachabhängigen Erkennen der Objekte ausgeht, deren Existenz somit nur vorausgesetzt werden kann. Bezüglich (...) der Form des Universums wird eine extensionali‐stische Haltung eingenommen, und die Frage nach der Rechtfertigung der Voraussetzungen empi‐rischer Erkenntnis wird im Sinne eines Kondilionalismus entschieden, welcher insbesondere ein apriorisches Beweisen dieser Voraussetzungen ablehnt und somit auch epistemologische Umschichtungen beim Wechsel von Erfahrungserkenntnis berücksichtigt. (shrink)

In 1929 Carnap gave a paper in Prague on Investigations in General Axiomatics; a briefsummary was published soon after. Its subject lookssomething like early model theory, and the mainresult, called the Gabelbarkeitssatz, appears toclaim that a consistent set of axioms is complete justif it is categorical. This of course casts doubt onthe entire project. Though there is no furthermention of this theorem in Carnap''s publishedwritings, his Nachlass includes a largetypescript on the subject, Investigations inGeneral Axiomatics. We examine this work here,showing (...) that it provides important insights intoCarnap''s development during this critical period, thetransition from Aufbau to Syntax,especially regarding the nature and motivation ofCarnap''s logicism. Moreover, we show how theAxiomatics influenced Carnap''s student Gödel inreaching the fundamental logical results that soonafterwards undermined Carnap''s project. (shrink)

"L'énigme majeure est la cause efficace" insiste Jean Largeault (1985). En effet, la physique contemporaine géométrise les phénomènes de la nature en transformant les causes efficientes en causalité formelle. Cependant elle nous invite aussi à accorder le structurel etle physique, le formel et le dynamique. Il convient donc de s'interroger sur le fondement du pouvoir créateur des mathématiques ou de leur caractère générateur en physique. Selon Charles de Koninck, la fécondité des mathématiques parait comme une intériorisation de la figure philosophique (...) de l'ange dans le cadre du projet d'une métamathématique comme angélologie thomiste. La raison poursuit un moyen de connaitre qui serait universel in repraesentando, par opposition à l'universel in praedicando. Cette tendance est essentielle à ce que l'on appelle le "mode platonicien". L'une des idées centrales de cet article consiste à établir une connexion profonde entre la notion de causalité en physique et cette manière platonicienne de connaitre. Plus précisément, l'idéalisation de la causalité efficace en physique mathématique est-il autre chose que ce mode dialectique de connaître abusivement porté à sa limite ? (shrink)