Julien Bernard

The programme of geometrical archaeology initiated by the last Husserlian texts merits being taken further with renewed emphasis on historical discontinuities. The revolutions that geometry has gone through have led to profound changes in meaning. The arch-foundations of geometry were not actually definitively set out at the time of the first factual institution of geometry, namely Greek geometry. Instead, the full plurality of the historical forms of geometry does not just consist of a movement to generalise axioms. It involves the reform of the archi-foundations themselves. We will show this using the example of two important revolutions: 1) the discovery of non-Euclidean geometries and 2) the transition to a differential geometry and a dynamic metric. We will also discuss the philosophical difficulties these two moments of re-origination brought up. These studies will follow an introductory section on historical phenomenology and the architecture of the original strata of geometry, the idea being to introduce the conceptual tools and vocabulary required for the studies in the final part.

I develop and comment on the controversy between Schlick, Husserl and his follower Weyl, concerning the ideal of a scientific philosophy. The main part of the article is divided into two sections. In the first one, I comment on the main texts of the controversy. Starting with Schlick’s attacks (in General Theory of Knowledge) toward the phenomenological method and Husserl’s response, I explain how Weyl progressively entered in the controversy in favor of Husserl. At the end of this section, I show that the debate between the two opposite conceptions of a scientific philosophy was blurred by very different conceptions of the notions of intuition and lived experience (Erlebnisse), which were then at the center of the debate. In the next section, I reconstruct Weyl’s solution to the problem of elaborating a transcendental-idealistic theory of knowledge that is attentive to the historicity of empirical sciences. I show that Weyl seems to consider the history of science as the locus of purification of the expression of a priori. In developing this philosophical position, Weyl provided Husserl with two different kinds of defense against Schlick’s attacks, firstly by showing that synthetic a priori remains an adequate epistemological concept, secondly by showing that certain phenomenological or transcendental philosophies (at least Weyl’s) are capable of taking into account the historicity of science, the importance of which was underestimated by Schlick.

In his first edition (1918) of Allgemeine Erkenntnislehre, on §17, Moritz Schlick ridiculed Husserl’s phenomenological method in a polemical text, where he used ironically Husserl’s vocabulary. This text was removed from the second edition (1925). As he explained in the preface to the second edition, Schlick preferred his readers to focus on the positive content of his theory of knowledge than to the correction of the mistakes of others. Because of this removal, mostly only German readers had an access to this text, the English and French translations of Allgemeine Erkenntnislehre being based on the second edition. For this reason, I publish here an English and a French translation of this passage, on the occasion of my article “Schlick, Husserl, Weyl: On Scientific Philosophy”. This translation has not been reviewed by a German nor an English native speaker. I hope nevertheless that this can be useful for researchers in history and philosophy of science, not able to read directly the German.

This article is devoted to the analysis of the remarks of Gödel's Maxims and Philosophical remarks (Max Phil) that present a solution to the paradoxes of set theory, and to the analysis of the context. It is divided in two parts. The first part contains two remarks from the notebook IX, (pp. 48b, 51) on the question of the strategies for the solution of paradoxes. They clearly show Gödel’s preference for the strategy of limited ranges of significance. The reasons why Gödel was also interested in the other strategies suggested by Russell is explained through two remarks of Max Phil IX (pp.69 and 72b) The second part presents a remark from Max Phil X (p. 28-29), and explains it from the perspective of Gödel analysis of concepts in the early 1943.

The hole argument is a story invented by Albert Einstein to set out the difficulties he had in reconciling his principle of covariance with the Mach's principle. Some modern presentations insist that the bare differential manifold loses its physical status and is just an expression of the mathematical framework of the new relativistic theory. In Space-Time-Matter, Hermann Weyl constructed an argument close to the modern hole argument, replacing the hole with a ball of clay. Beside some trivial technical differences, Weyl's argument is original because of the particular concept of mathematics that he inherited from the Gottingen school.

This book investigates Hermann Weyl’s work on the problem of space from the early 1920s onwards. It presents new material and opens the philosophical problem of space anew, crossing the disciplines of mathematics, history of science and philosophy. With a Kantian starting point Weyl asks: among all the infinitely many conceivable metrical spaces, which one applies to the physical world? In agreement with general relativity, Weyl acknowledges that the metric can quantitatively vary with the physical situation. Despite this freedom, Weyl “deduces”, with group-theoretical technicalities, that there is only one “kind” of legitimate metric. This construction was then decisive for the development of gauge theories. Nevertheless, the question of the foundations of the metric of physical theories is only a piece of a wider epistemological problem. Contributing authors mark out the double trajectory that goes through Weyl’s texts, from natural science to philosophy and conversely, always through the mediation of mathematics. Readers may trace the philosophical tradition to which Weyl refers and by which he is inspired, and explore the mathematical tradition that permitted Weyl to elaborate and solve his mathematical problem of space. Furthermore, this volume analyzes the role of the interlocutors with whom Weyl discussed the nature of physical space. This volume features the work of top specialists and will appeal to postgraduates and scholars in philosophy, the history of science, mathematics, or physics.

In The Continuum, Hermann Weyl gives new bases to the notions of set and function. With them, he constructs mathematics close to physics and solves the continuum problem. Those new notions are so unusual with respect to Set Theory that they are often misunderstood.We propose to explain the meaning of Weyl’s reform of those notions. We first make a synthesis of his main epistemological thesis, and then propose a comparative approach to stress the distance between the mathematical and logical principles of The Continuum and those of Set Theory. Our discussion will be centred on the distinction between intension and extension, and on the place Weyl gives to natural numbers for the foundations of analysis.