The paper focuses on the role of relativistic ideas in Wittgenstein’s philosophy. In particular, it focuses on On Certainty (1969), where in (305), Wittgenstein explicitly invokes Einstein’s theory of relativity: “Here once more there is needed a step like the one taken in relativity theory.” The aim of the paper is to establish a connection between Wittgenstein and Einstein that is both theoretically and exegetically sound. In particular, the paper argues that Wittgenstein’s reaction to scepticism closely resembles Einstein’s reaction to (...) the ether. (shrink)

This paper argues that Frege's notoriously long commitment to Kant's thesis that Euclidean geometry is synthetic _a priori_ is best explained by realizing that Frege uses ‘intuition’ in two senses. Frege sometimes adopts the usage presented in Hermann Helmholtz's sign theory of perception. However, when using ‘intuition’ to denote the source of geometric knowledge, he is appealing to Hermann Cohen's use of Kantian terminology. We will see that Cohen reinterpreted Kantian notions, stripping them of any psychological connotation. Cohen's defense of (...) his modified Kantian thesis on the unique status of the Euclidean axioms presents Frege's own views in a much more favorable light. (shrink)

In science as in mathematics, it is popular to know little and resent much about category theory. Less well known is how common it is to know little and like much about set theory. The set theory of almost all scientists, and even the average mathematician, is fundamentally different from the formal set theory that is contrasted against category theory. The latter two are often opposed by saying one emphasizes Substance, the other Form. However, in all known systems of mathematics (...) throughout history, mathematicians have moved fluidly between ideas conceived of as thing-like, property-like, and process-like. On the other hand one way to advance science is to better distinguish between thing, property, and process. All this constitutes a distracting background for those interested in, or distressed by, the possible application of category theory to science, and to mathematics as well. (shrink)

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)

In this paper, I will deal with the analogy between Cassirer’s interpretation of relativity and his philosophy of culture. As to the structure of the paper, it will be divided into six parts. I will start with a brief introduction, after which I will succinctly outline Cassirer’s reading of Einstein’s theory, and in particular of general covariance. I will then focus on the presentation of his project for a “systematic philosophy” in the last chapter of Einstein’s Theory of Relativity and (...) subsequently delve into the lexical references to relativity made in Philosophy of Symbolic Forms. After this, I will tackle Cassirer’s rectorship speech, where relativity and the philosophy of culture are explicitly interwoven, but with the important clarification (already provided in Einstein’s Theory of Relativity and Philosophy of Symbolic Forms) that not all kinds of knowledge align with de-anthropomorphized objectivity. The final section contains the concluding remarks. (shrink)

In this article, we analyse how Ernst Cassirer’s approach of a phenomenology of knowledge deals with the general question of disunity in science and society. By elaborating on the concept of functional unity, which presupposes difference, Cassirer’s work helps to revise foundational concepts of modern science and society, such as pluralism and truth. Relating Cassirer’s approach to the current interest in political epistemology, we show the implications of Cassirer’s theory of knowledge and analyses of modern science, particularly physics. In these (...) analyses, Cassirer carves out the relational logic of scientific knowledge and its consequences on epistemological and ethico-political levels. While this logic of relations relativises absolute claims on either level, it entails its distinct normative criteria as elements of the scientific ideal. Cassirer’s project defends this ideal and thus can simultaneously defend plurality _in_ science (including the humanities) in terms of methods, perspectives and aims, and preserve the unity _of_ science as a normative ideal and symbolic form in constant interaction with other forms. Thus, Cassirer’s pluralism must be distinguished from mere historicist or relativist conceptions. (shrink)

Philosophical Investigations, EarlyView.

The late 19th-century Ignorabimus controversy over the limits of scientific knowledge has often been characterized as proclaiming the end of intellectual progress, and by implication, as plunging Germany into a crisis of pessimism from which Liberalism never recovered. My research supports the opposite interpretation. The initiator of the Ignorabimus controversy, Emil du Bois-Reymond, was a physiologist who worked his whole life against the forces of obscurantism, whether they came from the Catholic and Conservative Right or the scientistic and millenarian Left. (...) Du Bois-Reymond’s doubt that scientists would ever elucidate consciousness must therefore be seen as an endorsement, and not a rejection, of his faith in reason. (shrink)

"Partial realism" is a common position in the contemporary philosophy of science literature. It states that the "essential" elements of empirically successful scientific theories accurately represent corresponding features the world. This thesis makes several novel contributions related to this position. Firstly, it offers a new definition of the concept of “empirical success”, representing a principled merger between the use-novelty and unification accounts. Secondly, it provides a comparative critical analysis of various accounts of which elements are "essential" to the success of (...) a theory, including structural realism and the divide et impera strategy. A novel account of essentialness, entitled the “empirically successful sub-theory "account", is defended. Thirdly, it is argued that the realism/anti-realism debate should put to the side metaphysical questions and focus instead on partial realism's commitment to the continuity of science. Because this commitment lacks metaphysical implications, it is referred to as "deflationary realism". Anti-realists cannot reject deflationary realism as a matter of a priori principle; its overall viability can therefore only be assessed by a careful examination of the history of science. Finally, another consequence of partial realism, named "partial rationalism", is defended. Partial rationalism states that, in cases where several competing theories have been suggested, scientists are rational just in case they accept the essential elements of each of the scientific theories on offer. This novel position subverts the existing literature on scientific "revolutions", as it sometimes demands that scientists devise a synthesis between competing scientific theories, instead of "choosing" only one. The philosophical points defended in this thesis are illustrated and supported by case studies from the history of science, including Fresnel’s wave theory of light, the Copernican revolution, the "neo-Darwinian synthesis" in evolutionary biology, the "prion revolution" in molecular biology, the miasma theory of disease, and the chemical revolution. (shrink)

Modern science was historically built by avoiding a direct treatment of cause-effect relationship questions. Recent developments in mathematical, probabilistic and statistical sciences make possible to pursue a more direct approach in cause-effect relationships leading to effective and systematic investigations in a wide range of scientific research fields.