The mathematical developments of the 19th century seemed to undermine Kant’s philosophy. Non-Euclidean geometries challenged Kant’s view that there is a spatial intuition rich enough to yield the truth of Euclidean geometry. Similarly, advancements in algebra challenged the view that temporal intuition provides a foundation for both it and arithmetic. Mathematics seemed increasingly detached from experience as well as its form; moreover, with advances in symbolic logic, mathematical inference also seemed independent of intuition. This paper considers various philosophical responses to (...) these changes, focusing on the idea of modifying Kant’s conception of intuition in order to accommodate the increasing abstractness of mathematics. It is argued that far from clinging to an outdated paradigm, programs based on new conceptions of intuition should be seen as motivated by important philosophical desiderata, such as the truth, apriority, distinctiveness and autonomy of mathematics. (shrink)

The issue is obscured by the fact that the word `space' can be used in four different ways. It can be used, first, as a term of pure mathematics, as when mathematicians talk of an `n-dimensional phase-space', an `n-dimensional vector-space', a `three-dimensional projective space' or a `twodimensional Riemannian space'. In this sense the word `space' means the totality of the abstract entities-the `points'-implicitly defined by the axioms. There is no doubt that there exist, iii this sense, non-Euclidean spaces, because all (...) that is claimed by such an assertion is that sets of non-Euclidean axioms constitute possible implicit definitions of abstract entities, that is to say that some sets of non-Euclidean axioms are consistent. If Kant or any other philosopher had denied this, he would have been wrong; but Kant himself took care not to deny it, 2 and there is little reason to suppose that any philosopher concerned about space has been using the word in this, the pure mathematician's, sense. (shrink)

Cette étude montre que les réflexions épistémologiques de Poincaré émergèrent dans le cadre de ses recherches scientifiques et qu’elles furent en partie inspirées par sa lecture de savants philosophes comme Helmholtz et surtout Maxwell. Elle donne une analyse systématique des textes philosophiques publiés par Poincaré vers 1900, au moment où il juge que la physique des principes constitue le sommet de l’évolution des théories. Enfin, elle met en rapport certaines de ses thèses sur la physique avec l’Analytique et la Dialectique (...) transcendantales kantiennes. (shrink)

The act of understanding is at the heart of all scientific activity; without it any ostensibly scientific activity is as sterile as that of a high school student substituting numbers into a formula. Ordinary language often uses visual metaphors in connection with understanding. When we finally understand what someone is trying to point out to us, we exclaim: “I see!” When someone really understands a subject matter, we say that she has “insight”. There appears to be a link between visualization (...) and understanding, and between visualizability and intelligibility. This applies in science no less than in daily life: visualization is regarded as a useful means of achieving scientific understanding, even in the .. (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)

This paper deals with Parmenides of Elea’s way of inquiry about reality and the opposition emerging from it. In more detail, it analyses how Parmenides’ concepts of logos and doxa present some analogies with Bergson’s thoughts about duration and Time and how these theories influenced the understanding of visual media, especially the cinematographic camera. This survey will allow us to demonstrate that some scientific theories about space that accompanied the development of the cinematographic camera progressively allowed for the birth of (...) a new understanding of this device. In the last section of this study, we will then focus on the way through which the film camera - understood as an intelligent device - passes from the sphere of doxa to the sphere of logos. (shrink)

In Origins of Objectivity Burge advances a theory of perception according to which perceptions are, themselves, objective representations. The possession of veridicality conditions by perceptual states—roughly, non-propositional analogues of truth-conditions—is central to Burge’s account of how perceptual states differ, empirically and metaphysically, from sensory states. Despite an impressive examination of the relevant empirical literatures, I argue here that Burge has not succeeded in securing a distinction between perception and “mere” sensation.

In this paper, we show that a restricted form of time travel both accords with special relativity kinematics and avoids several prima facie objections. We argue that such time travel provides a reasonable way to interpret certain phenomena which can readily be described, and the analogues of which have already been observed at the level of elementary particle reactions. We then describe how a time-traveling object could measure itself, and demonstrate how, in the appropriate circumstances, such an experiment could convince (...) a theorist who insisted on a single criterion for length measurements that his standard had itself changed in length. The same experiment can shed light on the possibility of detecting a universal expansion; and we show that, given certain experimental results, one must conclude that every member of a class of time travelers has changed in length simultaneously, though perhaps only while going backwards in time. (shrink)

The journal Mind is now a wholly philosophical journal. At the time of its founding, in 1876, however, its mission was rather different in character. Its aim was to discover whether scientific psychology was a truly viable enterprise and, if so, what its boundaries with philosophy, with other scientific disciplines, and with the earlier generation of discredited attempts at `scientific' studies of the mind (e.g. phrenology, mesmerism) might be. Although at first Mind published mostly philosophical pieces and literature reviews, by (...) the mid-1880s it was publishing primary experimental research, mostly by American psychologists who as yet had few outlets of their own. For a time it was the leading journal of experimental psychology in the English-speaking world. As the international competition among scientific and scholarly journals intensified in the 1890s, however, Mind started to lose its share of experimental contributions, and with the editorial takeover of the journal of George Stout in 1892, the journal soon became one dedicated purely to philosophy. (shrink)

The concept of natural kind is center stage in the debates about scientific realism. Champions of scientific realism such as Richard Boyd hold that our most developed scientific theories allow us to “cut the world at its joints” (Boyd, 1981, 1984, 1991). In the long run we can disclose natural kinds as nature made them, though as science progresses improvements in theory allow us to revise the extension of natural kind terms.

Faced with the mathematical possibility of non-Euclidean geometries, 19th Century geometers were tasked with the problem of determining which among the possible geometries corresponds to that of our space. In this context, the contribution of the Belgian philosopher-mathematician, Joseph Delboeuf, has been unduly neglected. The aim of this essay is to situate Delboeuf’s ideas within the context of the philosophies of geometry of his contemporaries, such as Helmholtz, Russell and Poincaré. We elucidate the central thesis, according to which Euclidean geometry (...) is given special status on the basis of the relativity of magnitudes, we uncover its hidden history and show that it is defensible within the context of the philosophies of geometry of the epoch. Through this discussion, we also develop various ideas that have some relevance to present-day methods in gravitational physics and cosmology. (shrink)

This volume, The Brazilian Studies in the Philosophy and History of Science, is the first attempt to present to a general audience, works from Brazil on this subject. The included papers are original, covering a remarkable number of relevant topics of philosophy of science, logic and on the history of science. The Brazilian community has increased in the last years in quantity and in quality of the works, most of them being published in respectable international journals on the subject. The (...) chapters of this volume are forwarded by a general introduction, which aims to sketch not only the contents of the chapters, but it is conceived as a historical and conceptual guide to the development of the field in Brazil. The introduction intends to be useful to the reader, and not only to the specialist, helping them to evaluate the increase in production of this country within the international context. (shrink)