Se distinguen dos acepciones del término “contexto de descubrimiento”: La acepción tradicional, que lo contrasta con el contexto de la justificación, y otra, más reciente, que lo relaciona con la metodología de inferencia causal. Curiosamente, el propio Reichenbach suscribió la segunda acepción, y no es coincidencia que su aportación al desarrollo del campo del descubrimiento causal haya sido capital. Se defiende la vigencia de esta metodología en todas las ciencias empíricas, incluidas las ciencias físicas.

In this paper, I critically discuss Frege’s philosophy of geometry with special emphasis on his position in The Foundations of Arithmetic of 1884. In Sect. 2, I argue that that what Frege calls faculty of intuition in his dissertation is probably meant to refer to a capacity of visualizing geometrical configurations structurally in a way which is essentially the same for most Western educated human beings. I further suggest that according to his Habilitationsschrift it is through spatial intuition that we (...) come to know the axioms of Euclidean geometry. In Sect. 3, I argue that Frege seems right in claiming in The Foundations, §14 that the synthetic nature of the Euclidean axioms follows from the fact that they are independent of one another and of the primitive laws of logic. If the former were dependent on the latter, they would be analytic in Frege’s sense of analyticity. But then they would not be independent of one another and due to their mutual provability would lose their status as axioms of Euclidean geometry, since according to Frege an axiom of a theory T is per definitionen unprovable in T. I further argue that only by invoking pure spatial intuition can Frege “explain” the epistemological status of the axioms of Euclidean geometry completely: their synthetic a priori nature. Finally, I argue that his view about independence in The Foundations, §14 seems to clash with his conception of independence in his mature period. In Sect. 4, I scrutinize Frege’s somewhat vague, but unduly neglected remarks in The Foundations, §26 on space, spatial intuition and the axioms of Euclidean geometry. I argue that for the sake of coherence Frege should have said unambiguously that space is objective, that it is independedent not only of our spatial intuition, but of our mental life altogether including our judgements about space, instead of encouraging the possible conjecture that in his view it contains an objective and a subjective component. I further argue that for Frege the objectivity of both space and the axioms of Euclidean geometry manifests itself in our universal and compulsory acknowledgement of the Euclidean axioms as true. I conclude Sect. 4 by arguing that there is a conflict between the subjectivity of our spatial intuitions as stressed in The Foundations, §26 and Frege’s thesis in his dissertation that the axioms of Euclidean geometry derive their validity from the nature of our faculty of intuition. To resolve this conflict, I propose that in the light of his avowed realism in The Foundations Frege could have replaced his early thesis by saying that although we come to know the axioms of Euclidean geometry through spatial intuition and are justified in acknowledging them as true on the basis of geometrical intuition, their truth is independent not only of the nature of our faculty of intuition and singular acts of intuition, but of our mental processes and activities in general, including the inner mental act of judging. In Sect. 5, I argue that Frege most likely did not adopt Kant’s method of acquiring geometrical knowledge via the ostensive construction of concepts in spatial intuition. In contrast to Kant, Frege holds that the axioms of three-dimensional Euclidean geometry express state of affairs about space obtaining independently of our spatial intuition. In Sect. 6, I conclude with a summarized assessment of Frege’s philosophy of geometry. (shrink)

The concept of quantity (Größe) plays a key role in Frege's theory of real numbers. Typically enough, he refers to this theory as ?theory of quantity? (?Größenlehre?) in the second volume of his opus magnum Grundgesetze der Arithmetik (Frege 1903). In this essay, I deal, in a critical way, with Frege's treatment of the concept of quantity and his approach to analysis from the beginning of his academic career until Frege 1903. I begin with a few introductory remarks. In Section (...) 2, I first analyze Frege's use of the term ?source of knowledge? (?Erkenntnisquelle?) with particular emphasis on the logical source of knowledge. The analysis includes a brief comparison between Frege and Kant's conceptions of logic and the logical source of knowledge. In a second step, I examine Frege's theory of quantity in Rechnungsmethoden, die sich auf eine Erweiterung des Größenbegriffes gründen (Frege 1874). Section 3 contains a couple of critical observations on Frege's comments on Hankel's theory of real numbers in Die Grundlagen der Arithmetik (Frege 1884). In Section 4, I consider Frege's discussion of the concept of quantity in Frege 1903. Section 5 is devoted to Cantor's theory of irrational numbers and the critique deployed by Frege. In Section 6, I return to Frege's own constructive treatment of analysis in Frege 1903 and succinctly describe what I take to be the quintessence of his account. (shrink)

It is often claimed that epistemological thought divides around the issue of the place of experience in knowledge: While empiricists argue that experience is the only legitimate source of knowledge, rationalists find other such sources. The trouble with such accounts is not that they are wrong, but that they are incomplete. On occasion, epistemological differences run deeper, raising the very notion of experience as an issue for epistemology. This paper looks at two epistemological debates which concerned not simply the place (...) of experience in knowledge but also the appropriate account of experience itself. The first episode is the rise of Marburg Neo-Kantianism in the 1870s – in particular the seminal work of Hermann Cohen in his Kants Theorie der Erfahrung (1871). Cohen's principal point was that Kant's significance as an epistemologist was in providing a new theory of experience, one that tied experience to exact science and led to a new stress on the formal conditions of exact knowledge. The second episode is Carnap's rejection of epistemology in the 1930s in favour of a program of the logic of science. My focus in each case will be the interplay between an epistemology focused on exact science as the locus of knowledge and a concomitant call for logical methods in epistemology. (shrink)

This paper compares Cohen’s Logic of Pure Knowledge and Cassirer’s Substance and Function in order to evaluate how in these works Cohen and Cassirer go beyond the limits established by Kantian philosophy. In his Logic, Cohen seeks to ground in pure thought all the elements which Kant distinguishes in empirical intuition: its matter (sensation) as well as its form (time and space). In this way, Cohen tries to provide an account of knowledge without appealing to any receptivity. In accordance with (...) Cohen’s project of reformulating the Kantian theory of sensibility, Cassirer undertakes in Substance and Function the task of developing an alternative doctrine of pure and empirical manifolds. But whereas Cohen analyzes the laws of pure thought, Cassirer aims to highlight the functional character of concepts in the development of modern mathematics and physics. I will discuss these two different approaches to the problems raised by Kantian philosophy and I will argue that Cassirer went further than Cohen in the project of critical idealism. (shrink)

ABSTRACT The aim of this paper is to discuss how Bruno Bauch deals with the problem of the coordination between empirical concepts and spatiotemporal objects. We shall argue that Bauch reformulates the Kantian distinction between concepts and intuitions by means of a philosophical consideration of differential calculus and that he thereby explains the possibility of such coordination, avoiding certain difficulties of the Kantian doctrine. RESUMO O propósito deste trabalho é discutir como o neokantismo de Bruno Bauch trabalha o problema da (...) coordenação de conceitos e objetos espaço-temporais. Sustentaremos que Bauch reformula a distinção kantiana de conceitos e intuições mediante uma consideração filosófica do cálculo diferencial e que, assim, explica a possibilidade de tal coordenação, evitando certas dificuldades da doutrina de Kant. (shrink)

German supporters of the Kantian philosophy in the late 19th century took one of two forks in the road: the fork leading to Baden, and the Southwest School of neo-Kantian philosophy, and the fork leading to Marburg, and the Marburg School, founded by Hermann Cohen. Between 1876, when Cohen came to Marburg, and 1918, the year of Cohen's death, Cohen, with his Marburg School, had a profound influence on German academia.

Marburg Neo-Kantianism has attracted substantial interest among contemporary philosophers drawn by its founding idea that the success of advanced theoretical science is a given fact and it is the task of philosophical inquiry to ground the objectivity of scientific achievement in its a priori sources (Cohen and Natorp 1906, p. i). The Marburg thinkers realized that recent advances and developments in the mathematical sciences had changed the character of Kant’s transcendental project, demanding new methods and approaches to establish the objectivity (...) of the latest insights into physical reality. Hermann Cohen, one of the founders of the Marburg School, attempted to base the objectivity of science on the concepts of .. (shrink)

We seek to elucidate the philosophical context in which one of the most important conceptual transformations of modern mathematics took place, namely the so-called revolution in rigor in infinitesimal calculus and mathematical analysis. Some of the protagonists of the said revolution were Cauchy, Cantor, Dedekind,and Weierstrass. The dominant current of philosophy in Germany at the time was neo-Kantianism. Among its various currents, the Marburg school (Cohen, Natorp, Cassirer, and others) was the one most interested in matters scientific and mathematical. Our (...) main thesis is that Marburg neo-Kantian philosophy formulated a sophisticated position towards the problems raised by the concepts of limits and infinitesimals. The Marburg school neither clung to the traditional approach of logically and metaphysically dubious infinitesimals, nor whiggishly subscribed to the new orthodoxy of the “great triumvirate” of Cantor, Dedekind, and Weierstrass that declared infinitesimals conceptus nongrati in mathematical discourse. Rather, following Cohen’s lead, the Marburg philosophers sought to clarify Leibniz’s principle of continuity, and to exploit it in making sense of infinitesimals and related concepts. (shrink)

On 11thOctober 2007, at the first international conference on Integrated History and Philosophy of Science (&HPS1) hosted by the Center for Philosophy of Science in Pittsburgh, Ernan McMullin (University of Notre Dame) portrayed a rather gloomy scenario concerning the current relationship between history and philosophy of science (HPS), on the one hand, and mainstream philosophy, on the other hand, as testified by a significant drop in the presence of HPS papers at various meetings of the American Philosophical Association (APA).

The metaphysical “Law of Continuity of Alterations” says that whenever an object alters from one state to another, it passes through a continuum of intermediate states. Kant treated LCA as a transcendental law of understanding. The primary purpose of the paper is to reconstruct and evaluate Kant’s three arguments for LCA. All three are found to be inadequate. However, a secondary goal of the paper is to show that LCA would have more naturally been construed as a regulative principle of (...) reason. I conclude with some remarks about how this could work. (shrink)

Frege claims that the laws of logic are characterized by their “generality,” but it is hard to see how this could identify a special feature of those laws. I argue that we must understand this talk of generality in normative terms, but that what Frege says provides a normative demarcation of the logical laws only once we connect it with his thinking about truth and science. He means to be identifying the laws of logic as those that appear in every (...) one of the scientific systems whose construction is the ultimate aim of science, and in which all truths have a place. Though an account of logic in terms of scientific systems might seem hopelessly antiquated, I argue that it is not: a basically Fregean account of the nature of logic still looks quite promising. (shrink)

Do you see now why it feels so good to be a critical mind? Why critique, this most ambiguous pharmakon, has become such a potent euphoric drug? You are always right! When naïve believers are clinging forcefully to their objects... you can turn all of those attachments into so many fetishes and humiliate all the believers by showing that it is nothing but their own projection, that you, yes you alone, can see. But as soon as naïve believers are thus (...) inflated by some belief in their own importance, in their own projective capacity, you strike them by a second uppercut and humiliate them again, this time by showing that, whatever they think, their behavior is entirely determined by the action of powerful causalities coming from objective reality they don't see, but that you, yes you, the never sleeping critic, alone can see. Isn't this fabulous? Isn't it really worth going to graduate school to study critique? (shrink)

In 1912, Ernst Cassirer contributed to the special issue of the Kant-Studien that honored Hermann Cohen's retirement—his mentor and teacher, and the recognized founding father of the so-called 'Marburg school' of Neo-Kantianism. In the context of an otherwise rather conventional presentation of Cohen's interpretation of Kant, Cassirer made a remark that is initially surprising. It is “anything but accurate,” he wrote, to regard Cohen's philosophy as focused “exclusively on the mathematical theory of nature,” as is usually done. A reconstruction of (...) the genesis of Cohen's thought, Cassirer continued, would already refute this interpretation. Actually, “[t]he... (shrink)

This article examines Cohen’s “transcendental method”, Windelband’s “critical method”, the neo-Kantian distinctions between natural science and the humanities (i. e., human or cultural sciences), and Weber’s account of ideal-typical explanations. The Marburg and the Southwest Schools of neo-Kantianism have in common that their respective philosophies of science focused on method, but they substantially differ in their approaches. Cohen advanced the “transcendental method”, which was taken up and transformed by Natorp and Cassirer; later, it became influential in neo-Kantian approaches to 20th (...) century physics. Windelband distinguished between facts and values, linking the former to the “genetic” method of history and the latter to the “critical” method of philosophy; and between the “nomothetic” and “idiographic” methods of the empirical sciences, a distinction further elaborated by Rickert. The distinction does not give rise to a sharp discrimination but is rather what Weber would later call an ideal type. All these approaches contribute in different ways to understanding the structure of scientific knowledge, focusing on different aspects of the general path of the empirical sciences between rationalism and empiricism. (shrink)

The use of the symbol ∨for disjunction in formal logic is ubiquitous. Where did it come from? The paper details the evolution of the symbol ∨ in its historical and logical context. Some sources say that disjunction in its use as connecting propositions or formulas was introduced by Peano; others suggest that it originated as an abbreviation of the Latin word for “or,” vel. We show that the origin of the symbol ∨ for disjunction can be traced to Whitehead and (...) Russell’s pre-Principia work in formal logic. Because of Principia’s influence, its notation was widely adopted by philosophers working in logic (the logical empiricists in the 1920s and 1930s, especially Carnap and early Quine). Hilbert’s adoption of ∨ in his Grundzüge der theoretischen Logik guaranteed its widespread use by mathematical logicians. The origins of other logical symbols are also discussed. (shrink)

Dialogo filosofijos mąstytojų Rosenzweig‘o ir Levino darbų esmė – mirties bedugnės ir asmens tapatumo santykis. Rosenzweig‘as niekį laiko galutiniu kantiškojo mąstymo tašku. Mirtis, kaip egzistencinis niekio patyrimas, buvo laikoma kiekvieno žmogaus realybe sudėtingu amžių sandūros laikotarpiu. Rosenzweig‘ui niekis buvo atspirties taškas, permąstant ir siekiant išsaugoti asmens tapatumą. Asmens tapatumas apsaugo nuo niekio, tačiau jis taip pat yra atviras pokyčiams. Savo ankstyvuosiuose tekstuose Levinas daro panašias prielaidas, laikydamas Buvimą asmens tapatumo pradžia. Levinas plėtojo dialektinę fenomenologiją pradėdamas nuo mirties. Asmens tapatumas traktuojamas (...) kaip hipostazė, tačiau Levino darbe „Totalité et Infini“ įvyksta svarbus lūžis – jame asmens tapatumo šaltiniu laikomas troškimas. Buvimas tampa dėmesio centru kaip antroji elementale pusė, o asmens tapatumas suvokiamas kaip atsiskyrimas. (shrink)

This paper argues that the principle of continuity that underlies Benjamin’s understanding of what makes the reality of a thing thinkable, which in the Kantian context implies a process of “filling time” with an anticipatory structure oriented to the subject, is of a different order than that of infinitesimal calculus—and that a “discontinuity” constitutive of the continuity of experience and (merely) counterposed to the image of actuality as an infinite gradation of ultimately thetic acts cannot be the principle on which (...) Benjamin bases the structure of becoming. Tracking the transformation of the process of “filling time” from its logical to its historical iteration, or from what Cohen called the “fundamental acts of time” in Logik der reinen Erkenntnis to Benjamin’s image of a language of language (qua language touching itself), the paper will suggest that for Benjamin, moving from 0 to 1 is anything but paradoxical, and instead relies on the possibility for a mathematical function to capture the nature of historical occurrence beyond paradoxes of language or phenomenality. (shrink)

The goal of this paper is to investigate the relation between Cohen's approach to differential calculus and his doctrine of pure thinking. We claim that Cohen's logic of origin is firmly based on his interpretation of infinitesimal analysis. More precisely, the transcendental method, when applied to differential calculus, reveals the productive capacity of thinking expressed by the judgment of origin.

One of the crucial elements of philosophising at the beginning of the twentieth century is the problem of grounding of philosophy. Representatives of neo-Kantianism fit in with this trend. They try to describe the grounding of philosophy by referring to the philosophy of Kant. That, however, raises a number of difficulties of interpretation that result from the appearing possibilities of interpretation. The article is an attempt to show the efforts of Hermann Cohen, who emphasized the importance of transcendental deduction and (...) transcendental apperception in Kant’s system. In accordance with the thesis of Fichte, Cohen searches for a basis that would allow building a system of knowledge and finds it is the concept of hypothesis. (shrink)

In the second edition of Hermann Cohen’s Kant’s Theory of Experience, he abandons the interpretation of Kant’s Anticipations of Perception that he gave in the first edition, in favourof a radically different one. On his early interpretation, the Anticipations is largely of psychological interest for its influence on, and continuing significance for, physiological psychology and psychophysics. But on his mature interpretation, it defends the superiority of a dynamic conception of nature over a mechanical conception. Further, on his early interpretation, Cohen (...) thought the Anticipations was not a central part of Kant’s critical theory of knowledge. But on his mature interpretation, he thinks it is absolutely central to that project. What is more, Cohen seems to have revised his interpretation in a relatively short period of time, in 1880-1. This paper argues that Cohen’s change in views about Kant’s Anticipations is explained by his reception of Leibniz in the very early 1880s, and specifically Cohen’s reception of Leibniz’s arguments against Descartes’ view that extension is the essence of matter. (shrink)

This essay addresses the attitude of some leading Neo-Kantian philosophers toward scientific psychology and psychophysics. Early influential figures like Friedrich A. Lange counted Gustav T. Fechner’s psychophysical law among their allies in the rehabilitation of the Kantian standpoint. Later on, however, Neo-Kantian philosophers firmly rejected psychological measurement as a whole and harshly criticized the methods adopted by several psychologists of their time. For example, the Marburg mathematician and philosopher August Stadler reduced the validity of Fechner’s law to the mere physiological (...) sphere, and Hermann Cohen conceived the application of mathematical integration to human sensations as an inane enterprise. (shrink)

The article elucidates and assesses the Marburg School’s account of the cognition. The characteristic feature of epistemology from this School is the rejection of the mirroring and acceptance of the cognitive transformation. The criticism of the mirroring theory is implicitly contained in Paul Natorp’s and Hermann Cohen’s cognitive relationism. Ernst Cassirer articulated this critical epistemology in his philosophy of the symbolic form and his conception of the symbolic representation. The historical bases of this criticism has been reconstructed as a main (...) purpose of this article. (shrink)