Boltzmann on Mathematics

Boltzmann’s lectures on natural philosophy point out how the principles of mathematics are both an improvement on traditional philosophy and also serve as a necessary foundation of physics or what the English call “Natura Philosophy”, a title which he will retain for his own lectures. We start with lecture #3 and the mathematical contents of his lectures plus a few philosophical comments. Because of the length of the lectures as a whole we can only give the main points of each but organized into a coherent study. Behind his mathematics stands his support of Darwinian evolution interpreted in a partly Lamarckian way. He also supported non-Euclidean geometry. Much of Boltzmann’s analysis of mathematics is an attempt to refute Kant’s static a priori categories and his identification of space with “non-sensuous intuition”. Boltzmann’s strong attention toward discreteness in mathematics can be seen throughout the lectures. Part II of this paper will touch on the historical background of atomism and focus on the discrete way of thinking with which Boltzmann approaches problems in mathematics and beyond. Part III briefly points out how Boltzmann related mathematics and discreteness to music. This revised version was published online in June 2006 with corrections to the Cover Date.     

A Comparison of Dewey’s and Russell’s Influences on China

John Dewey and Bertrand Russell visited China at around the same time in 1920. Both profoundly influenced China during the great transition period of this country. This article will focus on the differences between the two great figures that influenced China in the 1920s. This comparison will examine the following five aspects: 1. Deweyanization vs. Russellization; 2. Dewey’s “Populism” vs. Russell’s “Aristocraticism”; 3. Dewey’s “Syntheticalism” vs. Russell’s “Analyticalism”; 4. Dewey’s “Realism” vs. Russell’s “Romanticism”; 5. Dewey’s “Conservatism” vs. Russell’s “Radicalism”. This examination will highlight that, although their visit left indelible impressions among Chinese intellecturals, for the radical Marx–Leninists, any Western philosophy and socio-political theories, including Dewey’s and Russell’s, were prejudicial, outworn, and even counterrevolutionary. Soon “Marxi–Leninization” was gradually substituted for “Deweyanization” and “Russellization.”     

Knowing thyself ... in private: Masturbation and philosophy

Karl Marx once compared philosophy to masturbation, essentially seeing both as privative, idealistic, and impractical activities. Indeed, many lay folk see philosophers as “wankers.” While the present state of universities does throw doubt on the liberatory character of contemporary philosophy, Marx’s jibe nonetheless mischaracterizes masturbation. This paper is a brief attempt to correct Marx’s characterization of masturbation by drawing on the work of a thinker ofter associated with “intellectual onanism”: Martin Heidegger. Speaking ontologically, Heidergger’s theories can be developed to show that masturbation it is not privative, but “stretched” in time and place. Moreover, masturbation plays a practical role in the creative development of the self, including the self’s essential bodiliness. While not necessarily defending philosophy against Marx’s charges, this paper does show how even so-called “onanistic” philosophy might be redeemed. “Only a being which, like man, ‘had’ the word... can and must ‘have’ ‘the hand’” —Martin Heidegger “I have a dangerously supple wrist.” —Friedrich Nietzsche     

Kant’s Theory of Arithmetic: A Constructive Approach?

Kant’s theory of arithmetic is not only a central element in his theoretical philosophy but also an important contribution to the philosophy of arithmetic as such. However, modern mathematics, especially non-Euclidean geometry, has placed much pressure on Kant’s theory of mathematics. But objections against his theory of geometry do not necessarily correspond to arguments against his theory of arithmetic and algebra. The goal of this article is to show that at least some important details in Kant’s theory of arithmetic can be picked up, improved by reconstruction and defended under a contemporary perspective: the theory of numbers as products of rule following construction presupposing successive synthesis in time and the theory of arithmetic equations, sentences or “formulas”—as Kant says—as synthetic a priori. In order to do so, two calculi in terms of modern mathematics are introduced which formalise Kant’s theory of addition as a form of synthetic operation.

Evald Il’enkov and World Philosophy

To ascertain the context of Il’enkov’s philosophy, the author delves into the history of philosophy since the Sophists and Plato. For Il’enkov, philosophy is not an abstract science “about everything,” but a study of ideas – forms which are identical for thinking and being. These objective and universal forms of thought are explained as products and schemes of human activity creating the world of culture and reified in its “smart” things.     

Walter Pitts and “A Logical Calculus”

Many years after the publication of “A Logical Calculus of the Ideas Immanent in Nervous Activity,” Warren McCulloch gave Walter Pitts credit for contributing his knowledge of modular mathematics to their joint project.

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Meaning(fullness) Without Metaphysics: Another Look at Hume’s “Meaning Empiricism”

Although Hume has no developed semantic theory, in the heyday of analytic philosophy he was criticized for his “meaning empiricism,” which supposedly committed him to a private world of ideas, led him to champion a genetic account of meaning instead of an analytic one, and confused “impressions” with “perceptions of an objective realm.” But another look at Hume’s “meaning empiricism” reveals that his criterion for cognitive content, the cornerstone both of his resolutely anti-metaphysical stance and his naturalistic “science of human nature,” provides the basis for a successful response to his critics. Central to his program for reforming philosophy, Hume’s use of the criterion has two distinct aspects: a critical or negative aspect, which assesses the content of the central notions of metaphysical theories to demonstrate their unintelligibility; and a constructive or positive aspect, which accurately determines the cognitive content of terms and ideas.     

Structuralism and Meta-Mathematics

The debate on structuralism in the philosophy of mathematics has brought into focus a question about the status of meta-mathematics. It has been raised by Shapiro (2005), where he compares the ongoing discussion on structuralism in category theory to the Frege-Hilbert controversy on axiomatic systems. Shapiro outlines an answer according to which meta-mathematics is understood in structural terms and one according to which it is not. He finds both options viable and does not seem to prefer one over the other. The present paper reconsiders the nature of the formulae and symbols meta-mathematics is about and finds that, contrary to Charles Parsons’ influential view, meta-mathematical objects are not “quasi-concrete”. It is argued that, consequently, structuralists should extend their account of mathematics to meta-mathematics.     

How new is the new philosophy of psychiatry?

In their recent paper, Natalie Banner and Tim Thornton evaluate seven volumes of the Oxford University Press series “International Perspectives in Philosophy and Psychiatry,” an international book series begun in 2003 focusing on the emerging interdisciplinary field at the interface of philosophy and psychiatry. According to Natalie Banner and Tim Thornton, the series represents a clear indication that the interdisciplinary field of philosophy of psychiatry has been flourishing lately. Philosophers and psychiatrists face a “new philosophy of psychiatry”. However, the optimism which the “new” philosophy of psychiatry celebrates is precisely the exiling of philosophy from the foundations of psychiatry. The 150 year old belief that psychopathology cannot do without philosophical reflection has virtually disappeared from common psychiatric education and daily clinical practice. Though the discipline of psychiatry is particularly suited to contributions from philosophy, the impact of philosophy on psychiatry nowadays remains limited. With some exceptions, philosophical papers are embedded in a philosophical context inscrutable to ordinary psychiatrists. Much current philosophical work is perceived by psychiatrists as negativistic. I would encourage the field of psychiatry to incorporate once again basic philosophical attitudes which render possible true dialogue with philosophy and enrich both disciplines. The views developed here should not discredit the value and importance of Natalie Banner and Tim Thornton’s paper and the excellent series “International Perspectives in Philosophy and Psychiatry.” As Jaspers said “Everybody inclined to disregard philosophy will be overwhelmed by philosophy in an unperceived way”.     

How to Define a Number? A General Epistemological Account of Simon Stevin’s Art of Defining

This paper explores Simon Stevin’s l’Arithmétique of 1585, where we find a novel understanding of the concept of number. I will discuss the dynamics between his practice and philosophy of mathematics, and put it in the context of his general epistemological attitude. Subsequently, I will take a close look at his justificational concerns, and at how these are reflected in his inductive, a postiori and structuralist approach to investigating the numerical field. I will argue that Stevin’s renewed conceptualisation of the notion of number is a sort of “existential closure” of the numerical domain, founded upon the practice of his predecessors and contemporaries. Accordingly, I want to make clear that l’Aritmetique have to be read not as an ontological analysis or exploration of the numerical field, but as an explication of a mathematical ethos. In this sense, this article also intends to make a specific contribution to the broader issue of the “ethics of geometry.”     

How to be a structuralist all the way down

This paper considers the nature and role of axioms from the point of view of the current debates about the status of category theory and, in particular, in relation to the “algebraic” approach to mathematical structuralism. My aim is to show that category theory has as much to say about an algebraic consideration of meta-mathematical analyses of logical structure as it does about mathematical analyses of mathematical structure, without either requiring an assertory mathematical or meta-mathematical background theory as a “foundation”, or turning meta-mathematical analyses of logical concepts into “philosophical” ones. Thus, we can use category theory to frame an interpretation of mathematics according to which we can be structuralists all the way down.     

马克思的"感性世界"理论与现象学运动

The epistemological problems that are implicit in Marx’s theory on the “sensible world” indicate that Marx’s philosophy in fact contains within itself the topics of pure philosophy, but Marx did not involve himself in these topics. Through comparing with Husserl’s epistemological critique and Heidegger’s existentialism, we can clearly see that there are theoretical spaces in which we can develop Marx’s philosophy to the realm of pure philosophy, however, we must devote our creative efforts to the exploration of the spaces. Translated by Yang Xiaohua from Zhexue Yanjiu 哲学研究(Philosophical Research), 2006, (6): 20–26     

Different senses of finitude: An inquiry into Hilbert’s finitism

This article develops a critical investigation of the epistemological core of Hilbert’s foundational project, the so-called the finitary attitude. The investigation proceeds by distinguishing different senses of ‘number’ and ‘finitude’ that have been used in the philosophical arguments. The usual notion of modern pure mathematics, i.e. the sense of number which is implicit in the notion of an arbitrary finite sequence and iteration is one sense of number and finitude. Another sense, of older origin, is connected with practices of counting concrete things, and a third sense is linked up with the immediate intuitive experience of multitudes of concrete things. Hilbert’s finitism is examined with respect to these differences, and it will be shown that there is a tendency to conflate the different senses of number and finitude, a tendency which has been a source of problems in the discussion of the foundations of mathematics and in the philosophy of logic and language.     

W<Emphasis Type="SmallCaps">ang</Emphasis> Yangming’s 王陽明 Philosophy and Modern Theories of Democracy: A Reconstructive Interpretation

Liu Shipei 劉師培 (1884–1919) was the first scholar to locate intellectual resources of modern democracy in Wang Yangming’s theory of the “original knowing” (liangzhi 良知). In the 1950s there was a debate between Taiwanese liberals and the “New Confucians” over the relationship between the traditional Confucianism and modern democracy. Like Liu Shipei, the “New Confucians” justified modern democracy by means of Confucian philosophy (including that of Wang Yangming). For liberals, however, the Confucian tradition encompassed only the concept of “positive liberty,” which was irrelevant to or even incompatible with modern democracy. In this article, I try to argue for the position of the “New Confucians” by reconstructing Wang Yangming’s theory of the “original knowing” from a communitarian perspective.     

Bundling Hume with Kripkenstein

It is argued that the intuition driving Kripke’s famous version of Wittgenstein’s meaning skepticism is precisely the one that prompted Hume to despair of his bundle theory of the self: there are no necessary connections between distinct mental states. This interpretation is shown to throw light on Wittgenstein’s notorious idea that all proofs “create concepts.”

Wittgenstein has invented a new form of skepticism. Personally I am inclined to regard it as the most radical and original skeptical problem that philosophy has seen to date[.] – Saul Kripke

     

Heinrich Hertz’s Neo-Kantian Philosophy of Science, and its Development by Harald Høffding

Summary  This article is an investigation of parallel themes in Heinrich Hertz’s philosophy science and Kant’s theory of schemata, symbols and regulative ideas. It is argued that Hertz’s “pictures” bears close similarities to Kantian “schemata”, that is, they are rules linking concepts to intuitions and provide them with their meaning. Kant’s distinction between symbols and schemata is discussed and related to Hertz’s three pictures of mechanics. It is argued that Hertz considered his own picture of mechanics (the “hidden mass” picture) as symbolic in a different way than the force and energy pictures. In the final part of the article it is described how Harald H?ffding soon after the publication of Hertz’s Principles of Mechanics developed a general theory of analogical reasoning, relying on the ideas of Hertz and Kant.     

Rawls and Research on Cognitively Impaired Patients: A Reply to Maio

In his paper, “The Relevance of Rawls’ Principle of Justice for Research on Cognitively Impaired Patients” (Theoretical Medicine and Bioethics 23 (2002):45–53), Giovanni Maio has developed athought-provoking argument for the permissibility of non-therapeutic research on cognitively impaired patients. Maio argues that his conclusion follows from the acceptance of John Rawls’s principles of justice, specifically, Rawls’s “liberty principle” Maio has misinterpreted Rawls’s “libertyprinciple” – correctly interpreted it does notsupport non-therapeutic research on cognitivelyimpaired patients. Three other ‘Rawlsian’ arguments are suggested by Maio’s discussion –two “self-respect” arguments and a “presumed consent” argument – but none of them are convincing. However, an alternative argument developed from Rawls’s discussion of “justice in health care” in his most recent book, Justice as Fairness: A Restatement, may justify certain kinds of non-therapeutic research on some cognitively impaired patients in special circumstances. We should not expect anything more permissive from a liberal theory of justice. This revised version was published online in June 2006 with corrections to the Cover Date.     

Disputes over Philosophical Views in the First Half of the Twentieth Century and Development of Contemporary Chinese Philosophy

To explore the development of contemporary Chinese philosophy, fundamentally, is to explore the development of Marxist philosophy in contemporary China. The disputes over philosophical views in Chinese academic circles during the first half of the twentieth century have been focused on understanding Marxist philosophy from such aspects as “what kind of philosophy Chinese society needs,” “the relation of philosophy to science,” and “philosophy as an idea to reflect on one’s life.” These explorations have provided us a significant ideological insight into the development of Marxist philosophy and contemporary Chinese philosophy; that is, in contemporary China, Marxist philosophy, as a doctrine of the liberation and all-round development of human beings, exists not only as a kind of “doctrine” or “academy” but also as a kind of widely accepted “xueyuan (academic cultivations)” among people. Translated by Zhao Zhiyi from Jourmal of Jilin University (Social Sciences), 2005:1