The Meaning of Category Theory for 21st Century Philosophy

Among the main concerns of 20th century philosophy was that of the foundations of mathematics. But usually not recognized is the relevance of the choice of a foundational approach to the other main problems of 20th century philosophy, i.e., the logical structure of language, the nature of scientific theories, and the architecture of the mind. The tools used to deal with the difficulties inherent in such problems have largely relied on set theory and its “received view”. There are specific issues, in philosophy of language, epistemology and philosophy of mind, where this dependence turns out to be misleading. The same issues suggest the gain in understanding coming from category theory, which is, therefore, more than just the source of a “non-standard” approach to the foundations of mathematics. But, even so conceived, it is the very notion of what a foundation has to be that is called into question. The philosophical meaning of mathematics is no longer confined to which first principles are assumed and which “ontological” interpretation is given to them in terms of some possibly updated version of logicism, formalism or intuitionism. What is central to any foundational project proper is the role of universal constructions that serve to unify the different branches of mathematics, as already made clear in 1969 by Lawvere. Such universal constructions are best expressed by means of adjoint functors and representability up to isomorphism. In this lies the relevance of a category-theoretic perspective, which leads to wide-ranging consequences. One such is the presence of functorial constraints on the syntax–semantics relationships; another is an intrinsic view of (constructive) logic, as arises in topoi and, subsequently, in more general fibrations. But as soon as theories and their models are described accordingly, a new look at the main problems of 20th century’s philosophy becomes possible. The lack of any satisfactory solution to these problems in a purely logical and set-theoretic setting is the result of too circumscribed an approach, such as a static and punctiform view of objects and their elements, and a misconception of geometry and its historical changes before, during, and after the foundational “crisis”, as if algebraic geometry and synthetic differential geometry – not to mention algebraic topology – were secondary sources for what concerns foundational issues. The objectivity of basic geometrical intuitions also acts against the recent version of structuralism proposed as ‘the’ philosophy of category theory. On the other hand, the need for a consistent and adequate conceptual framework in facing the difficulties met by pre-categorical theories of language and scientific knowledge not only provides the basic concepts of category theory with specific applications but also suggests further directions for their development (e.g., in approaching the foundations of physics or the mathematical models in the cognitive sciences). This ‘virtuous’ circle is by now largely admitted in theoretical computer science; the time is ripe to realise that the same holds for classical topics of philosophy. Text of a talk given at the Workshop and Symposium on the Ramifications of Category Theory, Florence, November 18–22, 2003. For further documentation on the conference, see     

信息哲学与未来中国科技哲学的基础

The research programme of the philosophy of information (PI) proposed in 2002 made it an independent area or discipline in philosophical research. The scientific concept of ‘information’ is formally accepted in philosophical inquiry. Hence a new and tool-driven philosophical discipline of PI with its interdisciplinary nature has been established. Philosophy of information is an ‘orientative’ rather than ‘cognitive’ philosophy. When PI is under consideration in the history of Western philosophy, it can be regarded as a shift of large tradition. There are three large traditions at large, known as Platonic, Kantian and Leibniz-Russellian. In the discussion of the position of the possible worlds, we have modal Platonism and modal realism, but both of the theories are made in the framework of Western philosophy. In this essay, it is argued that possible worlds could be seen as worlds in information, which is then an interpretation of modal information theory (MIT). Our interpretation is made on the basis of Leibniz’s lifelong connection with China, a fact often overlooked by the Western philosophers. Possible world theory was influenced by the Neo-Confucianism flourishing since the Song Dynasty of China, the foundation of which is Yijing. It could be argued that Leibniz’s possible world theory was formulated in respect to the impact of the thoughts reflected in Yijing, in that one of the prominent features is the model-theoretic construction of theories. There are two approaches to theory construction, i.e., axiom-theoretic and model-theoretic. The origin of the former is from ancient Greece and the latter from ancient China. And they determined the different features of theoretic structures between the oriental and occidental traditions of science and technology. The tendency of the future development of science and technology is changing from the axiom-theoretic to the model-theoretic orientation, at least the two approaches being complementary each other. To some extent, this means the retrospective of tradition in the turning point of history, and some of the China’s cultural traditions might become the starting points in formulating the future Chinese philosophy of science and technology.     

The Transcendental Method and (Post-)Empiricist Philosophy of Science

This paper reconsiders the relation between Kantian transcendental reflection (including transcendental idealism) and 20th century philosophy of science. As has been pointed out by Michael Friedman and others, the notion of a “relativized a priori” played a central role in Rudolf Carnap’s, Hans Reichenbach’s and other logical empiricists’ thought. Thus, even though the logical empiricists dispensed with Kantian synthetic a priori judgments, they did maintain a crucial Kantian doctrine, viz., a distinction between the (transcendental) level of establishing norms for empirical inquiry and the (empirical) level of norm-governed inquiry itself. Even though Thomas Kuhn’s theory of scientific revolutions is often taken to be diametrically opposed to the received view of science inherited from logical empiricism, a version of this basically Kantian distinction is preserved in Kuhn’s thought. In this respect, as Friedman has argued, Kuhn is closer to Carnap’s theory of linguistic frameworks than, say, W.V. Quine’s holistic naturalism. Kuhn, indeed, might be described as a “new Kant” in post-empiricist philosophy of science. This article examines, first, the relativization of the Kantian a priori in Reichenbach’s work, arguing that while Reichenbach (after having given up his original Kantianism) criticized “transcendentalism”, he nevertheless retained, in a reinterpreted form, a Kantian-like transcendental method, claiming that the task of philosophy (of science) is to discover and analyze the presuppositions underlying the applicability of conceptual systems. Then, some reflections on Kuhn’s views on realism are offered, and it is suggested that Kuhn (as well as some other influential contributors to the realism debate, such as Hilary Putnam) can be reinterpreted as a (relativized, naturalized) Kantian transcendental idealist. Given the central importance of Kuhnian themes in contemporary philosophy of science, it is no exaggeration to claim that Kantian transcendental inquiry into the constitutive principles of empirical knowledge, and even transcendental idealism (as the framework for such inquiry), still have a crucial role to play in this field and deserve further scrutiny.     

Symposium “Analytical Philosophy and Philosophy of Science Today”, 23.–24. Juli 1995 in Peking, VR China

Report on a symposium “Analytical Philosophy of Science today”, July 23–24, 1995, in Beijing. The symposium demonstrates the actual interest and familiarity of Chinese researchers with Western philosophy of science and especially with analytical philosophizing. Main topics were diagnoses of the actual state of the art, discussion and critique of some classics and classical analytical conceptions, application of analytical thinking on hermeneutical problems, and its possible social function. This revised version was published online in August 2006 with corrections to the Cover Date.     

论马克思的实践——社会生产关系本体论

For a long time, under the influence of traditional Western philosophy, Orthodox interpreters have distorted Marx’s philosophy as the ontology of matter, thereby concealing the essence of Marx’s philosophy, and eliminating the fundamental difference between Marx’s philosophy and traditional philosophy. This paper proposes that Marx’s philosophy is not the ontology of matter, but on the contrary, by examining the ontology of matter, Marx put forward his own ontological theory, i.e., the ontology of the praxis-relations of social production, by which Marx linked the realms of phenomenon and essence, revealing the content and essence of his philosophy. __________ Translated by Kong Hui from Zhexue yanjiu 哲学研究 (Philosophical Researches), 2008, (3): 3–11     

Doing Ontology and Doing Justice: What Feminist Philosophy Can Teach Us About Meta-Metaphysics

Abstract

Feminist philosophy has recently become recognised as a self-standing philosophical sub-discipline. Still, metaphysics has remained largely dismissive of feminist insights. Here I make the case for the value of feminist insights in metaphysics: taking them seriously makes a difference to our ontological theory choice and feminist philosophy can provide helpful methodological tools to regiment ontological theories. My examination goes as follows. Contemporary ontology is not done via conceptual analysis, but via quasi-scientific means. This takes different ontological positions to be competing hypotheses about reality’s fundamental structure that are then assessed with a loose battery of criteria for theory choice. Such criteria make up the constitutive values of ontology (e.g. providing a unified, coherent, non-circular, simple, parsimonious total theory). These values are distinguished from contextual values of a practice: the political and moral values embedded in the social context of inquiry. Although we may be frank about some meta-metaphysical value commitments, bringing in feminist contextual values is viewed as an unacceptable move when thinking about ontological theory choice. This paper then asks: is this move unacceptable? I think not and I aim to motivate this methodological insight here by examining recent work on grounding.     

Emergence and reduction in chemistry: ontological or epistemological concepts?

In this paper I argue that the ontological interpretation of the concepts of reduction and emergence is often misleading in the philosophy of science and should nearly always be eschewed in favor of an epistemological interpretation. As a paradigm case, an example is drawn from the philosophy of chemistry to illustrate the drawbacks of “ontological reduction” and “ontological emergence,” and the virtues of an epistemological interpretation of these concepts.     

Differing ways, <Emphasis Type="Italic">Dao</Emphasis> and <Emphasis Type="Italic">Weg</Emphasis>: Comparative,metaphysical, and methodological considerations in Heidegger’s “Aus einem Gespräch von der Sprache”

This paper critically examines Heidegger’s 1959 dialogue, A Conversation from [von] Language – Between a Japanese and an Inquirer, across three distinct levels: as (1) a cross-cultural comparative exchange, (2) a meta-philosophical/ontological analysis of the fundamental relation between language and thought, and (3) a methodological inquiry into the phenomenology and hermeneutics of conversation. Despite the problematic nature of Heidegger’s explicit comparative engagement, I contend that his questioning of the possibility of “a conversation from house to house” provides a substantial clarification of the meta-philosophical difficulties inherent in comparative and cross-cultural philosophy. At the same time, his thinking with respect to hermeneutics provides a methodological clue to the possibility of and the normative conditions for understanding across such cultural differences.     

理论哲学与实践哲学:孰为第一哲学?

理论哲学与实践哲学涵括了哲学的全部领域。然而,一部西方哲学史实际上只是理论哲学即形而上学的历史,实践哲学则被隐于形而上学的阴影之下,为形而上学所遮蔽。其实,实践哲学作为一个重要的哲学领域,应当是贯穿于西方哲学史的、异于形而上学的一个十分重要而广阔的哲学领域。该     

Can Science Cope with More Than One World? A Cross-Reading of Habermas, Popper, and Searle

The purpose of this article is to critically assess the ‘three-world theory’ as it is presented—with some slight but decisive differences—by Jürgen Habermas and Karl Popper. This theory presents the philosophy of science with a conceptual and material problem, insofar as it claims that science has no single access to all aspects of the world. Although I will try to demonstrate advantages of Popper’s idea of ‘the third world’ of ideas, the shortcomings of his ontological stance become visible from the pragmatic point of view in Habermas’s theory of communicative acts. With regard to the critique that the three-world theory has met in both its pragmatic and ontological versions, I will take a closer look at John Searle’s naturalistic counter-position. By teasing out some problematic implications in his theory of causation, I aim to show that Searle’s approach is, in fact, much closer to Popper’s than he might think. Finally, while condoning Habermas’s distinction between the natural world and the lifeworld, I will opt for a pragmatically differentiated view of ‘the real’, rather than speaking of different worlds.     

Keeping quiet on the ontology of models

Stein once urged us not to confuse the means of representation with that which is being represented. Yet that is precisely what philosophers of science appear to have done at the meta-level when it comes to representing the practice of science. Proponents of the so-called ‘syntactic’ view identify theories as logically closed sets of sentences or propositions and models as idealised interpretations, or ‘theoruncula, as Braithwaite called them. Adherents of the ‘semantic’ approach, on the other hand, are typically characterised as taking them to be families of models that are set-theoretic, according to Suppes and others, or abstract, as Giere has argued. da Costa and French (Science and Partial Truth. OUP, Oxford, 2003) suggested that we should refrain from ontological speculation as to the nature of scientific theories and models and focus on their appropriate representation for various purposes within the philosophy of science. Such an approach allows both linguistic and non-linguistic resources to play their appropriate role (see also French and Saatsi, Philosophy of Science, Proceedings of the 2004 PSA Meeting, 78:548–559, 2006) and can be supported by recent case studies illustrating the heterogeneity of scientific practice. My aim in this paper is to further develop this ‘quietist’ view, and to indicate how it offers a fruitful way forward for the philosophy of science.     

结构实在论评析

The epistemological version of structural realism, proposed by Cao Tianyu, has great influence in the philosophy of science. Syntheses has published a special volume discussing the topic. Cao criticizes anti-realism, as well as the epistemic and ontic versions of structural realism. From the concepts of structure, ontology, and construction, he analyzes the objectivity of scientific theories as having five aspects: construction, historicity, holism, revision, and revolution. This paper systematically analyzes and comments on Cao's structural realism. The author agrees with his criticism of the under-determination thesis, is neutral to his argument against ontological discontinuity, and questions his universal language argument. Translated by Yu Jinlong from Ziran Bianzhengfa Yanjiu 自然辩证法研究 (Studies in Dialectics of Nature), 2006, (11): 34–38     

Dreamless Sleep and the Whole of Human Life: An Ontological Exposition

This paper explores the meaning of dreamless sleep. First, I consider four reasons why we commonly pass over sleep’s ontological significance. Second, I compare and contrast death and sleep to show how each is oriented to questions regarding the possibilities of “being-a-whole.” In the third and final part, I explore the meaning and implications of “being-toward-sleep,” arguing that human existence emerges atop naturally anonymous corporeality (i.e. living being). In sum, I try to show that we can recover an authentic – if somewhat ambiguous – sense of “being-a-whole” only by recognizing the ontological significance of dreamless sleep.     

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.     

中国哲学的认识主体修养论

The epistemology in Chinese philosophy remarkably emphasizes the cultivation of cognitive subjects. According to such epistemology, intelligence arises from benevolence, and thus morality should be valued to gain knowledge. In this way, epistemology is integrated with theories of values and cultivation. The cultivation of cognitive subjects in Chinese philosophy mainly involves a stance, attitudes, ways of thinking and feelings of a cognitive subject. To expatiate and develop the theory of the cultivation of cognitive subjects in Chinese philosophy has much meaning for the construction of a modern Chinese-style Marxist philosophy system. Translated by Huang Deyuan from Zhexue Yanjiu 哲学研究 (Philosophical Research), 2006, (8): 49–54     

Science, Democracy, and the Right to Research

Debates over the politicization of science have led some to claim that scientists have or should have a “right to research.” This article examines the political meaning and implications of the right to research with respect to different historical conceptions of rights. The more common “liberal” view sees rights as protections against social and political interference. The “republican” view, in contrast, conceives rights as claims to civic membership. Building on the republican view of rights, this article conceives the right to research as embedding science more firmly and explicitly within society, rather than sheltering science from society. From this perspective, all citizens should enjoy a general right to free inquiry, but this right to inquiry does not necessarily encompass all scientific research. Because rights are most reliably protected when embedded within democratic culture and institutions, claims for a right to research should be considered in light of how the research in question contributes to democracy. By putting both research and rights in a social context, this article shows that the claim for a right to research is best understood, not as a guarantee for public support of science, but as a way to initiate public deliberation and debate about which sorts of inquiry deserve public support.     

道德与自然:"形上之道"与"形而上学"的本质区别

Both thinkings on Dao in Chinese philosophy and metaphysics in Western philosophy investigate things on a spiritual level that transcends experience, but there are incommensurable differences between them. The objective of “metaphysics” is ontological knowledge about nature from the perspective of epistemological “truth-pursuing”. Western metaphysics is thus a “metaphysics of nature”. Dao in Chinese philosophy, on the other hand, more often manifests itself in “good-pursuing” by means of the internal, experiential pursuit of moral stature and spiritual security. Philosophy of Dao is thus a “metaphysics of ethics”. The cause of this difference can be traced back to the differences between the rational tradition of the West, characterized by the dualism of the subject and the object, and the moral tradition of China, characterized by the integration of man and nature. __________ Translated by Zhang Lin from Lunlixue yanjiu 伦理学研究 (Studies in Ethics), 2007, (4): 62–65     

Data and phenomena in conceptual modelling

The distinction between data and phenomena introduced by Bogen and Woodward (Philosophical Review 97(3):303–352, 1988) was meant to help accounting for scientific practice, especially in relation with scientific theory testing. Their article and the subsequent discussion is primarily viewed as internal to philosophy of science. We shall argue that the data/phenomena distinction can be used much more broadly in modelling processes in philosophy.     

Philosophy as Anti-Religion in the Work of Alain Badiou

The Heideggerian rupture in the history of philosophy in the name of a phenomenological and poetic ontology has provided an opening which many of the key figures in twentieth century continental thought have exploited. However, this opening was marked by Heidegger himself as an ambiguous one, insofar as metaphysics was perhaps integrally ‘onto-theology,’ that is, ultimately continuous with the world-historical capture of the thought of being. This piece argues that the philosophy of Alain Badiou, which departs from the recognition that Heidegger is the ‘last universally recognised philosopher’, provides the means for a radical reconsideration of the philosophy-theology relationship in its specifically Heideggerian form, involving as it does further questions of science and technology, the status of the poem, and the nature of ontological thought as such. We argue that, through the deployment of mathematics as ontology, the Gordian knot of onto-theology and its legion of consequences can be cut, and a new assemblage of many of the key Heideggerian motifs can be put into play: the poem, history, and philosophy itself.

Philosophy of science in Estonia

This paper presents a survey of the philosophy of science in Estonia. Topics covered include the historical background (science at the 17th century Academia Gustaviana, in the 19th century, during the Soviet period) and an overview of the current situation and main areas of research (the problem of demarcation, a critique of the traditional understandings of science, φ-science, classical and non-classical science, the philosophy of chemistry, the problem of induction, the sociology of scientific knowledge, semiotics as a methodology).