The author examines Kant’s transcendental doctrine of space and time in order to find out possible anthropological connotations of the German philosopher’s topology. The analysis allows us to draw the following conclusions: 1) the anthropological features of space and time significantly correct the transcendental understanding of space and time as forms of sensual intuition; 2) the anthropological connotations of the forms of space and time make it impossible to have both noumenal, intellectual intuition of things and intuition based (...) on a different topology, on configurations of the world that are different from those familiar to humans; 3) Kant’s achievement is his work «Metaphysical Foundations of Natural Science» (1786), which demonstrates the effectiveness of the transcendental method, in particular transcendental aesthetics, in substantiating the natural sciences (physics) of the time, which made it possible to prove the close connection of the natural sciences with the transcendental conditions of experience. (shrink)

Immanuel Kant's Metaphysical Foundations of Natural Science (1786) provides metaphysical foundations for the application of mathematics to empirically given nature. The application that Kant primarily has in mind is that achieved in Isaac Newton's Principia (1687). Thus, Kant's first chapter, the Phoronomy, concerns the mathematization of speed or velocity, and his fourth chapter, the Phenomenology, concerns the empirical application of the Newtonian notions of true or absolute space, time, and motion. This paper concentrates on Kant's second (...) and third chapters—the Dynamics and the Mechanics, respectively—and argues that they are best read as providing a transcendental explanation of the conditions for the possibility of applying the (mathematical) concept of quantity of matter to experience. Kant again has in mind the empirical measures of this quantity that Newton fashions in the Principia, and he aims to make clear, in particular, how Newton achieves a universal measure for all bodies whatsoever by projecting the static quantity of terrestrial weight into the heavens by means of the theory of universal gravitation. Kant is not attempting to prove a priori what Newton has established empirically but, rather, to clarify the character of Newton's mathematization by building Newton's empirical measures into the very concept of matter that is articulated in the Metaphysical Foundations. (shrink)

It is a philosophical naiveté to believe that the object of science is some ready-made world out there that the scientist, free of any preconceptions, simply stumbles upon. Of course, there is a world out there, given to us through the senses, but that must be intentionally elaborated to become a world for us and a possible object of scientific inquiry. The intentional constitution of the world of science supports and “justifies” a priori conceptions about the empirical world, (...) even those of a logical nature, that are, then, properly transcendental rather than metaphysical. My goal here is to investigate what these presuppositions are and on what they are based. (shrink)

In 1792 and 1798 Kant noticed two basic problems with hisMetaphysical Foundations of Natural Science (MAdN) which opened a crucial gap in the Critical system as a whole. Why is theMAdN so important? I show that the Analogies of Experience form an integrated proof of transeunt causality. This is central to Kant's answer to Hume. This proof requires explicating the empirical concept of matter as the moveable in space, it requires the specifically metaphysical principle that every physical (...) event has an external cause, and it requires a metaphysical principle regarding the individuation of spatio-temporal things. These three doctrines are not defended in the firstCritique, but only in theMAdN. Kant's transcendental analysis of the conditions of experience thus requires the special metaphysics of theMAdN. This marks an important shift in Kant's view of the metaphysical basis of the transcendental philosophy. (shrink)

The theory of space-time developed in Kant’s Critique of Pure Reason and his Metaphysical Foundations of Natural Science is connected to Leonhard Euler’s proof of invariance under Galilean transformations in the “On Motion in General” of the latter’s 1736 Analytical Mechanics. It is argued that Kant, by using the Principle of Relativity that is the output of Euler’s proof as an input to his own proof of the kinematic parallelogram law, makes essential use of absolute simultaneity. This (...) is why, in the Transcendental Aesthetic, he observes that “our theory of time explains as much a priori knowledge as the general theory of motion displays.” In conclusion, it is shown that the same proof-method, under a different definition of simultaneity, leads to the parallelogram law of the “Kinematic Part” of Einstein’s 1905 “On the Electrodynamics of Moving Bodies”. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Argumentative Structure of Kant’s Metaphysical Foundations Of Natural ScienceEric Watkinsone of kant’s most fundamental aims is to justify Newtonian science. However, providing a detailed explanation of even the main structure of his argument (not to mention the specific arguments that fill out this structure) is not a trivial enterprise. While it is clear that Kant’s Critique of Pure Reason (1781), his Metaphysical Foundations of (...) Natural Science (1786), and his unpublished (and incomplete) Opus postumum should in some way constitute the core of this justification, it is less clear how each of these works does so in detail. In this paper I shall first argue that the standard view of the relationship between the Critique of Pure Reason and the Metaphysical Foundations of Natural Science (hereafter simply Metaphysical Foundations) is mistaken. I shall then present my own interpretation of how the Metaphysical Foundations contributes to the justification of Newtonian science. Finally, I shall conclude by considering an important interpretation of the argument of the Metaphysical Foundations developed by Michael Friedman. However, it is first necessary to present briefly Kant’s conception of science (in particular what conditions a body of knowledge must satisfy for Kant in order to be considered science proper) as well as Kant’s own understanding of the relevant differences between his projects in the first Critique, the Metaphysical Foundations, and the Opus postumum.Kant’s conception of science is rather strict if measured by contemporary standards. For in the preface to the Metaphysical Foundations Kant establishes three substantive conditions that a body of knowledge must satisfy in order to be considered science proper.1 (1) It must not consist in empirical principles, [End Page 567] but rather must be obtained solely from pure, a priori principles;2 (2) It must be apodictically certain;3 (3)4 It must be a systematically ordered whole (which means that its various propositions must be related as, for example, antecedents and consequents).5 After stating these conditions, Kant then argues that all natural science proper requires a pure part upon which its apodictic certainty is based. In other words, satisfaction of the first condition immediately implies satisfaction of the second condition as well.6 Accordingly, these three conditions (and the first one in particular) imply that natural science proper requires (or rather presupposes) a justification by something distinct from it that Kant calls a metaphysics of nature.7 But what exactly does a metaphysics of nature encompass? Kant distinguishes two different parts of the metaphysics of nature: a transcendental part and a special part. A metaphysics of nature [End Page 568] is transcendental insofar as it concerns “the laws that make the concept of nature in general possible, even without relation to any determinate object of experience, and [insofar as it is] thus indeterminate with respect to the nature of this or that thing in the sensible world,” whereas a metaphysics of nature is special to the extent that “it is concerned with a special nature of this or that kind of thing of which an empirical concept is given, but so that except for what lies in this concept no other empirical principle is used for knowledge thereof.”8 In short, a transcendental metaphysics, revealing how experience in general is possible, is not supposed to presuppose an empirical concept, whereas a special metaphysics does make such an assumption insofar as it is concerned with the special natures of things.How do the three works cited above relate to Kant’s distinction between a transcendental and a special metaphysics of nature? In the preface to the Metaphysical Foundations Kant clearly indicates that he intends the Metaphysical Foundations to constitute the special metaphysics of nature. Although he does not explicitly refer to the first Critique in the preface, it is also relatively clear that he sees it (or at least the ‘System of Pure Reason’ that Kant foresees as following upon it and as incorporating its fundamental results)9 as constituting [End Page 569] the transcendental part of a metaphysics of nature.10 The Principles of Pure Understanding (‘Grundsätze des reinen Verstandes’) in the Transcendental Analytic argue for what could naturally be described as “laws... (shrink)

This paper deals with the interpretation of the Mechanics chapter of Kant’s Metaphysical Foundations of Natural Science. It is aimed at clarifying the procedure Kant invokes for the transcendental determination of the quantity of matter in mechanical respect. Kant’s intention is to ground mass measurement on the moving force that matter possesses by virtue of its motion, and that moving bodies display by setting other bodies in motion. An important issue in this context concerns the role (...) of gravitation as compared to mechanical processes in the narrow sense of “pressure and impact”. (shrink)

E. J. Lowe, a prominent figure in contemporary metaphysics, sets out and defends his theory of what there is. His four-category ontology is a metaphysical system which recognizes four fundamental categories of beings: substantial and non-substantial particulars and substantial and non-substantial universals. Lowe argues that this system has an explanatory power which is unrivalled by more parsimonious theories and that this counts decisively in its favour. He shows that it provides a powerful explanatory framework for a unified account of causation, (...) dispositions, natural laws, natural necessity and many other related matters, thus constituting a full metaphysical foundation for natural science. (shrink)

The thesis of this work may be summarized in the words of its author: "... the Social Sciences, which heretofore have wavered between literature and an impossible positivism after the fashion of the Natural Sciences, could establish their own scientific statute if, aided by special techniques, they began discovering their hypotheses and interpreting their observations in the light of the partial overlapping of objective man and subjective man within the idea of Universal Man possessed by all". Parain makes use (...) of the Cartesian idea of the Universal Man in her efforts to provide a solid foundation for the Human Sciences. In her dissatisfaction with procedures basing the human facts solely on scientific method, she frankly demands a framework that is truly ontological. She is confronted here with the same difficulties experienced by all those trying to define as facts our knowledge of self and our knowledge of other minds. Her solution, as in the above quote, constitutes a compromise between subjectivity and objectivity, between the lived and the reflective, between a postulated universal and an interpretative schema. The author is quite conscious of the special difficulty presented by passions and ideological biases in the definition of human facts. Here her attitude is resignation with the inevitable: an empirical observer will never quite do as a transcendental observer. In spite of this the author maintains and illustrates that we know a great deal more about man than we might suspect.—A. M. (shrink)

The goal of the present volume is to discuss the notion of a 'conceptual framework' or 'conceptual scheme', which has been dominating much work in the analysis and justification of knowledge in recent years. More specifi cally, this volume is designed to clarify the contrast between two competing approaches in the area of problems indicated by this notion: On the one hand, we have the conviction, underlying much present-day work in the philosophy of science, that the best we can (...) hope for in the justifi cation of empirical knowledge is to reconstruct the conceptual means actually employed by science, and to develop suitable models for analyzing conceptual change involved in the progress of science. This view involves the assumption that we should stop taking foundational questions of epistemology seriously and discard once and for all the quest for uncontrovertible truth. The result ing program of justifying epistemic claims by subsequently describing patterns of inferentially connected concepts as they are at work in actual science is closely connected with the idea of naturalizing epistemology, with concep tual relativism, and with a pragmatic interpretation of knowledge. On the other hand, recent epistemology tends to claim that no subsequent reconstruction of actually employed conceptual frameworks is sufficient for providing epistemic justification for our beliefs about the world. This second claim tries to resist the naturalistic and pragmatic approach to epistemology and insists on taking the epistemological sceptic seriously. (shrink)

In his Metaphysical Foundations of Natural Science, Kant accounts for the possibility of an acting-at-a-distance gravitational force, demonstrates the infinite divisibility of matter, and derives analogues to Newtonian laws of motion. The work is his major statement in philosophy of science, and was especially influential in German-speaking countries in the nineteenth century. However, this complex text has not received the scholarly attention it deserves. The chapters of this Critical Guide clarify the accounts of matter, motion, the (...) mathematization of nature, space, and natural laws exhibited in the Metaphysical Foundations; elucidate the relationship between its metaphysics of nature and Kant's critical philosophy; and describe the historical context for Kant's account of natural science. The volume will be an invaluable resource for understanding one of Kant's most difficult works, and will set the agenda for future scholarship on Kant's philosophy of science. (shrink)

This thesis presents an interpretation of Immanuel Kant’s theoretical philosophy in which the notion of ‘force’ is of central importance. My analysis encompasses the full span of Kant’s theoretical and natural-scientific writings, from the first publication to the drafts of an unfinished final work. With a close focus on Kant’s texts, I explicate their explicit references to force, providing a narrative of the philosophical role and significance of force in the various periods of the Kantian oeuvre. This represents an (...) intervention into Kant scholarship that seeks to correct the marginal role accorded to ‘force’. The central problem that emerges through the thesis’ attention to force is: how to interpret the simultaneous separation and connection of physical and psychological forces in Kant’s mature, critical philosophy? Physical and psychological forces are strictly separated, and yet a common, ontological conception of force underpins these two domains. I show that this issue has its basis in a tradition of philosophical ‘dynamics’ stemming from Leibniz, which is examined in part one. The three parts of the thesis proceed chronologically through the Kantian oeuvre. Part one reconstructs the historical context of Leibnizian and Newtonian conceptions of force, and presents a narrative of the employment of force in Kant’s pre-critical writings, in their relation to the broad problematic of Leibniz’s dynamics. Part two explores the account of physical and psychological forces, and the common, ontological notion of force, in the major critical-period discussions. Part three presents the late works, namely the third Critique and the Opus postumum, as a ‘philosophy of force’, in which force, with all its necessary ambiguities, plays central roles in Kant’s late systematising endeavours. I conclude that the perspective of this thesis makes possible a new understanding of the nature and unity of Kant’s philosophical project. (shrink)

In the mid-1760s, Johann Heinrich Lambert wrote a letter to Kant who offered cooperation with a view to reforming metaphysics. Based on the short correspondence between the two philosophers, it can be shown that this cooperation could never really come about. Nevertheless the thesis was sometimes put forward in research that Lambert had a defining influence on Kant’s Metaphysical Foundations of Natural Science, also, and above all, with regard to the Newton-critical moments of this natur­al theory. However, (...) this thesis can only be confirmed in relation to individual theorems, such as the relationship between attraction and repulsion force, even though the reasons for Lambert and Kant’s deviation from Newton’s theory of gravity also differ. For in its main features the transcendental metaphysics of Kant’s nature is substantially different from the mathematical methodology of Lambert’s theory of nature. In addition, Lambert stuck throughout his life to a theonomous natural teleology in the succession of Wolff, which was fundamentally made impossible by the Critique of Pure Reason: because the wise “intention of the creator”, which Lambert’s empirical-rationalistic cosmology could not and did not want to do without, could no longer be referred to in a rational context according to the Critique of Pure Reason. Even if Lambert certainly had moments of the Kantian theory of matter or — as Kant himself admitted — elements of the spatial theory of the first Critique, there is no way from his mathematisation of metaphysics and his natural teleology to the fundamental innovation of the Metaphysical Foundations. (shrink)

Ott (2009) identifies two kinds of philosophical theories about laws: top-down, and bottom-up. An influential top-down reading, exemplified by Ernst Cassirer, emphasized the ‘mere form of law’. Recent bottom-up accounts emphasize the mind-independent natures of objects as the basis of laws of nature. Stang and Pollok in turn focus on the transcendental idealist elements of Kant’s theory of matter, which leads to the question: is the essence of Kantian matter that it obeys the form of law? I argue that (...) Kant has an independent theory of matter in the Metaphysical Foundations of Natural Science, one that gives what Kant himself calls a ‘real definition’ of matter as a theory-independent (if not mind-independent) entity. I argue that this matter theory underpins physical arguments about inertia and impenetrability, which resemble Einstein’s arguments about the unification of fields in general relativity. (shrink)

Kant was centrally concerned with issues in the philosophy of natural science throughout his career. The Metaphysical Foundations of Natural Science presents his most mature reflections on these themes in the context of both his 'critical' philosophy, presented in the Critique of Pure Reason, and the natural science of his time. This volume presents a new translation, by Michael Friedman, which is especially clear and accurate. There are explanatory notes indicating some of the (...) main connections between the argument of the Metaphysical Foundations and the first Critique - as well as parallel connections to Newton's Principia. The volume is completed by an historical and philosophical introduction and a guide to further reading. (shrink)

Through an exploration of theoretical physics, this paper suggests the need for regrounding natural science in phenomenological philosophy. To begin, the philosophical roots of the prevailing scientific paradigm are traced to the thinking of Plato, Descartes, and Newton. The crisis in modern science is then investigated, tracking developments in physics, science's premier discipline. Einsteinian special relativity is interpreted as a response to the threat of discontinuity implied by the Michelson-Morley experiment, a challenge to classical objectivism that (...) Einstein sought to counteract. We see that Einstein's efforts to banish discontinuity ultimately fall into the “black hole” predicted in his general theory of relativity. The unavoidable discontinuity that haunts Einstein's theory is also central to quantum mechanics. Here too the attempt has been made to manage discontinuity, only to have this strategy thwarted in the end by the intractable problem of quantum gravity. The irrepressible discontinuity manifested in the phenomena of modern physics proves to be linked to a merging of subject and object that flies in the face of Cartesian philosophy. To accommodate these radically non-classical phenomena, a new philosophical foundation is called for: phenomenology. Phenomenological philosophy is elaborated through Merleau-Ponty's concept of depth and is then brought into focus for use in theoretical physics via qualitative work with topology and hypercomplex numbers. In the final part of this paper, a detailed summary is offered of the specific application of topological phenomenology to quantum gravity that was systematically articulated in The Self-Evolving Cosmos (Rosen 2008a). (shrink)

Natural Sciences and the Social Sciences contains a series of explorations of the different ways in which the social sciences have interacted with the natural sciences. Usually, such interactions are considered to go only `one way': from the natural to the social sciences. But there are several important essays in this volume which show how developments in the social sciences have affected the natural sciences - even the `hard' science of physics. Other essays deal with (...) various types of interaction since the Scientific Revolution. In his general introductory chapter, Cohen sets some general themes concerning analogies and homologies and the use of metaphors, drawing specific examples from the use of concepts of physics by marginalist economists and of developments in the life sciences by organismic sociologists. The remaining chapters, which explore the different ways in which the social sciences and the natural sciences have actually interacted, are written by leaders in the field of history of science, drawn from a wide range of countries and disciplines. The book will be of great interest to all historians of science, philosophers interested in questions of methodology, economists and sociologists, and all social scientists concerned with the history of their subject and its foundations. (shrink)

It has frequently been argued that there must be a necessary and important difference between the methods of the natural and social sciences, or that an empirical method in social science must be supplemented by or is inferior to an interpretative method. Often these claims have been supported by arguments using premises derived from the early Heidegger or the late Wittgenstein. These arguments, in turn, tend either to be transcendental in form or to follow a hermeneutic argument (...) strategy. This paper argues that neither of these types of argument, based on Heideggerian or Wittgensteinian premises, can be used successfully to show an important or essential difference between natural and social science. It does this by examining arguments proposed by Peter Winch and Hubert Dreyfus, showing how they are fallacious and misconstrue the import of the premises upon which they are based, and generalizing these objections to the transcendental and hermeneutic styles of argument in this field as such. The paper concludes with a consideration of Richard Rorty's Philosophy and the Mirror of Nature, which reaches conclusions in this area which are similar to those of this paper but which, it is argued, misconstrues the character of its own argument. (shrink)

Transcendental epistemology is an inquiry into conditions of human knowledge which reflect the structure of the human cognitive apparatus. The dependence thesis is the thesis that a proper investigation of such conditions must lean in important respects on the deliverances of science. I argue that Kant is right to object to the dependence thesis, but that the best objections to this thesis lead to the conclusion that the conditions of knowledge which Kant identifies are not, in any interesting (...) sense, a relection of the structure of the human cognitive apparatus. (shrink)

At various times in his "Pre-critical" and "Critical" periods, Kant presented an argument about the nature of space that has come to be called the "Incongruous Counterparts" argument. First presented in his 1768 essay, Concerning the Ultimate Foundation for the Differentiation of Regions in Space, the argument holds that two objects, such as two human hands, might be exact counterparts, that is, identical in "size and proportion and... the situation of the parts relative to each other," and yet might be (...) still "incongruent," that there is no continuous rigid motion which brings them into coincidence in space; or, that they are, though counterparts, incongruently left and right hands. This argument appears in 1768, in the Dissertation of 1770, the Prolegomena of 1783 and the Metaphysical Foundations of Natural Science in 1786. Unfortunately, while the details of the argument are virtually the same, the conclusions are not. Kant seems to have claimed that the argument shows: that a Leibnizean, relational theory of space was wrong; that a theory of absolute space was correct; that space was a pure form of sensibility and that space was transcendentally ideal, i.e., that space was not and could not be a feature of things in themselves. In the secondary literature, commentators who have dealt with this issue have simply noted the odd history of the argument and lamented it. Buroker's ambitious and interesting thesis in this book is not only that Kant's use of the argument is consistent and interconnected, but that the argument can be seen as the "origin" of Kant's idealism. She argues both of these points by arguing, in the great majority of cases, more for a logical than an actual or historical connection among the conclusions Kant drew from the argument; i.e., that she can illuminate the reasoning that led Kant from a rejection of Leibniz's relational view to his radical separation between sensibility and understanding, and then to his view that things in themselves are both unknowable and non-spatial. (shrink)

In this paper I contrast Husserlian transcendental eidetic phenomenology with some other views of what phenomenology is supposed to be and argue that, as eidetic, it does not admit of being ‘naturalized’ in accordance with standard accounts of naturalization. The paper indicates what some of the eidetic results in phenomenology are and it links these to the employment of reason in philosophical investigation, as distinct from introspection, emotion or empirical observation. Eidetic phenomenology, unlike cognitive science, should issue in (...) a ‘logic’ of consciousness. Instead of being derived from empirical investigations its results should consist of high-level background conditions that are necessary for cognitive science to be possible in the first place. To negate these conditions is to be faced with certain types of ‘material’ contradictions. Some analogies with science – mathematical science – are used to develop the argument. (shrink)

Mathematical logic is a branch of mathematics that takes axiom systems and mathematical proofs as its objects of study. This book shows how it can also provide a foundation for the development of information science and technology. The first five chapters systematically present the core topics of classical mathematical logic, including the syntax and models of first-order languages, formal inference systems, computability and representability, and Gödel’s theorems. The last five chapters present extensions and developments of classical mathematical logic, particularly (...) the concepts of version sequences of formal theories and their limits, the system of revision calculus, proschemes (formal descriptions of proof methods and strategies) and their properties, and the theory of inductive inference. All of these themes contribute to a formal theory of axiomatization and its application to the process of developing information technology and scientific theories. The book also describes the paradigm of three kinds of language environments for theories and it presents the basic properties required of a meta-language environment. Finally, the book brings these themes together by describing a workflow for scientific research in the information era in which formal methods, interactive software and human invention are all used to their advantage. The second edition of the book includes major revisions on the proof of the completeness theorem of the Gentzen system and new contents on the logic of scientific discovery, R-calculus without cut, and the operational semantics of program debugging. This book represents a valuable reference for graduate and undergraduate students and researchers in mathematics, information science and technology, and other relevant areas of natural sciences. Its first five chapters serve as an undergraduate text in mathematical logic and the last five chapters are addressed to graduate students in relevant disciplines. (shrink)

Although Wittgenstein’s influence on logic and foundations of mathematics is well recognized, nonetheless, his legacy concerning other sciences is much less elucidated, and in this article we aim at shedding new light on physics, artificial intelligence, and cognitive science from a Wittgensteinian perspective. We focus upon three issues amongst other things: the Chosmky versus Norvig debate on the nature of language; a Neo-Kantian parallelism between Bohr’s philosophy of physics and Hilbert’s philosophy of mathematics; the relationships between cognitive contextuality (...) and physical contextuality as shown by recent Bell-type results. The Chosmky versus Norvig debate may be seen as a battle between Wittgenstein’s earlier and later conceptions of meaning, i.e., picture theory and use theory. From a Wittgensteinian point of view, quantum physics may be seen as a physical version of the Linguistic Turn. The parallelism between Bohr’s philosophy of classical concepts and Hilbert’s philosophy of finitism builds upon transcendental philosophy in the Kantian tradition, both Bohr and Hilbert having been influenced by Neo-Kantian thinkers, such as Hertz, whose sign theory is actually a common root of Wittgenstein’s picture theory and Hilbert’s axiomatics. Wittgenstein is considered a root of contextualism in contemporary philosophy. Contextuality has different manifestations in physics and cognitive science, and contextuality studies across the sciences are rapidly developing in cutting-edge research. We elucidate both analogies and disanalogies between contextuality of reality and contextuality of reason in terms of the nature of probabilities involved. In passing, we also give a reformulation of Penrose’s quantum mind thesis. (shrink)

Although Wittgenstein’s influence on logic and foundations of mathematics is well recognized, nonetheless, his legacy concerning other sciences is much less elucidated, and in this article we aim at shedding new light on physics, artificial intelligence, and cognitive science from a Wittgensteinian perspective. We focus upon three issues amongst other things: the Chosmky versus Norvig debate on the nature of language; a Neo-Kantian parallelism between Bohr’s philosophy of physics and Hilbert’s philosophy of mathematics; the relationships between cognitive contextuality (...) and physical contextuality as shown by recent Bell-type results. The Chosmky versus Norvig debate may be seen as a battle between Wittgenstein’s earlier and later conceptions of meaning, i.e., picture theory and use theory. From a Wittgensteinian point of view, quantum physics may be seen as a physical version of the Linguistic Turn. The parallelism between Bohr’s philosophy of classical concepts and Hilbert’s philosophy of finitism builds upon transcendental philosophy in the Kantian tradition, both Bohr and Hilbert having been influenced by Neo-Kantian thinkers, such as Hertz, whose sign theory is actually a common root of Wittgenstein’s picture theory and Hilbert’s axiomatics. Wittgenstein is considered a root of contextualism in contemporary philosophy. Contextuality has different manifestations in physics and cognitive science, and contextuality studies across the sciences are rapidly developing in cutting-edge research. We elucidate both analogies and disanalogies between contextuality of reality and contextuality of reason in terms of the nature of probabilities involved. In passing, we also give a reformulation of Penrose’s quantum mind thesis. (shrink)

Wittgenstein’s philosophy of mathematics is often devalued due to its peculiar features, especially its radical departure from any of standard positions in foundations of mathematics, such as logicism, intuitionism, and formalism. We first contrast Wittgenstein’s finitism with Hilbert’s finitism, arguing that Wittgenstein’s is perspicuous or surveyable finitism whereas Hilbert’s is transcendental finitism. We then further elucidate Wittgenstein’s philosophy by explicating his natural history view of logic and mathematics, which is tightly linked with the so-called rule-following problem and (...) Kripkenstein’s paradox, yielding vital implications to the nature of mathematical understanding, and to the nature of the certainty and objectivity of mathematical truth. Since the incompleteness theorems, foundations of mathematics have mostly lost their philosophical driving force, and anti-foundationalism has become prevalent and pervasive. Yet new foundations have nevertheless emerged and come into the scene, namely categorical foundations. We articulate the foundational significance of category theory by explicating three forms of foundations, i.e., global foundations, local foundations, and conceptual foundations. And we explore the possibility of categorical unified science qua pluralistic unified science, arguing for the categorical unity of science on both mathematical and philosophical grounds. We then turn to an issue in conceptual foundations of mathematics, namely the nature of the concept of space. We elucidate Wittgenstein’s intensional conception of space in relation to Brouwer’s theory of space continua and to the modern conception of space as point-free structure in category theory and algebraic geometry. We finally give a bird’s-eye view of mathematical philosophy from a Wittgensteinian perspective, and further sheds new light on Wittgenstein’s constructive structuralism and his view of incompleteness and contradictions in mathematics. (shrink)

This volume is the first ever English translation of Kant's last major work, the so-called Opus Postumum, a work Kant himself described as his 'chef d'oeuvre' and as the keystone of his entire philosophical system. It occupied him for more than the last decade of his life. Begun with the intention of providing a 'transition from the metaphysical foundations of natural science to physics,' Kant's reflections take him far beyond the problem he initially set out to solve. (...) In fact, he reassesses a whole series of fundamental topics of transcendental philosophy: the thing in itself, the nature of space and time, the concept of the self and its agency, the idea of God, and the unity of theoretical and practical reason. Though never completed, the text reaches a logical albeit not fully developed, conclusion. (shrink)

Any attempt to assess the validity of Kant’s basic philosophical approach to the problems of physics must begin, not with a comprehensive metaphysical foundation of natural science but, rather, with the metaphysical foundation of the science directed to the primordial basis of nature, viz., the science of ponderomotive nature. The concrete aggregate of its constructive concerns is the aggregate of momenta. The synthesis of this aggregate is subject to a dynamic reciprocity of nature under the two (...) radical aspects of reality and unreality – factors or “aspects” reflected in cognition as subjective activity and its immediate objective correlate. The synthetic enterprise culminates in the recognition of a schematic event-unity, which is at the same time the basis of the possibility of emergence from the preceding sphere of ponderomotive nature into a higher-synthetic sphere of concrete, materio-formal nature. (shrink)

The concept of an operator is used in a variety of practical and theoretical areas. Operators, as both conceptual and physical entities, are found throughout the world as subsystems in nature, the human mind, and the manmade world. Operators, and what they operate, i.e., their substrates, targets, or operands, have a wide variety of forms, functions, and properties. Operators have explicit philosophical significance. On the one hand, they represent important ontological issues of reality. On the other hand, epistemological operators form (...) the basic mechanism of cognition. At the same time, there is no unified theory of the nature and functions of operators. In this work, we elaborate a detailed analysis of operators, which range from the most abstract formal structures and symbols in mathematics and logic to real entities, human and machine, and are responsible for effecting changes at both the individual and collective human levels. Our goal is to find what is common in physical objects called operators and abstract mathematical structures, with the name operator providing foundations for building a unified but flexible theory of operators. The paper concludes with some reflections on functionalism and other philosophical aspects of the ‘operation’ of operators. (shrink)

In this paper, I argue that in spite of suggestions to the contrary, Merleau-Ponty defends a positive account of the kind of abstract thought involved in mathematics and natural science. More specifically, drawing on both the Phenomenology of Perception and his later writings, I show that, for Merleau-Ponty, abstract thought and perception stand in the two-way relation of “foundation,” according to which abstract thought makes what we perceive explicit and determinate, and what we perceive is made to appear (...) by abstract thought. I claim that, on Merleau-Ponty's view, although this process can sometimes lead to falsification, it can also be carried out in such a manner that allows mathematics and natural science to articulate what we perceive in a way that is non-distortive and in keeping with the demands of perception itself. (shrink)

This study aims to understand scientific inference for the evolutionary procedure of Continental Drift based on abductive inference, which is important for creative inference and scientific discovery during problem solving. We present the following two research problems: (1) we suggest a scientific inference procedure as well as various strategies and a criterion for choosing hypotheses over other competing or previous hypotheses; aspects of this procedure include puzzling observation, abduction, retroduction, updating, deduction, induction, and recycle; and (2) we analyze the “theory (...) of continental drift” discovery, called the Earth science revolution, using our multistage inference procedure. Wegener’s Continental Drift hypothesis had an impact comparable to the revolution caused by Darwin’s theory of evolution in biology. Finally, the suggested inquiry inference model can provide us with a more consistent view of science and promote a deeper understanding of scientific concepts. (shrink)

This book offers a systematic interpretation of the relation between natural science and metaphysics in Husserl's phenomenology. It shows that Husserl's account of scientific knowledge is a radical alternative to established methods and frameworks in contemporary philosophy of science. The author's interpretation of Husserl's philosophy offers a critical reconstruction of the historical context from which his phenomenological approach developed, as well as new interpretations of key Husserlian concepts such as metaphysics, idealization, life-world, objectivism, crisis of the sciences, (...) and historicity. The development of Husserl's philosophical project is marked by the tension between natural science and transcendental phenomenology. While natural science provides a paradigmatic case of the way in which transcendental phenomenology, ontology, empirical science, and metaphysics can be articulated, it has also been the object of philosophical misunderstandings that have determined the current cultural and philosophical crisis. This book demonstrates the ways in which Husserl shows that our conceptions of philosophy and of nature are inseparable. Philosophy's Nature will appeal to scholars and advanced students who are interested in Husserl and the relations between phenomenology, natural science, and metaphysics. (shrink)

This volume is the first ever English translation of Kant's last major work, the so-called Opus Postumum, a work Kant himself described as his 'chef d'oeuvre' and as the keystone of his entire philosophical system. It occupied him for more than the last decade of his life. Begun with the intention of providing a 'transition from the metaphysical foundations of natural science to physics,' Kant's reflections take him far beyond the problem he initially set out to solve. (...) In fact, he reassesses a whole series of fundamental topics of transcendental philosophy: the thing in itself, the nature of space and time, the concept of the self and its agency, the idea of God, and the unity of theoretical and practical reason. Though never completed, the text reaches a logical albeit not fully developed, conclusion. (shrink)

The Fifth European Conference on Science and Theology, held in Freising and Munich, Germany, 1994, exemplified the growing worldwide interest in science-religion dialogue. The keys to this dialogue care the emergmg linkages and interfaces among all the sciences, on the one hand, and the enigmatic complexity of questions concerning the origin, nature, and destiny of man and the universe, on the other. Both increasingly address issues of meaning values, and ultimate causes, which lie well beyond the ken of (...) science as presently understood. Underlying the current science-religion dialogue is a sense of awe, humility, and wonder in the face of incomplete knowledge seeking understanding and transcendental faith seeking rational foundations. (shrink)

Kant famously distinguishes between the methods of mathematics and of metaphysics, holding that metaphysicians err when they avail themselves of the mathematical method. Nonetheless, in the Metaphysical Foundations of Natural Science, he insists that mathematics and metaphysics must jointly ground ‘proper natural science’. This article examines the distinctive contributions and unity of mathematics and metaphysics to the foundations of the science of body. I argue that the two are distinct insofar as they involve (...) distinctive sorts of grounding relations – mathematics pertains to formal grounding, while metaphysics concerns material grounding – while they are unified insofar as they treat motion, the fundamental determination of the science of body. (shrink)

The paper is a critical notice of Margaret Osler, "Divine Will and the Mechanical Philosophy". Criticism focuses on Osler's claim that theological voluntarism and intellectualism and associated ideas about the necessity of physical laws and the certainty of scientific beliefs provide an underlying framework for understanding Gassendi's and Descartes's natural philosophies.

In the opening sections of his Foundations of Natural Right, Fichte argues that mutual recognition is a condition for the possibility of self-consciousness. However, the argument turns on the apparently unconvincing claim that, in the context of transcendental philosophy, conceptions of the subject as an isolated individual give rise to a vicious circle the resolution of which requires the introduction of a second rational being to ‘summon’ the first. In this essay, my aim is to present a (...) revised account of the opening arguments on which they are more convincing. In particular, I argue that the problem of a circle is genuine and may be seen to result from a relation of mutual dependence between agency and cognition which ensures that for an exercise of either capacity to take place, an exercise of the other would have already had to have taken place with the result that neither can occur. Moreover, the solution is successful. The summons prevents us from being driven around the circle once more because it is a ‘synthesis’ that reconciles the constraint to which I am subject as a cognizer of independently given objects and my freedom as a self-determining subject. (shrink)

Consider your right hand and a mirror image duplicate of it. Kant calls such pairs incongruent counterparts. According to him they have the following puzzling features. The relation and situation of the parts of your hand with respect to one another are not sufficient to distinguish it from its mirror duplicate. Nevertheless, there is a spatial difference between the two. Turn and twist them how you will, you cannot make one of them occupy the exact boundaries now occupied by the (...) other. In his 1768 paper, ‘Concerning the Ultimate Foundations of the Differentiation of Regions in Space’, Kant uses these claims to argue against relational accounts of space and goes on to argue that the difference between incongruent counterparts depends on a relation to absolute space as a whole. In his 1770 Inaugural Dissertation he argued that this difference could not be captured by concepts alone but required appeal to intuition. In the Prolegomena (1783) and again in the Metaphysical Foundations of Natural Science (1786) Kant appealed to these puzzling features of incongruent counterparts to support his transcendental idealism about space. (shrink)

Kant's Metaphysical Foundations of Natural Science is one of the most difficult but also most important of Kant's works. Published in 1786 between the first and second editions of the Critique of Pure Reason, the Metaphysical Foundations occupies a central place in the development of Kant's philosophy, but has so far attracted relatively little attention compared with other works of Kant's critical period. Michael Friedman's book develops a new and complete reading of this work and reconstructs (...) Kant's main argument clearly and in great detail, explaining its relationship to both Newton's Principia and eighteenth-century scientific thinkers such as Euler and Lambert. By situating Kant's text relative to his pre-critical writings on metaphysics and natural philosophy and, in particular, to the changes Kant made in the second edition of the Critique, Friedman articulates a radically new perspective on the meaning and development of the critical philosophy as a whole. (shrink)