Poincaré's philosophy of mathematics

The primary concern of this thesis is to investigate the explicit philosophy of mathematics in the work of Henri Poincare. In particular, I argue that there is a well-founded doctrine which grounds both Poincare's negative thesis, which is based on constructivist sentiments, and his positive thesis, via which he retains a classical conception of the mathematical continuum. The doctrine which does so is one which is founded on the Kantian theory of synthetic a priori intuition. I begin, therefore, by outlining Kant's theory of the synthetic a priori, especially as it applies to mathematics. Then, in the main body of the thesis, I explain how the various central aspects of Poincare's philosophy of mathematics - e.g. his theory of induction; his theory of the continuum; his views on impredicativiti his theory of meaning - must, in general, be seen as an adaptation of Kant's position. My conclusion is that not only is there a well-founded philosophical core to Poincare's philosophy, but also that such a core provides a viable alternative in contemporary debates in the philosophy of mathematics. That is, Poincare's theory, which is secured by his doctrine of a priori intuitions, and which describes a position in between the two extremes of an "anti-realist" strict constructivism and a "realist" axiomatic set theory, may indeed be true

Schelling\u27s Naturalism: Motion, Space, and the Volition of Thought

This dissertation examines F.W.J. von Schelling\u27s Philosophy of Nature (or Naturphilosophie) as a form of early, and transcendentally expansive, naturalism that is, simultaneously, a naturalized transcendentalism. By focusing on space and motion, this dissertation argues that thought should be viewed as a natural activity through and through. This view is made possible by German Idealism historically, and yet, is complicated and obscured by contemporary philosophy\u27s treatment of German Idealism in both analytic and continental circles. The text engages with the foundations of Schelling\u27s theory of nature as well as geometry, field theory, inter-theory relations, epistemology, and pragmatism

An investigation of beauty and contemporary painting: Kant, Greenberg and Neuroscience

My motivation for my research stems from my practice as an abstract painter whose interests centre on form, pictorial space, surface quality and beauty in painting. For a long time I have been interested in the need for both freedom and restraint in the production of painting. In my practice I use an unusual material, containing translucent silicon polymers, because it provides a beautiful surface quality for my work. This is difficult to use; it cannot be applied with brushes, and so I developed a simple semi-autonomous machine for producing an image on canvas. The machine enabled me to paint with silicon polymers, to achieve a beautiful surface, but it imposed very severe restraints on the form of the images. This difficulty compelled me to consider the problem of the conflict between autonomy and freedom at a practical level and that in turn led to a reflection on the nature of this problem at the intellectual and emotional level. This thesis is, in large part, my response to this conflict. I begin my enquiry with a critical discussion of Greenberg's essay Modernist Painting in terms of the Kantian authority that he claims for it. I then tum to a critique of that Kantian authority itself. Common to both Greenberg and Kant is systematic argumentation in terms of wholly autonomous entities that makes a resolution of the conflict between freedom and necessity very difficult. In the second half of the thesis I use the concepts and empirical observations of affective neuroscience (which does not deal in autonomous entities) to develop my own theory of the beautiful and to use it as a critical tool in relation to both Kantian aesthetics and my own painting practice

A Long and Broken History of Western “Universalism”: Cosmopolitanism

With recent developments in political globalization, self-identifying “cosmopolitans” have overwhelmed the scholarly discourse. This article examines the moral claims behind the theory of cosmopolitanism—in its political universal form—while being especially cautious of claims of such true universalism, and its likely dangerous applications. This entails a brief analysis into certain justified universalist legal traditions; an example of such is found in the International Criminal Court (ICC). In examining the theory and application of western-originated cosmopolitanism, we not only see how theoretical claims of moral superiority are wrong, but that they are alive and well in western theories. In application, it follows that even (slightly) milder legal traditions, like the ICC, imply this unjustified moral superiority

Toward a Criticism of Theological Reason : Time and Timelessness as Primordial Presuppositions

This investigation studies the possibility of developing a theological criticism of Christian theological reason. The investigation proceeds by developing a phenomenological analysis of three major contexts within which reason has been interpreted and utilized by Christian theology for the constitution of its exegetical and systematic formulations: the philosophical, theological, and Biblical contexts. The philosophical context shows that the structure of reason requires the interpretation of Being\u27s dimensionality which determines its basic meaning and functioning. Moreover, it shows that Being\u27s dimensionality has been interpreted in two ways: as timeless and as temporal. The theological context, through the analysis of reason\u27s procedures as a tool for the constitution of meaning in Thomas Aquinas\u27s and Rudolf Bultmann\u27s systems, shows that theology has depended on philosophical critic is m of reason and its classical timeless interpretation of Being\u27s dimensionality. Thomas\u27s system, and with him conservative theology, follows the Aristotelian interpretation of reason while Bultmann\u27s system, and with him liberal theology, follows the Kantian interpretation. The Biblical context, through the analysis of Exodus 3:14, the locus classicus for the discussion about Being in Scripture, shows that theological criticism of theological reason is possible and that Biblical reflection on Being interprets its dimensionality as temporal. Moreover, considering the facts that the philosophical context uncovers the hypothetical nature of reason, and that Christian theology is rooted in the conceptuality of the Biblical reflection in which it is grounded, it is suggested that criticism of theological reason should be developed following the temporal interpretation of Being as rooted and developed in Scriptures. On this basis it is further suggested that such a criticism should be able to provide theology with the necessary starting point for advancing beyond the alternatives provided by the Aristotelian and Kantian interpretations of reason that so far have conditioned the interpretation and actual functioning of reason as a tool for the constitution of Christian theological meanings

Revelation and Christian learning.

SIGLEAvailable from British Library Document Supply Centre- DSC:D88161 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

Kierkegaard's post-enlightenment subject: the grammar and goal of belief

S0ren Kierkegaard's thesis, "Truth is Subjectivity", is presented in Concluding Unscientific Postscript to Philosophical Fragments, as the central philosophical concept of his pseudonymous authorship. Contrary to most readings, it is argued here that Kierkegaard's subjectivity principle is epistemologically normative, not for ethical and religious beliefs only, but for a wider, general epistemology as well. The significance of Kierkegaard's claim that truth is subjectivity is that Kierkegaard is recasting epistemological issues in theological and ethical terms.Part One argues that Kierkegaard formulates his subjectivity principle as a response to the Enlightenment epistemologies, specifically of Kant and Hegel, and more generally Descartes, that seek to ground epistemology infallibly in the metaphysical resources of human rationality. Kierkegaard limits the scope of reason and philosophy in a manner that is reminiscent of the late Wittgenstein, and understands the activity of philosophy as analogous to grammar. What is glossed over by Enlightenment epistemology is the human subject's involvement in any act of belief. Rather than seeing human subjectivity as a hindrance to the pursuit of truth, Kierkegaard understands subjectivity (for humans) to be the means of attaining truth.There are two basic types of subjectivity for Kierkegaard. Constitutional subjectivity refers to human persons as beings who achieve subjectivity, or a first person perspective on the world. Reflexive subjectivity, on the other hand, refers to the general subject-forming activities that comprise the process of becoming subjective, and has as its primary constituent a reflective component. These senses of subjectivity combine to provide Kierkegaard's subjectivity principle with its normative and critical capacity.Part Two outlines how Kierkegaard's two senses of subjectivity function normatively with respect to beliefs. This section demonstrates that Kierkegaard's grammar of subjectivity in the end is a grammar of belief also. The conclusion of the dissertation is that Kierkegaard's subjectivity principle is a meta-epistemological principle through which Kierkegaard details an ethic of belief that is ultimately theological in nature

Impredicativity and turn of the century foundations of mathematics : presupposition in Poincare and Russell

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Linguistics and Philosophy, 1993.Includes bibliographical references (leaves 145-158).by Joseph Romeo William Michael PicardPh.D

The role of concepts in Kant's account of aesthetic experience

The thesis begins by exploring Kant's account of cognition as it is presented within the Critique of Pure Reason, particularly with reference to the conceptualist/non-conceptualist debate as it has developed over recent years. I argue that there is an important non-conceptualist position within Kant's account that concerns the unity of space and time as non-conceptual intuitive wholes. This argument will be used in discussing and exploring Kant's account of both aesthetic receptivity and aesthetic creativity as presented within the Critique of Judgement. My exploration of this third Critique will begin by looking at Kant's account of the harmony of the faculties and how we should understand the sense in which our aesthetic response is a non-conceptually determined one. The same concern will apply to an analysis of Kant's account of the mathematical sublime, and in the later stages of this discussion we will find an interesting relation between Kant's account of the role of infinity (space and time as unified wholes), and our earlier argument concerning space and time as formal intuitive wholes. After this focus upon the conditions of aesthetic receptivity my focus shifts towards aesthetic creativity as presented in Kant's account of fine art and genius. The main focus here will be with Kant's remark that art, in order to be art, must seem like nature. I will argue that this statement must be understood in two interdependent ways, where the first element concerns the formal construction of a representation so that it looks like nature in the sense of being a unified and readable representation. I will argue that artistic creativity at this level is the precondition of the second sense in which art must seem like nature, which concerns the content of a representation, and that a non-conceptual intuitional base is essential to this end