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VOLUME LXVI, NUMBER 1
September 2012

 

Numerical Foundations: Arithmetic as Episteme, JEAN W. RIOUX

Mathematics has had its share of historical shocks, beginning with the discovery by Hippasus the Pythagorean that the integers could not possibly be the elements of all things. Likewise with Kurt Gödel’s Incompleteness Theorems, which presented a serious (even fatal) obstacle to David Hilbert’s formalism, and Bertrand Russell’s own discovery of the paradox inherent in his intuitively simple set theory. More recently, Paul Benacerraf presented a problem for the foundations of arithmetic in “What Numbers Could Not Be” and “Mathematical Truth.” Drawing out difficulties he found in mathematical realism, Benacerraf ended up proposing his own structuralist view of mathematics, according to which numbers could not be considered objects at all, but mere placeholders, wholly defined in terms of the structures within which they were found. While we do not intend to work through the intricacies of structuralism or other types of mathematical nonrealism, or even of any of the many other competing theories in contemporary philosophy of mathematics, our question concerns problems one finds in an earlier, and perhaps more naïve, view of mathematics which, though a realism of its own, begins with seemingly more problematic assumptions than these. Classically expressed, the question is: do numbers exist in the world, whether as substances or as attributes of things? These are among the things Benacerraf holds numbers could not be; still, we hope to dispel some of the confusion which might bring one prematurely to reject this account. Most precisely, we wish to address the problem whether there can be a science of arithmetic, as that term is understood by Aristotle and Thomas Aquinas.

Phronesis vs. Sophia: On Heidegger’s Ambivalent Aristotelianism, PANAGIOTIS THANASSAS

Heidegger’s first period in Freiburg (1919-23), where he taught as an assistant of Edmund Husserl, is characterized by a long, intense confrontation with the philosophy of Aristotle, manifested not only in the titles of his university lectures, but also in his explicit intention to write a book on Aristotle. This undertaking will recede in 1924 in Marburg, in view of the decision to write a treatise on time. This treatise will finally be composed in 1926 and will be published in 1927 under the title Being and Time. The shadow of Aristotle, however, still influences his philosophical work after 1924, and particularly in BT. The relevance of Heidegger’s Aristotle-interpretations can be determined in a twofold way: first, by tracing ‘tacit’ elements of Aristotelian thought, as they may emerge through Heidegger’s interpretations, and, secondly, by expounding the way in which the thought of Heidegger himself develops and takes shape in a dialogue with Aristotelian philosophy. Scholars agree that Heidegger’s confrontation with Aristotle does not amount to a passive adoption of Aristotelian positions, distinctions and evaluations, but is a kind of productive adaptation and reinterpretation of the Aristotelian heritage: appropriation, reappropriation, originelle Aneignung, “reinterprets and transforms”– these are the terms in which this relation has been described. But what precisely is the content and nature of this appropriation? A certain confusion is produced by an assumption implicitly shared by the vast majority of scholars, the conviction that Heidegger’s philosophy constitutes a unique corpus and that his thought evolves linearly and uniformly. Τhe paper attempts to challenge this assumption.—Correspondence to: This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Seeing Is Knowing: The Metaphysical Significance of Color Phenomenology, ZED ADAMS

There is a well-known tradition of thinkers who have argued that philosophical reflection on the lived character of everyday experience can reveal significant and sometimes surprising insights into the nature of things. Philosophers as diverse as William James, Edmund Husserl, and Ludwig Wittgenstein have all suggested that first-person experience can play an important, if not definitive, role in structuring our philosophical accounts of the world. One deep source of opposition to this tradition is the worry that first-person experience simply cannot do this kind of work, that mere armchair reflection on the lived character of everyday experience is an unreliable guide to the real natures of things. In this paper, I defend this tradition from this worry, but not by showing that everyday experience is infallible. There are, of course, many features of everyday experience that are deeply misleading: the earth does not feel like it is moving, after all. Rather than attempting the impossible—to defend the infallibility of everyday experience, or common sense more generally—I am going to adopt a different route. I will focus on a particular type of everyday experience and argue that “armchair” reflection upon it reveals serious constraints on what would count as an adequate account of the nature of the objects of that experience. The example on which I will focus is color. What, exactly, does first-person experience of colors reveal to us about their natures?

Mathematical Entities in the Divided Line, M. J. CRESSWELL

The second highest level of the divided line in Plato’s Republic (510b-511a) appears to be about the entities of mathematics—entities such as particular (though non-physical) triangles. It differs from the highest level in two respects. It involves reasoning from hypotheses, and it uses visible images. This article defends the traditional view that the passage is indeed about these mathematical ‘intermediates’; and tries to show how the apparently different features of the second level are related, by focussing on Plato’s need to give an account of how we can speak of many particulars of the same kind, without assuming that they are imperfect copies, in the way sensible things can be imperfect copies, of forms.—Correspondence to: This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Natural Law and the United States Constitution, ROBERT S. BARKER

The United States Constitution was written for the purpose of establishing an effective but limited national government, a government that would be capable of dealing with national and international problems, but that would not be able to violate the traditional liberties of the people. Thus, the Constitution was, and is essentially a practical-juridical document. One should not expect to find there pronouncements about the nature of man, society, law, or the state, such as are often found in many other national constitutions and international conventions. Nevertheless, several important characteristics of the Constitution—indeed its most important characteristics—are clear and admirable applications of the natural law. The principal drafters of the Constitution believed that God, in creating the universe, implanted in the nature of man a body of law to which all human beings are subject, which is superior to all manmade law, and which is knowable by human reason. Thus, the natural law of the American founders was traditional natural law as understood and expounded by classical and Medieval writers and carried forward in the English common law, and not the “Enlightenment” versions in vogue in eighteenth-century Europe. The classical-traditional natural law understanding of Madison, Hamilton, Wilson, and other leaders of the Philadelphia Convention are reflected in the three most important characteristics of the Constitution: the principle of limited government; the principle of subsidiarity (in both political and larger societal matters); and the practice of guaranteeing traditional rights, and only as against government.—Correspondence to: This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Last Updated ( Thursday, 06 November 2014 03:22 )