This article shows that there are square circles in the sense that there are mathematical objects that are at the same time both perfectly circular and perfectly square. The philosophical significance of this is discussed, especially in view of philosophy's widespread use of “square circle” as a typical example of an impossibility. In particular, the focus is on what the existence of square circles means for the possibility of conceptual analysis, and more generally what we (...) can learn about the nature of non-formal concepts and their use in philosophy. (shrink)

Hobbes ' geometrical disputes are significant since they highlight several important strands in his thought - issues concerning the right to make definitions, his anti-clericalism, the maker's knowledge argument and his objections to algebra. These are examined, and the foundational position, according to Hobbes, of geomentry in relation to philosophy, science and technology, explained and discussed.

Descartes' Meditations is one of the most thoroughly analyzed of all philosophical texts. Nevertheless, central issues in Descartes' thought remain unresolved, particularly the problem of the Cartesian Circle. Most attempts to deal with that problem have weakened the force of Descartes' own doubts or weakened the goals he was seeking. In this book, Stephen I. Wagner gives Descartes' doubts their strongest force and shows how he overcomes those doubts, establishing with metaphysical certainty the existence of a non-deceiving God and (...) the truth of his clear and distinct perceptions. Wagner's innovative and thorough reading of the text clarifies a wide range of other issues that have been left unclear by previous commentaries, including the nature of the cogito discovery and the relationship between Descartes' proofs of God's existence. His book will be of great interest to scholars and upper-level students of Descartes, early modern philosophy and theology. (shrink)

Epicurean ethics has been subject to withering ancient and contemporary criticism for the supposed irreconcilability of Epicurus’s emphatic endorsement of friendship and his equally clear and striking ethical egoism. Recently, Matthew Evans (2004) has suggested that the key to a plausible Epicurean response to these criticisms must begin by understanding why friendship is valuable for Epicurus. In the first section of this paper I develop Evans’ suggestion further. I argue that a shared conception of the human telos and of what (...) is required to attain it structures the confidence that characterizes friendship. In the second part of the paper I return to two contemporary criticisms of Epicurean friendship. The first criticism focuses on the problem of free riders. The second criticism points to a seeming inconsistency in Epicurean doctrine. I suggest that both criticisms can be adequately addressed once we understand Epicurean friendship in greater depth. (shrink)

Hobbes and Wallis's "battle of the books" illuminates the intimate relationship between science and crucial seventeenth-century debates over the limits of sovereign power and the existence of God.

The history of ideas about addiction often comes down to a history of debates over the use and meaning of language. Nowhere is this more clear than in the interminable “Is addiction a ‘disease’?” debate. In Marc Lewis’ excellent Biology of Desire and in his paper that centers this issue, there is far more agreement between his work and mine than there is disagreement on the “disease” question. Here, however, I make a case for greater compatibility between the “disease” view (...) and learning models of addiction than Lewis does, because I think the nuance is worth exploring. Indeed, if addiction science and ethics paid more attention to nuance in general, the whole field would be far better off. (shrink)

PrefaceList of AbbreviationsChapter One: The Mathematical Career of the Monster of MalmesburyChapter Two: The Reform of Mathematics and of the UniversitiesIdeological Origins of the DisputeChapter Three: De Corpore and the Mathematics of MaterialismChapter Four: Disputed FoundationsHobbes vs. Wallis on the Philosophy of MathematicsChapter Five: The "Modern Analytics" and the Nature of DemonstrationChapter Six: The Demise of Hobbesian GeometryChapter Seven: The Religion, Rhetoric, and Politics of Mr. Hobbes and Dr. WallisChapter Eight: Persistence in ErrorWhy Was Hobbes So Resolutely Wrong?Appendix: Selections from (...) Hobbes's Mathematical WritingsReferencesIndex Copyright © Libri GmbH. All rights reserved. (shrink)

IN THE FOLLOWING PAGES, I shall examine two questions. Is there an anticipation of the understanding that constitutes the act of interpretation? If so, does that anticipatory understanding possess a structure of the sort that stands to the act of interpretation as the ontological ground is held to stand to the ontic or factual consequences of that ground? These questions together make up the problem of the hermeneutical circle.

On 12 May 1962, a frail Douglas MacArthur delivered his final public speech to the cadets at the United States Military Academy. A West Point graduate himself, MacArthur served as Superintendent of...

Russell derived many of his logical symbols from the pioneering notation of Giuseppe Peano. Principia Mathematica (1910–13) made these “Peanese” symbols (and others) famous. Here I focus on one of the more peculiar notational derivatives from Peano, namely, Principia ’s dual use of a squared dot or dots for both conjunction and scope. As Dirk Schlimm has noted, Peano always had circular dots and only used them to symbolize scope distinctions. In contrast, Principia has squared dots and conventions such that (...) some dots mark scope distinctions while others symbolize conjunction. How did this come to pass? In this paper I trace a genealogy of Principia ’s square dots back to Russell’s appropriation of Peano’s use of circular dots. Russell never explicitly justifies appropriating Peano’s notations to symbolize two distinct notions, but below I explain why Russell deployed Peano’s dot notations in this manner. Further, I argue that it was Cambridge University Press who squared the circular dots. (shrink)

The early history of the attempts to unify quantum theory with the general theory of relativity is depicted through the work of the under--appreciated Italo-Brazilian physicist Gleb Wataghin, who is responsible for many of the ideas that the quantum gravity community is entertaining today.

This chapter contains sections titled: The Philosophical Tale.

First I delineate the three main variables which determine the basic strategies for defending descartes against the charges of circularity and inconsistency--His theory of mental activity, His interpretation of metaphysical certainty and its relation to truth, And his interpretation of compelled assent and its relation to metaphysical and moral certainty. Then I offer an account of descartes' method--Sensitive to his theories of time, Causality, And omnipotence, As well as consciousness--Which renders his descriptions of his procedure internally consistent, Mutually consistent, And (...) consistent with his practice, Which is exhibited as neither circular nor implausibly dogmatic. (shrink)

In 1682, Leibniz published an essay containing his solution to the classic problem of squaring the circle: the alternating converg-ing series that now bears his name. Yet his attempts to disseminate his quadrature results began seven years earlier and included four distinct approaches: the conventional (journal article), the grand (treatise), the impostrous (pseudepigraphia), and the extravagant (medals). This paper examines Leibniz’s various attempts to disseminate his series formula. By examining oft-ignored writings, as well as unpublished manuscripts, this paper answers (...) the question of how one of the greatest mathematicians sought to introduce his first great geometrical discovery to the world. (shrink)

Last year, as some of you may recall, I took it upon my chairly shoulders to solve the problem of causation, where this problem can be stated this way: What is causation? According to the analysis I offered, C is a cause of E if and only if C makes E happen. I am happy to report that, in the year since delivering this account of causation, no objections have arisen. The critics have been silenced. Indeed, my colleague Dan Hausman, (...) the Herbert Simon Professor of Philosophy, reports that he is no longer satisfied with the view he expressed in his recent book on causation, and I have no doubt that his change of mind is due in no small part to my seminal contribution to this subject. If you would permit me a joke, I think I “made happen” a change in Dan’s mind. I should also mention that we are now fortunate to have amongst us Carolina Sartorio, whose own analysis of causation, arrived at independently, seems but a stylistic variant of my own. Where I see causes as things that make things happen, she sees them as things that make a difference. I think, but can’t be certain, that our analyses come to the same thing. Perhaps if she hadn’t muddied the waters with all those numbered propositions and ‘ifs’ and ‘thens’ we could settle the matter. (shrink)

Journal Name: The Law & Ethics of Human Rights Issue: Ahead of print.

In Squaring the Circle in Descartes’ Meditations, Stephen Wagner aims to show that Descartes’ project in the Meditations is best understood as a ‘strong validation of reason’ i.e., as proving in a non-circular way that human reason is a reliable, truth-conducive faculty. For such an enterprise to qualify as a ‘strong’ validation, Wagner contends, skeptical doubt must be given its strongest force. The most stringent doubt available in the Meditations is the deceiving God. To rule out the possibility that (...) an omnipotent God created humans so that their best functioning cognitive faculties provide misleading information about what the world is like, Descartes must prove that a non-deceiving God exists. Furthermore, only a non-circular proof will count as a ‘validation.’ Wagner spells out the requirements of non-circularity as involving a proof for God’s existence that is not deductive, does not simply achieve a clear and distinct perception of God’s existence, and proceeds on the basis of perceptions that remain true even when the reasons underlying them are not attended to any longer by the meditator. (shrink)

In the rise of modern scientific philosophy, one can distinguish four general periods. Its early phase is part of the intellectual history of 19th-century Austria-Hungary. Second, we find it reaching its self-confident form in the 1920s and early ‘30s, chiefly in the collaborative achievements of the Vienna Circle and its analogous groups in Prague, Berlin, Lwow and Warsaw. Third is the period of its further growth and accommodation during the period roughly from the late 1930s to about 1960, especially (...) in the U.S.A., as mediated largely by the European refugees from fascism. Lastly, the movement’s fate from the 1960s on may be understood as its integration with, or dissolution into, other related modern streams. (shrink)

Despite the transformation it introduced in theories of democratic representation, the so-called ‘constructivist turn’ left unchallenged the epistemology that had characterised traditional accounts: the questions at stake in current debates on representation are still mostly elicited by a ‘passive’ image of representation as ultimately the phenomenon of being represented by others. Nowhere has the focus explicitly been placed on the experience of representing others. This article proposes a recalibration of current constructivist accounts of representation by introducing what I term the (...) representative standpoint, an epistemological perspective which discloses neglected aspects of the nature and the value of democratic representation. In particular, I suggest that from the representative standpoint, we are able to configure representation as the periodic motion between two spaces: the square, where the representative meets with their constituents, and the circle, where the representative meets with the representatives of other constituencies. The essence of democratic representation lies precisely in the constant moving back and forth between these two spaces. I finally suggest that, configured in these terms, representation may be acknowledged and valued also for providing liberal democracies with an in-built device for a kind of civic education, the beneficiaries of which are the representatives themselves. (shrink)

My final aim in this paper is to show that Descartes is not guilty, as is so often maintained, of circular argumentation in the Meditations. But first it is important to uncover and remove certain tenacious misconceptions and confusions concerning what goes on in the Meditations which lend credence to the charge of circular argumentation. In this connection Mr. Harry Frankfurt's recent article, “Memory and the Cartesian Circle,” is peculiarly instructive; for it presents not only a completely untenable defence (...) of Descartes but one that, implicitly at least, rests on the very misconceptions that give substance to the notion of a Cartesian Circle. With the intention, then, of clearing the ground for the construction of my own defence of Descartes, I shall spend the first part of this paper examining Frankfurt's central thesis, the errors contained in it, and their sources. This thesis is contained in his statement, which I shall henceforth designate by the letter “J,” “Descartes did not attempt to justify present clear and distinct perceptions.”. (shrink)

In the Trolley Case (Figure 1), as devised by Philippa Foot and modified by Judith Jarvis Thomson, a runaway trolley (i.e. tram) is headed down a main track and will hit and kill five unless you divert it onto a side track, where it will hit and kill one.

In the Trolley Case (Figure 1), as devised by Philippa Foot and modified by Judith Jarvis Thomson, a runaway trolley (i.e. tram) is headed down a main track and will hit and kill five unless you divert it onto a side track, where it will hit and kill one.

In the Trolley Case, as devised by Philippa Foot and modified by Judith Jarvis Thomson, a runaway trolley is headed down a main track and will hit and kill five unless you divert it onto a side track, where it will hit and kill one.

This article discusses the work of Cornelius Castoriadis, an important political thinker and theorist of democracy. Castoriadis developed not one but two theories of democracy based on two distinct understandings of autonomy. The first is compatible with the key features of representative government; the second is not. Unfortunately, Castoriadis models his interpretation of the idea of popular sovereignty on the second view, thereby concluding, like Rousseau before him, that it is incompatible with representative government. This article discusses both approaches and (...) presents a reinterpretation of political representation and of the idea of popular sovereignty in order to show how they can be made compatible. I argue that the discourse of popular sovereignty and the modern principles of representative government entail one another. (shrink)

Hume argues that respect for property (“justice”) is a convention-dependent (“artificial”) virtue. He does so by appeal to a principle, derived from his virtue-based approach to ethics, which requires that, for any kind of virtuous action, there be a “first virtuous motive” that is other than a sense of moral duty. It has been objected, however, that in the case of justice (and also in a parallel argument concerning promise-keeping) Hume (i) does not, (ii) should not, and (iii) cannot recognize (...) such a motive. This paper defends Hume’s argument against these three objections. (shrink)

Development law is an ethos-driven law reform paradigm that examines conditions from within the country and provides a frame of reference in which to evaluate the legal regime in the political, economic, social and cultural context. Moreover, development law provides a fresh approach to assessing existing national laws effectiveness generally; it assesses whether modifications are required to promote economic, political, and social progress, including protecting the rights of minority ethnic groups and disenfranchised peoples. By protecting rights, law can be an (...) instrument of social development and will not be alien to large segments of the population. Development law as a paradigm is the result of decision making within the country after careful examination by trained professionals whose sole interest is political, economical, social, cultural and national development. The enactment of laws and integration of customary norms that are embraced by the ruling authority, political elites, and other stake holders will best advance human rights. (shrink)