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22The Dispute between Two Accounts of the ContinuumJournal of Philosophy 119 (8): 425-443. 2022.The topic of this paper is the debate between two accounts of the continuum. On one account the continuum has discrete elements. On the other it has no discrete elements. Each account has its own strengths and weaknesses. The paper introduces several different explications of continuity before stating and discussing an antinomy and some options to resolve it. An assessment follows in which certain astute philosophical views are vetted. If the dispute concerns the reality of the continuum, there …Read more
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25Hintikka and the Functions of LogicLogica Universalis 13 (2): 203-217. 2019.Jaakko Hintikka points out the power of Skolem functions to affect both what there is and what we know. There is a tension in his presupposition that these functions actually extend the realm of logic. He claims to have resolved the tension by “reconstructing constructivism” along epistemological lines, instead of by a typical ontological construction; however, after the collapse of the distinction between first and second order, that resolution is not entirely satisfactory. Still, it does throw…Read more
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43A bibliography of Hao WangPhilosophia Mathematica 6 (1): 25-38. 1998.A listing is given of the published writings of the logician and philosopher Hao Wang (1921—1995), which includes all items known to the authors, including writings in Chinese and translations into other languages.
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52A Bibliography of Hao WangPhilosophia Mathematica 6 (1): 25-38. 1998.A listing is given of the published writings of the logician and philosopher Hao Wang , which includes all items known to the authors, including writings in Chinese and translations into other languages
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49Wittgenstein and logicSynthese 166 (1): 41-54. 2009.In his Tractatus Logico-Philosophicus Ludwig Wittgenstein (1889–1951) presents the concept of order in terms of a notational iteration that is completely logical but not part of logic. Logic for him is not the foundation of mathematical concepts but rather a purely formal way of reflecting the world that at the minimum adds absolutely no content. Order for him is not based on the concepts of logic but is instead revealed through an ideal notational series. He states that logic is “transcendental…Read more
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Suffolk UniversityAssociate Professor
APA Eastern Division
Boston, Massachusetts, United States of America
Areas of Specialization
Philosophy of Mathematics |