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50An Analysis of the Notion of Rigour in ProofsLogic and Philosophy of Science 9 (1): 165-171. 2011.We are told that there are standards of rigour in proof, and we are told that the standards have increased over the centuries. This is fairly clear. But rigour has also changed its nature. In this paper we as-sess where these changes leave us today.1 To motivate making the new assessment, we give two illustra-tions of changes in our conception of rigour. One, concerns the shift from geometry to arithmetic as setting the standard for rig-our. The other, concerns the notion of effective proof or c…Read more
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3Paul Tomassi, Logic: How to Think Logically Reviewed byPhilosophy in Review 20 (4): 240-244. 2000.
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9Introducing Philosophy of MathematicsRoutledge. 2007.What is mathematics about? Does the subject-matter of mathematics exist independently of the mind or are they mental constructions? How do we know mathematics? Is mathematical knowledge logical knowledge? And how is mathematics applied to the material world? In this introduction to the philosophy of mathematics, Michele Friend examines these and other ontological and epistemological problems raised by the content and practice of mathematics. Aimed at a readership with limited proficiency in math…Read more
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76Using Mathematics to Explain a Scientific TheoryPhilosophia Mathematica 24 (2): 185-213. 2016.We answer three questions: 1. Can we give a wholly mathematical explanation of a physical phenomenon? 2. Can we give a wholly mathematical explanation for a whole physical theory? 3. What is gained or lost in giving a wholly, or partially, mathematical explanation of a phenomenon or a scientific theory? To answer these questions we look at a project developed by Hajnal Andréka, Judit Madarász, István Németi and Gergely Székely. They, together with collaborators, present special relativity theory…Read more
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56The pluralist sheds the more traditional ideas of truth and ontology. This is dangerous, because it threatens instability of the theory. To lend stability to his philosophy, the pluralist trades truth and ontology for rigour and other ‘fixtures’. Fixtures are the steady goal posts. They are the parts of a theory that stay fixed across a pair of theories, and allow us to make translations and comparisons. They can ultimately be moved, but we tend to keep them fixed temporarily. Apart from conside…Read more
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3Leigh S. Cauman, First-order Logic, an Introduction Reviewed byPhilosophy in Review 20 (4): 240-244. 2000.
Washington, District of Columbia, United States of America
Areas of Specialization
Science, Logic, and Mathematics |
Metaphysics and Epistemology |
Philosophy, Misc |