Robert McNaughton. Axiomatic systems, conceptual schemes, and the consistency of mathematical theories. Philosophy of science, vol. 21 (1954), pp. 44–53. - Robert McNaughton. Conceptual schemes in set theory. The philosophical review, vol. 66 (1957), pp. 66–80.

1962 ◽  
Vol 27 (2) ◽  
pp. 221-222
Author(s):  
Y. Bar-Hillel
Keyword(s):  
Philosophy Of Science ◽  
Set Theory ◽  
Philosophical Review ◽  
Conceptual Schemes ◽  
Axiomatic Systems

George Boolos. The iterative conception of set. The journal of philosophy, vol. 68 (1971), pp. 215–231. - Dana Scott. Axiomatizing set theory. Axiomatic set theory, edited by Thomas J. Jech, Proceedings of symposia in pure mathematics, vol. 13 part 2, American Mathematical Society, Providence1974, pp. 207–214. - W. N. Reinhardt. Remarks on reflection principles, large cardinals, and elementary embeddings. Axiomatic set theory, edited by Thomas J. Jech, Proceedings of symposia in pure mathematics, vol. 13 part 2, American Mathematical Society, Providence1974, pp. 189–205. - W. N. Reinhardt. Set existence principles of Shoenfield, Ackermann, and Powell. Fundament a mathematicae, vol. 84 (1974), pp. 5–34. - Hao Wang. Large sets. Logic, foundations of mathematics, and computahility theory. Part one of the proceedings of the Fifth International Congress of Logic, Methodology and Philosophy of Science, London, Ontario, Canada–1975, edited by Robert E. Butts and Jaakko Hintikka, The University of Western Ontario series in philosophy of science, vol. 9, D. Reidel Publishing Company, Dordrecht and Boston1977, pp. 309–333. - Charles Parsons. What is the iterative conception of set?Logic, foundations of mathematics, and computahility theory. Part one of the proceedings of the Fifth International Congress of Logic, Methodology and Philosophy of Science, London, Ontario, Canada–1975, edited by Robert E. Butts and Jaakko Hintikka, The University of Western Ontario series in philosophy of science, vol. 9, D. Reidel Publishing Company, Dordrecht and Boston1977, pp. 335–367.

1985 ◽  
Vol 50 (2) ◽  
pp. 544-547 ◽  
Author(s):  
John P. Burgess
Keyword(s):  
Philosophy Of Science ◽  
Set Theory ◽  
American Mathematical Society ◽  
Publishing Company ◽  
Foundations Of Mathematics ◽  
Reidel Publishing Company ◽  
Pure Mathematics ◽  
Iterative Conception ◽  
The University ◽  
Axiomatic Set Theory

Stove's Discovery of the Worst Argument in the World

Philosophy ◽  
2002 ◽  
Vol 77 (4) ◽  
pp. 615-624 ◽  
Author(s):  
James Franklin
Keyword(s):  
Philosophy Of Science ◽  
Cultural Relativism ◽  
Ethical Relativism ◽  
Conceptual Schemes ◽  
The World

The winning entry in David Stove's Competition to Find the Worst Argument in the World was: “We can know things only as they are related to us/insofar as they fall under our conceptual schemes, etc., so, we cannot know things as they are in themselves.” That argument underpins many recent relativisms, including postmodernism, post-Kuhnian sociological philosophy of science, cultural relativism, sociobiological versions of ethical relativism, and so on. All such arguments have the same form as ‘We have eyes, therefore we cannot see’, and are equally invalid.

Philosophy of Mathematics

Philosophy ◽  
2010 ◽  
Author(s):  
Otávio Bueno
Keyword(s):  
Philosophy Of Science ◽  
Set Theory ◽  
Category Theory ◽  
Mathematical Reasoning ◽  
Philosophy Of Mathematics ◽  
Mathematical Practice ◽  
Mathematical Explanation ◽  
Excellent Work ◽  
Novel Approaches

Philosophy of mathematics is arguably one of the oldest branches of philosophy, and one that bears significant connections with core philosophical areas, particularly metaphysics, epistemology, and (more recently) the philosophy of science. This entry focuses on contemporary developments, which have yielded novel approaches (such as new forms of Platonism and nominalism, structuralism, neo-Fregeanism, empiricism, and naturalism) as well as several new issues (such as the significance of the application of mathematics, the role of visualization in mathematical reasoning, particular attention to mathematical practice and to the nature of mathematical explanation). Excellent work has also been done on particular philosophical issues that arise in the context of specific branches of mathematics, such as algebra, analysis, and geometry, as well as particular mathematical theories, such as set theory and category theory. Due to limitations of space, this work goes beyond the scope of the present entry.

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