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Justifying Definitions in Mathematics—Going Beyond Lakatos
definitions in mathematics justification of definitions Lakatos mathematical reasoning
2009/4/27
This paper addresses the actual practice of justifying definitions in mathematics. First, I introduce the main account of this issue, namely Lakatos's proof-generated definitions. Based on a case stud...
In this paper I argue that aim-oriented empiricism (AOE),
a conception of natural science that I have defended at some
length elsewhere, is a kind of synthesis of the views of
Popper, Kuhn and Laka...
Popper, Kuhn, Lakatos, and Aim-Oriented Empiricism
Scientific rationality Popper Kuhn Lakatos methodology scientific progress falsificationism empiricism metaphysics philosophy of physics research programmes
2011/9/7
In this paper I argue that aim-oriented empiricism (AOE), a conception of natural science that I have defended at some length elsewhere, is a kind of synthesis of the views of Popper, Kuhn and Lakatos...
What Lakatos Could Teach the Mathematical Physicist
Jaffe-Quinn debate theoretical mathematics Imre Lakatos's philosophy of mathematics rigor in mathematics and mathematical physics
2011/9/8
In their 1993 article "'Theoretical Mathematics': Toward a Cultural Synthesis of Mathematics and Theoretical Physics" published in the Bulletin of the American Mathematical Society, the eminent mathem...