Kuhn, Lakatos, and the Image of Mathematics
نویسندگان
چکیده
منابع مشابه
The Perils of Paradigm Mentalities: Revisiting Kuhn, Lakatos, and Popper
A common theme in the Centennial Issue of the American Political Science Review was how subfields have grown more specialized and insulated from one another. In this essay I argue that this trend has been hastened by the inappropriate incorporation of paradigm mentalities, first presented by Thomas Kuhn and later developed by Imre Lakatos. I show how paradigm mentalities help justify rigid oppo...
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1. In November of 1956, at the age of 31, Imre Lakatos left Hungary, going first to Vienna and then to Kings College, Cambridge, as a Ph.D. student. For his thesis he chose the topic of mathematical discovery and, at the suggestion of the Hungarian mathematician George Poly?, he based his research on an historical case study; the development of a conjecture, due to Euler, about polyhedra. This ...
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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 study of definitions of randomness in ergodic theory, I identify three other common ways of justifying definitions: natural-world-justification, condition-justification and redundancyjustification. Als...
متن کاملKuhn , Lakatos , and Laudan Applications in the History of Physics and Psychology
" Kuhnians depict the history of any scientific discipline as a succession of incommensurable paradigms. Empirical work done in one paradigm is of little relevance to another, and comparisons of paradigms on such familiar grounds as experimental adequacy are said to be inconclusive. Different paradigms do not agree on what constitutes knowledge or the meaning of truth. The recent work of other ...
متن کاملLakatos-style collaborative mathematics through dialectical, structured and abstract argumentation
The simulation of mathematical reasoning has been a driving force throughout the history of Artificial Intelligence research. However, despite significant successes in computer mathematics, computers are not widely used by mathematicians apart from their quotidian applications. An oft-cited reason for this is that current computational systems cannot do mathematics in the way that humans do. We...
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ژورنال
عنوان ژورنال: Philosophia Mathematica
سال: 1995
ISSN: 0031-8019,1744-6406
DOI: 10.1093/philmat/3.3.225