منابع مشابه
Mathematical Method and Proof
On a traditional view, the primary role of a mathematical proof is to warrant the truth of the resulting theorem. This view fails to explain why it is very often the case that a new proof of a theorem is deemed important. Three case studies from elementary arithmetic show, informally, that there are many criteria by which ordinary proofs are valued. I argue that at least some of these criteria ...
متن کاملLakatos and Hersh on Mathematical Proof
مفهوم اثبات در چند دهۀ اخیر مناقشهآمیز شده است. به طوری که افراد نظریه‌های مختلفی دربارۀ چیستی اثبات ارائه دادهاند. لاکاتوش و هرش از جملۀ این افراد هستند. نظریه‌های این دو فیلسوف شباهتها و اختلافات قابل توجهی دارند. به نظر می‌‌رسد که با مقایسه و بررسی نقادانۀ این دو نظریه فهم بهتری از مفهوم اثبات ریاضیاتی به دست خواهد آمد. دو وجه شباهت مهم بین این دو نظریه عبارتند از: دوگانه‌انگاری در اثبات ...
متن کاملlakatos and hersh on mathematical proof
the concept of mathematical proof has been controversial for the past few decades. different philosophers have offered different theories about the nature of mathematical proof, among which theories presented by lakatos and hersh have had significant similarities and differences with each other. it seems that a comparison and critical review of these two theories will lead to a better understan...
متن کاملRandomness and Mathematical Proof
The first is obviously constructed according to a simple rule; it consists of the number 01 repeated ten times. If one were asked to speculate on how the series might continue, one could predict with considerable confidence that the next two digits would be 0 and 1. Inspection of the second series of digits yields no such comprehensive pattern. There is no obvious rule governing the formation o...
متن کاملVote Counting as Mathematical Proof
Trust in the correctness of an election outcome requires proof of the correctness of vote counting. By formulating particular voting protocols as rules, correctness amounts to demonstrating that all rules have been applied correctly. A proof of the outcome of any particular election then consists of a sequence (or tree) of rule applications and provides and independently checkable certificate o...
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ژورنال
عنوان ژورنال: Synthese
سال: 2006
ISSN: 0039-7857,1573-0964
DOI: 10.1007/s11229-005-4064-5