منابع مشابه
Explanatory Proofs and Beautiful Proofs
This paper concerns the relation between a proof’s beauty and its explanatory power — that is, its capacity to go beyond proving a given theorem to explaining why that theorem holds. Explanatory power and beauty are among the many virtues that mathematicians value and seek in various proofs, and it is important to come to a better understanding of the relations among these virtues. Mathematical...
متن کاملFinding proofs and checking proofs
The classic dichotomy between proof discovery and proof presentation resurfaces in automated deduction. The LCF style of theorem proving offers a promising way to integrate formal deductive proof with higher-level algorithmic or heuristic forms of mathematical activity. One way of dealing with the potential inefficiency of a reduction to a formal deductive system is to exploit the separation of...
متن کاملWhy proofs by mathematical induction are generally not explanatory
Proposed accounts of scientific explanation have long been tested against certain canonical examples. Various arguments are paradigmatically explanatory, such as Newton’s explanations of Kepler’s laws and the tides, Darwin’s explanations of various biogeographical and anatomical facts, Wegener’s explanation of the correspondence between the South American and African coastlines, and Einstein’s ...
متن کاملDifferent Proofs are Good Proofs
In order to compare the quality of proofs, it is necessary to measure artifacts of the proofs, and evaluate the measurements to determine differences between the proofs. This paper discounts the approach of ranking proofs by their measured proof artifacts, and takes the position that different proofs are good proofs. The position is based on proofs in the TSTP solution library, which are genera...
متن کاملIndirect proofs and proofs from assumptions
By a proof by assumption, or for short an assumption proof, I mean the following. The proof proves a conclusion of the form ‘If P then Q’. It proceeds by making a sequence of statements S1, . . . , Sn (possibly with added commentary), where P is S1, Q is Sn, and for each Si with i > 1 there are earlier Sj . . . such that the conditional ‘If Sj . . . , then Si’ is already known. The reason for c...
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ژورنال
عنوان ژورنال: Journal of Humanistic Mathematics
سال: 2016
ISSN: 2159-8118
DOI: 10.5642/jhummath.201601.04