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O dowodzie matematycznym bardziej źródłowo

100%
Szumakowicz E.
Kwartalnik Filozoficzny
|
2014
|
vol. 42
|
issue 1
75-93
EN
What is a mathematical proof? Is formal logic capable of shedding light on its nature or essence? The author maintains that the answer is negative. Mathematical proof requires a more intrinsic investigation and explanation due to its specific structure. The crucial element is usually situated on the top level of the proof structure, so that an axiomatic basis is as a rule useless in mathematical thinking. The final conclusion is that the formal-logical foundations of mathematics should be complemented with a phenomenology of mathematical thinking. The latter should be developed in a manner that is understandable for ordinary mathematicians. Philosophy would thus show its applicability and usefulness beyond its own purely theoretical and speculative domain. The general should be embodied in the concrete. The author believes that this type of interdisciplinary, philosophico-mathematical research will attract mathematicians to philosophy with profit for their own domain.
2
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Rozumienie dowodu matematycznego a zagadnienie wyjaśnienia w matematyce

89%
Wójtowicz K.
Zagadnienia Filozoficzne w Nauce
|
2015
|
issue 58
89-114
EN
In the article, I present two possible points of view concerning mathematical proofs: (a) the formal view (according to which the formalized versions of mathematical proofs reveal their “essence”); (b) the semantic view (according to which mathematical proofs are sequences of intellectual acts, and a form of intuitive “grasp” is crucial). The problem of formalizability of mathematical proofs is discussed, as well as the problem of explanation in mathematics – in particular the problem of explanatory versus non-explanatory character of mathematical proofs. I argue, that this problem can be analyzed in a fruitful way only from the semantic point of view.
3
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Dowód matematyczny – argumentacja czy derywacja? – część II

88%
Wójtowicz K.
Zagadnienia Filozoficzne w Nauce
|
2011
|
issue 49
81-97
PL
In the first part of the paper, Azzouni’s derivation–indicator view was presented. In the second part it is analyzed in a detailed way. It is shown, that many problems arise, which cannot be explained in a satisfactory way in Azzouni’s theory, in particular the problem of the explanatory role of proof, of its epistemic role; the relationship between first–order and second–order versions of proofs is also not clear. It is concluded, that Azzouni’s theory does not provide a satisfactory account of mathematical proof, but inspires an interesting discussion. In the article, some of the mentioned problems are discussed.
4
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Dowód matematyczny – argumentacja czy derywacja? – część I

88%
Wójtowicz K.
Zagadnienia Filozoficzne w Nauce
|
2011
|
issue 49
63-80
PL
The article is devoted to the problem of status of mathematical proofs, in particular it tries to capture the relationship between the real, „semantic” notion of mathematical proof, and its formal (algorithmic) counterpart. In the first part, Azzouni’s derivation–indicator view is presented in a detailed way. According to the DI view, there is a formal derivation underlying every real proof.
5
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What are the limits of mathematical explanation? Interview with Charles McCarty by Piotr Urbańczyk

51%
McCarty D. C., Urbańczyk P.
Zagadnienia Filozoficzne w Nauce
|
2016
|
issue 60
119-137
EN
An interview with Charles McCarty by Piotr Urbańczyk concerning  mathematical explanation.
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