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Twórcza rola patologii w matematyce

100%
Pogonowski J.
Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia
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2014
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vol. 6
101-121
EN
We discuss the creative role of objects called pathologies by mathematicians.Pathologies may become “domesticated” and give rise to newmathematical domains. Thus they influence changes in mathematical intuition.
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Intuitive explanations of mathematical ideas

100%
Pogonowski J.
Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia
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2018
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vol. 10
123-137
EN
This short note is devoted to the role played by intuitive explanations in mathematical education. We provide a few examples of such explanations. They are related to: verbal commentaries, perception, physical models. We recall also some examples of internal explanations, inside mathematics itself.
3
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Rozumienie dowodu matematycznego a zagadnienie wyjaśnienia w matematyce

89%
Wójtowicz K.
Zagadnienia Filozoficzne w Nauce
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2015
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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.
4
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Realism in the philosophy of mathematics: Gödel and Ingarden

51%
Skowron B., Wójtowicz K., Skowron B., Wójtowicz K.
Przegląd Filozoficzny. Nowa Seria
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2020
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issue 4
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