“Cathedral Builders”: Mathematics and the Sublime

• Authors: Shaposhnikov Vladislav

Title variants

PL

„Budowniczy katedr”: matematyka a wzniosłość

• Languages of publication: EN

Abstracts

EN

The paper deals with aesthetic and religious dimensions of mathematics. These dimensions are considered as closely connected, though reciprocally non-reducible. “Mathematical beauty” is already firmly established as a term in the philosophy of mathematics. Here, an attempt is made to bring forward two additional candidates: “mathematical sublime” and “numinous mathematics”. The last one is meant to designate the recognition of some mathematical practices as inspiring anticipation of the meeting with the divine reality or producing a feeling of its presence. The first one is used here to designate the related feelings in disguise, i.e., being reinterpreted or transferred from the straightforwardly religious to the aesthetic sphere. Taking Kant’s theory of the sublime as a starting point, the paper introduces a related account of it that treats mathematical beauty through mathematical sublimity as a more fundamental category. Within this account, religious experience, the aesthetics of the sublime and mathematical practice are closely interlinked through an appropriate interpretation of the idea of the infinite. Both mathematical and art symbolism are seen as an endeavour to represent the infinite within the finite, which correlates well with the definition of mathematics as “the science of the infinite” (Hermann Weyl).

PL

Artykuł poświęcony jest estetycznemu wymiarowi matematyki, a także jego wymiarowi religijnemu. Wymiary te rozważane są jako silnie ze sobą powiązane, choć nie są do siebie sprowadzalne. „Piękno matematyczne” ugruntowało się już jako termin w filozofii matematyki. Podjęto tu próbę wysunięcia dodatkowych kandydatów: „matematyczna wzniosłość” i „matematyka numinotyczna”. Drugi z nich odnosi się do uznania pewnych praktyk matematycznych jako inspirujących do antycypacji spotkania z boską rzeczywistością lub jako wywołujących poczucie jej obecności. Z kolei pierwszy – do związanych z tym odczuć w „przebraniu”, to jest zreinterpretowanych i przeniesionych ze sfery wprost religijnej do estetycznej. Wychodząc od teorii wzniosłości Kanta, artykuł proponuje ujęcie matematycznego piękna poprzez matematyczną wzniosłość jako kategorię podstawową. W tym zakresie doświadczenie religijne, estetyka wzniosłości i praktyka matematyczna są wzajemnie silnie powiązane poprzez odpowiednią interpretację idei nieskończoności. Zarówno symbolizm matematyczny, jak i symbolizm w sztuce są tu postrzegane jako próba przedstawienia nieskończoności w tym, co skończone, co dobrze koreluje z definicją matematyki jako „nauki o nieskończoności” (Hermann Weyl).

Keywords

EN

philosophy of mathematics; philosophy of mathematical practice; mathematical aims; mathematical beauty; the sublime; numinous; the infinite; symbolism

PL

filozofia matematyki; filozofia praktyki matematycznej; cele matematyczne; matematyczne piękno; wzniosłość; numinosum; nieskończoność; symbolizm

• Publisher: University of Warsaw, Institute of Philosophy
• Journal: Edukacja Filozoficzna
• Year: 2019
• Issue: 68
• Pages: 195-226

Contributors

author

Shaposhnikov Vladislav

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