Principia mathematica

Zobacz też: Dzieło Issaca Newtona Philosophiae naturalis principia mathematica.

Principia mathematica – zamierzone na cztery tomy dzieło Bertranda Russella i Alfreda Northa Whiteheada dotyczące podstaw matematyki, tworzone i publikowane w latach 1910–1913. Jego celem było sprowadzenie matematyki do logiki i wyprowadzenie twierdzeń tej pierwszej z układu aksjomatów i reguł wnioskowania.

Dzieło Russella i Whiteheada inspirowane było wcześniejszymi pracami Gottloba Fregego z zakresu logiki, a dokładniej chęcią usunięcia z nich sprzeczności odkrytych przez Russella. Chodziło przede wszystkim o wyeliminowanie założeń prowadzących do paradoksów w rodzaju paradoksu Russella powstających w sytuacji, gdy dopuszczamy zdania mówiące o sobie samych.

Trzy tomy Principiów dotyczą jedynie teorii mnogości, liczb kardynalnych, porządkowych i rzeczywistych, lecz wydaje się, że dalsza droga jest jasna i w zasadzie całą matematykę można sprowadzić do logiki. Otwarty pozostał jednak problem niesprzeczności i zupełności systemu aksjomatów przyjętych przez Russella i Whiteheada. Dwadzieścia lat po napisaniu Principiów znalazł on nieoczekiwane rozwiązanie w twierdzeniu Gödla o niezupełności.

Ostatecznie powstały trzy tomy Principiów, Alfred North Whitehead zrezygnował z prac nad czwartym tomem.

Z wywiadu udzielonego przez Russella „Daily Herald” z okazji jego 90 urodzin pochodzi znana anegdota – Russell stwierdził żartobliwie, że Principia było zdolne przeczytać tylko sześciu ludzi, z których trzech było Polakami[1]. Według Klemensa Szaniawskiego żart ten kryje ziarno prawdy, gdyż istotnie niewielu jest ludzi zdolnych przeczytać długi i bardzo trudny tekst Principiów, a jednocześnie Russell bardzo cenił dokonania logików polskich, zwłaszcza Leona Chwistka.

Przypisy

  1. ↑ Klemens Szaniawski, Przedmowa do pierwszego wydania, w: Bertrand Russell, Autobiografia 1872-1914, Warszawa 1996

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