Naslov
Quine’s New foundations and paradoxes

Autori
Adlešić, Tin

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, stručni

Izvornik
Book of Abstracts / - , 2021, 62-63

Skup
Logica and Applications 2021

Mjesto i datum
Dubrovnik, Hrvatska, 20.09.2021

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Nije recenziran

Ključne riječi
Quine’s New foundations ; Stratification ; Russell’s paradox ; Burali-Forti’s paradox ; Cantor’s paradox

Sažetak
New foundations was introduced by Quine in 1937. as an improvement of Russell–Whitehead’s type theory. It was envisioned as a general theory of logical classes ; in the spirit of Frege. Eventually it’s nature shifted, and today it is viewed as an alternative set theory to ZF. NF is a set theory which allows universal set, and many more sets which are deemed too large in ZF. Nevertheless, it successfully (as far as we know) forbids common set theoretic paradoxes by a clever constraints imposed on the formula construction. The main goal of this talk is to briefly explain the development of NF. Starting form easy set theoretical constructions and continue towards more complex notions such as ordinal and cardinal numbers. A big stress will be made on set theoretical paradoxes, and how NF alludes them. Also, brief account of how ordinary mathematics can be described in NF will be presented.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA