Search results
Results from the WOW.Com Content Network
For example, the set containing only the empty set is a nonempty pure set. In modern set theory, it is common to restrict attention to the von Neumann universe of pure sets, and many systems of axiomatic set theory are designed to axiomatize the pure sets only. There are many technical advantages to this restriction, and little generality is ...
Alain Badiou (/ bɑːˈdjuː /; [ 3 ]French: [alɛ̃ badju] ⓘ; born 17 January 1937) is a French philosopher, formerly chair of Philosophy at the École normale supérieure (ENS) and founder of the faculty of Philosophy of the Université de Paris VIII with Gilles Deleuze, Michel Foucault and Jean-François Lyotard. Badiou's work is heavily ...
e. Philosophy of mathematics is the branch of philosophy that deals with the nature of mathematics and its relationship with other human activities. Major themes that are dealt with in philosophy of mathematics include: Reality: The question is whether mathematics is a pure product of human mind or whether it has some reality by itself.
t. e. In mathematical logic, Russell's paradox (also known as Russell's antinomy) is a set-theoretic paradox published by the British philosopher and mathematician Bertrand Russell in 1901. [1][2] Russell's paradox shows that every set theory that contains an unrestricted comprehension principle leads to contradictions. [3]
The foundational philosophy of formalism, as exemplified by David Hilbert, is a response to the paradoxes of set theory, and is based on formal logic. Virtually all mathematical theorems today can be formulated as theorems of set theory.
Scott–Potter set theory. An approach to the foundations of mathematics that is of relatively recent origin, Scott–Potter set theory is a collection of nested axiomatic set theories set out by the philosopher Michael Potter, building on earlier work by the mathematician Dana Scott and the philosopher George Boolos .
Mathematics. Pure mathematics studies the properties and structure of abstract objects, [1] such as the E8 group, in group theory. This may be done without focusing on concrete applications of the concepts in the physical world. Pure mathematics is the study of mathematical concepts independently of any application outside mathematics.
Coherentism is a view about the structure and system of knowledge, or else justified belief. The coherentist's thesis is normally formulated in terms of a denial of its contrary, such as dogmatic foundationalism, which lacks a proof-theoretical framework, or correspondence theory, which lacks universalism.