Realism in the philosophy of mathematics

By Blanchette, Patricia A.

Mathematical realism is the view that the truths of mathematics are objective, which is to say that they are true independently of any human activities, beliefs or capacities. ...

Antirealism in the philosophy of mathematics

By Moore, A.W.

Realism in the philosophy of mathematics is the position that takes mathematics at face value. According to realists, mathematics is the science of mathematical objects (numbers, sets, lines ...

Naturalized philosophy of mathematics

By Paseau, Alexander

There are three types of naturalism in the philosophy of mathematics: metaphysical, epistemological and methodological. Metaphysical naturalists maintain that all entities are natural. One reading of this claim ...

Realism and antirealism

By Craig, Edward

The basic idea of realism is that the kinds of thing which exist, and what they are like, are independent of us and the way in which we ...

Wittgenstein, Ludwig Josef Johann (1889–1951)

By Heal, Jane

Ludwig Wittgenstein was born in Vienna on 26 April 1889 and died in Cambridge on 29 April 1951. He spent his childhood and youth in Austria and Germany, ...

Fictionalism in the philosophy of mathematics

By Colyvan, Mark

Fictionalism in the philosophy of mathematics is the view that mathematical statements, such as ‘8+5=13’ and ‘∏ is irrational’, are to be interpreted at face value and, thus ...

Whitehead, Alfred North (1861–1947)

By Bradley, James

Whitehead made fundamental contributions to modern logic and created one of the most controversial metaphysical systems of the twentieth century. He drew out what he took to be ...

Wittgenstein, Ludwig Josef Johann (1889–1951)

Ludwig Wittgenstein was born in Vienna on 26 April 1889 and died in Cambridge on 29 April 1951. He spent his childhood and youth in Austria and Germany, ...

Metaphysics

By Craig, Edward

Metaphysics is a broad area of philosophy marked out by two types of inquiry. The first aims to be the most general investigation possible into the nature of ...

Numbers

By Priest, Graham

Numbers are, in general, mathematical entities whose function is to express the size, order or magnitude of something or other. Historically, starting from the most basic kind of ...

Intuitionistic logic and antirealism

By Pagin, Peter

The law of excluded middle (LEM) says that every sentence of the form A∨¬A (‘A or not A’) is logically true. This law is accepted in classical logic, ...

Gödel, Kurt (1906–78)

By Dawson, John W.

The greatest logician of the twentieth century, Gödel is renowned for his advocacy of mathematical Platonism and for three fundamental theorems in logic: the completeness of first-order logic; ...

Set theory, philosophy of

By Potter, Michael

The various attitudes that have been taken to mathematics can be split into two camps according to whether they take mathematical theorems to be true or not. Mathematicians ...

Mathematics, foundations of

By Detlefsen, Michael

Conceived of philosophically, the foundations of mathematics concern various metaphysical and epistemological problems raised by mathematical practice, its results and applications. Most of these problems are of ancient ...