Constructivism (mathematics) | Intuitionism | Philosophy of mathematics

Intuitionism

In the philosophy of mathematics, intuitionism, or neointuitionism (opposed to preintuitionism), is an approach where mathematics is considered to be purely the result of the constructive mental activity of humans rather than the discovery of fundamental principles claimed to exist in an objective reality. That is, logic and mathematics are not considered analytic activities wherein deep properties of objective reality are revealed and applied, but are instead considered the application of internally consistent methods used to realize more complex mental constructs, regardless of their possible independent existence in an objective reality. (Wikipedia).

Video thumbnail

Pascal Boyer - Aesthetic Cognitivism: Overview & Concepts

Free access to Closer to Truth's library of 5,000 videos: http://bit.ly/2UufzC7 Aesthetic Cognitivism is a theory about the value of the arts as sources of understanding—the arts as more than sources of delight, amusement, pleasure, or emotional catharsis (though they can certainly be all

From playlist Aesthetic Cognitivism: Overview & Concepts - CTT Interview Series

Video thumbnail

Chris Stewart (Pt. 1) - Aesthetic Cognitivism: Overview & Concepts

Free access to Closer to Truth's library of 5,000 videos: http://bit.ly/2UufzC7 Aesthetic Cognitivism is a theory about the value of the arts as sources of understanding—the arts as more than sources of delight, amusement, pleasure, or emotional catharsis (though they can certainly be all

From playlist Aesthetic Cognitivism: Overview & Concepts - CTT Interview Series

Video thumbnail

David Brown - Aesthetic Cognitivism: Overview & Concepts

Free access to Closer to Truth's library of 5,000 videos: http://bit.ly/2UufzC7 Aesthetic Cognitivism is a theory about the value of the arts as sources of understanding—the arts as more than sources of delight, amusement, pleasure, or emotional catharsis (though they can certainly be all

From playlist Art Seeking Understanding - Closer To Truth - Core Topic

Video thumbnail

Christopher R. Brewer (Pt. 1) - Aesthetic Cognitivism I: Overview and Concepts

Free access to Closer to Truth's library of 5,000 videos: http://bit.ly/2UufzC7 Aesthetic Cognitivism is a theory about the value of the arts as sources of understanding—the arts as more than sources of delight, amusement, pleasure, or emotional catharsis (though they can certainly be all

From playlist Aesthetic Cognitivism: Overview & Concepts - CTT Interview Series

Video thumbnail

Sarah Coakley - Alternative Concepts of God?

Is God, if there is a God, a personal, conscious, all-powerful Supreme Being? Some offer radically different concepts of 'God', exploring novel ideas of what God may be like. They challenge theism - the God of Judaism, Christianity and Islam - with radically new kinds of gods. Is this 'her

From playlist Big Questions About God - Closer To Truth - Core Topic

Video thumbnail

Nihilism: The Belief in Nothing

Nihilism: The Belief In Nothing - https://aperture.gg/nihilism Become smarter in 5 minutes by signing up for free today: http://cen.yt/mbaperture2 Follow me on Instagram: https://www.instagram.com/mcewen/ For some, the meaning of life is the love we share with friends, family, and our lov

From playlist Philosophy & Psychology 🧠

Video thumbnail

LambdaConf 2015 - Introduction to Intuitionistic Type Theory Vlad Patryshev

Traditionally, in Computer Science, sets are assumed to be the basis of a type theory, together with Boolean logic. In this version of type theory, we do not need sets or Boolean logic; intuitionism is enough ("no principle of excluded middle required"). The underlying math is Topos Theory

From playlist LambdaConf 2015

Video thumbnail

Klaus Mainzer: Constructivity and Computability. Perspectives for Mathematics [...]

Title: Klaus Mainzer: Constructivity and Computability. Perspectives for Mathematics, Computer Science, and Philosophy The lecture was held within the framework of the Hausdorff Trimester Program: Constructive Mathematics. Abstract: Since antiquity, mathematical proofs were realized by

From playlist Workshop: "Constructive Mathematics"

Video thumbnail

Giovanni Sambin: Pointfree topology is real and pointwise is ideal

The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: Both competing visions of mathematics in the past century, the thesis of formal- ism and the antithesis intuitionism, assume a notion of truth in which the quality of in

From playlist Workshop: "Constructive Mathematics"

Video thumbnail

Sets, logic and computability | Math History | NJ Wildberger

In this video we give a very quick overview of a highly controversial period in the development of modern mathematics: the rise of set theory, logic and computability in the late 19th and early 20th centuries. Starting with the pioneering but contentious work of Georg Cantor in creating S

From playlist MathHistory: A course in the History of Mathematics

Video thumbnail

Is Maths Discovered or Invented?

Tom Rocks Maths intern Kira Miller debates the age-old question of whether maths is discovered or invented by presenting the common arguments on each side. Arguments presented on the side of 'invented' include Formalism, Fictionalism, Art, and Social Construct. And in favour of 'discovere

From playlist Mathstars

Video thumbnail

Philosophy of Numbers - Numberphile

We revisit the philosophy department and the question of whether numbers really exist? Featuring Mark Jago from the University of Nottingham. More links & stuff in full description below ↓↓↓ Earlier video on numbers' existence: https://youtu.be/1EGDCh75SpQ Infinity paradoxes: https://yout

From playlist Infinity on Numberphile

Video thumbnail

The Case for Surrealism | The Art Assignment | PBS Digital Studios

Pre-order our book YOU ARE AN ARTIST (which includes new assignments!) here: http://bit.ly/2kplj2h "Surrealism" has become shorthand for the bizarre, the irrational, the hallucinatory. But what IS it? Or what WAS it? Today we delve into the history of Surrealism, as it formed in post-Worl

From playlist The Case For

Video thumbnail

Modern Anomaly and Novelty Detection: Exercise - Session 8

GMM (gaussian mixture model) HBOS (histogram-based outlier detection)

From playlist Modern Anomaly and Novelty Detection

Video thumbnail

Christopher R. Brewer (Pt. 2) - Aesthetic Cognitivism: Overview & Concepts

Free access to Closer to Truth's library of 5,000 videos: http://bit.ly/2UufzC7 Aesthetic Cognitivism is a theory about the value of the arts as sources of understanding—the arts as more than sources of delight, amusement, pleasure, or emotional catharsis (though they can certainly be all

From playlist Aesthetic Cognitivism: Overview & Concepts - CTT Interview Series

Video thumbnail

Galois theory: Field extensions

This lecture is part of an online course on Galois theory. We review some basic results about field extensions and algebraic numbers. We define the degree of a field extension and show that a number is algebraic over a field if and only if it is contained in a finite extension. We use thi

From playlist Galois theory

Video thumbnail

How To Be A Genius

The route to our best, most genius-like thoughts is not to be afraid of our stranger-sounding insights and hunches. If you like our films, take a look at our shop (we ship worldwide): https://goo.gl/qmKUmL Join our mailing list: http://bit.ly/2e0TQNJ Or visit us in person at our London H

From playlist SELF

Video thumbnail

What is Reductionism?

There are two different types of reductionism. One is called methodological reductionism, the other one theory reductionism. Methodological reductionism is about the properties of the real world. It’s about taking things apart into smaller things and finding that the smaller things determ

From playlist Philosophy of Science

Video thumbnail

What Is the Point of Spirituality?

A lot of people are - rightly - very sceptical of what goes on under the word 'spirituality.' But might there be something of value nevertheless in aspects of what people call the spiritual? A short guide to what a highly rational mind might learn to appreciate within the concept of 'the s

From playlist SELF

Related pages

Constructive analysis | Intuitionistic type theory | Brouwer–Hilbert controversy | Negation | Constructive set theory | Philosophy of mathematics | Gottlob Frege | Game semantics | Arend Heyting | Mind | Computability logic | Fuzzy set | David Hilbert | Model theory | Foundations of mathematics | Logical disjunction | Information theory | Zermelo–Fraenkel set theory | John von Neumann | Actual infinity | Alan Turing | Natural number | Mathematics | Stephen Cole Kleene | De Morgan's laws | Henri Poincaré | Rudolf Carnap | Leopold Kronecker | Jean van Heijenoort | Intuitionistic logic | Hilary Putnam | Michael Dummett | Bertrand Russell | Law of excluded middle | Russell's paradox | Fuzzy logic | Finitism