Metamathematics is the study of mathematics itself using mathematical methods. This study produces metatheories, which are mathematical theories about other mathematical theories. Emphasis on metamathematics (and perhaps the creation of the term itself) owes itself to David Hilbert's attempt to secure the foundations of mathematics in the early part of the 20th century. Metamathematics provides "a rigorous mathematical technique for investigating a great variety of foundation problems for mathematics and logic" (Kleene 1952, p. 59). An important feature of metamathematics is its emphasis on differentiating between reasoning from inside a system and from outside a system. An informal illustration of this is categorizing the proposition "2+2=4" as belonging to mathematics while categorizing the proposition "'2+2=4' is valid" as belonging to metamathematics. (Wikipedia).
Metacognition and speaking | Introduction | Part 1
In this video, I provide an overview of metacognition and discuss its role in speaking.
From playlist Metacognition
A Defense of Classical Theology (Part 4): Metaphysics, Being, and the Analogy of Being
In part 4 of this series, we'll discuss what metaphysics is, the fundamental notion of "being" and whether it is a generic notion, how it is said of many things, the modes of predication, and the analogy of being, and its relation to natural theology. In this video series, I will make th
From playlist Theology
Definitions, specification and interpretation | Arithmetic and Geometry Math Foundations 44
We discuss important meta-issues regarding definitions and specification in mathematics. We also introduce the idea that mathematical definitions, expressions, formulas or theorems may support a variety of possible interpretations. Examples use our previous definitions from elementary ge
From playlist Math Foundations
Intuitive Introduction to Category Theory
Category Theory offers a different style of thinking about mathematics. I describe how using functions and sets as examples. Join our Discord to engage with other Mathematics enthusiasts ! https://discord.gg/yyDzhKXUBV Patreon: https://www.patreon.com/MetaMaths Source code for animatio
From playlist Category Theory course
Wolfram Physics Project: Working Session Sept. 15, 2020 [Physicalization of Metamathematics]
This is a Wolfram Physics Project working session on metamathematics and its physicalization in the Wolfram Model. Begins at 10:15 Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by visiting our website: http://wolfr.am/physics Check out the
From playlist Wolfram Physics Project Livestream Archive
Introduction to Parametric Equations
This video defines a parametric equations and shows how to graph a parametric equation by hand. http://mathispower4u.yolasite.com/
From playlist Parametric Equations
Wolfram Physics Project: Working Session Tuesday, Aug. 10, 2021 [Physicalization of Metamathematics]
This is a Wolfram Physics Project working session on physicalization of metamathematics in the Wolfram Model. Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by visiting our website: http://wolfr.am/physics Check out the announcement post: ht
From playlist Wolfram Physics Project Livestream Archive
Wolfram Physics Project: Working Session Tuesday, Sept. 7, 2021 [Metamathematics]
This is a Wolfram Physics Project working session on metamathematics in the Wolfram Model. Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by visiting our website: http://wolfr.am/physics Check out the announcement post: http://wolfr.am/physi
From playlist Wolfram Physics Project Livestream Archive
Wolfram Physics Project: Working Session Tuesday, Feb 1, 2022 [Metamathematics]
This is a Wolfram Physics Project working session on metamathematics in the Wolfram Model. Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by visiting our website: http://wolfr.am/physics Check out the announcement post: http://wolfr.am/
From playlist Wolfram Physics Project Livestream Archive
Wolfram Physics Project: Working Session Tuesday, Dec. 21, 2021 [Metamathematics]
This is a Wolfram Physics Project working session on metamathematics in the Wolfram Model. Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by visiting our website: http://wolfr.am/physics Check out the announcement post: http://wolfr.am/
From playlist Wolfram Physics Project Livestream Archive
Wolfram Physics Project: Working Session Tuesday, Jan. 18, 2022 [Metamathematics]
This is a Wolfram Physics Project working session on metamathematics in the Wolfram Model. Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by visiting our website: http://wolfr.am/physics Check out the announcement post: http://wolfr.am/
From playlist Wolfram Physics Project Livestream Archive
Divine Proportions: Rational Trigonometry to Universal Geometry
I discuss my book Divine Proportions: Rational Trigonometry to Universal Geometry, which gives a novel way of thinking not only about trigonometry, but also Euclidean geometry. It also lays the ground work for a more rational and logical approach to other geometries, including hyperbolic g
From playlist MathSeminars
Wolfram Physics Project: Working Session Tuesday, Aug. 4, 2020 [Empirical Physical Metamathematics]
This is a Wolfram Physics Project working session on empirical physical metamathematics. Stephen discusses this in A New Kind of Science: https://www.wolframscience.com/nks/notes-12-9--empirical-metamathematics/ Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-dat
From playlist Wolfram Physics Project Livestream Archive
Wolfram Physics Project: Axiomatization of the Computational Universe Tuesday, Feb. 16, 2021
This is a Wolfram Physics Project working session about the axiomatization of the Computational Universe. Begins at 1:36 Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by visiting our website: http://wolfr.am/physics Check out the announceme
From playlist Wolfram Physics Project Livestream Archive
A short demo of getting a keycode for a board at metauni and using it to view the board in a web browser, and of using a URL for a board to jump into metauni at the exact location of a board. Music by Lucas Cantor.
From playlist Metauni
Wolfram Physics Project: Working Session Thursday, July 23, 2020 [Metamathematics | Part 1]
This is a Wolfram Physics Project progress update at the Wolfram Summer School. Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by visiting our website: http://wolfr.am/physics Check out the announcement post: http://wolfr.am/physics-announce
From playlist Wolfram Physics Project Livestream Archive
4 Ways of Thinking About Abstract Objects - Philosophy Tube
Are numbers, sets, colours and Hamlet really objects? Are they abstract? What does that mean? Metaphysics playlist: https://www.youtube.com/playlist?list=PLvoAL-KSZ32cX32PRBl1D4b4wr8DwhRQ4 Subscribe! http://www.youtube.com/subscription_center?add_user=thephilosophytube Patreon: http://ww
From playlist METAPHYSICS
MAG - Lecture 3 - Monomial orderings
metauni Algebraic Geometry (MAG) is a first course in algebraic geometry, in Roblox. In Lecture 3 we introduce monomial orderings, and some examples that suggest how monomial orderings control the division process. The webpage for MAG is https://metauni.org/mag/. This video was recorded
From playlist MAG
Wolfram Physics Project: Working Session Aug 18, 2020 [Physicalization of Empirical Metamathematics]
This is a Wolfram Physics Project working session on empirical metamathematics and its physicalization. Begins at 3:00 Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by visiting our website: http://wolfr.am/physics Check out the announcement
From playlist Wolfram Physics Project Livestream Archive