Logic: The Structure of Reason
As a tool for characterizing rational thought, logic cuts across many philosophical disciplines and lies at the core of mathematics and computer science. Drawing on Aristotle’s Organon, Russell’s Principia Mathematica, and other central works, this program tracks the evolution of logic, be
From playlist Logic & Philosophy of Mathematics
Basic Methods: We note the different methods of informal proof, which include direct proof, proof by contradiction, and proof by induction. We give proofs that sqrt(2) is irrational and that there are infinitely many primes, among others.
From playlist Math Major Basics
There is a great deal of confusion about the term 'grammar'. Most people associate with it a book written about a language. In fact, there are various manifestations of this traditional term: presecriptive, descriptive and reference grammar. In theoretical linguistics, grammars are theory
From playlist VLC107 - Syntax: Part II
Teach Astronomy - Epistemology
http://www.teachastronomy.com/ The study of knowledge is called epistemology. There are two fundamental routes or paths for the study of knowledge. One is the idea of empiricism which dates back to Aristotle 25 hundred years ago. In the empirical approach to the method of science everyt
From playlist 01. Fundamentals of Science and Astronomy
A group is (in a sense) the simplest structure in which we can do the familiar tasks associated with "algebra." First, in this video, we review the definition of a group.
From playlist Modern Algebra - Chapter 15 (groups)
This video lists an explains propositional, predicate calculus axioms, as well as a set theoretical statement that goes with it, including ZF and beyond. Where possible, the explanations are kept constructive. You can find the list of axioms in the file discussed in this video here: https:
From playlist Logic
Quantum Mechanics -- a Primer for Mathematicians
Juerg Frohlich ETH Zurich; Member, School of Mathematics, IAS December 3, 2012 A general algebraic formalism for the mathematical modeling of physical systems is sketched. This formalism is sufficiently general to encompass classical and quantum-mechanical models. It is then explained in w
From playlist Mathematics
What Are Numbers? Philosophy of Mathematics (Elucidations)
What is mathematics about and how do we acquire mathematical knowledge? Mathematics seems to be about numbers, but what exactly are numbers? Are numbers and other mathematical objects something discovered or invented? Daniel Sutherland discusses some of these issues in the philosophy of ma
From playlist Logic & Philosophy of Mathematics
Stanford Seminar - On the Origin of Experience: The Shaping of Sense and the Complex World
"On the Origin of Experience: The Shaping of Sense and the Complex World" -Steven Ericsson-Zenith Colloquium on Computer Systems Seminar Series (EE380) presents the current research in design, implementation, analysis, and use of computer systems. Topics range from integrated circuits to
From playlist Engineering
Sergei Artemov: Hyperderivations
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: A well-principled notion of epistemic theory as an axiomatic description of a given scenario incorporated into the possible worlds environment is conspicuously absent in
From playlist Workshop: "Proof, Computation, Complexity"
Early Philosophical Thought (East Asia and India)
Philosophy has its roots all over the world, and although the best preserved documents are from the Western world, which is why this topic is so frequently studied from a Western perspective, there are a number of Eastern thinkers that are very much worth discussing. Let's visit Egypt, Ira
From playlist Philosophy/Logic
Hegel's Phenomenology of Spirit - Introduction (Bernstein - 2007)
Professor J.M. Bernstein introduces Hegel and discusses his initial moves and philosophical project, including the departure from Kant and Kantianism. This is the first lecture in his 2007 course on Hegel's Phenomenology of Spirit, known as "the Bernstein Tapes". Note, the audio has been h
From playlist Hegel
Introduction to Philosophy and Logic
Humans are on a quest to understand the world around us. How did this quest begin? What are the tools we use to gather knowledge? How do we know what is possible to know? What do we mean when using words like ethics, ontology, metaphysics, aesthetics, and logic? This series is going to get
From playlist Philosophy/Logic
Furio Honsell - Tribute to Ennio De Giorgi - 20 September 2016
Honsell, Furio "Implementing Cantor’s paradise in constructive type theory"
From playlist A Mathematical Tribute to Ennio De Giorgi
Stanford Seminar - Should you believe Wikipedia?
Should you believe Wikipedia? An introduction to social and virtue epistemology, with questions about the utility of philosophy for HCI researchers Amy Bruckman Georgia Institute of Technology May 7, 2021 How do we know what is "true"? Understanding the fundamental nature of truth and kn
From playlist Stanford Seminars
Inference: A Logical-Philosophical Perspective with Alexander Paseau
In this talk, Professor Alexander Paseau, Faculty of Philosophy, University of Oxford, will describe some of his work on inference within mathematics and more generally. Inferences can be usefully divided into deductive or non-deductive. Formal logic studies deductive inference, the obviou
From playlist Franke Program in Science and the Humanities
Introduction to Predicate Logic
This video introduces predicate logic. mathispower4u.com
From playlist Symbolic Logic and Proofs (Discrete Math)
