Logical calculi | Propositional calculus | Systems of formal logic
In mathematical logic, Frege's propositional calculus was the first axiomatization of propositional calculus. It was invented by Gottlob Frege, who also invented predicate calculus, in 1879 as part of his second-order predicate calculus (although Charles Peirce was the first to use the term "second-order" and developed his own version of the predicate calculus independently of Frege). It makes use of just two logical operators: implication and negation, and it is constituted by six axioms and one inference rule: modus ponens. Frege's propositional calculus is equivalent to any other classical propositional calculus, such as the "standard PC" with 11 axioms. Frege's PC and standard PC share two common axioms: THEN-1 and THEN-2. Notice that axioms THEN-1 through THEN-3 only make use of (and define) the implication operator, whereas axioms FRG-1 through FRG-3 define the negation operator. The following theorems will aim to find the remaining nine axioms of standard PC within the "theorem-space" of Frege's PC, showing that the theory of standard PC is contained within the theory of Frege's PC. (A theory, also called here, for figurative purposes, a "theorem-space", is a set of theorems that are a subset of a universal set of well-formed formulas. The theorems are linked to each other in a directed manner by inference rules, forming a sort of dendritic network. At the roots of the theorem-space are found the axioms, which "generate" the theorem-space much like a generating set generates a group.) (Wikipedia).
C73 Introducing the theorem of Frobenius
The theorem of Frobenius allows us to calculate a solution around a regular singular point.
From playlist Differential Equations
Propositional Logic and the Algebra of Boole | MathFoundations273 | N J Wildberger
We give an overview of classical Propositional Logic, which is a branch of philosophy concerned with systematizing reason. This framework uses "atomic statements" called "propositions", and "relations", or "connectives", between them, prominently AND, OR, NOT, IMPLIES and EQUIVALENT, and t
From playlist Boole's Logic and Circuit Analysis
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
Philosophy of Mathematics & Frege (Dummett 1994)
Michael Dummett gives a talk on Frege and the philosophy of mathematics. For a good introduction to the philosophy of mathematics, check out: https://www.youtube.com/watch?v=UhX1ouUjDHE Another good introduction to the philosophy of mathematics: https://www.youtube.com/watch?v=XyXWnGFKTkg
From playlist Logic & Philosophy of Mathematics
The Ultimate Guide to Propositional Logic for Discrete Mathematics
This is the ultimate guide to propositional logic in discrete mathematics. We cover propositions, truth tables, connectives, syntax, semantics, logical equivalence, translating english to logic, and even logic inferences and logical deductions. 00:00 Propositions 02:47 Connectives 05:13 W
From playlist Discrete Math 1
Differential Equation in terms of Dependent Variable (1 of 2: Partial Fractions)
More resources available at www.misterwootube.com
From playlist Applications of Calculus
Crisis in the Foundation of Mathematics | Infinite Series
Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi What if the foundation that all of mathematics is built upon isn't as firm as we thought it was? Note: The natural numbers sometimes include zero and sometimes don't -
From playlist An Infinite Playlist
Faulhaber's Formula and Bernoulli Numbers | Algebraic Calculus One | Wild Egg
This is a lecture in the Algebraic Calculus One course, which will present an exciting new approach to calculus, sticking with rational numbers and high school algebra, and avoiding all "infinite processes", "real numbers" and other modern fantasies. The course will be carefully framed on
From playlist Algebraic Calculus One from Wild Egg
Thoughts, Thinking, & Thinkers (Tim Crane - 2017 Frege Lectures)
Professor Tim Crane gives a series of talks called "Thoughts, Thinking, & Thinkers" as part of the 2017 Frege Lectures in theoretical philosophy at the University of Tartu. Note, this is a re-upload. One of Frege’s most famous principles was ‘always to separate sharply the psychological
From playlist Philosophy of Mind
1.11.9 Russell's Paradox: Video
MIT 6.042J Mathematics for Computer Science, Spring 2015 View the complete course: http://ocw.mit.edu/6-042JS15 Instructor: Albert R. Meyer License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 6.042J Mathematics for Computer Science, Spring 2015
Russell's Paradox - A Ripple in the Foundations of Mathematics
Bertrand Russell's set theory paradox on the foundations of mathematics, axiomatic set theory and the laws of logic. A celebration of Gottlob Frege. Thank you to Professor Joel David Hamkins for your help with this video. Hi! I'm Jade. Subscribe to Up and Atom for physics, math and com
From playlist Math
Most Famous Ethical Puzzle: The Frege-Geach Problem - Philosophy Tube
One of the most famous and difficult problems in ethics! The issue that killed moral noncognitivism – The Frege-Geach Problem! Ethics Playlist: https://www.youtube.com/playlist?list=PLvoAL-KSZ32ecfEjoNjMJyKTFUS5-hNr9 Subscribe! http://www.youtube.com/subscription_center?add_user=thephilos
From playlist A-Level Philosophy
!!Con 2020 - Programming from an alternate timeline! by Matthew Dockrey
Programming from an alternate timeline! by Matthew Dockrey We take ANDs and ORs for granted, but for millennia there was only the IMPLIES of classical Aristotelian syllogisms. It wasn’t until the 19th century that mathematical logic started to emerge, and it was a long time before it look
From playlist !!Con 2020
The Philosophy of Language - John Searle & Bryan Magee (1978)
In this program, John Searle discusses the philosophy of language with Bryan Magee. This is from a 1978 series on Modern Philosophy called Men of Ideas. #Philosophy #BryanMagee #Searle
From playlist Bryan Magee Interviews - Modern Philosophy: Men of Ideas (1977-1978)
The Frenet Serret equations (example) | Differential Geometry 19 | NJ Wildberger
Following from the last lecture on the Frenet Serret equations, we here look in detail at an important illustrative example--that of a helix. The Fundamental theorem of curves is stated--that the curvature and torsion essentially determine a 3D curve up to congruence. We introduce the osc
From playlist Differential Geometry
Frege, Russell, & Modern Logic - A. J. Ayer & Bryan Magee (1987)
In this program, A. J. Ayer discusses the work of Gottlob Frege, Bertrand Russell, and modern logic with Bryan Magee. This is from the 1987 series on great philosophers. #Philosophy #Bryanmagee #BertrandRussell
From playlist Bryan Magee Interviews - The Great Philosophers (1987)
This is one of my all-time favorite differential equation videos!!! :D Here I'm actually using the Wronskian to actually find a nontrivial solution to a second-order differential equation. This is amazing because it brings the concept of the Wronskian back to life! And as they say, you won
From playlist Differential equations
The Holy Grail of Propositional Logic | MathFoundations 279 | N J Wildberger
How can we mechanically systematize reasoning? This is the Holy Grail of Propositional Logic, implicit in the aims of Aristotle and the Stoics, envisioned by Leibniz, and charted by George Boole. Here we summarize our claim that the new approach of the Algebra of Boole to Propositional log
From playlist Boole's Logic and Circuit Analysis