In logic, a categorical proposition, or categorical statement, is a proposition that asserts or denies that all or some of the members of one category (the subject term) are included in another (the predicate term). The study of arguments using categorical statements (i.e., syllogisms) forms an important branch of deductive reasoning that began with the Ancient Greeks. The Ancient Greeks such as Aristotle identified four primary distinct types of categorical proposition and gave them standard forms (now often called A, E, I, and O). If, abstractly, the subject category is named S and the predicate category is named P, the four standard forms are: * All S are P. (A form, ) * No S are P. (E form, ) * Some S are P. (I form, ) * Some S are not P. (O form, ) Surprisingly, a large number of sentences may be translated into one of these canonical forms while retaining all or most of the original meaning of the sentence. Greek investigations resulted in the so-called square of opposition, which codifies the logical relations among the different forms; for example, that an A-statement is contradictory to an O-statement; that is to say, for example, if one believes "All apples are red fruits," one cannot simultaneously believe that "Some apples are not red fruits." Thus the relationships of the square of opposition may allow immediate inference, whereby the truth or falsity of one of the forms may follow directly from the truth or falsity of a statement in another form. Modern understanding of categorical propositions (originating with the mid-19th century work of George Boole) requires one to consider if the subject category may be empty. If so, this is called the hypothetical viewpoint, in opposition to the existential viewpoint which requires the subject category to have at least one member. The existential viewpoint is a stronger stance than the hypothetical and, when it is appropriate to take, it allows one to deduce more results than otherwise could be made. The hypothetical viewpoint, being the weaker view, has the effect of removing some of the relations present in the traditional square of opposition. Arguments consisting of three categorical propositions — two as premises and one as conclusion — are known as categorical syllogisms and were of paramount importance from the times of ancient Greek logicians through the Middle Ages. Although formal arguments using categorical syllogisms have largely given way to the increased expressive power of modern logic systems like the first-order predicate calculus, they still retain practical value in addition to their historic and pedagogical significance. (Wikipedia).
IAML2.7: Categorical (nominal) attributes
From playlist Thinking about Data
Introduction to Propositional Logic and Truth Tables
This video introduces propositional logic and truth tables. mathispower4u.com
From playlist Symbolic Logic and Proofs (Discrete Math)
Categorical actions in geometry and representation theory - Clemens Koppensteiner
Short talks by postdoctoral members Topic: Categorical actions in geometry and representation theory Speaker: Clemens Koppensteiner Affiliation: Member, School of Mathematics Date: September 29, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
From playlist e. Sets and Logic
Categorical joins - Alex Perry
Workshop on Homological Mirror Symmetry: Methods and Structures Title: Categorical joins Speaker: Alex Perry Affiliation: Harvard Date: November 7, 2016 For more video, visit http://video.ias.edu
From playlist Mathematics
Introduction to Predicate Logic
This video introduces predicate logic. mathispower4u.com
From playlist Symbolic Logic and Proofs (Discrete Math)
Towards elementary infinity-toposes - Michael Shulman
Vladimir Voevodsky Memorial Conference Topic: Towards elementary infinity-toposes Speaker: Michael Shulman Affiliation: University of San Diego Date: September 13, 2018 For more video please visit http://video.ias.edu
From playlist Mathematics
Implication and Biconditional Statements
The definition of implication and biconditional connectives along with some laws for working with them, plus the definition of tautology and contradiction. (In the part I got hung up on in the video, "p is necessary for q" can be read "p if q" (or "if q, then p"), and "p is sufficient fo
From playlist Linear Algebra
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
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
Perverse schobers and semi-orthogonal decompositions - Mikhail Kapranov
Vladimir Voevodsky Memorial Conference Topic: Perverse schobers and semi-orthogonal decompositions Speaker: Mikhail Kapranov Affiliation: Institute for Advanced Study Date: September 14, 2018 For more video please visit http://video.ias.edu
From playlist Mathematics
Category Theory 8.2: Type algebra, Curry-Howard-Lambek isomorphism
Type algebra, Curry-Howard-Lambek isomorphism
From playlist Category Theory
The synthetic theory of ∞-categories vs the synthetic theory of ∞-categories - Emily Riehl
Vladimir Voevodsky Memorial Conference Topic: The synthetic theory of ∞-categories vs the synthetic theory of ∞-categories Speaker: Emily Riehl Affiliation: Johns Hopkins University Date: September 12, 2018 For more video please visit http://video.ias.edu
From playlist Mathematics
Distinguishing fillings via dynamics of Fukaya categories - Yusuf Baris Kartal
Symplectic Dynamics/Geometry Seminar Topic: Distinguishing fillings via dynamics of Fukaya categories Speaker: Yusuf Baris Kartal Affiliation: Massachusetts Institute of Technology Date: November 12, 2018 For more video please visit http://video.ias.edu
From playlist Symplectic Dynamics
Laurent Lafforgue - 1/4 Classifying toposes of geometric theories
Course at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Slides: https://aroundtoposes.com/wp-content/uploads/2021/07/LafforgueSlidesToposesOnline.pdf The purpose of these lectures will be to present the theory of classifying topose
From playlist Toposes online
Univalent foundations and the equivalence principle - Benedikt Ahrens
Vladimir Voevodsky Memorial Conference Topic: Univalent foundations and the equivalence principle Speaker: Benedikt Ahrens Affiliation: University of Birmingham Date: September 12, 2018 For more video please visit http://video.ias.edu
From playlist Vladimir Voevodsky Memorial Conference
From playlist STAT 200 Lectures (OER)
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
This video focuses on how to write the converse of a conditional statement. In particular, this video shows how to flip the hypothesis and conclusion of a conditional statement. The concepts of truth value and logical equivalence are explored as well. Your feedback and requests are encour
From playlist Geometry
Olivia Caramello - 3/4 Introduction to sheaves, stacks and relative toposes
Course at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Slides: https://aroundtoposes.com/wp-content/uploads/2021/07/CaramelloSlidesToposesOnline.pdf This course provides a geometric introduction to (relative) topos theory. The fir
From playlist Toposes online