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Categorical Logic·Intermediate·6 lessons·~300 min
How class statements support traditional deductive reasoning
What you'll learn
Lessons
Introduces categorical propositions as class-inclusion claims, distinguishes subject and predicate terms, explains quantity and quality, and teaches students to classify every standard-form proposition as A, E, I, or O.
Introduces the square of opposition, explains the relationships of contradiction, contrariety, subcontrariety, and subalternation among A, E, I, and O propositions, and distinguishes the traditional and modern treatments of existential import.
Teaches students to represent single categorical propositions with two-circle Venn diagrams, introduces the conventions for shading and 'x' marks, and sets up the three-circle diagram used in the next lesson for syllogisms.
Teaches students to analyze the structure of a categorical syllogism by identifying its major, minor, and middle terms and classifying each premise by form, as a prerequisite for evaluation.
Applies the five classical rules of the syllogism to evaluate validity and introduces the three-circle Venn diagram as an alternative decision procedure, giving students two independent ways to check syllogistic arguments.
An integrative lesson that asks students to take mixed categorical arguments in ordinary language, put them into standard form, test them against the full rule set, and either validate or repair them.
How to study
Each lesson opens with a guided walkthrough — read it before the activity.
Look at why each step follows, not just what the answer is.
Know which rule applies and what would make the response weak before you start.
Optional context for the unit. Each lesson surfaces the concepts and rules it uses — these are here when you want the bigger picture.
A proposition asserting inclusion or exclusion between two classes, namely the subject class and the predicate class.
The term in a categorical proposition that names the class about which something is being asserted.
The term in a categorical proposition that names the class asserted to contain, exclude, or partially overlap with the subject class.
Quantity is whether a proposition is universal (about every member) or particular (about at least one member); quality is whether it is affirmative or negative.
The four standard forms of categorical proposition: A (universal affirmative), E (universal negative), I (particular affirmative), and O (particular negative).
A term is distributed in a categorical proposition if the proposition refers to every member of the class named by that term.
A diagram that represents the logical relationships among A, E, I, and O propositions sharing the same subject and predicate terms.
The question of whether a proposition, especially a universal one, carries the claim that its subject class has at least one member.
A diagram using overlapping circles to represent classes; shading indicates an empty region and an 'x' indicates at least one member.
A deductive argument consisting of exactly two categorical premises and a categorical conclusion involving exactly three terms.
The major term is the predicate of the conclusion; the minor term is the subject of the conclusion; the middle term appears in both premises but not the conclusion.