Logic

What is Dialectics? Its definition as the science of correct thinking, its formal and material objects, its importance, and its three-part division.

What is an idea? Its description as the mind's grasp of an essence, its formation through abstraction, its constituents (Comprehension and Extension), and its formal definition.

Ideas classified by five aspects: their origin (intuitive or derivative), perfection (clear, distinct, complete), comprehension (simple/compound, concrete/abstract), extension (singular, universal, particular, transcendental), and mutual relations.

The Universal idea examined in two aspects: as Reflex Universal (the five Predicables — Species, Genus, Specific Difference, Property, Accident), and as Direct Universal (the ten Categories or Predicamentals).

What is a term? Its definition as a sensible, arbitrary sign that manifests an idea, and its classification by exactness (univocal, equivocal, analogous), by Comprehension, and by Extension.

How a term is actually used in context: Supposition (the term taken in a definite sense — material or formal) and Appellation (the application of one term to the reality expressed in another).

How ideas are explained by defining them: the types of definition (nominal, real essential, descriptive) and the four rules every valid definition must satisfy.

How ideas are explained by dividing them: the doctrine of Logical Division (its three elements — Principle, Totality, Dividing Members) and the four rules that govern a correct division.

The second mental operation: what the Judgment is, how it is defined as the mind's pronouncement on the agreement or disagreement of two ideas, and what its constituent elements are.

Just as the idea is expressed in the term, the judgment is expressed in the proposition. Its definition, three elements (subject, predicate, copula), logical form, and the properties of quality and quantity.

The full taxonomy of propositions: simple (A, E, I, O) with the two distribution principles, and compound (modal, categorical, hypothetical, complex, multiple) in all their varieties.

Propositions considered in relation to one another: Opposition (contradiction, contrariety, subcontrariety, subalternity) displayed in the Logical Square; Equipollence; and Conversion — all as means of immediate inference.

The third mental operation: reasoning described as mediate inference, defined in terms of both ideas and judgments, and divided into its two methods — induction (from particular to universal) and deduction (from universal to particular).

The syllogism defined, its terms and propositions named, correctness distinguished from truth, and the kinds of syllogism (categorical and hypothetical) enumerated and illustrated.

The eight general laws of the categorical syllogism (four laws of terms, four laws of propositions) with reasons and examples; followed by the special laws governing conditional, conjunctive, and disjunctive hypothetical syllogisms.

The four Figures of the syllogism (determined by the position of the middle term), the special laws governing each Figure, and the valid Moods — the 19 combinations of A, E, I, O propositions that survive the laws of syllogism.

Shortened and lengthened forms of the syllogism: the Enthymeme, Epichirema, Polysyllogism, Sorites, and Dilemma; followed by a note on Argument from Analogy and Argument from Hypothesis.

The five principal fallacies: Equivocation, Composition and Division, Evading the Point, Begging the Question, and False Cause — with examples and principles for detecting each.

The complete method for reducing syllogisms of the Second, Third, and Fourth Figures to the First Figure, using the mnemonic Latin names (Barbara, Celarent, etc.) and the reduction consonants s, p, m, c.