Logic

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 mind's second operation: comparing two ideas and pronouncing their agreement or disagreement. Description, definition, and the three elements of judgment.

The proposition defined as a judgment expressed in terms, with its three elements (subject, predicate, copula), the reduction of propositions to logical form, and the properties of quantity and quality.

Propositions classified as simple (the A, E, I, O forms, and the two principles governing distribution of the predicate) and compound (modal, categorical, hypothetical, complex, and multiple), with worked examples of every type.

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.

Reasoning described as mediate inference — arriving at a judgment indirectly through a third idea — and defined in terms of its three ideas (major, middle, minor) and three judgments (two premisses and a conclusion). The two methods, Induction and Deduction, with the Dictum de Omni and Dictum de Nullo.

The syllogism defined as an argument of three propositions in which the third necessarily follows from the first two; its terms and premisses named; the distinction between correctness and truth; and the classification into categorical and hypothetical syllogisms.

The eight laws of correctness for the categorical syllogism (four Laws of Terms, four Laws of Propositions), each explained and justified, plus the laws governing the three types of hypothetical syllogism, with extensive worked examples and practice syllogisms for the student to test.

The four Figures of the syllogism, determined by the position of the middle term, with their special laws; and the Moods of the syllogism, the valid arrangements of A, E, I, O propositions, sifted down from sixty-four possibilities to nineteen valid moods distributed across the figures.

The shortened or lengthened forms of the syllogism — Enthymeme, Epichirema, Polysyllogism, Sorites, and Dilemma — each with its law of correctness and worked examples, plus a note on Argument from Analogy and Argument from Hypothesis.

Five commonly used fallacies — Equivocation, Composition and Division, Evading the Point, Begging the Question, and False Cause — defined, illustrated, and equipped with practical guidance for recognizing them in everyday argument.