https://teddyrookbook.com/logic/traditional-logic/Recent content in Traditional Logic on Teddy Rook Bookhttps://teddyrookbook.com/img/share.jpghttps://teddyrookbook.com/img/share.jpgHugoenhttps://teddyrookbook.com/logic/traditional-logic/three-acts/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/three-acts/Simple apprehension grasps a term, judgment joins terms into a proposition, and reasoning moves from propositions to a conclusion. Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/terms/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/terms/A term is a word or phrase that names a class or an individual; singular terms name one thing, general terms name a class. Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/extension-intension/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/extension-intension/A term's extension is the set of things it applies to; its comprehension (intension) is the set of features it implies. Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/genus-species/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/genus-species/A genus is a wider class divided into species; the same class can be a species of one genus and a genus of narrower species. Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/predicables/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/predicables/A predicate can relate to its subject as genus, species, difference, property (always goes with it) or accident (may or may not). Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/division/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/division/A good division splits a genus into species by one principle, so that the parts are exclusive and together exhaustive. Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/categorical-propositions/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/categorical-propositions/A categorical proposition relates two classes: quantifier, subject term, copula (are or are not) and predicate term. Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/aeio/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/aeio/A: All S are P. E: No S are P. I: Some S are P. O: Some S are not P. Quantity is universal or particular; quality is affirmative or negative. Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/translating-nonstandard/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/translating-nonstandard/Turn verbs into "are" plus a class, singular statements into "All S are P", and words like "every", "none" and "a few" into the four quantifiers. Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/only-exceptives/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/only-exceptives/"Only S are P" and "None but S are P" become "All P are S"; "All except S are P" makes two claims. Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/distribution/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/distribution/A term is distributed when the proposition says something about every member of its class: A distributes S, E both, I neither, O the predicate. Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/venn-propositions/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/venn-propositions/Shade a region to show it is empty; put an X in a region to show something is there. A and E shade; I and O place an X. Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/existential-import/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/existential-import/In the modern (Boolean) reading, A and E say nothing about whether S exists; I and O do. The traditional reading assumes the subject class is not empty. Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/square/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/square/A, E, I and O with the same terms sit at the corners of a square; its sides and diagonals name how their truth values are tied. Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/contradictories/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/contradictories/A and O, and E and I, are contradictories: exactly one of each pair is true. Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/contraries-subcontraries/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/contraries-subcontraries/A and E cannot both be true but can both be false; I and O cannot both be false but can both be true. Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/subalternation/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/subalternation/On the traditional square, truth flows down from A to I and from E to O, and falsity flows up from I to A and from O to E. Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/square-inferences/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/square-inferences/Given the truth value of one corner, work out each other corner as true, false or undetermined. Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/modern-square/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/modern-square/Without existential import only the contradictory diagonals survive; contrariety, subcontrariety and subalternation can fail when a class is empty. Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/complements/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/complements/The complement of a class is everything outside it: non-P. The complement of non-P is P. Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/conversion/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/conversion/Conversion swaps subject and predicate. It is valid for E and I, not for A or O (A converts only by limitation, on the traditional reading). Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/obversion/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/obversion/Obversion changes the quality (affirmative to negative or back) and replaces the predicate with its complement; it is valid for all four forms. Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/contraposition/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/contraposition/Contraposition swaps subject and predicate and replaces both with their complements. It is valid for A and O, not for E or I. Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/immediate-chains/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/immediate-chains/Combine conversion, obversion, contraposition and the square to decide whether one proposition follows from another. Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/syllogism-parts/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/syllogism-parts/A categorical syllogism has three propositions and three terms: the major term (predicate of the conclusion), minor term (subject of the conclusion) and middle term. Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/syllogism-standard-form/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/syllogism-standard-form/In standard form the major premise (with the major term) comes first, then the minor premise, then the conclusion. Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/mood/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/mood/The mood is the three letters of the major premise, minor premise and conclusion, in that order, such as AII or EAE. Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/figure/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/figure/The figure (1 to 4) records where the middle term sits: subject then predicate, predicate twice, subject twice, or predicate then subject. Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/venn-syllogism/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/venn-syllogism/Draw three circles, diagram both premises, and the syllogism is valid when the conclusion is already shown without drawing anything more. Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/venn-particular/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/venn-particular/Diagram universal premises first; place an X in a region only if the other region it could go in is shaded, otherwise put it on the line. Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/rules-terms/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/rules-terms/The middle term must be distributed at least once, and a term distributed in the conclusion must be distributed in its premise. Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/rules-quality/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/rules-quality/Two negative premises prove nothing; a negative premise requires a negative conclusion, and a negative conclusion requires a negative premise. Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/syllogism-fallacies/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/syllogism-fallacies/Each broken rule has a name: undistributed middle, illicit major, illicit minor, exclusive premises, affirmative from a negative, the existential fallacy, four terms. Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/valid-forms/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/valid-forms/Fifteen mood-and-figure combinations are valid on the modern reading, such as AAA-1 (Barbara), EAE-1 (Celarent) and AII-3 (Datisi). Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/conditional-validity/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/conditional-validity/Nine more forms, such as AAI-1 and EAO-2, are valid only if a class is assumed to have members; the Venn test shows which class. Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/reducing-terms/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/reducing-terms/When an argument seems to have four or more terms, use synonyms, complements and obversion to bring it down to three. Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/everyday-syllogisms/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/everyday-syllogisms/Put each statement in standard form, find the three terms, arrange the syllogism, then test it by the rules or a Venn diagram. Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/enthymemes/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/enthymemes/An enthymeme is a syllogism with a premise or the conclusion left unstated; supply the missing part so the syllogism is valid, then judge whether it is true. Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/sorites/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/sorites/A sorites is a chain of premises that leads to one conclusion through several hidden intermediate conclusions; it is valid when every link is a valid syllogism. Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/hypothetical-propositions/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/hypothetical-propositions/A hypothetical proposition joins an antecedent and a consequent: "If P, then Q". "Q if P", "P only if Q" and "Q provided that P" say the same. Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/modus-ponens/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/modus-ponens/From "If P, then Q" and "P", conclude "Q". Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/modus-tollens/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/modus-tollens/From "If P, then Q" and "not Q", conclude "not P". Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/hypothetical-fallacies/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/hypothetical-fallacies/Affirming the consequent (Q, so P) and denying the antecedent (not P, so not Q) are invalid; the consequent can come about some other way. Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/pure-hypothetical/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/pure-hypothetical/From "If P, then Q" and "If Q, then R", conclude "If P, then R"; the links must run in the same direction. Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/disjunctive-syllogism/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/disjunctive-syllogism/From "P or Q" and "not P", conclude "Q". From "P or Q" and "P", nothing follows about Q unless the "or" is exclusive. Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/conjunctive-syllogism/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/conjunctive-syllogism/From "Not both P and Q" and "P", conclude "not Q". From "not P", nothing follows. Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/dilemmas/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/dilemmas/A constructive dilemma reasons from "If P then Q, and if R then S" and "P or R" to "Q or S"; a destructive dilemma from "not Q or not S" to "not P or not R". Traditional Logic · Logic Ladderhttps://teddyrookbook.com/logic/traditional-logic/answering-dilemmas/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/logic/traditional-logic/answering-dilemmas/Escape between the horns (show a third option), grasp a horn (deny a conditional premise), or offer a counterdilemma. Traditional Logic · Logic Ladder