Chapter 8 Categorical Syllogisms Flashcards
Categorical syllogism
An argument that contains three categorical statements: the statements contain three different terms altogether, each statement contains two different terms, and no two statements contains the same two terms.
Axiom system
An organized collection of propositions in which some statements (called theorems) are deducted from others (called axioms) on the basis of definitions and strict deductive reasoning.
counterexample
a circumstance in which the premises of an argument are true while the conclusion is false.
Distributed term
a term within a categorical statement is said to be distributed is the statement makes an assertion about every member of the class denoted by the term.
Figure of a categorical syllogism
A specification of the pattern of the placement, inside the syllogism, of the syllogisms middle term. Four possible patterns exist, resulting in four possible figures.
Figure 1- middle term appears in the major premise as the subject term and in the minor premise, as the subject term.
Figure 2- middle term appears as predicate in both premises
Figure 3- middle term appears as subject in both premises
Figure 4- middle term appears as predicate in the major premise and as the subject term in the minor premise.
formally invalid argument
an argument that displays an invalid form
formally valid argument
an argument that displays a valid form
logical form of a categorical syllogism
the syllogism’s general logical structure, expressed by listing the syllogism’s mood and figure.
major premise
the premise containing the major term.
major term
the conclusion’s predicate term
middle term
the term pairing both the premises (and thus not listed in the conclusion)
minor premise
the premise containing the minor term
mood of the categorical syllogism
something that is specified by listing in order the type (AEIO) of each syllogism’s statements when it is expressed in standard form.
Perfect syllogism
a syllogism in the first figure that is self-evidently valid.
Proof by contradiction
proving a syllogistic form valid by showing that we contradict ourselves if we suppose that an instance of the corm could have true premises with a false conclusion.
