Logic and Categorical Syllogisms
Standard Form Categorical Syllogisms
SYLLOGISMS
* A syllogism is composed of two statements, from which a third one, the conclusion, is inferred.
CATEGORICAL SYLLOGISMS * Are syllogisms made up of three categorical propositions. * They are a type of deductive argument, that is, the conclusion (provided the argument form is valid) follows with necessity from the premises.
TWO EXAMPLES OF CATEGORICAL SYLLOGISMS 1.) All Greeks are mortal. All Athenians are Greeks. Therefore all Athenians are mortal. 2.) All mammals are animals. All humans are mammals. Therefore all humans are animals These are arguments typically known as syllogism. It has been studied and taught for more than 2 centuries.
Mood and Figure * Every standard form categorical syllogism will have three terms, with each one used twice in the three propositions which make up the syllogism. * The predicate term will be used in the major premise and the conclusion, the subject term in the minor premise and conclusion and the middle term in the two premises. * The arrangement of the four propositions--A, E, I or O--determines the mood, or ordering of the three propositions which make up the syllogism. * A syllogism with all A propositions, such as those above, is one in mood AAA. * One with E propositions as the major premise and conclusion and an I proposition as the minor premise would be in mood EIE. * Thus the order of propositions determines the mood of a categorical syllogism. * Since there are four kinds of categorical propositions and three propositions in each syllogism, there are 64 possible syllogistic moods. * Moreover, there are 16 possible arrangements of the four kinds of propositions
SYLLOGISMS
* A syllogism is composed of two statements, from which a third one, the conclusion, is inferred.
CATEGORICAL SYLLOGISMS * Are syllogisms made up of three categorical propositions. * They are a type of deductive argument, that is, the conclusion (provided the argument form is valid) follows with necessity from the premises.
TWO EXAMPLES OF CATEGORICAL SYLLOGISMS 1.) All Greeks are mortal. All Athenians are Greeks. Therefore all Athenians are mortal. 2.) All mammals are animals. All humans are mammals. Therefore all humans are animals These are arguments typically known as syllogism. It has been studied and taught for more than 2 centuries.
Mood and Figure * Every standard form categorical syllogism will have three terms, with each one used twice in the three propositions which make up the syllogism. * The predicate term will be used in the major premise and the conclusion, the subject term in the minor premise and conclusion and the middle term in the two premises. * The arrangement of the four propositions--A, E, I or O--determines the mood, or ordering of the three propositions which make up the syllogism. * A syllogism with all A propositions, such as those above, is one in mood AAA. * One with E propositions as the major premise and conclusion and an I proposition as the minor premise would be in mood EIE. * Thus the order of propositions determines the mood of a categorical syllogism. * Since there are four kinds of categorical propositions and three propositions in each syllogism, there are 64 possible syllogistic moods. * Moreover, there are 16 possible arrangements of the four kinds of propositions