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    The document defines categorical syllogisms as logical arguments with two premises and a conclusion made up of categorical statements containing exactly three terms. It discusses the standard form of syllogisms, including defining the major term, minor term, and middle term. Mood is defined as a string indicating the form of the major premise, minor premise, and conclusion. Figure is determined by the position of the middle term and can be first, second, third, or fourth. The form of a syllogism is completely determined by its mood and figure.

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    The document defines categorical syllogisms as logical arguments with two premises and a conclusion made up of categorical statements containing exactly three terms. It discusses the standard form of syllogisms, including defining the major term, minor term, and middle term. Mood is defined as a string indicating the form of the major premise, minor premise, and conclusion. Figure is determined by the position of the middle term and can be first, second, third, or fourth. The form of a syllogism is completely determined by its mood and figure.

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    The document defines categorical syllogisms as logical arguments with two premises and a conclusion made up of categorical statements containing exactly three terms. It discusses the standard form of syllogisms, including defining the major term, minor term, and middle term. Mood is defined as a string indicating the form of the major premise, minor premise, and conclusion. Figure is determined by the position of the middle term and can be first, second, third, or fourth. The form of a syllogism is completely determined by its mood and figure.

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    80 views5 pages

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    Uploaded by

    Rez Adolfo
    The document defines categorical syllogisms as logical arguments with two premises and a conclusion made up of categorical statements containing exactly three terms. It discusses the standard form of syllogisms, including defining the major term, minor term, and middle term. Mood is defined as a string indicating the form of the major premise, minor premise, and conclusion. Figure is determined by the position of the middle term and can be first, second, third, or fourth. The form of a syllogism is completely determined by its mood and figure.

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    of 5

    Standard Form, Mood, and Figure

    Definition:

    A syllogismis an argument with two premises and a conclusion

    Definition:

    A categorical syllogismis a syllogism whose premises and conclusion are


    all categorical statements and which contains exactly three terms.

    Because each categorical statement contains exactly two (distinct)


    terms, it follows from this definition that each term in a categorical syllogism
    must occur exactly twice in the argument.
    Definition:
    The major term in a categorical syllogism is the predicate term of the
    conclusion. The minor term is the subject
    term of the conclusion. The middle term is the term that occurs in each
    premise.

    Example 1: A Categorical Syllogism

    1. All good logicians are beer lovers.


    2. No politicians are good logicians.
    3. Some politicians are not beer lovers.

    Major term: beer lovers


    Minor term: politicians
    Middle term: good logicans
    Definition :

    A categorical syllogism is in standard form iff

    1. Its component statements are all in standard form (i.e., not


    stylistic variants)
    2. Its first premise contains the major term,
    3. Its second premise contains the minor term, and
    4. The conclusion is stated last.

    Example 2

    1. No birds are mammals.


    2. All dogs are mammals.
    3. Therefore, no dogs are birds.

    Definition:
    The major premise of a categorical syllogism (in standard form) is the
    premise containing the major term.
    Definition:

    The minor premise of a categorical syllogism (in standard form) is the


    premise containing the minor term.

    It follows that, in a standard form categorical syllogism, the first


    premise is the major premise and the second premise is the minor premise
    Mood and Figure

    Themoodof a categorical syllogism in standard form is a string of three


    letters indicating, respectively, the forms of the major premise, minor
    premise, and conclusion of the syllogism. Thus,the mood of the syllogism in
    Example 2 above is EAE.

    Note, however, that syllogisms can have the same mood but still differ in
    logical form. Consider the following example:

    1. No mammals are birds.


    2. All mammals are animals.
    3. Therefore, no animals are birds.

    Example 3 also has the form EAE


    But, unlike Example 2, it is invalid. Whats the difference?
    The syllogisms in Examples 2 and 3 have the following forms, respectively:

    No P are M.
    No M are P.
    All S are M.

    All M are S.
    No S are P.
    No S are P.

    These two syllogisms differ in figure


    The figure of a categorical syllogism is determined by the position of the
    middle term. There are four possible figures

    FIRST FIGURE SECOND THIRD FIGURE FOURTH


    FIGURE FIGURE
    M-P P-M M-P P-M
    S-M S-M M-S M-S
    S-P S-P S-P S-P

    The syllogism in Example 2 exhibits second figure. The one in Example 3


    exhibits third figure.

    Now for the central fact about syllogistic validity:

    The form of a categorical syllogism is completely determined


    by its mood and figure

    Aristotle worked out exhaustively which combinations of mood and


    figurec result in valid forms and which result in invalid forms. Thus,
    the form of Example 2 ( EAE-2) is valid; that of example 3 (EAE-3) is
    invalid.

    There are 256 combinations of mood and figure (64 ( 4 x 4 x 4 )


    moods x 4 ) only fifteen are valid
    The valid syllogistic forms

    FIRST FIGURE AAA , EAE , AII , EIO


    SECOND FIGURE EAE , AEE , EIO , AOO
    THIRD FIGURE IAI , AII , OAO , EIO
    FOURTH FIGURE AEE , IAI , EIO

    In working out the valid forms, Aristotle made an assumption that is


    rejected by most modern logicians, namely, that all terms denote nonempty
    classes. On this assumption, nine more forms turn out valid in addition to
    the fifteen above.

    Forms valid in Aristotelian logic only

    FIRST FIGURE AAI , EAO


    SECOND FIGURE AEO , EAO
    THIRD FIGURE AII , EAO
    FOURTH FIGURE AEO , EAO , AII

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