Categorical Syllogisms Notes

Categorical Syllogisms and the Logic of Arguments

Argument and Syllogisms

Argument

  • An argument contains a minimum of two statements:

    • Premise

    • Conclusion

  • Instances of reasoning concerning which it is claimed that some statement(s) provides evidence for the truth of some other statement.

Deductive vs. Inductive Arguments

  • Deductive: Conclusion proceeds from a universal proposition to a particular proposition.

    • General to Specific/Particular.

  • Inductive: Conclusion proceeds from a particular instance to a universal proposition.

    • Specific/Particular to General.

Syllogism

  • A syllogism is a deductive argument consisting of:

    • Two premises

    • One conclusion

  • Includes categorical propositions.

  • Must be in standard form.

  • Represents a connected thought.

Syllogism: Standard Form

  • Major Premise

  • Minor Premise

  • Conclusion

Example

  • Major Premise: All persons are intellectual beings.

  • Minor Premise: Plato is a person.

  • Conclusion: Therefore, Plato is an intellectual being.

Syllogism: Terms

  • Major Term (P)

  • Minor Term (S)

  • Middle Term (M)

Example

  • All wide readers are knowledgeable.

  • Alex is a wide reader.

  • Hence, Alex is knowledgeable.

Major Term (P)

  • In the example:

    • All wide readers are knowledgeable.

    • Alex is a wide reader.

    • Hence, Alex is knowledgeable.

  • The major term is "knowledgeable."

  • It is the predicate of the conclusion.

  • It is the predicate of the major premise.

Minor Term (S)

  • In the example:

    • All wide readers are knowledgeable.

    • Alex is a wide reader.

    • Hence, Alex is knowledgeable.

  • The minor term is "Alex."

  • It is the subject of the conclusion.

  • It is the subject of the minor premise.

Middle Term (M)

  • In the example:

    • All wide readers are knowledgeable.

    • Alex is a wide reader.

    • Hence, Alex is knowledgeable.

  • The middle term is "wide reader."

  • It is found in both premises, but not in the conclusion.

Validity and Soundness

Form and Content

  • Form: Refers to the structure or pattern of an argument.

  • Content: Refers to the subject matter of an argument.

Validity

  • Analyze the form of the argument.

  • Concerns only the form, not the content.

  • Only deductive arguments can be valid or invalid.

Soundness

  • Only attributed to deductive arguments.

  • Concerns both content and form.

  • A valid argument that contains only true premises is sound.

Figures of Categorical Syllogisms

First Figure: SUB-PRE


\begin{aligned}
M &P \
S &M \
\therefore S &P
\end{aligned}

  • M is the subject of the major premise and the predicate of the minor premise.

Second Figure: PRE-PRE


\begin{aligned}
P &M \
S &M \
\therefore S &P
\end{aligned}

  • M is the predicate of the major premise and the predicate of the minor premise.

Third Figure: SUB-SUB


\begin{aligned}
M &P \
M &S \
\therefore S &P
\end{aligned}

  • M is the subject of the major premise and the subject of the minor premise.

Fourth Figure: PRE-SUB


\begin{aligned}
P &M \
M &S \
\therefore S &P
\end{aligned}

  • M is the predicate of the major premise and the subject of the minor premise.

Moods of Categorical Syllogisms

  • Refers to the different arrangements of the four types of propositions (A, E, I, O).

  • Only 19 of these arrangements follow the rules of correct deduction (VALID).

  • These 19 moods are derived from mnemonic verses.

First Figure Moods

  • BARBARA

  • CELARENT

  • DARII

  • FERIO

Second Figure Moods

  • CESARE

  • CAMESTRES

  • FESTINO

  • BAROCO

Third Figure Moods

  • DARAPTI

  • FELAPTON

  • DISAMIS

  • DATISI

  • BOCARDO

  • FERISON

Fourth Figure Moods

  • CAMENES

  • DIMARIS

  • FESAPO

  • FRESISON

  • BRAMANTIP

Example Application

  • Some deadly weapons are grenades; But, all grenades are explosives; Therefore, some explosives are deadly weapons.

    1. Identify the figure (position of middle term)

    2. Identify the proposition of each premise

    3. Look for the mood (arrangement of premises)

Next Steps

  • Exercise on Categorical Syllogisms:

    • SFC Syllogism

    • Figures

    • Moods

  • Lecture: Rules on Categorical Syllogisms