Syllogism

Syllogism: A syllogism is a form of reasoning in which a conclusion is drawn from two premises.

It was defined by Aristotle and consists of a major premise and a minor premise to form a deducted conclusion.

Example:
Socrates is a man (Minor Premise)
All men are mortal (Major Premise)
Socrates is mortal (Conclusion)

Categorical Syllogisms

Categorical syllogisms consist of three parts:
major premise = incontrovertible fact
minor premise = inestablished fact
conclusion = minor term and middle term and major term

Each part is a categorical proposition which asserts or denies that all or some of the members of one category are members of another.
Each of the premises is in the form "All A are B," "Some A are B," and "No A are B."

It is easy to commit logical fallacies using syllogisms. For example:
All women like to shop
John likes to shop
Therefore, John is a woman

This false because of the fact that if we take "All women like to shop" as being true, it doesn't mean all people that shop are women and just because John likes to shop, he does not have to be a woman.
The validity of a categorical syllogism depends on its logical form. An argument is valid when, if its premises were true, then its conclusion would also have to be true. The application of this definition in no way depends upon the content of a specific categorical syllogism. If a syllogism is valid, it is impossible for the premises to be true while the conclusion is false.

The Laws of Distribution

Subject: Noun Phrase; thing that does or is
Predicate: Verb Phrase; complete action done by subject
Distributed terms: Terms that refer to all members of a class
Undistributed terms: Terms that refer to less than all members of a class

Proposition Subject Predicate Example
A Distributed Undistributed All cats are mammals
E Distributed Distributed No cats are dogs
I Undistributed Undistributed Some cats are tabbies
O Undistributed Distributed Some cats are not tabbies

Syllogistic Fallacy

Syllogistic Fallacies are formal fallacies that occur in syllogisms.
there are eight rules to these that we talked about in class.
Rule 1: A valid affirmative conclusion cannot be reached if at least one of its premises are negative.

  • A: Universal Affirmatives - All S are P
  • E: Universal Negative - No S are P
  • I: Particular Affirmatives - Some S are P
  • O: Particular Negative - Some S are not P

Rule 2: A valid conclusion cannot be reached if both premises are negative.
Rule 3: A valid syllogism cannot be constructed with more than three terms.
Rule 4: If the major term is distributed in the conclusion, it must also be in the major premise.
Rule 5: If the minor term is distributed in the conclusion, it must also be in the minor premise.
Rule 6: A valid negative conclusion cannot be reached if both premises are affirmative.
Rule 7: The middle term must be distributed in at least one premise.
Rule 8: A particular conclusion from universal premises cannot be valid if no members of the referenced class exist.

*This rule is disputed and only implied that it exists, this rule states that every M is P, every M is S, and some S are P
P - Major term
S - Minor term
M - Middle term

Logical Syllogisms

There is a way of remembering the 15 valid syllogisms by looking at the vowels of the following test:
Adamant teacher maligning Hesiod-
teacher alleges Hesiods aloof.
"Hesiods orator: Maligning villain;"
alleges villain Hesiod.
Figure 1 Figure 2 Figure 3 Figure 4
AAA EAE EIO AEE
EAE AEE OAO IAI
AII EIO AII EIO
EIO AOO IAI
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