# Non-Categorical Syllogisms

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1. The Enthymeme
A syllogism missing one of the propositions:        John will never get a good job because he      didn’t graduate.

To formulate a syllogism, find the conclusion, then the major, minor and middle terms:              Those who did not graduate will not get          a good job. John did not graduate.                Therefore, John will not get a good job.
2. Sorites
a series of syllogisms without conclusions.
3. Progressive (Aristotelian) Sorites
• First premise contains the Subject:
•  Every man is an animal.
•  Every animal is a living thing.
•  Every living thing is a substance.
•  Every substance is an existing thing.  Therefore, every man is an existing.
•                   vs.
•  Every man is an animal.
•  Every animal is a living thing.
•  Therefore, every man is a living thing. etc.

Rules: Only the first premise may be particular, and only the last negative.
4. Regressive (Goclenian) Sorites
• First premise contains the Predicate:
•  Every substance is an existing thing.
•  Every living thing is a substance.
•  Every animal is a living thing.
•  Every man is an animal.
•  Therefore, every man is an existing thing.

Rules: Only the first premise may be negative, and only the last particular.
5. The Epicheirema
a syllogism with a causal premise (a “double syllogism”)

• Every doctor is smart because they all study hard.
• Lenny is a doctor.
• Therefore, Lenny is smart.

• This is actually two syllogisms:
•  Everyone who studies hard is smart.
•  Doctors study hard.
•  Therefore, doctors are smart.
•                         +
•  Every doctor is smart.
•  Lenny is a doctor.
•  Therefore, Lenny is smart.
6. Compound Syllogisms: Conditional Syllogisms
• the first proposition contains an “if…then” statement:
•  If Socrates is eating, then he exists.  Socrates is eating.
•  Therefore, Socrates exists.

The antecedent must be affirmed or the consequent denied for the conclusion to be affected. There must be a necessary connection between antecedent and consequent.
7. Compound Syllogisms: Disjunctive Syllogisms
• the first proposition contains an “either…or” statement:
• Strong disjunct (cannot both be true):
•  The number 4 must be either even or odd.  The number 4 is not odd.
•  Therefore, the number 4 is even.
•
• Weak disjunct (both can be true):
•  Either Socrates is walking or talking.
•  Socrates is not walking.
•  Therefore he is talking.
8. Compound Syllogisms: The Dilemma
• - the first proposition contains two contradictories:
•  No whole number can be both odd and even.  This whole number is not even.
•  Therefore, this whole number is odd
9. The Dilemma:
Has two “horns” either pointing to one conclusion or to two impossibilities.

•  Either A or B.
•  If A then C.
•  If B then C.
•  Therefore, C.
•         or:
•  Either A or B.
•  If A then C.
•  If B then D.
•  Therefore either C or D.
10. Ways out of a Dilemma:
• 1. Escaping between the horns - discovering         a third possibility.
• 2. Taking the dilemma by the horns - denying         one of the possibilities.
• 3. Rebutting a dilemma - comes up with a             counter dilemma.
11. Expository Syllogisms
Have a singular middle term:

•  Socrates was a philosopher.
•  Socraes was a Greek.
•  Therefore, a Greek was a philosopher.
•  Not really a syllogism, or useful in any way

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 Author: mgalang ID: 264699 Filename: Non-Categorical Syllogisms Updated: 2014-03-02 21:18:44 Tags: Logic Folders: Description: Non-Categorical Syllogisms Show Answers:

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