Non-Categorical Syllogisms

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mgalang
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264699
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Non-Categorical Syllogisms
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2014-03-02 16:18:44
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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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