4.1 The Components of Categorical Propositions - ppt download

4.1 Continued Standard Form: Requires the quantifiers “all,” “no,” or “some.” The subject term is a noun or noun phrase. The copula, or links between subject and predicate terms are “are” or “are not.” The predicate term is a noun or noun phrase.
4.1 The Components of Categorical Propositions
Relate subject terms and predicate terms. Either all or part of the class denoted by the subject term is included or excluded from the class denoted by the predicate term.
Requires the quantifiers all, no, or some. The subject term is a noun or noun phrase. The copula, or links between subject and predicate terms are are or are not. The predicate term is a noun or noun phrase.
Affirmative: All S are P. Some S are P. Negative: No S are P. Some S are not P.
Some S are P. Some S are not P.
E: universal negative. I: particular affirmative. O: particular negative.
Is something being asserted about every member of the s or p class
Aristotle held that universal propositions about existing things have existential import. George Boole held that no universal propositions have existential import. John Venn (who perfected Boole’s theory) developed a system of diagrams to represent the information they express.
4.3 Continued The Modern Square of Opposition: a relationship of mutually contradictory pairs of propositions.
Some trade spies are not masters of bribery. Therefore it is false that all trade spies are masters of bribery.
Testing immediate inferences for validity: It is false that all A are B. It is false that some A are B. We diagram the following way:
Therefore, it is false that some T are M. We diagram the following way: It is false that all M are C. Therefore, no M are C. And finally, All S are W. Some S are W.
The Existential Fallacy is a formal fallacy that occurs whenever an argument is invalid merely because the premise lacks existential import. All A are B. Therefore some A are B. It is false that some A are not B. Therefore it is false that no A are B.
Subject and predicate switch places. No cats are dogs; no dogs are cats.
Replace predicate with its term complement. All horses are animals, no horses are non-animals.
Replace each with its term complement. All horses are animals; all non-animals are non-horses.
Adopts the Aristotelian standpoint that universal propositions about existing things have existential import. Contradictory = opposite truth value. Contradictories: A-O and E-I (same as modern square). Contrary = at least one is false. Contraries: A-E.
Subcontraries: I-O. Subalternation: Truth Flows Down from A-I and E-O. Falsity Flows Up from I-A and O-E.
All Swiss watches are true works of art. Therefore it is false that no Swiss watches are works of art. The Existential Fallacy: from the Aristotelian standpoint, committed only when contrary, sub- contrary and subalternation are correctly used to draw inferences about things that do not exist.
Conditionally Valid applies to an argument from the Aristotelian standpoint, when we are not certain whether the subject term of the premise actually denotes an existing thing.
Symbolize Universal categorical propositions from the Aristotelian standpoint. The Aristotelian standpoint is that universal propositions have existential import when they refer to existing things.
4.6 Continued Proving the Traditional Square of Opposition Through the Use of Venn Diagrams
If inferences are valid, they are valid from both Aristotelian and Boolean standpoints. Invalid Boolean references may be valid from the Aristotelian standpoint. Test an inference form for validity from the Boolean Standpoint. Then adopt the Aristotelian standpoint (above).
Then, since it is invalid from the Boolean standpoint, adopt the Aristotelian standpoint.
Terms Without Nouns. If a term consists only of an adjective, a plural noun or pronoun should be introduced to make the term genuinely denotative. Some roses are red. Some roses are red flowers.
Statements in ordinary usage often incorporate forms of the verb to be rather than are and are not. Some college students will become educated. Some college students are people who will become educated.
This proposition makes an assertion about a specific noun, while the parameter affects the form, not the meaning. George went home. All people identical to George are people who went home.
Spatial and temporal adverbs may be respectively translated in terms of places and times. He is always clean shaven. All times are times he is clean shaven.
Be guided by the most probable quantifier. Emeralds are green gems. All emeralds are green gems. Or. There are lions in the zoo. Some lions are animals in the zoo.
Other than All , Some or No. Standard quantifier: Some soldiers are heroic. Nonstandard quantifier: A few soldiers are heroes.
If it is a mouse then it is a mammal. All mice are mammals. If it is a turkey, then it is not a mammal. No turkeys are mammals.
Only, None but, None except, None but the brave deserve the fair. All people who deserve the fair are brave people.
The only animals that live in this canyon are skunks. All animals that live in this canyon are skunks.
Take the forms, All except S are P and All but S are P. All except students are invited. No students are invited people and all non-students are invited people.

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