Lesson_Two_and_Test - LESSON 2 Categorical Logic Part 1...

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Section 4: Categorical Sentences , Barker, pp. 25-30. ***Read the section, then the following additional comments. Long ago in the history of logic, someone discovered that all language could ultimately be reduced to four basic types of sentences. Obviously, one would have to forego a lot of the subtlety and complexity of normal communication, but on the other hand, one could do a rigorous logical analysis on the basis of those sentences. These sentences are sometimes called “categorical” sentences. When we have presented a sentence in its proper form we say that it is a “well-formed formula,” or “categorical form.” Each categorical sentence has certain properties: a. the subject: the first category mentioned; b. the predicate: the second category mentioned; c. the copula: the word “are” which links the two categories; d. the quantity: whether the sentence is universal— indicated by the words, “all” or “no,” or particular— indicated by the word, “some”; e. the quality: whether the sentence is affirmative or negative ; f. certain levels of distribution: to what extent the subject or the predicate refer to all members of their category. 1. The first categorical sentence expresses something universal. E.g. All frogs are amphibians. Note what the components of this sentence are. a. It links two categories of things, frogs and amphibians. In this sentence “frogs” is the subject term, while “amphibians” is the predicate term. b. The two categories are brought together by a form of the verb “to be,” namely “are.” This verb is known as the copula . 1 LESSON 2 Categorical Logic, Part 1
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c. The sentence is preceded by a quantifier, “all.” It indicates the scope of the statement, viz. it refers to all frogs (though, of course, not to all amphibians). We can write this sentence as All F are A This formulation would constitute a categorical form. A sentence such as All frogs are green. could be understood as synonymous with All frogs are green things. and be symbolized as All F are G Note that we use capital letters to represent categories. Even a statement that does not have a form of “to be” in it originally can be translated that way. All frogs breathe air. translates to All F is B which you could think of as All frogs are breathers of air. (though I don’t recommend making things any more stilted than they already are). This type of sentence is referred to as an A sentence, not because “all” starts with an A, but from the Latin “ a ffirmo,” which means, “I affirm.” Thus an A sentence is a universal affirmative sentence. We can diagram it the following way. First we can make a circle containing all frogs. All the frogs in the universe, grass frogs, bull frogs, tree frogs, etc. are contained in that circle. (What a jumping, croaking collection that is!) 2
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Then we can draw a second circle containing all amphibians, not only frogs, but also salamanders and cecilians. In order to allow for the possibility that some animals belong in both categories, we draw the circles so that they overlap.
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