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Lesson_Four_and_Test

# Lesson_Four_and_Test - LESSON 4 Categorical Logic Part 3...

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Section 7: The Syllogism , Barker, pp. 44-50. ***Read the section, then the following additional comments. For the next little while the focus of our attention will be on the syllogism . To qualify as an authentic syllogism, an argument must follow some very strict rules; in order to be a valid syllogism it must observe even more rules. First the basic ones: 1. A syllogism consists of three categorical sentences: two premises and a conclusion. 2. The three categorical sentences share exactly three category terms among themselves. That means that each term appears twice. E.g. All wheels are round objects. All tires are wheels. Therefore, all tires are round objects. Note that there are three terms, “wheels,” “round,” and “tires.” Each term shows up in two different sentences. 3. The term, “wheels,” appears in the two premises, but not the conclusion. There will always be one such term in a syllogism. We call the term that is in both premises, but not the conclusion, the middle term. 4. The other two terms, “round” and “tires,” both show up in the conclusion. “Tires” is the subject of the conclusion, “round” is the predicate. 5. The term that is the predicate of the conclusion is called the major term. We write the premise that contains the major term first, and we refer to it as the major premise . 6. The term that is the subject of the conclusion is called the minor term. We write the premise that contains the minor term second, and we refer to it as the minor premise . Thus in our example, “round” is the major term, “tires” is the minor term. If we were to invert major and minor premises, the logical validity of the syllogism would not be changed, but we would not be able to apply our standard evaluation techniques to it. 7. Based on the categorical sentences used in a syllogism, we have the mood of the syllogism. In the example, there are three A sentences used; consequently the mood of the syllogism is AAA. Theoretically, there can be EAE, III, OAI, or any other possible combinations of categorical sentences to be the moods of syllogisms. You will shortly realize that many moods are so patently invalid that there is little need to worry about them. 1 LESSON 4 Categorical Logic, Part 3

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8. Where in a syllogism the middle term appears reveals to us the figure of a syllogism. There are four possible combinations, so syllogisms come in four figures. The convention of how to determine the figure of a syllogism is well portrayed by Barker’s “shirt collar” diagram on page 45. Here is another summary: first second third fourth major premise: mid -maj maj- mid mid -maj maj- mid \ | | / minor premise: min- mid min- mid mid -min mid -min 9. If you apply the categories of mood and figure to our example, you see that its mood is AAA; it is in the first figure. We shall abbreviate this classification as “AAA-1.” Let us look at what happens if we take the same example and put it into different figures: AAA-1: All wheels are round objects.
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Lesson_Four_and_Test - LESSON 4 Categorical Logic Part 3...

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