Notes on Introduction to Logic -- Phil A101

William Jamison - Instructor

Lecture 5:

CHAPTER 4

Aristotelian Logic: Arguments 155

4.1 The Categorical Syllogism 156

Exercises 157

4.2 Standard-Form Syllogisms 158  

Exercises 161

4.3 Mood and Figure 164

Exercises 166

4.4 Testing the Validity of  Syllogisms 166

4.5 Testing by Counterexamples 167

Exercises 169

4.6 Testing with Venn  Diagrams 170

Exercises 171

4.7 Testing by Rules 182

Exercises 190

4.8 The Boolean Interpretation 191

In general, while the Boolean issue must be taken seriously, for the most part it only affects the Square of Opposition when it is not clear that the subject set contains exiting members. Since an A statement implies the truth of the I statement, it appears that the truth of an A statement such as, "All unicorns are animals with one horn." implies the statement, "Some unicorn is an animal with one horn." Since in English an I statement appears to indicate the existence of the particular item in the subject set, it seems that the relationships on the Square as Aristotle used it would force the conclusion that imaginary items, such as unicorns, exist -- when they do not.

4.9 Syllogistic Arguments in Ordinary Language 192

Exercises 192

Summary 199

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