WEEK 7B: CHAPTER 10, cont.

READ Copi/Cohen, Section 10.4, pp. 367-78

10.4: ARGUMENT FORMS AND ARGUMENTS

--TRUTH TABLES

1. [Copi/Cohen, 371] In this discussion of truth tables, "row" refers to a HORIZONTAL line of truth values, "column" refers to a VERTICAL line of truth values. For example, in the truth table on this page, the first row of values is T T T; the first column of values is T T F F.

An argument form is INVALID if there is one row of truth values where ALL the premisses are true and the conclusion is false. Remember that arguments are either VALID or INVALID. Therefore, if in the truth table there are no rows such that all the premisses are true and the conclusion is false, then the argument is NOT INVALID--or, more simply put, VALID. The point of truth tables is to determine whether or not a particular argument form is INVALID. If investigation reveals that a given argument is not invalid, then it is valid. There is no middle ground between validity and invalidity in logic. All arguments are either valid or invalid.

In the truth table on p. 371, which row shows that this argument is invalid? The answer: Row 3; in this row, all the premisses [in this case, there are only two] are true and the conclusion is false.

--DISJUNCTIVE SYLLOGISM

2. [Copi/Cohen, 372] The truth table for the Disjunctive Syllogism appears at the bottom of the page. In the paragraph just before the start of "C. Some Common Valid Argument Forms," Copi/Cohen notes that the order in which the columns of a given argument are arranged depends on the person evaluating the argument. For example, the order of columns for the truth table for the Disjunctive Syllogism could have been as follows: p p p v q q This way is acceptable, even though it locates the conclusion of the argument--q, in this case--at the end of the row. For some people it will be easier to read a truth table if the last column represents the conclusion. But, again, the order does not matter--what does matter, as Copi/Cohen stresses, is that the table be read CORRECTLY.

3. [Copi/Cohen, 373, 374] "modus ponens" and "modus tollens" are Latin expressions, as you may already know. Note that Copi/Cohen provides translations. The Latin names are commonly used for these very basic argument forms so you should learn them.

4. [Copi/Cohen, 376] Note the simple algebraic formula for determining the number of rows in an argument of "n" variables. The truth tables studied in this course will never contain more than three variables; in general, arguments with four (or more) variables become very cumbersome to evaluate using the truth table method. For these types of argument, other methods of determining validity have been formalized.

5. [Copi/Cohen, 376] The fallacies of affirming the consequent and denying the antecedent are FORMAL fallacies, i.e., they pertain to the form of their respective arguments. It does not matter what someone is trying to prove or what it is they are talking about--if either of these fallacious arguments is used, the conclusion does not follow logically from whatever is said in the premisses.

INSTRUCTIONS: Do Exercises, pp. 380, III only.