Unit 3: Clarifying Meaning

Study Guide

Analysis of statements consists of techniques for analyzing and clarifying meaning. The three main skills to acquire are: learning to recognize and classify the various "fallacies of clarity" (1), and then, to avoid them, learning what a "definition" is, and how to criticize such a thing (2, 3, 4).

  1. Identifying some "fallacies of clarity".
  2. Some persuasive but invalid arguments rely upon a shift in meaning of a key term, so that two distinct premises can appear to be one. Learning how to recognize and identify these is the first main skill listed above. Various arguments in ordinary English will be given, and you will be asked to identify which of the fallacies of clarity they commit. (It may be helpful to look at the beginning of section 6.1, on fallacies in general, before trying these.) There will be seven such arguments in all, worth 30% of the final grade.
    Identifying fallacies is much harder than it looks; you will need to practice with as many sample problems as you can. The critical exercises for this skill are 3.7 and 3.8. See also the following slide shows:
    See also the following slide shows:

    Equivocation and Slippery Slope

    Composition and Division

  3. Some technical definitions.
  4. Talking about the meaning of words is a finicky business. As you might imagine, one must be very careful about the meanings of the words one uses when one talks about the meanings of words. So the first order of business is to learn (and be able to state) the technical definitions for
    extension / intension / connotation
    ambiguous / vague
    collective attribution / distributive attribution (§ 3.3)
    definiens / definiendum
    necessary condition / sufficient condition
    too broad / too narrow
    See sections 3.2, 3.4, 3.5. You will be asked to provide three definitions, in all worth 21% of the final grade.

  5. Principles of adequate definitions.
  6. There will be some true-false questions on the principles of adequate definitions. Some will require you to tell whether or not some condition S is a necessary (or sufficient) condition for some condition P. Try the examples given in exercises 3.1 - 3.6. (There will be eight such questions, worth 17% of the final grade.)
  7. Demonstrating that a definition is too broad or too narrow.
You will be given two items that include inadequate definitions. If the definition is too broad, you should be able to think of an example to show that it is too broad. Similarly if the definition is too narrow. These two aspects require different sorts of examples, and be sure you understand what sort of example is needed for each. Try to do this with exercise 3.9. Review the connections between necessary conditions, sufficient conditions, too broad, and too narrow.
One item will ask you to criticize a bad definition for a technical term introduced in unit 1 of this course, so you might review those definitions. The two "inadequate definition" items together are worth 31% of the final grade.
For items 2-4, see the other two lecture slide shows for this unit:

Principles of Adequate Definitions

Criticizing Definitions as Too Broad, Too Narrow

Recommended sections from Patrick Hurley’s Concise Introduction to Logic:

This is the optional but recommended text for this course, and it has some useful material for this unit.
Hurley describes the Slippery Slope fallacy on p 146, and the other fallacies of clarity (Equivocation, Composition, and Division) in Section 3.4, pp. 164 ff. Because they are mixed in with a large collection of other fallacies, his exercises for 3.3 and 3.4 will probably be far too difficult at this point. (They will be useful for unit 6, where the fallacies of clarity are included again, together with a bunch of other ones.)
Chapter 2 of Hurley is very useful as a supplemental explanation of varieties of meaning and principles of definition. See sections 2.1 and 2.2 on varieties of meaning and the extension/intension distinction. Exercise 2.2, part II, p. 92, and ex. 2.3, part III, p 100, might be helpful for our part 3.
Sections 2.3 and 2.4 go into considerable detail on principles of definition; he explains purposes and techniques of definition more fully than I do. Likewise section 2.5 gives eight rules for adequate definitions, while for our purposes the only essential rule is rule 3 ("a definition should be neither too broad nor too narrow"). Exercises 2.4, part I, p 107 and 2.5, part I, p 214, provide many examples of inadequate definitions to be criticized, as in our part 4. These exercises are also both found in the "LogicCoach" software on the CD Rom that comes with the book.