6B Mood and Figure

  • Mood and figure give you two important pieces of information about a categorical syllogism. Mood tells you the quantity and quality of the major premise, the minor premise, and the conclusion of a categorical syllogism; for example, EIO means that the major premise is an E-proposition, the minor premise is an I- proposition, and the conclusion is an O-proposition. Figure tells you the placement of the middle term in the premises:

A table is titled The Four Figures of Categorical Syllogisms. Four “figures,” labelled Figure 1, Figure 2, Figure 3, and Figure 4, appear in a row. Figure 1 shows the premise M, the premise S, and the conclusion S. Beside it is the premise P, the premise M, and the conclusion P. The two Ms are circled by a single circle. Figure 2 has premise P, premise S, and conclusion S; then premise M, premise M, and conclusion P, and the two Ms are circled by a single circle. Figure 3 has premise M, premise M, and conclusion S; then beside that premise P, premise S, and conclusion P. The two Ms are circled by a single circle. Figure 4 has premise P, then premise M, and conclusion S; next to it is premise M, premise S, and conclusion P. The two Ms are circled by a single circle.

Thus, EIO-4 represents the following categorical syllogism, in which the middle term is in Figure 4:

  • No P are M.
  • Some M are S.
  • Some S are not P.

6C Diagramming in the Modern Interpretation

  • Categorical syllogism:
  • All S. are M.
  • No P are M.
  • No S are P.

A Venn diagram featuring 3 circles is shown. The top circle is labelled M. The bottom left circle is labelled S. The bottom right circle is labelled P. The are of circle S excluding the part that overlaps with circle M is shaded blue. The area that is shared in common by circles M and P is shaded orange. The label “First premise” appears next to circle S, and a blue arrow points to the area of that circle that is shaded blue. The label “Second premise” appears to the side of circle P, and an orange arrow points to the area common to circles M and P that is shaded orange.

Conclusion “No S are P” is represented in diagram. Argument is VALID.

6I Sorites

  • Both Chapter 1 and section H of this chapter cover incomplete arguments. If you understand how to identify what’s missing in an argument, you can successfully tackle the special type of enthymeme called a sorites.

    Unlike a categorical syllogism with only two premises and a conclusion, a sorites has more than two premises and a conclusion. Your job is to organize the argument so that you can create a series of categorical syllogisms out of a sorites.

Follow these steps:

  1. Be sure the argument is translated into standard-form categorical propositions, paraphrasing as appropriate.
  2. Reveal the form of the argument by replacing terms with letters.
  3. Put the argument elements in order by identifying the conclusion’s predicate. Then locate that same term in one of the premises. This becomes the first premise. Repeat until you’ve accounted for all of the premises. The subject term of the conclusion will be found in the last premise of the sorites.
  4. The first two premises should yield a conclusion that is presently missing. Assert that conclusion.
  5. You are now ready to diagram the first two premises. If the argument is valid, you can use the conclusion as the first premise in the next leg of the argument.