10. ILLUSTRATIVE EXERCISES.
(1a) Make use of the proper symbols and indicate the three terms of each of the attending syllogisms:
(1) All fixed stars twinkle,
Vega is a fixed star,
∴ Vega twinkles.
(2) All men are rational beings,
No tree is a rational being,
∴ No trees are men.
(3) All good citizens are law abiding,
All good citizens vote,
∴ Some who vote are law abiding.
I recall that the three terms are the middle, the major and the minor, and that the “middle” does not occur in the conclusion, whereas the “major” is always the predicate and the “minor” the subject of the conclusion. The symbols M, G and S being the initial letters of middle, greater and smaller, I make use of these in designating the three terms, as the following will illustrate:
(1) All M
fixed stars G
twinkle,
S
Vega is a M
fixed star,
∴ S
Vega G
twinkles.
“Twinkles” being the predicate of the conclusion is designated as being the major term by putting the letter G above it. Then “G” is placed above the term “twinkle” in the first premise.
“S” is placed above the subject of the conclusion to indicate that it is the minor term. “S” is also placed above “Vega,” the minor term, as found in the second premise.
The remaining term, “fixed stars,” must be the middle term, therefore I place “M” above it. The fact that “fixed star” does not occur in the conclusion verifies this.
Using only the symbols, the syllogism takes this form:
All M is G
S is M
∴ S is G
Using the symbols to represent the other syllogisms, we have
(2) All G is M
No S is M
∴ No S is G
(3) All M is G
All M is S
∴ Some S is G
(1b) Indicate by symbols the three terms of the following syllogisms:
(1) No trees are men,
All rational beings are men,
∴ No rational being is a tree.
(2) All men have the power of speech,
You are a man,
∴ You have the power of speech.
(3) Some men are wise,
All men are rational,
∴ Some rational beings are wise.
(2a) Illustrate by syllogism the fallacy of undistributed middle. An easy way is to use the middle term as the predicate of two A premises. This yields the fallacy because an A proposition does not distribute the predicate.
The illustration: distributed terms underscored.
All true teachers are students,
All scholars are students,
———————————————
∴ All scholars are true teachers.
(2b) Give two illustrations of undistributed middle.
(3a) Give syllogistic illustrations of the fallacies of illicit major and minor.
Illicit Major.
Use the middle term as the subject of an A proposition, and then as the predicate of an E proposition. This would necessitate a negative conclusion in which the major term is distributed. But the major term is not distributed in the major premise, hence the fallacy.
Illustration in which the distributed terms are underscored:
All men are mortal,
No trees are men,
——————————
∴ No trees are mortal.
Illicit Minor.
To illustrate this fallacy one may use the middle term as the subject of two A premises. This would give an A conclusion in which the subject is distributed. But this same term is not distributed in its premise because here it is used as the predicate of an A. Illustration:
All earnest students study,
All earnest students desire to succeed,
———————————————————
∴ All who desire to succeed study.