Studies and Exercises in Formal Logic

by John Neville Keynes

which is absurd.[164]

[¹⁶⁴] Compare De Morgan, Formal Logic, p. 25. Granting the validity of obversion, the contraposition of E and the contraposition of O may be established similarly.

All the above are interesting, as illustrating the processes of immediate inference; but regarded as proofs they labour under the disadvantage of deducing the less complex by means of the more complex.

EXERCISES.

111. Give all the logical opposites of the proposition,—Some rich men are virtuous; and also the converse of the contrary of its contradictory. How is the latter directly related to the given proposition?
Does it follow that a proposition admits of simple conversion because its predicate is distributed? [K.]

112. Point out any ambiguities in the following propositions, and give the contradictory and (where possible) the converse of each of them:—(i) Some of the candidates have been successful; (ii) All are not happy that seem so; (iii) All the fish weighed five pounds. [K.]

113. State in logical form and convert the following propositions:—(a) He jests at scars who never felt a wound; (b) Axioms are self-evident; (c) Natives alone can stand the climate of Africa; (d) Not one of the Greeks at Thermopylae escaped; (e) All that glitters is not gold. [O.]

114. “The angles at the base of an isosceles triangle are equal.” What can be inferred from this proposition by obversion, conversion, and contraposition respectively? [L.]

154 115. Give the obverse, the contrapositive, and the inverse of each of the following propositions:—The virtuous alone are truly noble; No Athenians are Helots. [M.]

116. Give the contrapositive and (where possible) the inverse of the following propositions:—(i) A stitch in time saves nine; (ii) None but the brave deserve the fair; (iii) Blessed are the peacemakers; (iv) Things equal to the same thing are equal to one another; (v) Not every tale we hear is to be believed. [K.]