72. Determine the quality of each of the following propositions, and the distribution of its terms: (a) A few distinguished men have had undistinguished sons; (b) Few very distinguished men have had very distinguished sons; (c) Not a few distinguished men have had distinguished sons. [J.]
73. Examine the significance of few, a few, most, any, in the following propositions; Few artists are exempt from vanity; A few facts are better than a great deal of rhetoric; Most men are selfish; If any philosophers have been wise, Socrates and Plato must be numbered among them. [M.]
74. Everything is either X or Y ; X and Y are coextensive ; Only X is Y ; The class X comprises the class Y and something more. Express each of these statements by means of ordinary A, I, E, O categorical propositions. [C.]
75. Express each of the following statements in one or more of the forms recognised in the traditional scheme of categorical propositions: (i) No one can be rich and happy unless he is also temperate and prudent, and not always then; (ii) No child ever fails to be troublesome if ill taught and spoilt; (iii) It would be equally false to assert that the rich alone are happy, or that they alone are not. [V.]
76. Express, as nearly as you can, each of the following statements in the form of an ordinary categorical proposition, and determine its quality and the distribution of its terms:
(a) It cannot be maintained that pleasure is the sole good; 108
(b) The trade of a country does not always suffer, if its exports are hampered by foreign duties;
(c) The man who shews fear cannot be presumed to be guilty;
(d) One or other of the members of the committee must have divulged the secret. [C.]
77. Find the categorical propositions, expressed in terms of cases of Q or non-Q and of R or non-R, which are directly or indirectly implied by each of the following statements:
(a) The presence of Q is a necessary, but not a sufficient, condition for the presence of R ;
(b) The absence of Q is a necessary, but not a sufficient, condition for the presence of R ;
(c) The presence of Q is a necessary, but not a sufficient, condition for the absence of R.
In what respects, if any, does the categorical form fail to express the full significance of such propositions as the above? [J.]
78. “Honesty of purpose is perfectly compatible with blundering ignorance.”
“The affair might have turned out otherwise than it did.”
“It may be that Hamlet was not written by the actor known by his contemporaries as Shakespeare.”
Employ the above propositions to illustrate your views in regard to the modality of propositions; and examine the relations between each of the propositions and any assertoric proposition which may be taken to be its ground or to be partially equivalent to it. [C.]