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A Few Specimens of Exercises in the Art of Reasoning

April-May 1887

Houghton Library

CONFIDENTIALLY COMMUNICATED. N.B. IT MUST NOT BE SUPPOSED THAT THESE REPRESENT MORE THAN A FEW OUT OF A LARGE NUMBER OF VARIETIES OF EXERCISES.

If your making your men work in your powder-mill at night would lose you much money, you would get your property insured. If fire is dropped into a barrel of gunpowder, there will be a terrific explosion. If the certainty that a terrific explosion would lose you much money would lead you to insure your property, you would be sure to find that no company would take the risk. Hence, if your making your men work in your powder-mill at night would make danger of fire being dropped into a barrel of gunpowder, you cannot get any company to insure your property. Show whether or not this follows.

A young king, on coming to the throne, found himself attacked by a powerful neighbor, and thereupon made the following reflections. I shall either prove myself to be a great man and conquer in the first campaign, or a prudent man and trust implicitly in my chancellor, or a fool and ruin the dynasty by headstrong rashness. If I am a great man, or popular with the army, my soldiers will stand by me. If I am a prudent man, or have good counsellors, I shall obtain the assistance of some of the neighboring princes. If I am a fool, or behave like a coward, I shall alienate my people. If my soldiers stand by me and I conquer in the first campaign, I shall reduce my enemy to vassalage, unless I ruin the dynasty by headstrong rashness in spite of good counsellors. If I gain the assistance of a neighboring prince, and trust implicitly to my chancellor, I shall certainly be compelled to behave like a coward, but I shall not ruin the dynasty by headstrong rashness. If I do not conquer in the first campaign, I shall not be positively popular with the army Of all these things I am profoundly convinced; and they afford me a legitimate ground of confidence; for I have only to resolve that I will do nothing to alienate my people unless it assures my popularity with the army, and that if I have good counsellors I will trust implicitly to my chancellor, and thus I shall be assured of reducing my enemy to vassalage. Was this conclusion well-drawn?

In a certain college, there is at least one student having an examiner and never studying unless during the recitation of some one or other of his examiners. (But it is not herein implied that there are any recitations.) Moreover, every examiner lectures at some time during the studying of all those whom he examines. Draw two conclusions, one without saying anything about examining, the other without saying anything about studying.

Required the conclusion from the following premises: 1st. There is somebody who accuses everybody to everybody, unless perhaps not to some persons who have servants who love the parties who would otherwise be accused. 2nd. There are two persons one of whom accuses every servant of the other to everybody whom that other does not benefit.

Explain how the conclusion of the following argument might be false, though the premises were true, and give the additional premise required to make it irrefragable.

Every Corsican kills a Corsican;

But nobody is killed by more than one person;

Hence, every Corsican is killed by a Corsican.

Truth being the conformity of a statement with fact, what are the facts conformity with which constitutes the truth of a hypothetical proposition, such as, “If A is true, then B is true”?

It has been held that a man is responsible for the proximate, but not for the remote, effects of his actions and negligences. Define these two kinds of effects.

Criticise the ordinary definition of a pronoun, showing that it yields no positive idea; and propose a better definition.

Show that the ordinary definition of a circle contains something superfluous.