Page images
PDF
EPUB

APPENDIX.

ARTICLE I.

AN ANALYSIS OF SOME TRAINS OF REASONING.

To elucidate and at the same time to test the accuracy of those views of the reasoning process which have been unfolded in the preceding chapters, perhaps the most effectual way will be to examine some specimens of argumentation, not fashioned for the purpose, but taken from productions written without reference to theories or canons of logic. The usual course in logical treatises is to frame syllogisms or enthymemes specially adapted to exemplify the rules and observations brought forward; and this has its advantages; but it ought not to supersede an examination and analysis of the actual reasoning employed by men in their ordinary discourse and writings to convince each other. The latter procedure may be expected to bring out some points which would have otherwise escaped remark, and, at all events, it is likely enough to put to the test the soundness of any theory on the subject.

SECTION 1.

Analysis of a Demonstration in Euclid.

The first instance of reasoning which I shall select for this purpose, is the demonstration of a theorem in Euclid.

THEOREM.

An exterior angle of a triangle is equal to both its opposite interior angles, and all the interior angles of a triangle are together equal to two right angles.

B

C

E

The exterior angle BCD formed by the production of the side AC of the triangle ABC, is equal to the two opposite interior angles CAB and CBA, and all the interior

angles CA B, CBA, and BCA, are together equal to two right angles.

Through the point c draw the straight line CE parallel

to AB.

1. The interior angle BAC is equal to the exterior angle ECD, because AD is a straight line falling upon the parallel lines AB and CE. (book i. prop. 29.*) 2. Again, the alternate angles ABC and BCE are equal, because BC is a straight line falling upon the parallel lines AB and CE. (i. 29.)

3. Wherefore the two interior angles BAC and ABC are together equal to the two angles ECD and BCE or the whole angle BCD.

4. When to each of these equals is added the angle BCA, the angles BCA, BAC, and ABC, which are the three interior angles of the triangle, are together equal to the angles BCA and BCD.

5. But the angles BCA and BCD being made by the straight line BC on the same side of the straight line AD, are together equal to two right angles. (i. 13.) 6. Wherefore the three interior angles of the triangle are also together equal to two right angles.

Simson's Euclid.

In this demonstration there are six distinct steps of reasoning. The first and second steps, although in appearance enthymemes, are in reality syllogisms, having the major premises not indeed formally stated nor yet suppressed, but only referred to as propositions formerly proved, viz., "a straight line falling upon two parallel straight lines makes the exterior angle equal to the interior opposite one," and "a straight line falling upon two parallel straight lines makes the alternate angles equal."

The general principle or maxim exemplified by these two arguments, is the dictum de omni et nullo. In the latter argument, for example, the equality of the alternate angles ABC and BCE is not self-evident, but proved by the allegation previously demonstrated that all such angles are equal.

The third step is an argument not requiring a major premise. The angles BAC and ABC having been shown to be respectively equal to ECD and BCE, the first pair together are intuitively discerned to be equal to the second pair together, or to BCD.

To such reasoning, indeed, a major premise is, as we all know, sometimes appended, by citing the maxim (forming the 2nd Axiom in Simpson's Euclid) "if equals are added to equals the wholes are equal," but, as already explained, this can bring no confirmation to the argument, which is in itself perfectly conclusive. The axiom cited is only the general principle exemplified by the reasoning, and when introduced as a major premise is a logical impertinence.

The fourth step is also a self-evident argument requiring no major premise, and exemplifies the same axiom, "when equals are added to equals the wholes are equal," or more correctly, "when the same quantity is added to equals, the wholes are equal."

The fifth step is again an apparent enthymeme, with the major premise not formally stated but indicated as having been previously proved, viz. " the angles which one straight

line makes with another on the same side of it are equal to two right angles." The general principle exemplified is here, as in the first and second steps, the dictum de omni et nullo.

The sixth step, like the third and fourth steps, is a selfevident argument, not properly admitting or requiring any major premise, being complete as an enthymeme; but it exemplifies a different axiom, viz. "things which are equal to each other are equal to the same thing;" which is the converse of Euclid's, "things which are equal to the same are equal to each other."

In this demonstration, then, consisting of six steps of reasoning, three of the arguments require respectively a major premise, and three do not: the three former exemplify the dictum de omni et nullo, and the three latter exemplify respectively a mathematical axiom.

SECTION 2.

Analysis of a Passage in Burke's Letter on the French
Revolution.

The next specimen of argumentative composition which I purpose to examine, is a passage from Burke, requesting the reader to bear in mind that it is not my design to discuss the validity of the reasoning (although I may hazard incidental remarks on that point), but to exhibit the nature of the various arguments adduced.

may

It be useful to observe, before quoting the passage, that there is one very marked distinction between mathematical and what is usually called moral reasoning, or rather argumentative composition on moral and political topics. In the former, no proposition which is not selfevident is introduced without being proved. The latter, on the contrary, often abounds with mere assertions as well as arguments, presenting the two so intermingled that it

is not always easy to separate them. The reasoning, moreover, is not seldom elliptical, disjointed, and irregular, so that both skill and patience are required to reduce it into a definite shape and proper order. The portion of argumentative composition which I have now to analyse, is as follows:

1. "All persons possessing any portion of power ought to be strongly and awfully impressed with an idea that they act in trust; and that they are to account for their conduct in that trust to the one great master, author, and founder of society.

This principle ought even to be more strongly impressed upon the minds of those who compose the collective sovereignty than upon those of single princes. 2. Without instruments, these princes can do nothing. Whoever uses instruments, in finding helps finds also impediments. Their power is, therefore, by no means complete.

3. Nor are they safe in extreme abuse. Such persons, however elevated by flattery, arrogance, and self-opinion, must be sensible that whether covered or not by positive law, in some way or other they are accountable even here for the abuse of their trust. If they are not cut off by a rebellion of their people, they may be strangled by the very janissaries kept for their security against all other rebellion. Thus we have seen the King of France sold by his soldiers for an increase of pay.

4. But where popular authority is absolute and unrestrained, the people have an infinitely greater, because a far better-founded, confidence in their own power. They are themselves, in a great measure, their own instruments. They are nearer to their objects.

5. Besides, they are less under responsibility to one of the greatest controlling powers on earth, the sense of fame and estimation.

« PreviousContinue »