These two aspects are sometimes positive and negative, as,

The man we are speaking of is enslaved by his appetites;

Therefore he is not free.

They are sometimes active and passive, as,

The Duke of Wellington vanquished Bonaparte;
Therefore Bonaparte was vanquished by the
Duke.*

Sometimes such inferences amount to little more than varieties in the expression of the same fact, and many of them undoubtedly seem puerile, but they are demonstrative, and, notwithstanding their apparent puerility when standing alone, they are often convenient stepping-stones in argumentative discourse, when their trivial character is merged in their transitional utility.†

All these we may rank amongst convenient and useful inferences, and with equal reason we may place in the same class such as we have been engaged in discussing those, namely, of really demonstrative syllogisms - notwithstanding the un

* A modern author, in reference to a similar example, says, "We either think that Philip was beaten by Peter, or that Peter beat Philip; two distinct thoughts, though relating to one fact. In reading from the tablet of our mind, we may bring forward the images in one order, or in another.". Outline of the Laws of Thought, p. 109.

† For some actual examples of such inferences as are here described, see Examination of a passage from Burke in the Appendix, Article 1.

deniable fact that the conclusion is always contained in the major premise.

The admission of this truth detracts, it must be owned, from the importance of demonstrative classreasoning as it stands in general estimation, and circumscribes such reasoning within very narrow boundaries.

It is an obvious reflection, that if no fact can be inferred in syllogistic reasoning but what is contained in the major proposition, no science can possibly be constructed by a series of real or legitimate syllogisms alone. Hence there must be a fallacy in the assertion that the science of Geometry can be exhibited in such a series. This feat has, I am aware, been ostensibly accomplished, and the way in which it has been performed presents no difficulty *; but, as I shall hereafter have occasion to show, it has been done solely by the introduction of redundant propositions, merely incumbering the demonstration, and disguising the real source of the validity of those arguments into which they are so unavailingly intruded. Such syllogisms may be fairly termed spurious.

* In Stewart's Elements, vol. ii. p. 260, it is stated that the first six books of Euclid had been exhibited in syllogisms by two writers named Herlinus and Dasypodius. See also Sir Wm. Hamilton's Edition of Reid's Works, p. 702, where the same fact is mentioned.

CHAP. IV.

CONTINGENT UNDER THE FORM OF DEMONSTRATIVE

REASONING.

I HAVE now taken a survey of contingent and demonstrative reasoning, and endeavoured to show the nature and cogency of each species, and also the general principles on which they proceed or which they exemplify.

But I have still to notice a large class of cases in reasoning which partake of the character of both; which, while they are contingent in reality, are demonstrative in form.

It has been already explained that the formation of general laws, extending beyond the observed facts from which they are derived, is, in every instance, an act of contingent reasoning; that general laws rest on the same evidence or are deduced from the same premises as particular inferences.

It is, nevertheless, a common and often a very convenient practice, first to deduce the general law, and afterwards from the general law to draw the particular inference, which then wears the appearance of a demonstrated truth.

The subject may be elucidated by an instance of reasoning similar to one before given.

All human beings, as far as observation has extended, have been found fallible

Therefore the unknown author of the book just put into my hands is fallible.

This, which is a good material argument, an instance of forcible contingent reasoning, may be converted into the following demonstration by assuming as a major premise the general law which is deducible from the preceding uniform fact. All human beings are fallible;

Therefore the author of this book is fallible. It is obvious, nevertheless, that the real nature of the reasoning cannot be altered by changing the form in which it is expressed. The evidence of the fallibility of human beings consists in previous known instances of the intellectual qualities exhibited by them; and the conclusion drawn from these instances is as to the intellectual qualities of a writer concerning whom we know nothing. The process is really inferring from what has existed in all similar, i. e. all other cases, what exists in this

case.

As a further illustration, let us examine a piece of reasoning often cited in logical treatises.

All horned quadrupeds are ruminant;

Therefore this horned quadruped is ruminant. Whether we take this enthymeme as it is, or make it, by the introduction of a minor premise, into a regular syllogism, the conclusion drawn is

irresistible. You cannot admit the premise and deny the conclusion, without self-contradiction.

But the form into which the reasoning is thrown by using the general law as a major premise masks the real nature of the evidence for the conclusion. The real argument is,

All other horned quadrupeds have been found to be ruminant;

Therefore this horned quadruped is ruminant. It is because we have found horned quadrupeds to have been ruminant in all other cases, as far as our knowledge has extended, that we conclude that the horned animal before us is ruminant. The fact or collection of facts gathered from observation without any contrary instance, is sufficient to determine the mind to believe the conclusion; but there would be no self-contradiction, although a want of sound sense, in admitting the premise and denying the inference. The reason is not what is usually designated logical or demonstrative, but material or contingent. It is, nevertheless, all that we can possibly have in the case.

Laying down the general law, that all horned quadrupeds are ruminant, has not the slightest power to change either the character of the facts of which it is the indication, or that of the conclusion to which it may lead. Material arguments cannot be converted into demonstrative proofs by any arrangement of propositions, or by any translation from one form into another.