system to strengthen the masculine efficiency of our reasoning powers in dealing with the important questions of moral, political, and philosophical science, or the multifarious business of actual life.

Regarded as a discipline of the mind, indeed, I cannot see why the arguments brought against the study of some departments of mathematics should not be brought against the study of technical logic. The latter appears to me to be nearly, in this respect, in the position of the modern calculus, the formulæ of which have been said to transport the mathematician from the data to the conclusion in a carriage with the blinds down; unlike geometrical demonstration, which compels him to walk over every inch of the road, and be cognizant of every step in his journey.

But the modern calculus, although it may be of questionable value as a discipline of the mind, is unquestionably a most powerful and an indispensable instrument for attaining results which pure geometrical operations could never reach; while technical logic is not only equally low in value as an intellectual exercise, but is besides a clumsy and circuitous method of arriving at its proposed ends.

Placed in a scene where we are surrounded by objects and immersed in events, we are perpetually obliged to reason about them.

To train the mind to do this by directing its attention upon words, to the completest practicable

exclusion of things, through the medium of a verbal and literal mechanism, however ingenious, instead of habituating it to face realities and question their significance, seems to me to unfit it for the business in which it is destined to be engaged.

In former times, when the Aristotelian system had no rival in physical investigation, the bad effects here traced were seen in all their extent; but fortunately in our own day the mischievous influence of such a discipline is greatly counteracted by the far different discipline of sciences, in which no step of reasoning can be taken without bringing into view the actual phenomena of life and nature.

CHAP. XII.

THE SOURCES OF ERRONEOUS CONCLUSIONS.

FROM the survey which we have now taken of the field of reasoning, we shall be prepared to enter upon that most important question to which any theory on the subject of this treatise necessarily leads, viz. "what are the sources of erroneous conclusions ?”*

Reasoning consists in coming to conclusions, and the sole legitimate object of the process is to come to such as are correct. Why we do not always succeed in attaining this end it must be instructive to inquire. By erroneous conclusions I here mean false propositions at which we have arrived by inference, whatever may have been the sources of the error, whether false facts in the premises, or some false step in the reasoning process itself. This

* I have not entered into the consideration of fallacies except in so far as the subject of this chapter required it, partly because a minute exposition of them belongs rather to the art than to the theory of reasoning, and partly because they have been very excellently and fully explained by several modern writers, particularly by Dr. Whately and Mr. John Mill in their works already referred to, and by Mr. De Morgan in his "Formal Logic."

remark indicates two of the great sources of erroneous conclusions, viz., wrong facts or premises, and wrong processes of inference.

When we undertake a journey, we may fail to reach the proposed end, either by setting out in a wrong direction, or, if we set out right, by deviating from the true path in the course of our progress.

In contingent, as indeed in all other reasoning, the premises are of course wrong when the facts asserted in them are either wholly or partially incorrect. We We may, from inaccurate observation, or misconception, or misrecollection, or other causes, be led to propound that all A's, as far as our knowledge has extended, have been found possessed of the attribute B, when, in truth (to take an extreme case), no A's have been found to possess that attribute.

If from such false observation, or undue assumption, we proceed to infer that all A's possess B, or that any unobserved A possesses B, it is an instance of an erroneous conclusion, of which the source is an erroneous premise.

On the other hand, the process of inferring a conclusion in contingent reasoning is wrong when the facts contained in the premises, although they are correct, are not sufficient to warrant the inference we draw from them.

Thus we may lay down a universal law in the form of, all A's possess the attribute B, when the

facts warrant us only in the inference that all A's probably possess the attribute B.

The universal law in this case would not be a false conclusion from false facts, but would proceed from an erroneous estimate of what the correct facts of the case enable us legitimately to infer. It would be an instance of undue or unwarranted generalisation.

In demonstrative reasoning there are two cases to be noted.

In such as consist of one premise, of the nature of a minor, and an inference, erroneous conclusions are scarcely possible, except from false facts; and these latter are almost excluded from the principal species of such reasoning, viz. mathematical, by the circumstance that the facts about which it is conversant are few and simple.

With the greater part of syllogistic reasoning the case is otherwise. Here erroneous conclusions may proceed both from wrong premises and from wrong processes of inference. The wrong premises, as in the case of contingent reasoning, assert false facts, and frequently owe their origin to false general laws obtained by such reasoning; but in a far greater proportion they may be traced to pure gratuitous assumption of general propositions which are not true.

The wrong processes of inference, or at least the only ones claiming attention, are of two kinds, technically called non-distribution of the middle