Part III, Chapter 1: Of the Nature of Reasoning, and of the different Kinds of it (with the Preface to the Part)
THAT part of which we now have to treat, and which comprehends the rules of reasoning, is regarded as the most important in logic, and is almost the only one which has been treated of with any care. But it may be doubted whether it is really as useful as it has been supposed to be. The greater part of the errors of men, as we have already said elsewhere, arises much more from their reasoning on false principles, than from their reasoning wrongly on their principles. It rarely happens that men allow themselves to be deceived by reasonings which are false, only because the consequences are ill deduced; and those who are not capable of discovering such errors by the light of reason alone, would not commonly understand the rules which are given for this purpose, much less the application of them. Nevertheless, considering these rules simply as speculative truths, they may always be useful as mental discipline; and, further than this, it cannot be denied that they are of service on some occasions, and in relation to those persons who, being of a lively and inquiring turn of mind, allow themselves, at times, for want of attention, to be deceived by false consequences, which attention to these rules would probably rectify. Be this as it may, the following chapters contain what is commonly said on this subject, and, indeed, somewhat more.
THE necessity of reasoning is founded exclusively on the narrow limits of the human mind, which, having to judge of the truth or falsehood of a proposition—which is, in this connection, termed the question—is not always able to do this by the consideration of the two ideas which compose it, of which that which is the subject is also called the minor term, because the subject is generally less extended than the attribute; and that which is the attribute is also called the major term, for a contrary reason. When, therefore, the consideration of these two ideas is not sufficient to enable us to determine whether we should affirm or deny the one of the other, it is necessary to have recourse to a third idea, either complex or incomplex (according to what we have said of complex terms), and this third idea is called the mean (or middle term).
Now, it would be of no service, for the purpose of effecting this comparison of the two ideas through the medium of this third idea, to compare it with only one of the two terms. If I wish to know, for example, whether the soul is spiritual, and not seeing clearly into the question at first, should choose the idea of thought in order to make it clear to me, it is manifest that it would be useless to compare thought with the soul, unless I conceive that it had some relation to the attribute spiritual, by means of which I might be able to judge whether it belonged, or did not belong, to the soul. I may say, indeed, for example, the soul thinks; but I shall not be able to conclude that it is therefore spiritual, unless I conceive some relation to exist between the terms thinking and spiritual.
It is necessary, therefore, that the middle term be compared both with the subject or minor term, and with the attribute or major term,—whether this be done separately with each of these terms, as in the syllogisms which are for this reason called simple; or with both the terms at once, as in the arguments which are called conjunctive.
But in either way this comparison demands two propositions. We shall speak of the conjunctive arguments in detail; but in relation to the simple ones this is clear, since the middle term, being once compared with the attribute of the conclusion (which can only be done by affirming or denying), makes the proposition which is called the major, because this attribute of the conclusion is called the major term.
And being again compared with the subject of the conclusion, makes what is called the minor (proposition), because the subject of the conclusion is called the minor term.
And then the conclusion, which is the proposition itself which had to be proved, and which, before it was proved, was called THE QUESTION.
It is well to know that the two first propositions are also called premises (premissce), because they are placed (in the mind at least) before the conclusion, which ought to be a necessary consequence from them, if the syllogism be good: that is to say, that, supposing the truth of the premises, the truth of the conclusion necessarily follows.
It is true that the two premises are not always expressed, because often one alone is sufficient to enable the mind to conceive them both; and when we thus express only two propositions, this sort of reasoning is called enthymeme, which is a real syllogism in the mind, since it applies the proposition which is not expressed, but which is imperfect in expression, and affords its conclusion only in virtue of that suppressed proposition.
I said that there were at least three propositions in a reasoning; but there may be many more without rendering it defective on that account, provided always that the rules be observed. For if, after having consulted a third idea, in order to know whether an attribute belongs, or does not belong, to a subject, and after having compared it with one of the terms, not knowing as yet whether it belongs, or does not belong, to the second term,—I might choose a fourth in order to make this clear to me, and a fifth, if that is not sufficient, until I arrive at an idea which connects the attribute of the conclusion with the subject.
If I question, for example, whether avaricious men are miserable, I may consider, first, that the avaricious are full of desires and passions; if this does not afford ground for the conclusion, that therefore they are miserable, I may examine what it is to be full of desires, and I shall find in this idea that of being without many things which are desired, and misery in this privation of things which are desired; which will enable me to form this reasoning:—Avaricious men are full of desires; those who are full of desires want many things, since it is impossible for them to satisfy all their desires; those who are without that which they desire are miserable; therefore avaricious men are miserable.
Such reasonings as these, composed of many propositions, of which the second depends on the first, and so of the rest, are called sorites, and are those which are most common in mathematics. But because, when they are long, the mind has more difficulty in following them, and the three propositions are better adapted to the capacity of the mind, we have taken more pains in examining the rules of good and bad syllogisms, that is to say, of arguments of three propositions. This it is well to follow, since the rules which are given for these may be easily applied to all the reasonings which are composed of many propositions, inasmuch as they may all be reduced to syllogisms, if they are good.