from condition to conclusion. Suppose, for example, a business man has postponed embarking on a certain enterprise because it would have begun on Friday, unconscious that this assumes that "all enterprises begun on Friday are likely to be unsuccessful." Through the delay thus caused his enterprise meets failure. He may thus be led to consider whether the inference he had made were really well grounded, or whether the association between Friday and failure were due simply to emotional attachment or uncriticized tradition. He may then be willing on a future occasion to try an inference whose assumption could be better justified in terms of empirical fact. The first step will be made toward forming the habit of guarding his reasoning against the play of illogical influences.

This does not mean, of course, that in people's actual thinking they may ever come to state all their deductions in the complete and exact form required to reveal their validity. It does mean that they acquire a vague sense of what that form would be, and more and more develop the habit of respecting it in subconscious fashion when they follow out any suggestion to its consequences. Thus it is natural for a primitive mind to reason that a particularly striking or interesting consequence that has been observed to follow a given event must follow it again when it recurs, as victory in war after a certain configuration of the omens, but experience gradually teaches that it is regularity of connection. between condition and consequence that validates the reasoning rather than an occasional connection of unusual vividness. Gradually the habit is formed, as experience develops, of implicitly recognizing the authority of this principle and of reasoning in ways whose underlying ground, if stated, would be in accordance with its demands. Then, as nations appear with certain classes given freedom from absorbing economic pursuits, who are able to devote themselves to inquiries of no immediate and pressing practical concern, and as the importance of the mental development just sketched draws the conscious attention of certain members of such classes, the problem sooner or later becomes clearly faced of the explicit formulation of the conditions of correct reasoning which have become gradually recognized

implicitly. Thus deductive logic arises as a formulated science of correct reasoning. In the ancient world this development took place among both the Greeks and the Hindus, though in an inadequate form due to their general assumptions about the nature of thinking and the inadequacy of generally current beliefs about the world. Among the Greeks, Aristotle was the great formulator of the principles of correct reasoning, and his scholastic followers in the Middle Ages worked them out with subtle and minute attention to all the detailed relations involved. The history of deductive logic in the modern world has been marked by the correction of certain mistakes in Aristotle's assumptions about thinking and the inclusion of his main results. as an integral part of a far more extensive system of deductive thinking.

correct reasoning

Now let us return to the difference noted at the beginning of The this chapter between the usual form of the deductive process as articulaoccurring in our actual thinking and the form in which we were tion of a piece of forced to put it when we wished to test its correctness—that is, to the first of our two illustrations. What is the most noticeable difference between those two forms? Obviously, that the second contains a general statement not contained in the first-in this case the statement: trips downtown on the bus are apt to take forty minutes. In what ways, now, does the correctness of the conclusion we draw from the suggested condition (if I make this trip on the bus) depend on that general statement? Obviously, in two ways. In the first place the deduction is not correct unless that implicitly involved general statement is justified by the facts it attempts to summarize. If it is not empirically verifiable that trips downtown on the bus are apt to take forty minutes, then I cannot legitimately conclude that if I take such a trip now it will be likely to consume so much time. In the second place the deduction is not correct unless, taking the truth of this general statement for granted together with that expressed in the suggested condition (this projected trip is a trip on the bus), the asserted conclusion necessarily follows. That is, the general statement must so articulate the entire piece of reasoning that if it and the suggested condition be admitted

Further

or asserted together, the conclusion must also be admitted. Its meaning, in other words, is seen to be so bound up with their meaning that you cannot grant them without granting it also. The importance of this may be seen if we consider a bit of reasoning which is otherwise sound but which does not meet this condition, and one which somebody might unwarily assume to be correct.

Great men have been ridiculed.
I am ridiculed.

Hence I must be a great man.

Here a careful examination of the meaning of the first statement discloses that it does not at all say that everybody who is ridiculed is a great man, but only that some great men have been ridiculed. But the former alone could yield, in conjunction with the second statement, the asserted conclusion. It does not necessarily follow from the latter.

Now while a study of the first of these requirements about the general statement involved in any deduction might properly limitation be taken up in this chapter, it will be better to postpone it. For we must remember that when we are at the fourth step of problem of deduc- any actual act of thought we have to take for granted (explicitly tive logic or implicitly) the best available general principle that our past

of the

experience seems to justify. When my problem is that of getting downtown at a given time, I ordinarily have no leisure to determine whether the best formulation I can make in terms. of past experience of the time it takes to make the trip on the bus is correct for the purposes of that problem; I make the best estimate that I can, and on the basis of its acceptance decide whether the bus is the best means to my chosen end. Furthermore, if I did raise the question of the correctness of that formulation and seriously set about answering it, I should have dropped my original problem for a quite different one; it would no longer be, How shall I get to that appointment? but, How long does it really take to go downtown on the bus? And I should find, when I came to the fourth step of this new problem, that I should there, too, have to take for granted general principles derived from past experience, without, at least at the time,

raising any question about their correctness.

So it will be de

cidedly best to leave to the next part of the book the inquiry into how we establish true general statements of this sort, and restrict the study of the present chapter to the conditions of correct reasoning revealed in the other requirement—that is, that the general assertion implied by our reasoning be such that when we grant both it and the suggested condition, we must necessarily grant the conclusion also.

and truth

The task of the present chapter thus coincides with that of Difference the branch of logic which since the very beginning of the formal between study of the science has been termed deductive. Under what validity conditions, given certain assertions, do other assertions necessarily follow from them (can be deduced from them), as their consequences or implications? Such is our problem. And we should become familiar at this point with a technical term. This is a study of the validity of reasoning. A piece of reasoning whose conclusion does really follow from the assertions which purport to imply it, is valid. One whose conclusion does not follow is invalid. Notice that validity is not the same as truth. An assertion may be untrue, and yet, if its meaning is clear, it is possible to tell whether another assertion necessarily follows from it or not. For example:

All negroes live in the Southern states.

'Rastus Johnson is a negro.

Therefore, 'Rastus lives in a Southern state.

""Fruth">

Here the first statement is palpably false, yet the reasoning is valid—that is, the conclusion follows from the statements which purport to yield it. Observe also that without further information we do not know whether the conclusion here is true or false. isn't this It might happen to be true, in spite of the (falsity of the first the opposite premise. On the other hand, of course, it might be false in spite of the validity of the reasoning. Hence there is no necessary relation between the validity of any reasoning and the truth of its conclusion, or of the other assertions which function in it. But, and this is the fundamental point for our present analysis, if those assertions are true and the reasoning is valid, the conclusion must be true. We see, then, the vital importance

Illustrations of valid reasoning

of a systematic study of the conditions of validity. Unless the reasoning is valid, correct premises cannot guarantee correct conclusions. And until we have confirmed the conclusions in other ways the only assurance we can have of their soundness is founded on the assumed truth of the premises plus the validity of the reasoning. Since such further confirmation always involves effort and often risk, it is highly desirable that we understand clearly the conditions of valid reasoning and form the habit of rigorous adherence to them in our own thinking on whatever subject. Knowledge will aid practice here as elsewhere. If, therefore, we wish to avoid error in our deductions, it is essential to understand the conditions of valid deduction.

Section 2. THE SYLLOGISM

Consider the following pieces of valid reasoning:

Cæsar conquered Gaul.

Cæsar was charmed by Cleopatra.

Therefore, a conqueror of Gaul was charmed by Cleopatra.

Chicago will build a subway.

The cost per mile of a subway is very high.

Therefore, Chicago will build a means of transportation whose cost

per mile is very high.

This key is in tune with the G string.

The G string is in tune with that bell.

Therefore, this key is in tune with that bell.

Most business men are progressive.

Most business men are Republicans.

Therefore, some progressive people are Republicans.

Henry is the father of James.

James is the father of Sally.

Therefore, Henry is grandfather of Sally.

Omaha is west of Chicago.

Topeka is south of Omaha.

Therefore, Topeka is southwest of Chicago.