8-4. Drawing The Line
from 8. DeductionClear Thinking by R W Jepson

I conclude this chapter with a reference to two examples of what may be termed false logic, i.e., attempts to use obvious and self-evident logical rules or formulae to arrive at unwarrantable or inconclusive conclusions.

The first concerns the application of two fundamental logical laws—the Law of Contradiction and the Law of the Excluded Middle. The former states that A is not not-A, i.e., that the same person or thing cannot be in the same sense A and not-A. The second that a person or thing is either A or not-A, i.e., that there is no middle ground between them. (Observe in passing that either . . . or is here strictly disjunctive in meaning, i.e., equivalent to not both . . . and; the alternatives they introduce are mutually exclusive.)

Now in these rules and formulae A and not-A are clearly contradictories-terms or notions that are absolute, and between which a hard and fast line can be drawn. Mortal and immortal are such terms; a man cannot be both mortal and immortal; he must be one or the other; there is no middle, undetermined, "no man's land" between the two.

But, unfortunately, we often confuse with contradictories and with each other two additional classes of terms or notions: (a) those that in some particular respect or other are merely different, and (b) those that are opposite or contrary, representing two opposite extremes of a continuous series of variations. Under different I would place such notions as knave and fool, man and woman. No hard and fast line can be drawn between knave and fool; the qualities of a knave and a fool may exist side by side in varying proportions in the same person. Men and women may from some points of view be contrasted or even placed at opposite poles; in some churches, for example, men sit on one side of the nave and women on the other; but from other points of view they are not opposites, far less contradictories. We must always know what other facts are involved before we can determine whether such notions are really incompatible.

Under opposites or contraries we may class such relative terms as young and old, sweet and sour, sane and insane, civilised and uncivilised; between them there is a real difference, which can be more or less accurately measured in some quantitative way; but we cannot draw a hard-and-fast line of distinction between them, i.e., if we do employ some quantitative means of measurement, we cannot say precisely at what point a person or thing ceases to be one and becomes the other. In fact they shade off by almost imperceptible degrees into each other. Hence the delimitation or definition of such terms, in the strict sense, is bound to be difficult, if not impossible; and any attempt at precise definition might be used by an unscrupulous or captious opponent to force you to admit opinions which you do not hold. Socrates employed these tactics with devastating effect upon the Sophists.

People who make a great pretence of being logical, on whose lips "logical" and "logically" constantly recur, are often the first to apply the Law of Contradiction and the Law of the Excluded Middle in cases where opposite and not contradictory terms are in question, either to their own confusion or to the confusion of others. The following simple dialogue may help to make this clear.

X.: "I shouldn't call Senor Fulano old; he is only 55.
Y.: "When then exactly would you say that a man becomes old? 56, 57, 58, 59 ."
X.: "I can't exactly say. It all depends... "
Y.: "Come! Come! No hedging! You must draw the line somewhere. Be logical."
[Y. is wrong: logic cannot help; logic cannot provide a rule that can be applied in every case.]
X.:"But so much depends on the man himself. After all a man may be quite grey and yet possess all the vitality of youth."
Y.:"Well, then, give me your definition of old."
[Y. is here attempting to pin X. down to a definition, which he may subsequently use to X.'s discomfiture; but X. is not to be drawn.]
X.:"You are asking me to do the same thing as when you asked me where I would draw the line. I tell you it can't be done. Between the two extremes there are almost any number of stages at which it is impossible to say whether any particular man has ceased to be young and has become old."
Y.: "In other words, logically, according to you, there is really no difference between young and old."
[Y.'s third mistake; note how X. deals with him.]
X.:"Not at all. Just because it is impossible to say, to a year, where youth ends and old age begins,it does not follow that there is no difference between a baby in a cradle and a man of 90 in a bath-chair."

Classification into categories is, as we saw at the beginning of Chapter Seven, a necessary preliminary to exact thinking, and when such categories are clearly defined or delimited, then the laws of formal logic will tell us whether an argument based on them is valid or not. But there are facts which cannot, owing to their own nature, be fitted into clear-cut categories, and any attempt to do so is likely to lead to error. It is just as foolish, however, to use this as an excuse for vacillation or indecision in a specific case where opposite or contrary notions are involved. Zealous partisans would have us believe that all that their party stands for is good and all that the other party stands for is bad. We may doubt this, especially when we have seen the claims of the other side. But that is no valid excuse for shrugging one's shoulders and saying that the policies of both parties are equally good or equally bad, and that therefore there is no point in choosing one or other. We are not thereby absolved from the duty of weighing and considering the rival policies, of estimating to the best of our ability how much good and how much bad is likely to accrue from each, and of coming to decision after setting one against the other.

One more illustration before we pass on. To state categorically that the Middle Ages ended and Modern Times began in 1453 would reveal a very imperfect interpretation of the movements and tendencies in European History; it is no doubt a convenient date to remember, but the statement is an oversimplified summary of a complicated variety of changes spread over a long period of time. But that is no reason why we should not continue to distinguish between those two successive periods and to label them "Middle Ages "and "Modern Times ; nor why we should not continue to make generalisations about the contrasting characteristics of each.

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