THREE:Inventions in machine improvement, no matter what their nature, must of course consist in and conform to certain fixed modes of operating, and no plan of urging the truth of a proposition is so common, even with a chance inventor, as to trace out the 'principles' which govern his discovery.Disjunction is, in truth, the primordial form of all reasoning, out of which the other forms are successively evolved; and, as such, it is common to man with the lower animals. You are taking a walk in the country with your dog. You come to a stream and jump over it. On measuring the distance with his eye, the animal is afraid to follow you. After waiting a little, he first runs up stream in search of a crossing, and, finding none, returns to look for one in the opposite direction. Failing there also, he comes back once more, and either ventures on the leap or makes his way home by some other route. Now, on considering the matter a little more382 closely, we shall find that hypothetical reasoning takes its rise from the examination of each separate alternative presented by a disjunctive premise. A plurality of courses being open to us, we consider what will ensue on the acceptance or rejection of each. The dog in our illustration thinks (after a canine fashion) that if he jumps he may fall in; if he does not, he will be left behind. Hector will not take refuge within the walls, because, if he does, Polydamas will triumph over him; nor will he offer terms of peace, because, if he does, Achilles will refuse them. Once more, categorical reasoning is developed out of hypothetical reasoning by the necessity of deducing consequences from a general rule. Hector must have argued from the known characters of Polydamas and Achilles, that in certain circumstances they would act after a certain manner. We may add, that this progress of conscious reasoning is a reproduction of the unconscious logic according to which life itself is evolved. All sorts of combinations are spontaneously produced, which, in consequence of the struggle for existence, cannot all survive. Those adapted to the conditions of life are selected, on trial, at the expense of the rest; and their adaptation or non-adaptation is determined in accordance with categorical laws. Furthermore, the framing of a disjunctive proposition necessitates the systematic distribution of possibilities under mutually exclusive heads, thus involving the logical processes of definition, division, and classification. Dialectic, as Plato understood it, consisted almost entirely in the joint performance of these operations;a process which Aristotle regards as the immediate but very imperfect precursor of his own syllogistic method.276 You cannot, he says, prove anything by dividing, for instance, all living things into the two classes, mortal and immortal; unless, indeed, you assume the very point under discussionto which class a particular species belongs. Yet this is how he constantly reasons himself; and even demonstrative reason383ing, as he interprets it, implies the possession of a ready-made classification. For, according to him, it consists exclusively of propositions which predicate some essential attribute of a thingin other words, some attribute already included in the definition of the subject; and a continuous series of such definitions can only be given by a fixed classification of things.
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THREE:I was not afraid of an inquiry, but asked for it as a matter of fact, by writing in my report:
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THREE:Larry and Dick straightened and stared in surprise. It was very plain to be seen that Sandy was not joking.
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ONE:Leona Lalage fell back with a faint cry. Just for a moment she covered her eyes with her hands. Lalage stood like a statue. He smiled, but there was nothing of mirth in it."Come along," she said. "I've got the key of the courtyard. Not that we are in the least likely to find anything there?"
ONE:"Yes," I reply, "it is bad, very bad, but is it really all true?"Lawrence came in puffing one of his eternal cigarettes. His manner was full of confidence.
ONE:In working out his theory of logic, the point on which Bacon lays most stress is the use of negative instances. He seems to think that their application to reasoning is an original discovery of his own. But, on examination, no more seems to be meant by it than that, before accepting any particular theory, we should consider what other explanations of the same fact might conceivably be offered. In other words, we should follow the example already set by Aristotle and nearly every other Greek philosopher after Socrates. But this is not induction; it is reasoning down from a disjunctive proposition, generally assumed without any close scrutiny, with the help of sundry conditional propositions, until we reach our conclusion by a sort of exhaustive process. Either this, that, or the other is the explanation of something. But if it were either that or the other, so and so would follow, which is impossible; therefore it must be this. No other logic is possible in the infancy of enquiry; but one great advantage of experiment and mathematical analysis is to relieve us from the necessity of employing it.
