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Chapter V: Knowledge of the Essence cannot be attained by DivisionEdit

Nor can demonstration be attained by means of Division, which never proves necessary connection, and can never give the cause. Thus definitions founded on division are invalid as lacking the element of necessity.

Nor does the method of Division produce syllogistic conclusions, as has been pointed out in the analysis of the figures of the syllogism (Pr. An. I. 31). There is never any necessity that the thing to be defined should be exactly what it is stated to be because the other terms of the division are so; and the method of division is even less demonstrative than induction. One ought not to ask that the conclusion should be admitted, nor ought it to be held to be true because another admits it, but it must necessarily be true if those particular premises are true, even though our companion refuses to accept it. Thus, in division the question might be asked. ‘Is Man an animate or inanimate creature?’ Though the other may decide in favour of ‘animate,’ yet no real conclusion has been arrived at. Suppose the question to follow, ‘As every animate creature is terrestrial or aquatic, which is man?’ and the other decides for terrestrial. Yet it is not a necessary consequence of these admissions that man is a terrestrial animate creature, but that also is an assumption.

It makes no difference whether the division has many or few parts; for the same charge may be brought against every instance of it. Even in the case of arguments which might proceed syllogistically, when division is resorted to the method is not syllogistic. There is in fact nothing to shew that these qualities, though they may all be true of man, really express his Nature or essential Form. Also there is nothing to prevent Division from adding to, subtracting from, or entirely passing over the substance of the thing.

It is in this connection that mistakes are generally made; but the difficulty may be solved by taking all the essential attributes of the thing, arranging them in order by means of division, making a postulate of the first attribute and passing over none of the later ones. Here necessity will be secured so long as everything falls within the division, nothing being omitted, and so long as no term is admitted which is capable of a further subdivision. This process, however, involves no regular syllogism, or if division does convey scientific knowledge it conveys it in a different way from syllogism. Nor is there anything strange in this; for Induction does not properly speaking demonstrate, but yet it makes something known. In the present case, however, one who announces a definition after an inspection of a division does not really give us a syllogism. Just as in the case of conclusions without any middle term, if it be asserted that this conclusion must follow from this premise, one is entitled to ask, ‘Why so?’ so also with definitions which depend on division. E.g. ‘What is man?’ ‘A mortal, footed, biped, featherless animal.’ ‘Why?’ will be asked at every additional attribute. The answer will be that it may, as the speaker supposes, be proved by division that everything is either mortal or immortal. No reasoning of this kind can have any of the characteristics of definition. Hence even if division did demonstrate something, definition would not thereby become the same as syllogism.