Chapter XXXII: On the difference of Principles corresponding to the difference of SyllogismsEdit
- The principles of demonstration cannot be the same in all cases, for true conclusions may be drawn from false premises, and even in the case of true syllogisms the principles may differ generically. Further all principles may be divided into Common and Special, corresponding to the grounds and the subjects (ξ ν κα περ ) of demonstration.
It is impossible that all syllogisms should have the same elementary principles, and this may be proved by purely dialectical considerations, Some syllogisms are true, others false, and it is also possible to deduce a true conclusion from false premises, though only in one particular class of circumstances. For instance the proposition C is A may be true, but the middle term B is false, since B is not A, nor yet is C B. But if the middle terms to these premises be expressed, the falsity of the premises will become obvious; since a false conclusion presupposes false premises, while true conclusions result from true premises, and false and true premises are different from one another. Nor do false conclusions follow only from premises which are false in the same manner as themselves, for things which are false may be both the contrary to and inconsistent with each other, as may be illustrated by the assertions ‘Justice is either injustice or cowardice’; ‘Man is either a horse or an ox’; ‘Equal is either greater or less.’ That all syllogisms have not the same principles may also be proved as follows from conclusions already arrived at. Even true conclusions are not invarably derived from the same elementary principles, for in many cases the principles differ and do not suit every kind of argument: e.g. the conception of ‘unit’ cannot be used as a principle when theorizing concerning points, since units, unlike points, have no special position. In order to make the same principles suit various forms of syllogism it is necessary to use them as predicates of the major term, as subjects of the minor or as intermediate between major and minor; or else they must be variously related, some being intermediate between major and minor, others superior to the major or inferior to the minor.
No common principles can exist from which everything may be demonstrated (by ‘common principles,’ I mean those resembling the proposition,—‘it is possible either to affirm or deny everything.’) Existing things differ generically; some predicates can only be assigned to the genus quantity, others to that of quality, and these subjects and predicates together with the common principles of science join in producing a demonstration. Moreover the principles are not much less numerous than the conclusions, since the principles constitute premises, and may become formal premises by inserting a term between major and minor or adding a term either superior to the major or inferior to the minor. Further the conclusions are unlimited, the terms limited. Again some principles are necessary, some contingent.
If we consider the matter in this way we see that these limited principles cannot be identical, since the conclusions are unlimited. If an objector were to assert that these are the principles of geometry, those of calculation, those again of medicine, his assertion would simply amount to saying that different sciences have different principles. It is however absurd to say that they are the same principles in all cases just because they are principles and not something else; for by that method all distinct things might be proved identical. Nor can it be meant that every premise will prove every conclusion, which would be equivalent to claiming that all sciences should have the same principles—a ridiculous assumption, for this is not the case with existing kinds of exact science, nor is it possible in logical analysis. The immediate premises are principles, and distinct from them is the conclusion which is attained by means of the addition of an immediate premise. If it be asserted that it is the primary immediate premises that constitute those principles which are identical in every science, we should answer that there is a unique premise in each branch of science. If then it be agreed that not everything can be proved from any principle whatsoever, and yet that the principles of various sciences are not so unlike one another as to fall into distinct classes, there remains the suggestion that the principles of every science are akin, while the conclusions drawn from them differ. This however is clearly untrue, for it has been proved that the principles of sciences which differ generically are themselves generically different. Principles are in fact of two kinds, being either the sources or the subject of science. The former are common, the latter, such as ‘number’ or ‘magnitude,’ are peculiar to each science.