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prior analytics-第27章

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takes one of these; along with the contradictory of the original



conclusion。 Also in the ostensive proof it is not necessary that the



conclusion should be known; nor that one should suppose beforehand



that it is true or not: in the other it is necessary to suppose



beforehand that it is not true。 It makes no difference whether the



conclusion is affirmative or negative; the method is the same in



both cases。 Everything which is concluded ostensively can be proved



per impossibile; and that which is proved per impossibile can be



proved ostensively; through the same terms。 Whenever the syllogism



is formed in the first figure; the truth will be found in the middle



or the last figure; if negative in the middle; if affirmative in the



last。 Whenever the syllogism is formed in the middle figure; the truth



will be found in the first; whatever the problem may be。 Whenever



the syllogism is formed in the last figure; the truth will be found in



the first and middle figures; if affirmative in first; if negative



in the middle。 Suppose that A has been proved to belong to no B; or



not to all B; through the first figure。 Then the hypothesis must



have been that A belongs to some B; and the original premisses that



C belongs to all A and to no B。 For thus the syllogism was made and



the impossible conclusion reached。 But this is the middle figure; if C



belongs to all A and to no B。 And it is clear from these premisses



that A belongs to no B。 Similarly if has been proved not to belong



to all B。 For the hypothesis is that A belongs to all B; and the



original premisses are that C belongs to all A but not to all B。



Similarly too; if the premiss CA should be negative: for thus also



we have the middle figure。 Again suppose it has been proved that A



belongs to some B。 The hypothesis here is that is that A belongs to no



B; and the original premisses that B belongs to all C; and A either to



all or to some C: for in this way we shall get what is impossible。 But



if A and B belong to all C; we have the last figure。 And it is clear



from these premisses that A must belong to some B。 Similarly if B or A



should be assumed to belong to some C。



  Again suppose it has been proved in the middle figure that A belongs



to all B。 Then the hypothesis must have been that A belongs not to all



B; and the original premisses that A belongs to all C; and C to all B:



for thus we shall get what is impossible。 But if A belongs to all C;



and C to all B; we have the first figure。 Similarly if it has been



proved that A belongs to some B: for the hypothesis then must have



been that A belongs to no B; and the original premisses that A belongs



to all C; and C to some B。 If the syllogism is negative; the



hypothesis must have been that A belongs to some B; and the original



premisses that A belongs to no C; and C to all B; so that the first



figure results。 If the syllogism is not universal; but proof has



been given that A does not belong to some B; we may infer in the



same way。 The hypothesis is that A belongs to all B; the original



premisses that A belongs to no C; and C belongs to some B: for thus we



get the first figure。



  Again suppose it has been proved in the third figure that A



belongs to all B。 Then the hypothesis must have been that A belongs



not to all B; and the original premisses that C belongs to all B;



and A belongs to all C; for thus we shall get what is impossible。



And the original premisses form the first figure。 Similarly if the



demonstration establishes a particular proposition: the hypothesis



then must have been that A belongs to no B; and the original premisses



that C belongs to some B; and A to all C。 If the syllogism is



negative; the hypothesis must have been that A belongs to some B;



and the original premisses that C belongs to no A and to all B; and



this is the middle figure。 Similarly if the demonstration is not



universal。 The hypothesis will then be that A belongs to all B; the



premisses that C belongs to no A and to some B: and this is the middle



figure。



  It is clear then that it is possible through the same terms to prove



each of the problems ostensively as well。 Similarly it will be



possible if the syllogisms are ostensive to reduce them ad impossibile



in the terms which have been taken; whenever the contradictory of



the conclusion of the ostensive syllogism is taken as a premiss。 For



the syllogisms become identical with those which are obtained by means



of conversion; so that we obtain immediately the figures through which



each problem will be solved。 It is clear then that every thesis can be



proved in both ways; i。e。 per impossibile and ostensively; and it is



not possible to separate one method from the other。







                                15







  In what figure it is possible to draw a conclusion from premisses



which are opposed; and in what figure this is not possible; will be



made clear in this way。 Verbally four kinds of opposition are



possible; viz。 universal affirmative to universal negative;



universal affirmative to particular negative; particular affirmative



to universal negative; and particular affirmative to particular



negative: but really there are only three: for the particular



affirmative is only verbally opposed to the particular negative。 Of



the genuine opposites I call those which are universal contraries; the



universal affirmative and the universal negative; e。g。 'every



science is good'; 'no science is good'; the others I call



contradictories。



  In the first figure no syllogism whether affirmative or negative can



be made out of opposed premisses: no affirmative syllogism is possible



because both premisses must be affirmative; but opposites are; the one



affirmative; the other negative: no negative syllogism is possible



because opposites affirm and deny the same predicate of the same



subject; and the middle term in the first figure is not predicated



of both extremes; but one thing is denied of it; and it is affirmed of



something else: but such premisses are not opposed。



  In the middle figure a syllogism can be made both



oLcontradictories and of contraries。 Let A stand for good; let B and C



stand for science。 If then one assumes that every science is good; and



no science is good; A belongs to all B and to no C; so that B



belongs to no C: no science then is a science。 Similarly if after



taking 'every science is good' one took 'the science of medicine is



not good'; for A belongs to all B but to no C; so that a particular



science will not be a science。 Again; a particular science will not be



a science if A belongs to all C but to no B; and B is science; C



medicine; and A supposition: for after taking 'no science is



supposition'; one has assumed that a particular science is



supposition。 This syllogism differs from the preceding because the



relations between the terms are reversed: before; the affirmative



statement concerned B; now it concerns C。 Similarly if one premiss



is not universal: for the middle term is always that which is stated



negatively of one extreme; and affirmatively of the other。



Consequently it is possible that contradictories may lead to a



conclusion; though not always or in every mood; but only if the



terms subordinate to the middle are such that they are either



identical or related as whole to part。 Otherwise it is impossible: for



the premisses cannot anyhow be either contraries or contradictories。



  In the third figure an affirmative syllogism can never be made out



of opposite premisses; for the reason given in reference to the



first figure; but a negative syllogism is possible whether the terms



are universal or not。 Let B and C stand for science; A for medicine。



If then one should assume that all medicine is science and that no



medicine is science; he has assumed that B belongs to all A and C to



no A; so that a particular science will not be a science。 Similarly if



the premiss BA is not assumed universally。 For if some medicine is



science and again no medicine is science; it results that some science



is not science; The premisses are contrary if the terms are taken



universally; if one is particular; they are contradictory。



  We must recognize that it is possible to take opposites in the way



we said; viz。 'all science is good' and 'no science is good' or



'some science is not good'。 This does not usually escape notice。 But



it is possible to establish one part of a contradiction through



other premisses; or to assume it in the way suggested in t
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