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第15章

prior analytics-第15章

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the terms the supposable and the opinable in preference to the



phrase suggested。







                                40







  Since the expressions 'pleasure is good' and 'pleasure is the



good' are not identical; we must not set out the terms in the same



way; but if the syllogism is to prove that pleasure is the good; the



term must be 'the good'; but if the object is to prove that pleasure



is good; the term will be 'good'。 Similarly in all other cases。







                                41







  It is not the same; either in fact or in speech; that A belongs to



all of that to which B belongs; and that A belongs to all of that to



all of which B belongs: for nothing prevents B from belonging to C;



though not to all C: e。g。 let B stand for beautiful; and C for



white。 If beauty belongs to something white; it is true to say that



beauty belongs to that which is white; but not perhaps to everything



that is white。 If then A belongs to B; but not to everything of



which B is predicated; then whether B belongs to all C or merely



belongs to C; it is not necessary that A should belong; I do not say



to all C; but even to C at all。 But if A belongs to everything of



which B is truly stated; it will follow that A can be said of all of



that of all of which B is said。 If however A is said of that of all of



which B may be said; nothing prevents B belonging to C; and yet A



not belonging to all C or to any C at all。 If then we take three terms



it is clear that the expression 'A is said of all of which B is



said' means this; 'A is said of all the things of which B is said'。



And if B is said of all of a third term; so also is A: but if B is not



said of all of the third term; there is no necessity that A should



be said of all of it。



  We must not suppose that something absurd results through setting



out the terms: for we do not use the existence of this particular



thing; but imitate the geometrician who says that 'this line a foot



long' or 'this straight line' or 'this line without breadth' exists



although it does not; but does not use the diagrams in the sense



that he reasons from them。 For in general; if two things are not



related as whole to part and part to whole; the prover does not



prove from them; and so no syllogism a is formed。 We (I mean the



learner) use the process of setting out terms like perception by



sense; not as though it were impossible to demonstrate without these



illustrative terms; as it is to demonstrate without the premisses of



the syllogism。







                                42







  We should not forget that in the same syllogism not all



conclusions are reached through one figure; but one through one



figure; another through another。 Clearly then we must analyse



arguments in accordance with this。 Since not every problem is proved



in every figure; but certain problems in each figure; it is clear from



the conclusion in what figure the premisses should be sought。







                                43







  In reference to those arguments aiming at a definition which have



been directed to prove some part of the definition; we must take as



a term the point to which the argument has been directed; not the



whole definition: for so we shall be less likely to be disturbed by



the length of the term: e。g。 if a man proves that water is a drinkable



liquid; we must take as terms drinkable and water。







                                44







  Further we must not try to reduce hypothetical syllogisms; for



with the given premisses it is not possible to reduce them。 For they



have not been proved by syllogism; but assented to by agreement。 For



instance if a man should suppose that unless there is one faculty of



contraries; there cannot be one science; and should then argue that



not every faculty is of contraries; e。g。 of what is healthy and what



is sickly: for the same thing will then be at the same time healthy



and sickly。 He has shown that there is not one faculty of all



contraries; but he has not proved that there is not a science。 And yet



one must agree。 But the agreement does not come from a syllogism;



but from an hypothesis。 This argument cannot be reduced: but the proof



that there is not a single faculty can。 The latter argument perhaps



was a syllogism: but the former was an hypothesis。



  The same holds good of arguments which are brought to a conclusion



per impossibile。 These cannot be analysed either; but the reduction to



what is impossible can be analysed since it is proved by syllogism;



though the rest of the argument cannot; because the conclusion is



reached from an hypothesis。 But these differ from the previous



arguments: for in the former a preliminary agreement must be reached



if one is to accept the conclusion; e。g。 an agreement that if there is



proved to be one faculty of contraries; then contraries fall under the



same science; whereas in the latter; even if no preliminary



agreement has been made; men still accept the reasoning; because the



falsity is patent; e。g。 the falsity of what follows from the



assumption that the diagonal is commensurate; viz。 that then odd



numbers are equal to evens。



  Many other arguments are brought to a conclusion by the help of an



hypothesis; these we ought to consider and mark out clearly。 We



shall describe in the sequel their differences; and the various ways



in which hypothetical arguments are formed: but at present this much



must be clear; that it is not possible to resolve such arguments



into the figures。 And we have explained the reason。







                                45







  Whatever problems are proved in more than one figure; if they have



been established in one figure by syllogism; can be reduced to another



figure; e。g。 a negative syllogism in the first figure can be reduced



to the second; and a syllogism in the middle figure to the first;



not all however but some only。 The point will be clear in the



sequel。 If A belongs to no B; and B to all C; then A belongs to no



C。 Thus the first figure; but if the negative statement is



converted; we shall have the middle figure。 For B belongs to no A; and



to all C。 Similarly if the syllogism is not universal but



particular; e。g。 if A belongs to no B; and B to some C。 Convert the



negative statement and you will have the middle figure。



  The universal syllogisms in the second figure can be reduced to



the first; but only one of the two particular syllogisms。 Let A belong



to no B and to all C。 Convert the negative statement; and you will



have the first figure。 For B will belong to no A and A to all C。 But



if the affirmative statement concerns B; and the negative C; C must be



made first term。 For C belongs to no A; and A to all B: therefore C



belongs to no B。 B then belongs to no C: for the negative statement is



convertible。



  But if the syllogism is particular; whenever the negative



statement concerns the major extreme; reduction to the first figure



will be possible; e。g。 if A belongs to no B and to some C: convert the



negative statement and you will have the first figure。 For B will



belong to no A and A to some C。 But when the affirmative statement



concerns the major extreme; no resolution will be possible; e。g。 if



A belongs to all B; but not to all C: for the statement AB does not



admit of conversion; nor would there be a syllogism if it did。



  Again syllogisms in the third figure cannot all be resolved into the



first; though all syllogisms in the first figure can be resolved



into the third。 Let A belong to all B and B to some C。 Since the



particular affirmative is convertible; C will belong to some B: but



A belonged to all B: so that the third figure is formed。 Similarly



if the syllogism is negative: for the particular affirmative is



convertible: therefore A will belong to no B; and to some C。



  Of the syllogisms in the last figure one only cannot be resolved



into the first; viz。 when the negative statement is not universal: all



the rest can be resolved。 Let A and B be affirmed of all C: then C can



be converted partially with either A or B: C then belongs to some B。



Consequently we shall get the first figure; if A belongs to all C; and



C to some of the Bs。 If A belongs to all C and B to some C; the



argument is the same: for B is convertible in reference to C。 But if B



belongs to all C and A to some C; the first term must be B: for B



belongs to all C; and C to some A; therefore B belongs to some A。



But since the particular statement is convertible; A will belong to



some B。 If the syllogism is negative; when the terms are universal



we must take them in a similar way。 Let B belong to all C; and A to no



C: then C will belong to some B; and A to no C; and so C will be



middle term。 Similarly if the negative statement is universal; the



affirmative particular: for A will belong to no C; and C to some of



the Bs。 But if the negative statement is particular; no resolution



will be possible; e。g。 if B belongs to all C; and A not belong to some



C: convert the statement BC and both premisses will be particular。



  It is clear that in order to resolve the figures into one another



the premiss which concerns the minor extreme must be converted in both



the figures: for when this premiss is altered; the transition to the



other figure is made。



  One of the syllogisms in the middle figure can; the other cannot; be



resolved into the third figure。 Whenever the universal statement is



negative; resolution is possible。 For if A belongs to no B and to some



C; both B and C alike are convertible in relation to A; so that B



belongs to no A and C to some A。 A therefore is middle term。 But



when A belongs to all B; and not to some C; resolution will not be



possible: for neither of the premisses is universal after conversion。



  Syllogisms in the third figure can be resolved into the middle



figure; whenever the negative statement is universal; e。g。 if A



belongs to no C; and B to some or all C。 For C then will belong to



no A and to some B。 But if the negative statement is particular; no



resolution will be possible: for the particular negative does not



admit of conversion。



  It is clear then that the same syllogisms cannot be resolved in



these figures which could not be resolved into the first figure; and



that when syllogisms are reduced to the first figure thes

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