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posterior analytics-第13部分

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property; and that which alters a property changes。 Again; we can



predicate A of G without falsehood; and G of B; for to feel pleasure



is to relax; and to relax is to change。 So the conclusion can be drawn



through middles which are different; i。e。 not in the same series…yet



not so that neither of these middles is predicable of the other; for



they must both be attributable to some one subject。



  A further point worth investigating is how many ways of proving



the same conclusion can be obtained by varying the figure;







                                30







  There is no knowledge by demonstration of chance conjunctions; for



chance conjunctions exist neither by necessity nor as general



connexions but comprise what comes to be as something distinct from



these。 Now demonstration is concerned only with one or other of



these two; for all reasoning proceeds from necessary or general



premisses; the conclusion being necessary if the premisses are



necessary and general if the premisses are general。 Consequently; if



chance conjunctions are neither general nor necessary; they are not



demonstrable。







                                31







  Scientific knowledge is not possible through the act of



perception。 Even if perception as a faculty is of 'the such' and not



merely of a 'this somewhat'; yet one must at any rate actually



perceive a 'this somewhat'; and at a definite present place and



time: but that which is commensurately universal and true in all cases



one cannot perceive; since it is not 'this' and it is not 'now'; if it



were; it would not be commensurately universal…the term we apply to



what is always and everywhere。 Seeing; therefore; that



demonstrations are commensurately universal and universals



imperceptible; we clearly cannot obtain scientific knowledge by the



act of perception: nay; it is obvious that even if it were possible to



perceive that a triangle has its angles equal to two right angles;



we should still be looking for a demonstration…we should not (as



some say) possess knowledge of it; for perception must be of a



particular; whereas scientific knowledge involves the recognition of



the commensurate universal。 So if we were on the moon; and saw the



earth shutting out the sun's light; we should not know the cause of



the eclipse: we should perceive the present fact of the eclipse; but



not the reasoned fact at all; since the act of perception is not of



the commensurate universal。 I do not; of course; deny that by watching



the frequent recurrence of this event we might; after tracking the



commensurate universal; possess a demonstration; for the



commensurate universal is elicited from the several groups of



singulars。



  The commensurate universal is precious because it makes clear the



cause; so that in the case of facts like these which have a cause



other than themselves universal knowledge is more precious than



sense…perceptions and than intuition。 (As regards primary truths there



is of course a different account to be given。) Hence it is clear



that knowledge of things demonstrable cannot be acquired by



perception; unless the term perception is applied to the possession of



scientific knowledge through demonstration。 Nevertheless certain



points do arise with regard to connexions to be proved which are



referred for their explanation to a failure in sense…perception: there



are cases when an act of vision would terminate our inquiry; not



because in seeing we should be knowing; but because we should have



elicited the universal from seeing; if; for example; we saw the



pores in the glass and the light passing through; the reason of the



kindling would be clear to us because we should at the same time see



it in each instance and intuit that it must be so in all instances。







                                32







  All syllogisms cannot have the same basic truths。 This may be



shown first of all by the following dialectical considerations。 (1)



Some syllogisms are true and some false: for though a true inference



is possible from false premisses; yet this occurs once only…I mean



if A for instance; is truly predicable of C; but B; the middle; is



false; both A…B and B…C being false; nevertheless; if middles are



taken to prove these premisses; they will be false because every



conclusion which is a falsehood has false premisses; while true



conclusions have true premisses; and false and true differ in kind。



Then again; (2) falsehoods are not all derived from a single identical



set of principles: there are falsehoods which are the contraries of



one another and cannot coexist; e。g。 'justice is injustice'; and



'justice is cowardice'; 'man is horse'; and 'man is ox'; 'the equal is



greater'; and 'the equal is less。' From established principles we



may argue the case as follows; confining…ourselves therefore to true



conclusions。 Not even all these are inferred from the same basic



truths; many of them in fact have basic truths which differ



generically and are not transferable; units; for instance; which are



without position; cannot take the place of points; which have



position。 The transferred terms could only fit in as middle terms or



as major or minor terms; or else have some of the other terms



between them; others outside them。



  Nor can any of the common axioms…such; I mean; as the law of



excluded middle…serve as premisses for the proof of all conclusions。



For the kinds of being are different; and some attributes attach to



quanta and some to qualia only; and proof is achieved by means of



the common axioms taken in conjunction with these several kinds and



their attributes。



  Again; it is not true that the basic truths are much fewer than



the conclusions; for the basic truths are the premisses; and the



premisses are formed by the apposition of a fresh extreme term or



the interposition of a fresh middle。 Moreover; the number of



conclusions is indefinite; though the number of middle terms is



finite; and lastly some of the basic truths are necessary; others



variable。



  Looking at it in this way we see that; since the number of



conclusions is indefinite; the basic truths cannot be identical or



limited in number。 If; on the other hand; identity is used in



another sense; and it is said; e。g。 'these and no other are the



fundamental truths of geometry; these the fundamentals of calculation;



these again of medicine'; would the statement mean anything except



that the sciences have basic truths? To call them identical because



they are self…identical is absurd; since everything can be



identified with everything in that sense of identity。 Nor again can



the contention that all conclusions have the same basic truths mean



that from the mass of all possible premisses any conclusion may be



drawn。 That would be exceedingly naive; for it is not the case in



the clearly evident mathematical sciences; nor is it possible in



analysis; since it is the immediate premisses which are the basic



truths; and a fresh conclusion is only formed by the addition of a new



immediate premiss: but if it be admitted that it is these primary



immediate premisses which are basic truths; each subject…genus will



provide one basic truth。 If; however; it is not argued that from the



mass of all possible premisses any conclusion may be proved; nor yet



admitted that basic truths differ so as to be generically different



for each science; it remains to consider the possibility that; while



the basic truths of all knowledge are within one genus; special



premisses are required to prove special conclusions。 But that this



cannot be the case has been shown by our proof that the basic truths



of things generically different themselves differ generically。 For



fundamental truths are of two kinds; those which are premisses of



demonstration and the subject…genus; and though the former are common;



the latter…number; for instance; and magnitude…are peculiar。







                                33







  Scientific knowledge and its object differ from opinion and the



object of opinion in that scientific knowledge is commensurately



universal and proceeds by necessary connexions; and that which is



necessary cannot be otherwise。 So though there are things which are



true and real and yet can be otherwise; scientific knowledge clearly



does not concern them: if it did; things which can be otherwise



would be incapable of being otherwise。 Nor are they any concern of



rational intuition…by rational intuition I mean an originative



source of scientific knowledge…nor of indemonstrable knowledge;



which is the grasping of the immediate premiss。 Since then rational



intuition; science; and opinion; and what is revealed by these



terms; are the only things that can be 'true'; it follows that it is



opinion that is concerned with that which may be true or false; and



can be otherwise: opinion in fact is the grasp of a premiss which is



immediate but not necessary。 This view also fits the observed facts;



for opinion is unstable; and so is the kind of being we have described



as its object。 Besides; when a man thinks a truth incapable of being



otherwise he always thinks that he knows it; never that he opines



it。 He thinks that he opines when he thinks that a connexion; though



actually so; may quite easily be otherwise; for he believes that



such is the proper object of opinion; while the necessary is the



object of knowledg
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