Azione Romana

Analitici secondiLibro I

Aristotele (384–322 a.C.) · Analytica posteriora · Ἀναλυτικὰ ὕστερα · Bekker 71a–100b

Libro I, capitolo 1 Upon the Nature of Demonstration.71a1–71b8

Inglese

All doctrine, and all intellectual discipline,1 arise from pre-existent knowledge. Now this is evident, if we survey them all, for both mathematical sciences are obtained in this manner, and also each of the other arts. It is the same also with arguments, as well those which result through syllogisms, as those which are formed through induction, for both teach through things previously known, the one assuming as if from those who understood them,2 the other3 demonstrating the universal by that which is evident as to the singular. Likewise also do rhetoricians persuade, for they do so either through examples, which is induction, or through enthy-mems, which is syllogism.†4 It is necessary however to possess previous knowledge in a twofold respect; for with some things we must pre-suppose that they are, but with others we must understand what that is which is spoken of; and with others both must be known, as for instance, (we must pre-assume,) that of every thing it is true to affirm or deny that it is, but of a triangle, that it signifies so and so, and of the monad (we must know) both, viz. what it signifies and that it is, for each of these is not manifest to us in a similar manner.5 It is possible however to know from knowing some things previously,6 and receiving the knowledge of others at the same time, as of things which are contained under universals, and of which a man possesses knowledge.7 For he knew before that every triangle has angles equal to two right angles, but that this which is in a semi-circle is a triangle, he knew by induction at the same time. For of some things knowledge is acquired after this manner, nor is the extreme known through the middle, as such things as are singulars, and are not predicated of any subject. Perhaps however we must confess that we possess knowledge after a certain manner before induction or the assumption of a syllogism, but in another manner not.8 For what a man is ignorant about its existence at all, how could he know at all that it has two right angles? But it is evident that he thus knows because he knows the universal, but singly he does not know it. Still if this be not admitted, the doubt which is mentioned in the Meno9 will occur, either he will learn nothing, or those things which he knows,10 for he must not say, as some endeavour to solve the doubt, “ Do you know that every duad is an even number or not?” for since if some one says that he does, they would bring forward a certain duad which he did not think existed, as therefore not even; and they solve the ambiguity, not by saying that he knew every duad to be even, but that he was ignorant as to what they know is a duad. Nevertheless they know that of which they possess and have received the demonstration, but they have received it not of every thing which they know to be a triangle or a number, but of every number and triangle singly, for no proposition is assumed of such a kind as the number which you know, or the rectilinear figure which you know, but universally. Still there is nothing (I think) to prevent a man who learns, in a certain respect knowing and in a certain respect being ignorant,11 for it is absurd, not that he should in some way know what he learns, but that he should thus know it, as he does when he learns it, and in the same manner.

Note del traduttore
  1. 1 Doctrine and discipline are the same in reality, but differ in relation, being called “ doctrine ” when applied to teaching, and “ discipline ” as pertaining to learning. Taylor defines Διανοία, that power of the soul which reasons scientifically, deriving the principles of its reasoning from intellect: and these principles are axioms and definitions. Comp. Poetic. ch. 6, where the word is applied to a certain part of tragedy. Ethics, b. vi. c. 2. Waitz notices the similarity between the commencement of this ch. and the opening ch. of the Ethics. For the principle stated, consult Hill’s Logic, p. 137, and for the word, see Biese, i. p. 89.
  2. 2 That is, syllogisms contain propositions, assumed to be known either by demonstration or per se.
  3. 3 Induction.
  4. 4 Vid. Rhet. b. i. ch. 2. It was shown (b. ii. ch. 24, Anal. Pri.) that example is reduced to a syllogism in the 1st figure, the major prop. of which is proved by an imperfect deduction; wherefore as the whole force of the example consists in that induction, it is not undeservedly said to be a certain induction. Tay-or.
  5. 5 Quæ antequam disciplina ipsa quæcunque nobis tradatur, cognoscere debemus ὅτι ἐστιν, axiomata sunt, quæ vero cognoscere debemus τί τὸ λεγόμενόν ἐστι, definitiones sunt : unde fit ut disciplinam ipsam quamcunque, præcede redebeant, axiomata et definitiones.—Nam etsi definitio rei naturam non patefaciat, tamen quam vim habeat nomen quo res significetur exponit, ut etiam definitio nominalis, quæ dicitur utilitatem quandam habeat. Waitz. See also Meditationes de cognitione Veritatis et Ideis : Leibnitz Opera, p. 80, ed. Erdmann.
  6. 6 i. e. to prove the principal conclusion, from certain propositions being proved, pro-syllogistically.
  7. 7 Learning them not from antecedent knowledge nor pro-syllogistically, but immediately, just as sensibles are known by the senses. Taylor. Compare also Ethics, b. vi. ch. 3, and Whately's Logic.
  8. 8 i. e. the conclusion may be known by universal, yet it cannot be by proper or peculiar knowledge ; for instance, in the case below he knows that this triangle has angles equal to two right, because he knows this to be the case universally of a triangle, but he does not know it singly, absolutely, and perfectly by proper knowledge.
  9. 9 Meno, Plato-
  10. 10 The passage in the Meno of Plato is that commencing καὶ τνα τρόπoυ
  11. 11 Knowing by universal, being ignorant by proper knowledge.

San Tommaso: Libro I, lezione I · Libro I, lezione II · Libro I, lezione III

Libro I, capitolo 2 Of Knowledge, and Demonstration, and its Elements.71b9–72b4

Inglese

We think that we know each thing singly, (and not in a sophistical manner, according to accident,) when we think that we know the cause on account of which a thing is, that it is the cause of that thing, and that the latter cannot subsist otherwise; wherefore it is evident that knowledge is a thing of this kind, for both those who do not, and those who do know, fancy, the former, that they in this manner possess knowledge, but those who know, possess it in reality, so that it is impossible that a thing of which there is know-

ζητήσεις. The doubt (ἀπόρημα) is, that if we can learn nothing, therefore that nothing is to be investigated, since what we know we need not investigate, and it is vain to search after what we know not, since not knowing the object of our search, we shall be ignorant of it, even when found. Socrates solves this (λύει) by declaring that to discover and to learn, are nothing else than to remember, because the soul, being immortal, formerly knew every thing, of which knowledge, becoming oblivious by being merged in the body, she endeavours to recall knowledge to memory by investigation. ledge simply should subsist in any other way.1 Whether therefore there is any other mode of knowing we shall tell hereafter, but we say also that we obtain knowledge through demonstration, but I call demonstration a scientific2 syllogism, and I mean by scientific that according to which, from our possessing it, we know. If then to know is what we have laid down, it is necessary that demonstrative science should be from things true, first, immediate, more known than, prior to, and the causes of the conclusion, for thus there will be the appropriate first principles of whatever is demonstrated.3 Now syllogism will subsist even without these, but demonstration will not, since it will not produce knowledge. It is necessary then that they should be true, since we cannot know that which does not subsist, for instance, that the diameter of a square is commensurate with its side. But it must be from things first and indemonstrable, or otherwise a man will not know them, because he does not possess the demonstration of them,4 for to know those things of which there is demonstration not accidentally is to possess demonstration. But they must be causes, and more known, and prior; causes indeed, because we then know scientifically when we know the cause; and prior, since they are causes; previously known also, not only according to the other mode by understanding (what they signify), but by knowing that they are.5 Moreover they are prior and more known in two ways, for what is prior in nature, is not the same as that which is prior in regard to us, nor what is more known (simply) the same as what is more known to us. Now I call things prior and more known to us, those which are nearer to sense, and things prior and more known simply, those which are more remote from sense; and those things are most remote6 which are especially universal,7 and those nearest which are singular, and these are mutually opposed. That again is from things first, which is from peculiar principles,8 and I mean by first, the same thing as the principle, but the principle of demonstration is an immediate proposition, and that is immediate to which there is no other prior. Now a proposition is one part of enunciation, one of one,9 dialectic indeed, which similarly assumes either (part of contradiction), but demonstrative which definitely (assumes) that one (part) is true. Enunciation is either part of contradiction, and contradiction is an opposition10 which has no medium in respect to itself. But that part of contradiction (which declares) something, of somewhat, is affirmation, and that (which signifies) something from somewhat is negation.11 Of an immediate syllogistic principle, I call that the thesis, which it is not possible to demonstrate, nor is it necessary that he should possess it, who intends to learn any thing; but what he who intends to learn any thing must necessarily possess, that I call an axiom,12 for there are certain things of this kind, and in denominating these, we are accustomed generally to use this name. But of thesis, that which receives either part of contradiction, as for instance, I mean that a certain thing is, or that it is not, is hypothesis, but that which is without this, is definition. For definition is a thesis, since the arithmetician lays down unity to be that which is indivisible, according to quantity, yet it is not hypothesis, since what unity is, and that unity is, are not the same thing.

Notwithstanding, since we must believe in and know a thing from possessing such a syllogism as we call demonstration, and this is, because these are so, of which syllogism consists—it is necessary not only to have a previous knowledge of the first, or all, or some things, but that they should be more known, for that on account of which any thing exists, always exists itself in a greater degree; for example, that on account of which we love is itself more beloved. Hence if we know and believe on account of things first, we also know and believe those first things in a greater degree, because through them (we know and believe) things posterior. A man however cannot believe more than what he knows, those things which he does not know, nor with respect to which he is better disposed than if he knew.13 This however will happen, unless some one should previously know of those who give credence through demonstration, since it is more necessary to believe either in all or in certain first principles, than in the conclusion. It is not only however requisite that he who is to possess knowledge through demonstration, should know in a greater degree first principles, and believe rather in them than in the thing demonstrated, but also that nothing else should be more credible or more known to him than the opposites of the principles, from which a syllogism of contra-deception may consist, since it behoves him who possesses knowledge singly to be unchangeable.14

Note del traduttore
  1. 1 True science requires, 1st, that the cause of a thing be known, i. e. that the middle term be the cause of the conclusion; 2nd, that the cause be compared with the effect, so that we know it to be the cause of the conclusion; 3rd, that we know the conclusion to subsist thus necessarily, and that it cannot subsist otherwise. Taylor. Comp. Rhet. i. c. 7. Magna Moralia, i. c. 34. Metap. i. 1, and 10, 3, and 7. Cause and ἀρχὴ must not be confounded, since the cause precedes the ἀρχή; vide Buckley's note in Bohn's edition of the Rhetoric quoted above.
  2. 2 Syllog. qui scire facit. Buhle.
  3. 3 Vide Hill's Logic, page 289, also Mansel, p. 104, et seq.; in the appendix note H. of the latter's work, the reader will find the statement of the nature of demonstrative syllogism fully set forth. The words first and immediate, signify that they are not demonstrable by a middle term from any higher truth. The demonstration, “propter quid sit per causam non primam,” would only form a subordinate portion of a complex demonstration. Vide Wall's Log. lib. iii. cap. 22. As post demonstrations depend upon those prior, therefore all are said to be from things first.
  4. 4 Either they would be unknown or not be principles, because they might be demonstrated by other things prior to them, ad infinitum. Vide Whately's Logic, book iv.
  5. 5 Principles are prior in a two-fold respect, they cause a thing to be, and also cause the same to be known. Taylor. Comp. Anal. Post. i. 24. The inquiry into the definition of a thing is identical with that of its cause, with the difference that the cause of attributes is to be sought in their subject, but in the case of substances per se the cause must be sought in themselves only. Cf. Metap. v. 1, 2; x. 7, 2.
  6. 6 i. e. from sense.
  7. 7 Aristotle here intimates his concurrence with the Platonic theory, that the soul contains in itself essentially the “universal,” or true principle of demonstration; vide the Commentary of Proclus on the Parmenides of Plato, in which he exhibits the priority of universals to singulars, and the method of their reception by the dianœtic faculty. Cf. also Ritter and Cousin upon the Old Academy. Arist. Ethics, b. vi. c. 11, and Metap. books i. iv. vi. and xii. (Leip. ed.) If demonstration be from universals prior by nature, it follows, according to Aristotle, that it is alone from forms essentially inherent in the soul, since abstract forms are not naturally prior, because they are universals of a posterior origin.
  8. 8 That principles ought to be peculiar to the science, and to what is to be demonstrated, he shows, ch. vii. and ix.
  9. 9 One enunciation signifies one thing of one. Vide ch. 8, on Interpretation.
  10. 10 Vide ch. 10. Categories.
  11. 11 Ch. 6, on Interpretation.
  12. 12 Axioms are common, according to Aristotle, to several classes, but in the case of a single science need only be assumed to an extent commensurate with the object-matter of that science. As Mansel well observes, the places in which the axioms are mentioned in connexion with demonstration, have never been satisfactorily explained on the usual scholastic interpretation. I entirely agree with him, that the supposition that axioms are virtually, but not actually, employed in demonstration, and the distinction drawn between immediate propositions and axioms, are equally unfounded ; in fact it subverts Aristotle’s own expression. Vide Mansel’s Logic, App. 66. Compare also Zabarella in I. An. Post. Cont. 57, 58. Crakanthorpe, Logic, lib. iv. c. 1. Aquinas Opusc. 48, de Syllo. Dem. cap. 6.
  13. 13 By being better disposed, Aristotle, who is here speaking of demonstrative knowledge, means the intuitive apprehension of intellect. Cf. Waitz and Biese in loc.
  14. 14 That is, free from lapsing into error, which he would fall into by not knowing opposites, since he might believe that the opposites to true principles are true. For the better elucidation of the above chapter, the following table of the principles of science is given :

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Libro I, capitolo 3 Refutation of certain opinions as to Science and Demonstration.72b5–73a20

Inglese

To some, because it is necessary that first things should be known, science does not appear to exist, but to others to exist indeed, yet (they think) there are demonstrations of all things, neither of which opinions is true or necessary.1 For those who suppose that knowledge does not subsist at all, these think that we are to proceed to infinity as if we may not know things subsequent by things prior, of which there are no first, reasoning rightly, since it is impossible to penetrate infinites.2 And if (they say) we are to stop, and there are principles, these are unknown, since there is no demonstration of them, which alone they say is to know scientifically; but if it is not possible to know first things, neither can we know either simply or properly things which result from these, but by hypothesis, if these exist.

Others however assent with respect to knowledge, for (they assert) that it is only through demonstration, but that nothing prevents there being a demonstration of all things, for demonstration may be effected in a circle, and (things be proved) from each other. We on the contrary assert, that neither is all science demonstrative, but that the science of things immediate is indemonstrable. And this is evidently necessary, for if it is requisite to know things prior, and from which demonstration subsists, but some time or other there is a stand made at things immediate, these must of necessity be indemonstrable. This therefore we thus assert, and we say that there is not only science,3 but also a certain principle of science, by which we know terms.4 But that it is impossible to demonstrate in a circle simply is evident, since demon-

“firsts” on the other hand, still there is no science, for the latter being from things prior, there can be nothing prior to “firsts.” stration must consist of things prior and more known, as it is impossible that the same should be prior and posterior to the same, unless in a different way, as for instance, some things with reference to us, but others simply in the manner in which induction makes known. If however this be so, to know simply will not be well defined, but it is two-fold,5 or the other demonstration is not simply so which is produced from things more known to us. Still there happens to those who assert there is demonstration in a circle, not only what has now been declared, but that they say nothing else than this is if it is, and in this manner we may easily demonstrate all things. Nevertheless it is evident that this occurs, when three terms are laid down, for to assert that demonstration recurs through many or through few terms, or whether through few or through two, makes no difference. For when A existing, B necessarily is, and from this last C, if A exists C will exist, if then, when A is, it is necessary that B should be, but this existing, A exists, (for this were to demonstrate in a circle,) let A be laid down in the place of C. To say therefore that because B is A is, is equivalent to saying that C is, and this is to say that A existing C is, but C is the same as A, so that it happens that they who assert there is demonstration in a circle, say nothing else than that A is because A is, and thus we may easily demonstrate all things. Neither however is this possible, except in those things which follow each other as properties: from one thing however being laid down, it has been proved that there will never necessarily result something else, (I mean by one thing, neither one term, nor one thesis being laid down,) but from two first and least theses, it is possible (to infer necessarily something else), since we may syllogize. If then A is consequent to B and to C, and these to each subvert demonstration by a procession to infinity, that we not only say there is demonstration, but that things do not proceed to infinity, because there is a certain principle of demonstration by which we know the terms or boundaries of things, when we obtain illumination from thence. Perhaps, however, by a “certain principle of science,” Aristotle means our intellect, and by terms, axioms. Cf. Metap. lib. ii. and x. other, and to A, thus indeed it is possible to demonstrate all those things which are required from each other in the first figure, as we have shown in the books on Syllogism. It has also been shown that in the other figures there is either not a syllogism, or not one concerning the subjects assumed;6 but it is by no means possible to demonstrate in a circle those which do not reciprocate. Hence, since there are but few such in demonstrations, it is evidently vain and impossible to say, that there is demonstration of things from each other, and that on this account universal demonstration is possible.

Note del traduttore
  1. 1 The argument is as follows: there are, or are not, certain πρῶτα; if there are not, but we admit a process ad infinitum, there is no science, since the latter ultimately depends on certain πρῶτα: if there are
  2. 2 They are right in saying we cannot know things posterior through the prior, unless the progress of investigation stop at certain “firsts;” they are wrong in asserting that these firsts cannot be known. Cf. Physics, lib. i. and iii.
  3. 3 That is, demonstrative science.
  4. 4 A certain knowledge antecedent to demonstrative science. The word ὅροι, here, Pacius mistakes for “simple terms;” it signifies rather, as St. Hilaire observes, “les propositions immediates,” i. e. axioms. The following is the interpretation by Ammonius of this place. The principle of science is intellect, not our intellect, but that which is divine and above us; but terms are intelligible and divine forms, which are called terms in consequence of being the boundaries of all things. For as multitude originates from the monad, and is dissolved into the monad, and tens are the boundaries of hundreds, and hundreds of thousands, but the monad is the common boundary of all numbers; thus also with respect to things, we may say that the boundaries of sensibles are the celestial bodies, of the celestial bodies intelligible essences, and of all things in common the first cause. And this may be said in answer to those who
  5. 5 The one from things more known and prior, according to nature; the other from those more known and prior, according to us.
  6. 6 Both assumed prop. are not proved, because in the 2nd fig. the conclusion is negative, wherefore we cannot prove an affirmative prop. in a circle ; and in the 3rd fig. the conclusion is particular, wherefore an universal cannot be demonstrated in a circle.

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Libro I, capitolo 4 Upon the terms “every,” “per se,” and “universal.”.73a21–74a3

Inglese

Since it is impossible that a thing, of which there is simply science, should have a various subsistence, it will be also necessary that what we know should pertain to demonstrative science, and demonstrative science is that which we possess from possessing demonstration, hence a syllogism is a demonstration from necessary (propositions). We must comprehend then of what, and what kind (of propositions), demonstrations consist; but first let us define what we mean by “of every,” and “per se,” and “universal.”

I call that “of every,” which is not in a certain thing, and in another certain thing is not, nor which is at one time, and not at another; as if animal is predicated of every man, if it is truly said that this is a man, it is true also that he is an animal, and if now the one is true, so also is the other; and in like manner, if a point is in every line. Here is a proof, for when we are questioned as it were of every, we thus object, either if a thing is not present with a certain individual, or if it is not sometimes. But I call those “per se” which are inherent in (the definition of) what a thing is,1 as line is in triangle, and point in line, (for the essence of them is from these, and they are in the definition explaining what it is:)2 also those things which are inherent in their attributes in the definition declaring what a thing is,3 as the straight and the curved are inherent in a line, and the odd and even in number, and the primary4 and composite, the equilateral and the oblong:5 and they are inherent in all these, in the definition declaring what a thing is, there indeed line, but here number. In a similar manner, in other things, I say that such are per se inherent in each, but what are in neither way inherent (I call) accidents, as the being musical, or white in an animal. Moreover, that which is not predicated of any other subject, as that which walks being something else, is that which walks, and is white, but essence and whatever things signify this particular thing, not being any thing else, are that which they are. Now those which are not predicated of a subject, I call “per se,” but those which are so predicated, I call accidents. Again, after another manner, that which on account of itself is present with each thing is “per se,” but that which is not on account of itself is an accident;6 thus it is an accident if while any body was walking it should lighten, for it did not lighten on account of his walking, but we say that it accidentally happened. If, however, a thing is present on account of itself, it is per se, as if any one having his throat cut should die, and through the wound, because he will die in consequence of his throat being cut, but it did not accidentally happen that he whose throat was cut died.

Those therefore which are predicated in things which are simply objects of science per se, so as to be inherent in the things predicated, or which 1st mode. are themselves inherent in subjects, are on ac- † 2nd mode. count of themselves, and from necessity, for it does not happen that they are not inherent either simply or as opposites, as the straight and the curved in a line, and the even or odd in number. For a contrary is either privation or contradiction in the same genus, as that is even which is not odd in numbers, so far as it follows:7 hence if it is requisite to affirm or deny, it is also necessary that those which are per se should be inherent.

Let then the expressions “of every” and “per se” be thus defined: I call that universal, however, which is both predicated “of every” and “per se,” and so far as the thing is.8 Now it is evident that whatever are universal are inherent in things necessarily, but the expressions “per se,” “and so far as it is,” are the same; as a point and straightness are per se present in a line, for they are in it, in as far as it is a line, and two right angles in a triangle, so far as it is a triangle, for a triangle is per se equal to two right angles. But universal is then present, when it is demonstrated of any casual and primary thing, as to possess two right angles is not universally inherent in figure, yet it is possible to demonstrate of a figure that it has two right angles, but not of any casual figure, nor does a demonstrator use any casual figure, for a square is indeed a figure, yet it has not angles equal to two right. But any isosceles has angles equal to two right, yet not primarily, for triangle is prior. Whatever therefore is casually first demonstrated to possess two right angles, or any thing else, in this first is the universal inherent, and the demonstration per se of this is universal, but of other things after a certain manner not per se, neither is it universally present in an isosceles, but extends farther.

Note del traduttore
  1. 1 Four senses are given of this expression, τὸ καθ' ατό: 1. When the predicate is part of the definition of the subject. 2. When the subject is part of the definition of the predicate. 3. When existence is predicated of a substance. 4. When the subject is the external efficient cause of the predicate. In proper demonstration, propositions must be “per se” either in the first or second meaning. Cf. Mansel’s Logic, note H. on the Demonstrative Syllogism.
  2. 2 Thus a triangle is defined to be a figure contained by three straight lines.
  3. 3 As, to use Aristotle’s graphic illustration, in the definition of nose, flatness of nose is not employed, but flatness of nose is defined to be a curvature of nose.
  4. 4 As 3, 5, 7, &c.
  5. 5 An oblong number is that which a number produces, not multiplied by itself, but by another number, as six is from twice three. Taylor.
  6. 6 This relates to the efficient cause.
  7. 7 Contraries may, however, be both absent from a subject, as a body may be neither white nor black ; but the even and odd are opposed as contradictories, so that one of them must be present in a subject. Vide Categ. ch. 10. The even is compared to the not odd, because it is necessarily consequent to it.
  8. 8 As man is risible, because every man is, both “per se” and “quatenus ipsum ;” upon the apparent inconsistency of Aristotle in the use of the word καθόλου, see Waitz, l. Ana. Post. p. 315. The reader will find some valuable remarks upon the demonstratio potissima, especially in reference to this place, in Mansel’s Logic, Appendix, note H., where the example is regularly stated.

San Tommaso: Libro I, lezione IX · Libro I, lezione X · Libro I, lezione XI

Libro I, capitolo 5 Of Errors about the primary Universal.74a4–74b4

Inglese

We ought not to be ignorant that frequently error arises, and that what is demonstrated is not primarily universal, in so far as the primarily universal appears to be demonstrated. Now we are deceived by this mistake, when either nothing higher can be assumed, except the singular or singulars, or when something else can be assumed, but it wants a name in things differing in species, or when it happens to be as a whole in a part, of which the demonstration is made, for demonstration will happen to particulars, and will be of every individual, yet nevertheless it will not be the demonstration of this first universal. Still I say the demonstration of this first, so far as it is this, when it is of the first universal. If then any one should show that right lines do not meet, it may appear to be (a proper) demonstration of this, because it is in all right lines, yet this is not so, since this does not arise from the lines being thus equal, but so far as they are in some way or other equal. Also if a triangle should be no other than isosceles, so far as isosceles it may appear to be inherent: alternate proportion also, so far as regards numbers and lines and solids and times (as was once shown separately) it is possible at least to be demonstrated of all by one demonstration, but inasmuch as all these, numbers, length, time, are not one denominated thing, and differ from each other in species, they were assumed separately. But now the demonstration is universal, for it is not in so far as they are lines or numbers, that it is inherent, but in so far as this thing which they suppose to be universally inherent. For this reason neither if one should demonstrate each several triangle by one or another demonstration, that each has two right angles, equilateral, the scalene, and the isosceles separately, would he yet know that the triangle (itself) has angles equal to two right, except in a sophistical manner,2 nor triangle universally, though there should be no other triangle besides these. For he does not know it so far as it is triangle, nor does he know every triangle, except according to number, but not every, according to species, even if there be no one that he does not know.3 When then does he not know universally, and when knows he simply? It is clear that if there is the same essence of a triangle, and of an equilateral either of each or of all, he knows,[†2] but if there is not the same, but different, and it is inherent so far as it is triangle, he does not know.4 Whether however is it inherent, so far as it is triangle, or so far as it is isosceles? And when, according to this, is it primary? And of what is the demonstration universally? It is evident that it then is, when, other things being taken away, it is inherent in the primary, thus two right angles will be inherent in a brazen isosceles triangle, when the being brazen and the being isosceles are taken away, but not if the figure or boundary is taken away, nor if the primary are. But what primary? if indeed triangle (is taken away); according to this it is inherent in others, and of this universally is the demonstration.

Note del traduttore
  1. 1 All universals are gained by abstraction, i. e. by separating the phenomena in which a certain number of individuals resemble each other, from those in which they differ ; Locke calls all universals, abstract ideas. Upon generalization as distinguished from abstraction, vide Stewart, Phil. of the Human Mind ; Whately's Logic, Outline of Laws of Thought, p. 44. The causes of the error which a person commits who demonstrates of the inferior as of species, what he ought to demonstrate of the superior as of genus, are four. 1st, When one particular being under universal, we demonstrate the former instead of the latter : 2nd, when we demonstrate of all contained under a proper subject when we seem to do so of the proper subject itself: 3rd, when the particular is demonstrated because the universal has no name : 4th, when we conclude that an universal demonstration of a thing has been given because the demonstration is of every individual. Cf. Waitz, p. 387, et seq.
  2. 2 Vide supra.
  3. 3 That is, in number. Triangles are here said to be as many in number as in species.
  4. 4 That is, by demonstration of a species of triangle, he does not know the universal property as demonstrated of triangle, viz. the possession of three angles equal to two right.
  5. Universally and simply mean nearly the same thing, because when a man knows not sophistically, i. e. simply, he knows universally, hence Taylor and Buhle insert, the one “universally,” the latter “simpliciter,” as equivalent in this place.

San Tommaso: Libro I, lezione XII

Libro I, capitolo 6 Demonstration consists of Principles per se; and of a necessary Medium.74b5–75a37

Inglese

If then demonstrative science is from necessary principles, (for what is scientifically known cannot subsist otherwise,) and those which are per se inherent are necessarily so in things, (for some are inherent in the definition of what a thing is, but others are they in the very nature of which the subjects are inherent, of which they are so predicated, that one of opposites is necessarily present,) it is evident that the demonstrative syllogism will consist of certain things of this kind, for every thing is either thus inherent, or according to accident, but accidents are not necessary.

Either therefore we must say this, or that demonstration is a necessary thing, if we lay down this principle, and that if demonstration is given that a thing cannot subsist otherwise, wherefore the2 syllogism must be from necessary (matter). For it is possible without demonstration to syllogize from what are true, but we cannot do so from things necessary, except by demonstration, for this is now (the essence) of demonstration. An indication also that demonstration is from things necessary is, that we thus object to those who think they demonstrate that (the conclusion) is not necessary, whether we think that the matter may altogether be otherwise possible, or on account of the argument. Hence too the folly of those appears, who think they assume principles rightly, if the proposition be probable and true, as the Sophists (assume) that to know is to possess knowledge.3 For it is not the probable or improbable, which is the principle, but that which is primary of the genus about which the demonstration is made, nor is every thing true appropriate. But that it is necessary that the syllogism should consist of necessary things appears also from these; for if he who cannot assign a reason why a thing is, when there is a demonstration, does not possess knowledge, let A4 be necessarily predicated of C, but B the medium through which it is demonstrated not of necessity, (in this case) he does not know the cause. For this is not on account of the medium, for the latter may not exist, yet the conclusion is necessary. Besides, if some one does not know, though he now possesses a reason, and is safe, the thing also being preserved, he not having forgotten it, neither did he before know it. But the medium may perish if it is not necessary, so that he, being safe, will have a reason, the thing being preserved, and yet not know it, wherefore neither did he know it before.5 But if the medium is not destroyed, yet may possibly perish, that which happens will be possible and contingent, it is impossible however that one so circumstanced should know.6 When therefore the conclusion is from necessity, there is nothing to prevent the medium through which the demonstration was made from being not necessary, since it is possible to syllogize the necessary even from things not necessary, just as we may the true from things not true. Still when the medium is from necessity the conclusion is also from necessity, as the true (results) from the true always: for let A be of necessity predicated of B, and this of C, then it is sesses science: he who possesses science knows what science is: therefore, he who knows any thing knows what science is. necessary that A should be with C. But when the conclusion is not necessary, neither possibly can the medium be necessary: for let A be present with C, not of necessity, but let it be with B, and this with C of necessity; A then will also be of necessity present with C, yet it was not supposed so.7 Since therefore what one knows demonstratively must be inherent of necessity, we must evidently obtain the demonstration through a necessary medium also, for otherwise, he will neither know why a thing exists, nor that it is necessary for it to exist, but he will either imagine not knowing, if he assumes what is not necessary as if it were necessary,8 or in like manner he will not imagine if he knows that it is through media, and why it is through the Cf. ch. 2. immediate.*9 Of accidents however which are not per se after the manner in which things per se have been defined, there is no demonstrative science, since it is not possible to demonstrate the conclusion of necessity, because accident may possibly not be present, for I speak of accident of this kind.10 Still some one may perhaps doubt why we must make such investigations about these things, if it is not necessary that the conclusion should be, for it makes no difference if any one interrogating casual things*11 should afterwards give the conclusion: nevertheless we must interrogate not as if (the conclusion) were necessary on account of things interrogated, but because it is necessary for him who asserts these should assert this, and that he should speak truly if the things are truly inherent.

Since, however, whatever are inherent per se are necessarily inherent in every genus, and so far as each is, it is clear that scientific demonstrations are of things “per se” inherent, and consist of such as these. For accidents are not necessary: wherefore it is not necessary to know the conclusion why it is, nor if it always is, but not as, for instance, syllogisms formed from signs. For what is “per se” will not be known “per se,” nor why it is, and to know why a thing is, is to know through cause, wherefore the middle must “per se” be inherent in the third, and the first in the middle.

Note del traduttore
  1. 1 If things per se or essential are necessary, and the principles of demonstration are necessary; therefore the principles of demonstration are per se. As Taylor observes, by conversion of the major, Aristotle's argument here may become a syllogism in Barbara.
  2. 2 i. e. the demonstrative.
  3. 3 It was thus argued by Protagoras: Whoever knows any thing, pos-
  4. 4 The minor
  5. 5 Scientia quam quis habet, non perditur, nisi aut ipse perit aut obliviscitur aut res quam scivit, interit. Waitz. For a general analysis of the argument, see Waitz, page 320, in locum.
  6. 6 Vide Prior Anal. book ii. chap. 2—4. The argument that the medium, the source of science as containing the cause, does not perish, though it may do so, and therefore by its remaining that science may be possessed, Aristotle shows to be ineffectual, since they who advance it are compelled to confess that to be possible, viz. that the medium may perish, which is impossible, and hence that we may be ignorant of what we know. By being “so circumstanced,” is meant “to be ignorant without forgetfulness” Cf. Whately’s Logic, b. iv. c. ii. sec. 2.
  7. 7 The necessary relations between premises and conclusion may be considered as four: 1. If the conclusion is necessary, the propositions may be non-necessary. 2. If the conclusion is non-necessary, the prop. are non-necessary. 3. If the prop. are necessary, the conclusion is always necessary. 4. If the prop. are non-necessary, the conclusion may be necessary. Granting that the last (number 4.) may be true, yet Aristotle denies that in such a case the person who thus infers demonstrates, because demonstration produces true science, but such a man is ignorant that the conclusion is necessary. Vide also Hill's Logic, p. 285, et seq.
  8. 8 Sanderson defines thus: Error est habitus quo mens inclinatur ad assentiendum sine formidine falsitati. Opinio est habitus quo mens inclinatur ad assentiendum cum formidine alicui propositioni propter probabilitatem quam videtur habere. Error, therefore, as Mansel observes, implies certainty of the subject, but not of the object; whilst opinion cannot consist with certainty of the subject, nor yet, strictly, with that of the object. It is of course clear, that what one may scientifically know, another may only think, but to constitute real science two things are necessary: 1. A correct ascertainment of the data from which we are to reason; 2. Correctness in deduction of conclusions from them. Cf. Whately, b. iv. c. 2, sect. 3. Error, as defined above, comes under the state of mind described in the text by Aristotle.
  9. 9 Cf. Aquinas, Op. 48, cap. 1; Occam, Log. p. 3, c. 2. If the premise is not the first cause, though it contains the cause of the conclusion, the syllogism is not δι' ἀμέσων, and there is no demonstration: neither if the premise be an effect and not a cause of the conclusion, nor if the premise, though immediate, be a remote cause of it, since in all these cases we know the fact only, but not the cause. Cf. Mansel and Wai.'s Log. ib. iii. cap. 22.
  10. 10 i. e. about common accident—for proper accident is predicated in the second mode per se of a subject. Taylor.
  11. 11 Ad veram demonstrationem nihil attinet si quis sumat quæ in casu posita, et mutationi obnoxia sint et quæ inde consequantur, declaret. Waitz. The casual, here alluded to, are propositions not belonging to the conclusion.

San Tommaso: Libro I, lezione XIII · Libro I, lezione XIV

Libro I, capitolo 7 That we may not demonstrate by passing from one Genus to another.75a38–75b20

Inglese

It is not therefore possible to demonstrate passing from one genus to another, as, for instance, (to demonstrate) a geometrical (problem) by arithmetic, for there are three things in demonstrations, one the demonstrated conclusion, and this is that which is per se inherent in a certain genus. Another are axioms, but axioms are they from which (demonstration is made), the third is the subject genus, whose properties and essential accidents demonstration makes manifest. Now it is possible that the things from which demonstration consists may be the same, but with those whose genus is different, as arithmetic and geometry, we cannot adapt an arithmetical demonstration to the accidents of magnitudes, except magnitudes are numbers, and how this is possible to some shall be told here-after. But arithmetical demonstration always has the genus about which the demonstration (is conversant), and others in like manner, so that it is either simply necessary that there should be the same genus, or in a certain respect,2 if demonstration is about to be transferred; but that it is otherwise impossible is evident, for the extremes and the middles must necessarily be of the same genus, since if they are not per se, they will be accidents. On this account we cannot by geometry demonstrate that there is one science of contraries, nor that two cubes make one cube,3 neither can any science (demonstrate) what belongs to any science, but such as are so related to each other as to be the one under the other, for instance, optics to geometry, and harmonics to arithmetic. Nor if any thing is inherent in lines not so far as they are lines, nor as they are from proper principles, as if a straight line is the most beautiful of lines, or if it is contrary to circumference, for these things are inherent not by reason of their proper genus, but in so far as they have something common. demonstrative syllogism, the minor term is the subject; the major, the attribute; the middle, the cause.

Note del traduttore
  1. 1 Cf. Anal. Post. i. 10. Eth. i. 2. Keckermann Syst. Log. iii. Tract. 2. cap. 1. Zabarella de Meth. lib. ii. cap. 7. Genus here signifies the object or materia circa quam, often, but improperly, called the subject; the species are the subdivisions of the general subject. In the
  2. If it always is inherent, i. e. if the propositions be always true.
  3. 2 Of subaltern sciences, the subject is not entirely the same, as the subject of geometry is a line, but of optics an optical line. Taylor. Vide also Trendelenburg, p. 118.
  4. 3 That is, geometry cannot teach a method of doubling the cube. Vide Reimer de Duplicatone Cubi. Omnis demonstratio genus suum, non excedere sed in eo consistere debet. Waitz.

San Tommaso: Libro I, lezione XV

Libro I, capitolo 8 Things which are subject to Change are incapable of Demonstration per se.75b21–36

Inglese

It is also evident that if the propositions of which a syllogism consists are universal, the conclusion of such a demonstration. and in short of the demonstration of itself, must necessarily be perpetual. There is not then either demonstration, nor in short science of corruptible natures, but so as by accident, because there is not universal belonging to it, but sometimes, and after a certain manner. But when there is such, it is necessary that one proposition should not be universal, and that it should be corruptible, corruptible indeed, because the conclusion will be so if the proposition is so, and not universal, because one of those things of which it is predicated will be, and another will not be,1 hence it is not possible to conclude universally, but that it is now. It is the same in the case of definitions, since definition is either the principle of demonstration, or demonstration, differing in the position (of the terms), or a certain conclusion of demonstration. The demonstrations and sciences however of things frequently occurrent, as of the eclipse of the moon, evidently always exist, so far as they are such, but so far as they are not always, they are particular,2 and as in an eclipse, so also is it in other things.

Note del traduttore
  1. 1 Hoc quidem (tempore) erit quod asseritur, hoc vero (tempore) non erit. Buhle. I prefer Buhle’s translation for its clearness, but have followed Taylor’s on account of its exactness. The science of things subject to change is not simply science, but with the addition of κατὰ συμβεβηκός. Upon the relation of science to its subject matter, see Rhet. book i. ch. 7. Cf. also Rhet. ii. ch. 24. Anal. Prior, i. ch. 13. The subject of science, he expressly says in the Ethics, (b. vi. ch. 4,) has a necessary existence, therefore it is eternal and indestructible.
  2. 2 Particular cases, (of eclipses, for instance,) as they are not always the same, do not fall under demonstration.

San Tommaso: Libro I, lezione XVI

Libro I, capitolo 9 That the Demonstration of a thing ought to proceed from its own appropriate Principles: these last indemonstrable.75b37–76a30

Inglese

Since however it is evident that we cannot demonstrate each thing except from its own principles, if what is to be demonstrated is inherent in a subject so far as the subject is that (which it is), to have a scientific knowledge of that thing is not this, if it should be demonstrated from true, indemonstrable, and immediate (propositions).1 For we may so demonstrate possibly, as Bryso did, the quadrature of the circle, since such reasonings prove through something common, that which is inherent in another thing, hence these arguments are adapted to other things not of the same genus.2 Wherefore that thing would not be scientifically known, as far as it is such, but from accident, for otherwise the demonstration would not be adapted also to another genus.

We know however each thing not accidentally when we know it according to that, after which it is inherent from principles which are those of that thing, so far as it is that thing;3* as that a thing has angles equal to two right angles, in which the thing spoken of4 is essentially inherent from the principles of this thing. Hence if that is essentially inherent in what it is inherent, it is necessary that the middle should be in the same affinity,|| but if not, yet it will be as harmonics are proved through an arithmetical principle.5 Such things however are demonstrated after a similar manner, yet they differ,6 for that they are, is part of another science, (for the subject genus is another,†) but why they are, is a province of a superior science, of which they are the essential qualities. Hence from these things also it is apparent that we cannot demonstrate each thing simply, but from its proper principles, and the principles of these7 have something common.

If then this is evident, it is also clear that it is impossible to demonstrate the proper principles of each thing, for they will be the principles of all things, and the science of them the mistress of all (sciences):8 for the man has more scientific knowledge who knows from superior causes, since he knows from prior things when he knows not from effects, but from causes. So that if he knows more, he knows also most, and if that be science, it is also more, and most of all such. Demonstration however is not suitable to another genus, except as we have said, geometrical to mechanical or optical, and arithmetical to harmonical demonstrations.

Nevertheless it is difficult to know whether a man possesses knowledge or not, since it is hard to ascertain if we know from the principles of each thing or not, which indeed constitutes knowledge. We think however that we know, if we have got a syllogism from certain primary truths, but it is not so, since it is necessary that they § should be of a kindred nature with the primary.

Note del traduttore
  1. 1 That is, the propositions must also be appropriate to the subject of demonstration.
  2. 2 According to Alexander Aphrodisiensis—Bryso endeavoured to demonstrate the quadrature of the circle thus : Where the greater and less are found, there also is the equal found, but a square greater and less than a circle is found, therefore a square equal to the circle may also be found. The minor is proved, because a square inscribed in a circle is less, and circumscribed about a circle is greater than the circle, but the demonstration is founded on a common principle, because the greater, the less, and the equal are found not only in a square and circle, but also in other things. Neither is the major universally true, because a rectilinear angle may be given greater or less than the angle in a semicircle, but one equal to it cannot be given. Vide Euclid Elem. Prop. xvi. b. 3.
  3. 3 The examples of Aristotle are principally taken from the Mathematics, and the tests of καθ' αὐτό and ᾗ αὐτό are expressly applied to a geometrical theorem. Mansel. Vide the 4th chap. of this book.
  4. 4 The possession of three angles equal to two right.
  5. 5 That is, by the application of the principle of a superior science, to a problem belonging to a subaltern science, as music is subaltern to arithmetic.
  6. 6 Where the principle is assumed from the same science, or from a superior one, the difference is, that, in the former case, the ὅτι and διότι are known; but in the latter, the διότι is known in the superior, the ὅτι in the inferior science.
  7. 7 Of subaltern sciences.
  8. 8 Metaphysics. See the third book of Aristotle’s treatise on that subject; also Magna Moralia, lib. i.; De Animâ, books i. ii. iii.

San Tommaso: Libro I, lezione XVII · Libro I, lezione XVIII

Libro I, capitolo 10 Of the Definition and Division of Prin- ciples.*.76a31–77a4

Inglese

I CALL those principles in each genus, the existence of which it is impossible to demonstrate. What then first things, and such as result from these signify, is assumed, but as to principles, we must assume that they are, but demonstrate the rest, as what unity is, or what the straight and a triangle are; it is necessary however to assume that unity and magnitude exist, but to demonstrate the other things.1

Of those which are employed in demonstrative sciences, some are peculiar to each science, but others are common, and common according to analogy, since each is useful, so far as it is in the genus under science. The peculiar indeed are such as, that a line is a thing of this kind, and that the straight is, but the common are, as that if equals be taken from equals the remainders are equal. Now each of these is sufficient, so far as it is in the genus, for (a geometrician) will effect the same, though he should not assume of all, but in magnitudes alone, and the arithmeticían in respect of numbers2 (alone).

Proper principles, again, are those which are assumed to be, and about which science considers whatever are inherent per se, as arithmetic assumes unities, and geometry points and lines, for they assume that these are, and that they are this particular thing. But the essential properties of these, what each signifies, they assume, as arithmetic, what the odd is, or the even, or a square, or a cube; and geometry, what is not proportionate, or what is to be broken, or to incline; but that they are, they demonstrate through things common, and from those which have been demonstrated. So also astronomy, for all demonstrative science is conversant with three things, those which are laid down as existing, and these are the genus, (the essential properties of which the science considers,) and common things called axioms, from which as primaries they demonstrate; and thirdly, the affections, the signification of each of which the demonstrator assumes.3 There is nothing however to prevent certain sciences overlooking some of these, as if the genus is not supposed to be, if it be manifest4 that it exists, (for it is not similarly manifest that number is, as that the cold and hot are,) and if (the science) does not assume what the affections signify, if they are evident, as neither does it assume what things common signify, (as what it is) to take away equals from equals, because it is known; nevertheless these things are naturally three, viz. that about which demonstration is employed, the things demonstrated, and the principles from which they are.

Neither however hypothesis nor postulate is that which it is necessary should exist per se, and be necessarily seen,|| for demonstration does not belong to external speech, but to what is in the soul,5 since neither does syllogism. For it is always possible to object to external discourse, but not always to internal. Whatever things then, being demonstrable, a man assumes without demonstration, these, if he assumes what appear probable to the learner, he supposes, and this is not an hypothesis simply, but with reference to the learner alone; but if, there being no inherent opinion, or when a contrary is inherent, the demonstrator assumes, he requires the same thing to be granted to him. And in this hypothesis and postulate differ, for postulate is any thing sub-contrary to the opinion of the learner, which though demonstrable a man assumes, and uses without demonstration.

Definitions then are not hypotheses, (for they are not asserted to be or not to be,) but hypotheses are in propositions. Now it is only necessary that definitions should be understood, but this is not hypothesis, except some one should say that the verb to hear is hypothesis. But they are hypotheses, from the existence of which, in that they are, the conclusion is produced. Neither does the geometrician suppose falsities, as some say, who assert, that it is not right to use a false (principle), but that the geometrician does so, when he calls a line a foot long when it is not so, or the line which he describes a straight line when it is not straight. The geometrician indeed concludes nothing from the lines being so and so, as he has said, but concludes those, which are manifested through these (symbols). Moreover postulate and every hypothesis are either as a whole or as in a part, but definitions are neither of these.6

fitably compare Locke's Essay, b. iv. 5, 5, and 6, 2; also Sanderson. The former's distinction between mental and verbal propositions is well known. The words in the text are only enunciative of oral as contrasted with mental reasoning, but are not decisive against Whately's opinion. Vide De Animâ, b. i. and iii.; Eth. b. i. c. 13. Dr. Hessey speaks sensibly enough of the "absurdity of maintaining that logic regards the accident of the external language, and not the necessity of the internal thought" (p. 4, Intro. Schem. Rhet.). It appears to be, after all, "splitting a straw;" for such an opinion is not only "absurd," but self-destructive, we never do, because we never can, practically adopt it.

Note del traduttore
  1. 1 The above clears Aristotle from the charge unjustly brought against him by Mill, since the former states here the necessity of assuming the existence of the subject, as clearly as the latter asserts it. (Vide Mill's Logic, vol. i.) The principles (ἐξ ὧν) from which Aristotle demonstrates are axioms of which he gives a specimen below: “If equals, &c.” Vide the table of the principles of science, given before. Cf. also Euclid, b. vi. Prop. 11.
  2. 2 The geometrician and arithmeticían each assume the principle, only so far as it is analogous to his subject science ; thus the former does not assume every whole to be greater than its part, but that every magnitude is so, and the latter that every whole number is greater than its part. Cf. Waitz in loc.
  3. 3 Vide Trendelenburg Erläuterungen, p. 118. For a full enunciation of the statement made here by Aristotle, the reader is referred to Mansel’s Logic, p. 109, and Appendices.
  4. 4 It is not made the subject of hypothesis, if it is manifest; in other words, it is tacitly assumed.
  5. 5 The two kinds of speech were, 1st, λόγος ὁ ξω, καὶ προφορικὸς, καὶ κατὰ τν φωνήν, i. e. the external, and (2nd) the internal, ἔσω, καὶ ἐνδιάθετος, καὶ κατὰ τὴν ψυχήν. Plut. in Philo. et Damascen. Both Whately and Aldrich regard language as the principal object of logic; the former declares that “if any process of reasoning can take place in the mind without any employment of language, orally or mentally, such a process does not come within the province of the science here treated of.” Mansel, on the contrary, considers “the laws of such process, equally with any other, matters of logical investigation.” The reader may pro-
  6. 6 Definitio ab hypothesi eo differt quod nihil edicit de existentia rei quæ definitur : nam si quis contendat definitionem, licet non ponat aliquid esse vel non esse, sed intelligi tantum velit id quod dicat, tamen esse hypothesin, quodcunque auribus percipimus, si quod dictum est intelleximus, hypothesis dicenda erit. Verum ὑποθέσεις dicuntur quibus positis (ὄσων ὄντων) et ex quibus aliud quid colligitur. Alia causa cur definitio non appellari possit hypothesis in eo est, quod hæc aut universalis est aut particularis, in illa, vero quod subjectum est æquale esse debet ei quod prædicatur. Waitz. Vide also scheme of principles of science. Cf. Locke’s Essay, b. iii. 4, 7. Occam’s Logic, part i.

San Tommaso: Libro I, lezione XVIII · Libro I, lezione XIX

Libro I, capitolo 11 Of certain Common Principles of all Sciences.77a5–35

Inglese

That there should then be forms, or one cer- * εἴδη—species. Buhle. tain thing besides the many, is not necessary, to the existence of demonstration,1 but it is necessary truly to predicate one thing of the many, for there will not be the universal unless this be so, and if there be not an universal, there will not be a medium, so that neither will there be a demonstration. It is essential then that there should be one and the same thing, which is not equivocal in respect of many: no demonstration however assumes that it is impossible to affirm and deny the same thing at one and the same time, unless it is requisite also thus to demonstrate the conclusion. It is demonstrated however by assuming the first to be true of the middle, and that it is i. e. the major prop. not true to deny it, but it makes no difference whether we assume the middle to be or not to be, and in a similar manner also in respect of the third.2 For if that be granted in respect of which it is true to predicate man, even if (some one should think that man is) not man, (the conclusion) will be true, if only it is said that man is an animal, and not that he is not an animal, for it will be true to say that Callias, even if he be not Callias, yet is still an animal, but not that which is not an animal. The cause however is, that the first is not only predicated of the middle, but also of something else, in consequence of its being common to many, so that neither if the middle be that thing itself, or not that thing, does it make any difference in respect to the conclusion. But the demonstration which leads to the impossible, assumes that of every thing affirmation or negation is true, and these|| it does not always (assume) universally, but so far as is sufficient, and it is sufficient (which is assumed) in respect of the genus. I mean by the genus, as the genus about which a person introduces demonstrations, as I have observed before. All sciences communicate with each other according to common (principles), and I mean by common those which men use as demonstrating from these, but not those about which they demonstrate, nor that which they demonstrate, and dialectic is (common) to all (sciences). If also any one3 endeavours to demonstrate universally common (principles), as that of every thing it is true to affirm or deny, or that equals remain from equals, or others of this kind. Dialectic however does not belong to certain things thus definite, nor to one particular genus; for it would not interrogate, since it is impossible for the demonstrator to interrogate, because the same thing is not proved from opposites:4 this however has been shown in the treatment of syllogism.

Note del traduttore
  1. 1 The Platonic theory of Idea, to which Aristotle here refers, so highly commended by St. Augustine, is not free from much error, arising from Plato’s opinion that the ideas in man’s soul are inherently good. The remark which Aristotle makes in this place, seems chiefly, as Taylor thinks, to prevent the misconception of Plato’s theory, by those who imagined his ideas to be corporeally separate from matter, and not incorporeal forms residing in a divine intellect; but the real case is, that Aristotle elsewhere impugns the doctrine of the idea as not practical. Vide Ethics, lib. i. c. 6, Browne’s note, Bohn’s edition; also Metaphysics, lib. xii. De Animâ; Brewer’s Ethics; Ritter, vol. ii. The province of the Platonic dialectic was to investigate the true nature of that connexion, which existed between each thing and the archetypal form or idea which made it what it was, and to awaken the soul to a full remembrance of what she had known prior to her being imprisoned in the body. Hence, dialectic, with Plato, is the science of the immutable, and takes cognizance of the universal principle; in fact, is an object identical with the Metaphysics of Aristotle, whereas the dialectic of the latter partook of the essentially practical nature of his mind, and is merely “the art of disputing by question and answer.” Cf. Gorgias, Theætetus, Meno, and the Commentaries of Syrianus, and upon the doctrine of universals, see Locke’s Essay, b. iv.; Stewart, Phil. of Human Mind; Whately’s and Mansel’s Logics.
  2. 2 Though the minor should not be assumed both to be and not to be that which it is, nevertheless the conclusion will be right.
  3. 3 The major.
  4. 4 Here is a proof of the difference between the dialectic of Plato and

San Tommaso: Libro I, lezione XIX · Libro I, lezione XX

Citato nell'enciclopedia: IDEA · SILLOGISMO

Libro I, capitolo 12 Of Syllogistic Interrogation.77a36–78a21

Inglese

If syllogistic interrogation is the same as a pro-position of contradiction,1 but there are proposi-tions in each science, from which the syllogism which belongs to each consists, there will be a certain scientific interrogation, from which the syllogism,2 which is appropriate to each science, is drawn. It is clear, then, that not every inter-rogation would be geometrical, or medical, and so of the rest, but from what any thing is demonstrated about which geo-metry is conversant, or which are demonstrated from the same principles as geometry, as optics, and in like man-ner with other sciences. These3 also must be discussed from geometrical principles and conclu-sions, but the discussion of principles is not to be carried on by the geometrician so far as he is such; likewise with other sciences. Neither is every one who possesses science to be interrogated with every question, nor is every question about each to be answered, but those which are defined about the science. It is evident then that he does well, who disputes with a geometrician thus, so far as he is such, if he demon-strate any thing from these principles, but if not, he will not do well. Again, it is clear that neither does he confute the geometrician except by accident, so that there cannot be a discussion of geometry by those who are ignorant of geometry, since the bad reasoner will escape detection, and it is the same with other sciences.

Since there are geometrical interrogations, are there also those which are ungeometrical? and that of Aristotle, pointed out above. Moreover the dialectician interro-gates so that his opponent may either affirm or deny, but the demon-strator proves or interrogates in order to make the thing evident from principles better known to his hearer; again, the dialectician may em-ploy affirmation or negation, but the demonstrator has to prove a certain conclusion. false syllogism in each science are those ignorant questions which appertains. are of a certain quality4 geometrical? whether also is a syllogism, from ignorance, a syllogism composed from opposites or a paralogism,5 but according to geometry, or from another art, as a musical interrogation is ungeometrical, about geometry, but to imagine that parallel lines meet is in a certain respect geometrical, and after another manner ungeometrical?† For this is two-fold, in the same way as what is without rhythm; and the one is ungeometrical because it possesses not (what is geometrical), as what is without rhythm; but the other because it possesses it wrongly—and this ignorance which is from such principles, is contrary.|| In mathematics however there is not in like manner a paralogism, because the middle is always two-fold,6 for (one thing) is predicated of every individual of this, and this again of another every, but the predicate is not called universal;7 those, nevertheless, it is possible, we may see by common perception, but in argument they escape us. Is then every circle a figure? If any one should delineate it, it is clear. But what, are verses a circle? They are evidently not so.8 Still it is improper to object to it, if it be an inductive proposition; for as neither is that a proposition which is not in respect of many things, (since it will not be in all, but syllogism is from universals,) neither, it appears clear, is that an objection, for propositions and objections are the same, as the objection which one adduces, may become either a demonstrative or a dialectic proposition.9† It occurs that some argue contrary to syllogism, from assuming the consequences of both (extremes), as Cæneus does,10 that fire is in a multiple proportion, because, as he says, both fire and this proportion are rapidly generated. But thus there is no syllogism,11 though there will be, if totle says, they may be seen by common perception, (τῇ νοήσει,) the verb νοεῖν being said of self-evident truths, because mathematicians represent these things by diagrams, and therefore if a circle was similarly described, it would be manifest; κύκλος however signifies both a mathematical figure and a kind of period or verse. Vide Hermo. et Demet. the multiple is consequent to the most rapid proportion, and the most rapid proportion to fire in motion. Sometimes it does not happen that a conclusion is made from the assumptions, and sometimes it happens, but is not perceived: if however it were impossible to demonstrate the true from the false, it would be easy to resolve, for (the terms) would be necessarily converted.12 Thus let A13 exist, and this existing, these things also exist14 the existence of which I know, as B, from these then § I will demonstrate that that || exists. What pertain however to mathematics, are rather converted, because they take nothing accidental, (and in this they differ from dialectical subjects,) but definitions.

Yet they are increased, not through media, but through additional assumption, as A of B, this of C, this again of D, and so on to infinity. Also transversely, as A both of C and of E, as there is a number so great or even infinite, which is A, an odd number so great B, and an odd number C. A then is (true) of C, and the even is a number so great D, the even number is E, wherefore A is (true) of E.

Note del traduttore
  1. 1 Interrogation and proposition are the same in reality, but differ in definition. A proposition is such as, “Every man is an animal;” an interrogation is such as, “Is not every man an animal?” Taylor.
  2. 2 i. e. the de-monstrative syllogism.
  3. 3 What are proved in geo-metry, &c.
  4. 4 Ignorance is two-fold; 1st, From pure negation; 2nd, From a depraved disposition. Vide chapters 16, 17, and 18; also Eth. b. iii. ch. 1. Cf. Metap. lib. iii.
  5. 5 Utrum syllogismus ἀγεωμέτρητος dicendus est is, qui fiat ex propositionibus veritati repugnantibus, sive etiam qui ex propositionibus veris non recte colligat (ὁ παραλογισμός) dummodo propositiones ex quibus fiat geometriæ sint propriæ an syll. qui ex aliâ doctrinâ desumtus ad geometriam omnino non pertineat? Waitz. Aristotle says (afterwards) that certain interrogations, entirely geometrical, are assumed from another art or science, and correspond to the ignorance which is said to be of pure negation, as “Is number even or odd?” but that there are others which are in a certain respect geometrical, and in a certain respect not, and which are falsely conceived of geometrical points, as “Will not parallel lines meet?” Cf. Philop. fol. 34.
  6. 6 That is, the middle term is twice assumed, viz. in the major and in the minor prop.
  7. 7 The majus extremum is universally attributed to the middle term in the major prop. in the first figure, (to which Aristotle refers,) and the middle term is universally attributed to the minor extreme in the minor proposition; but the expression of universality is not added to the predicate, but to the subject only.
  8. 8 I read the concluding paragraph according to Waitz’s stopping. Aris-
  9. 9 The following is the note of Julius Pacius on Anal. Prior, c. 28, (Pacian Division,) as to the apparently conflicting statement made by Aristotle here. “Discrimen ponit Aristoteles (lib. ii. Prior, cap. 28) inter objectionem et propositionem, id est propositionem illam cui objicitur: alioquin etiam ipsa objectio est propositio, ut dictum fuit in definitione. Discrimen est, quod objectio est universalis, vel particu- laris: propositio verò, si sit pars syllogismi universalis, necessario est universalis. Sensus est propositiones constituentes syllogismum esse universales: everti autem vel per objectiones universales, ut contrarias; vel per particulares ut contradicentes. Huic sententiæ opponitur quod ait Aristoteles, lib. i. Post. cap. 12, par. 11, omnem instantiam esse universalem. Existimo hæc loca per distinctionem esse concilianda. Aristoteles in Prior. considerat instantiam sive objectionem quatenus evertit propositionem contrariam; hæc objectio potest esse tam universa- lis quam particularis. In Poster. autem considerat objectionem quatenus per eam, non solum evertitur propositio adversarii, sed etiam demon- stratio erigitur. Quoniam igitur demonstratio constat ex propositionibus universalibus, etiam hæc objectio necessario est universalis.” On the con- sideration of the enstatic enthymeme, and of the passages relative to the Ἔνστασις, vide Dr. Hessey’s Schem. Rhet. Supple. Table 5. Cf. also Waitz in loc.
  10. 10 Cæneus argued: “That which is increased by multiple proportion is rapidly increased Fire is rapidly increased ∴ Fire is increased by multiple proportion.” The last expression means that by every addition it becomes double or triple, etc.
  11. 11 Because both prop. affirm. in the 2nd fig.
  12. 12 Difficilius est ad dijudicandum ex quibus propositionibus coactum sit, quod syllogismus conficit (τὸ ἀναλύειν). Waitz. Aristotle means that the truth of the prop. might easily be collected from the truth of the conclusion, for they might be converted.
  13. 13 Propositions.
  14. 14 This conclusion which I know is true.

San Tommaso: Libro I, lezione XXI · Libro I, lezione XXII

Libro I, capitolo 13 The difference between Science, “that” a thing is, and “why” it is.78a22–79a16

Inglese

Now there is a difference between knowing that a thing is, and why it is, first in the same science, and in this in two ways, the one, if the syllogism is not formed through things immediate, (since the primary cause is not assumed, but the science of the why has respect to the first cause,) but the other if it is through things immediate indeed, yet not through the cause, but through that which is more known of the things, which reciprocate.1 Now nothing prevents that which is not a cause being sometimes more known amongst things which are mutually predicated, so that demonstration shall accrue through this, as that the planets are near, because they do not twinkle. Let C be the planets, B not to twinkle, A to be near, B therefore is truly predicated of C, since the planets do not twinkle, A also of B, for what does not twinkle is near, but this2 may be assumed by induction or by sense.3 It is necessary then that A should be present with C, so that it is demonstrated that the planets are near. This syllogism then is not of the “why,” but of the “that” (a thing is), for the planets are not near because they do not twinkle, but they do not twinkle because they are near. It happens indeed that the one may be proved through the other, and the demonstration will be of the “why,” as let C be the planets, B to be near, A not to twinkle, B then is present with C, so that A “not to twinkle” will be with C. It is also a syllogism of the “why,” for the first cause was assumed. Again, as they show the moon to be spherical through increments (of light), for if what is thus increased be spherical, and the moon is increased, it is evident that the moon is spherical, thus then a syllogism of the “that” is produced, but if the middle is placed contrarily, there is a syllogism of the “why,” for it is not spherical on account of the increments, but from being spherical she receives such increments: let the moon be C, spherical B, increase A. Where again the media do not reciprocate,4 and what is not the cause is more known, the “that” is indeed demonstrated, but not the “why;” further, where the middle is placed externally,5 for in these the demonstration is of the “that,” and not of the “why,” as the cause is not assigned. For example, why does not a wall breathe? because it is not an animal, for if this was the cause of its not breathing, it would be necessary that animal should be the cause of its breathing, since if negation is the cause of a thing not being, affirmation is the cause of its being, thus if the disproportion of hot and cold is the cause of not being well, the proportion of these is the cause of being well. Likewise if affirmation is the cause of being, negation is the cause of not being, but in things which have been thus explained, what has been stated does not occur, for not every animal respires.6 A syllogism of such a cause is nevertheless produced in the middle figure, for example, let A be animal, B to respire, C a wall, A then is present with every B, (for whatever respires is animal,) but with no C, so that neither is B present with any C, wherefore a wall does not respire.7 Such causes however resemble things spoken hyperbolically,8 and this is, when we turn aside to speak of the middle, which is more widely extended, as for instance, that saying of Anacharsis, that amongst the Scythians there are no pipers, since neither are there any vines.9 As to the same science then, and the position of the media, these are the differences between a syllogism of, that a thing is, and of why it is, but in another respect the why differs from the that, because each is beheld in a different science. Now such are those things which so subsist with reference to each other, as that the one is under the other, such as optics with reference to geometry, mechanics to the measurement of solids, harmonics to arithmetic, and celestial phenomena to astronomy. Some of these sciences are almost synonymous, as astronomy is both the mathematical and the nautical; and harmony is both mathematical and that which belongs to the ear. For here to know that a thing is, is the province of those who exercise the sense, but to know why it is, belongs to mathematicians, since these possess the demonstrations of causes, and often are ignorant of the that, as they who contemplating universals, frequently are ignorant of singulars from want of observation. But these10 are such as being essentially something else11 use forms, for mathematics are conversant with forms, since they do not regard one certain subject, for though the geometrical are of a certain subject, yet not so far as they are geometrical are they in a subject. As optics also to geometry, so is some other science related to optics, as for example, the science about the rainbow, for to know that it is, appertains to the natural philosopher, but why it is, to the optician either simply or mathematically. Many sciences also which are not arranged under each other subsist thus, for example, medicine with regard to geometry, for to know that circular wounds heal more slowly is the province of the physician, but why (they do so) of the geometrician.12

Note del traduttore
  1. 1 When the effect immediately follows the cause, the two are said to reciprocate, because one being admitted, the other is necessarily so, though sometimes the effect is more known than the cause, as he says below. For the two senses of the word ἄμεσος, cf. Anal. Post. i. 2, and ii. 19; here it signifies a premise immediate, as regards its conclusion, i. e. not requiring the insertion of lower middle terms, to connect its terms with those of the conclusion. On the particular meaning of the word “cause,” and in fact in relation to the whole chapter, see Hill’s Logic, under “Demonstrationis species,” pp. 287, et seq., and Mansel’s Logic, 106, Appendix, pp. 63, et seq.
  2. 2 i. e. the two propositions.
  3. 3 The major by induction, because a lamp, gold, etc., when they are near, do not twinkle; the minor by sense, because we see the planets do not twinkle. Taylor.
  4. 4 The cause is the middle, in the demonstration of the “why,” and the effect is the middle, in the demonstration of the “that.” By media not reciprocating, is meant when we reason affirmatively, from the effect to the remote cause; as, man is risible, therefore he is animal: here we miss the proximate cause, “is rational.”
  5. 5 i. e. before both extremes, in the 2nd figure, in which demonstration through a remote cause (as he will show) occurs.
  6. 6 But only those which have lungs, hence the proximate cause of respiration is not animal, but the possession of lungs, which cause however is not assigned.
  7. 7 Example (4.)
  8. 8 Remote causes being adduced resemble hyperboles, in that more is said than is requisite, for a remote is of wider extension than a proximate cause.
  9. 9 When we leave (the proximate cause) to speak of that middle which is more widely extended than (cause). Taylor. The demonstration of Anacharsis is thus framed in the 2nd figure. There are no pipers where there are no vines, but there are no vines among the Scythians, ∴ among the Scythians there are no pipers. Now the successive causes to the first or major premise are, there are no vines because there are no grapes; no grapes is the cause of no wine; no wine is the cause of no intoxication; no intoxication cause of no pipers; but these intermediate causes are omitted, and the effect is at once connected with the remote cause.
  10. 10 i. e. the superior sciences.
  11. 11 Essentially different from their subject sciences.
  12. 12 Viz. because he knows that the capacity of the circle is the largest of all figures, having equal perimeters, hence the parts of a circular wound coalesce more slowly. For the development of the chapter, the following scheme of demonstration is introduced :

San Tommaso: Libro I, lezione XXIII · Libro I, lezione XXIV · Libro I, lezione XXV

Libro I, capitolo 14 The first Figure most suitable to Science.79a17–32

Inglese

Of the figures, the first is especially adapted to science, for both the mathematical sciences carry out their demonstrations by this, as arithmetic, geometry, optics, and nearly, so to speak, whatsoever sciences investigate the “why,” since either entirely or for the most part, and in most sciences, the syllogism of the why is through this figure. Wherefore also, on this account, it will be especially adapted to science, for it is the highest property of knowledge to contemplate the “why;” in the next place, it is possible through this figure alone to investigate the science of what a thing is; for in the middle figure, there is no affirmative syllogism, but the science of what a thing is belongs to affirmation, and in the last figure, there is an affirmative, but not an universal; but the what a thing is belongs to universals, for man is not a biped animal in a certain respect. Moreover this has no need of those, but they are condensed and enlarged1 through this, till we arrive at things immediate: it is evident, then, that the first figure is in the highest degree adapted to scientific knowledge.

Note del traduttore
  1. 1 By prosyllogisms. § i. e. indemonstrable. || Vide Anal. Prior i. ch. 1. ¶ In Camestres.

San Tommaso: Libro I, lezione XXVI

Libro I, capitolo 15 Of immediate negative Propositions.79a33–79b22

Inglese

As it happened that A was present with B individually, so also it may happen not to be present, and I mean by being present with, or not, individually, that there is no medium between them, for thus the being present with or not, will not be according to something else. When then either A or B is in a certain whole,|| or when both are, it is impossible that A should not be primarily present with B. For let A be in the whole of C, if then B is not in the whole of C, (for it is possible that A may be in a certain whole, but that B may not be in this,) there will be a syllogism that A is not present with B, for if C is present with every A, but with no B A will be present with no B. In like manner also, if B is in a certain whole, as for instance, in D, for D is with every B, but A with no D, so that A will be present with no B by a syllogism. In the same way1 it can be shown2 if both also are in a certain whole, but that it is possible that B may not be in the whole in which A is, or again A in which B is, is evident from those co-ordinations3 which do not interchange.4 For if none of those, which are in the class A C D, is predicated of any of those in B E F, but A is in the whole of H, which is co-arranged with it, it is evident that B will not be in H, for otherwise the co-ordinates would intermingle. Likewise also if B is in a certain whole, but if neither is in any whole, and A is not present with B, it is necessary that it should not be present individually, § for if there shall be a certain middle, one of them must necessarily be in a certain whole, for there will be a syllogism either in the first, or in the middle figure. If then it is in the first, B will be in a certain whole, (for it is necessary that the proposition in regard to this should be affirmative,) but if in the middle figure either of them || may be (in the whole), for the negative being joined to both, ¶ there is a syllogism, * but there will not be when both the propositions are negative.

It is manifestly possible then, that one thing may not be individually present with another, also when, and how this may happen, we have shown.

Note del traduttore
  1. 1 i. e. they are reduced to the first figure.
  2. i. e. the definition affirms.
  3. The other figures condensed by this one.
  4. 2 That A is not with B.
  5. 3 συστοιχίαι.
  6. 4 By co-ordinations, he means the series deduced from each of the ten categories, as substances, body, etc. Now what belongs to one class can- not be arranged in another ; thus body, which is in the category of sub- stance, cannot be in the category of quality. Ex. 1. Substance. H. B. Quality. Body. A. E. Colour. Animated. C. F. Whiteness. Rational. } D. Animal. }

Libro I, capitolo 16 Of Ignorance, according to corrupt position of the Terms, where there are no Media.79b23–80b16

Inglese

The ignorance which is denominated not according to negation, but according to disposition, is a deception produced through syllogism, and this happens in two ways, in those things which are primarily present, or not present; for it happens either when one simply apprehends the being present, or not being present, or when he obtains this opinion through syllogism: of simple opinion, then, the deception is simple, but of that which is through syllogism, it is manifold. For let A not be present with any B individually, if then A is concluded to be present with B, assuming C as the middle, a person will be deceived through syllogism. Hence it is possible that both propositions may be false, but it is also possible that only one may be so, for if neither A is present with any C, nor C with any B, but each proposition is taken contrary, both will be false. But it may be that C so subsists with reference to A and B, as neither to be under A nor universally (present) with B, for it is impossible that B should be in a certain whole, since it was said that A is not primarily present with it; but A need not be universally present with all beings, so that both propositions are false.

Nevertheless, we may assume one proposition as true, not either of them casually, but the proposition A C, for the proposition C B will be always false, because B is in none; but A C may be (true), for instance, if A is present individually, both with C and B, for when the same thing is primarily predicated of many things, neither will be predicated of neither; it makes no difference however if it (A) be not individually present with it (C).

The deception then of being present, is by these and in this way only, (for there was not a syllogism of being present in another figure,*) but the deception of not being present with, is in the first and middle figure. Let us first then declare in how many ways it occurs in the first, and under what propositional circumstances. It may then happen when both propositions are false, e. g. if A is present individually with C and B, for if A should be assumed present with no C, but C with every B, the propositions will be false. But (deception) is possible, when one proposition is false, and either of them casually; for it is possible that A C may be true, but C B false; A C true, because A is not present with all beings, but C B false, because it is impossible that C should be with B, with nothing of which A is present; for otherwise the proposition A C will be no longer true, at the same time, if both are true, the conclusion also will be true. But it is also possible that C B may be true, when the other proposition is false, as if B is in C and in A, for one must necessarily be under the other, so that if A should be assumed present with no C, the proposition will be false.|| It is clear then, that when one proposition is false, and also when both are, the syllogism will be false. In the middle figure, however, it is not possible that both propositions should be wholly false, for when A is present with every B, it will be impossible to assume any thing, which is present with every individual of the one, but with no individual of the other; † but we must so assume the propositions that the (middle) may be present with one (extreme), and not be present with the other, if indeed there is to be a syllogism. If then, when they are thus assumed, they are false, it is clear that, when taken contrarily, they will subsist vice versâ, but this is impossible.2 Still there is nothing to prevent each being partly false, as if C is with A, and with a certain B; for if it should be assumed present with every A, but with no B, both propositions indeed would be false, yet not wholly, but partially. The same will occur when the negative is placed vice versâ. But it is possible that one proposition, and either of them, may be false, for what is present with every A, will be also with B,|| if then C is assumed present with the whole of A, but not present with the whole of B, C A will be true, but the proposition C B false. Again, what is present with no B, will not be present with every A; for if with A, it would also be with B, but it was not present; if then C should be assumed present with the whole of A, but with no B, the proposition C B will be true, but the other false. The same will happen if the negative is transposed, for what is in no A, will neither be in any B; if then C is assumed not present with the whole of A, but present with the whole of B, the proposition A C will be true, but the other false. Again, also, it is false to assume that what is present with every B, is with no A; for it is necessary, if it is with every B, that it should be also with a certain A; if then C is assumed present with every B, but with no A, the proposition C B will be indeed true, but C A false. Hence, it is evident that when both propositions are false, and when one only is so, there will be a syllogism deceptive in individuals.3

Note del traduttore
  1. 1 Vide Whately, b. iii. sec. 15—19.
  2. 2 They will be true when the arrangement is such that negation results from affirmation, and affirmation from negation ; but this will be impossible, because when the conclusion is false, the prop. cannot be true.
  3. 3 In those cases which have no medium.

San Tommaso: Libro I, lezione XXVII · Libro I, lezione XXVIII

Libro I, capitolo 17 Continuation of the same with Media.80b17–81a37

Inglese

In those which are not individually present,|| or which are not present, when a syllogism of the false is produced through an appropriate medium, both propositions cannot be false, but only the major. But I mean by an appropriate medium, that through which there is a syllogism of contradiction. For let A be with B through the medium of C, since then we must take C B as affirmative, if there is to be a syllogism, it is clear that this will be always true, for it is not converted. A C, on the other hand, will be false, for when this is converted, a contrary syllogism arises.1 So also if the middle is assumed from another affinity, as for instance, if D is in the whole of A, and is predicated of every B, for the proposition D B must necessarily remain,2 but the other proposition must be converted, so that the one (the minor) will be always true, but the other (the major) always false. Deception also of this kind is almost the same as that which is through an appropriate medium, but if the syllogism should not be through an appropriate medium,3 when indeed the middle is under A, but is present with no B, it is necessary that both propositions should be false. For the propositions must be assumed contrary to the way in which they subsist, if a syllogism is to be formed,4 for when they are thus assumed both are false, as if A is with the whole of D, but D present with no B, for when these are converted, there will be a syllogism, and both propositions will be false. When however the medium is not under A, for instance, D, A D will be true, but D B false, for A D is true, because D was not in A, but D B false, because if it were true the conclusion also would be true, but it was false.

Through the middle figure however, when deception is produced, it is impossible that both propositions should be wholly false, (for when B is under A, it is possible for nothing to be present with the whole of the one, but with nothing of the other, as has been observed before,†) but one proposition may be false whichever may happen. For if C is with A and with B, if it be assumed present with A, but not present with B, the proposition A C will be true, but the other false; again, if C be assumed present with B, but with no A, the proposition C B will be true, but the other false.

If then the syllogism of deception be negative, it has been shown when and through what the deception will occur, but if it be affirmative, when it is through an appropriate medium, it is impossible that both should be false, for C B must necessarily remain, if there is to be a syllogism,|| as was also observed before. Wherefore C A will be always false, for it is this which is converted. Likewise also, if the middle be taken from another class, as was observed in negative deception, for the proposition D B must of necessity remain, but A D be converted, and the deception is the same as the former. But when it is not through an appropriate medium, if D be under A, this5 indeed will be true, but the other6 false, for A may possibly be present with many things which are not under each other.7 If however D is not under A, this8 will evidently be always false, (for it is assumed affirmative,) for D B may be as well true as false, since nothing prevents A being present with no D, but D with every B, as animal with (no) science, but science with (all) music. Again, (nothing prevents) A from being present with no D, and D with no B: it is clear then that when the medium is not under A, both propositions, and either of them, as it may happen, may be false.

In how many ways then, and through what, syllogistic deceptions are possible, both in things immediate, and in those which are demonstrated, has been shown.

Note del traduttore
  1. 1 A syllogism with a conclusion opposite to the true conclusion, and which produces deception opposed to true science.
  2. 2 Because the minor in the 1st fig. must continue affirm.
  3. i. e. the major must be changed into a negative.
  4. 3 When it is through a medium by which a true conclusion cannot be proved: thus, through “brute,” it can never be proved that “man is a living being.” Taylor.
  5. 4 i. e. to form a negative in the 1st figure, (Celarent,) it is necessary in the major prop. that the first be denied of the middle, and in the minor that the middle should be affirmed of the last.
  6. 5 The major.
  7. 6 The minor.
  8. 7 The expression, present with, must be taken generally, for the being attributed, whether affirmatively or negatively, to many things not under each other; thus “brute” is affirmatively attributed to “quadruped,” but negatively to “man;” but “man” is not subjected to “brute.” Taylor.
  9. 8 The major.

San Tommaso: Libro I, lezione XXIX

Citato nell'enciclopedia: LOGICA

Libro I, capitolo 18 Of the Dependence of Universals upon Induction, and of the latter upon Sense.81a38–81b9

Inglese

It is clear, also, that if any sense be deficient, a certain science must be also deficient, which we cannot possess, since we learn either by induction or by demonstration. Now demonstration is from universals, but induction from particulars, it is impossible however to investigate universals, except through induction, since things which are said to be from abstraction, will be known through induction;1 if any one desires to make it apparent that some things are present with each genus, although they are not separable, so far as each is such a thing. Nevertheless, it is impossible for those who have not sense to make an induction, for sense is conversant with singulars, as the science of them cannot be received, since neither (can it be obtained) from universals without induction, nor through induction without sense.

Note del traduttore
  1. 1 Vide Hill’s Logic, and Aldrich de Prædicab. form.; Whately’s Logic, book ii. ch. 5, and book iv. ch. 1. Universals are gained by abstraction, because we separate the points of concord, concomitant with a certain number of individuals, from those points in which they differ, hence Locke calls all universals abstract terms. Properly speaking, abstraction

San Tommaso: Libro I, lezione XXX

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Libro I, capitolo 19 Of the Principles of Demonstration, whether they are Finite or Infinite.81b10–82a20

Inglese

Every syllogism consists of three terms, and one indeed is able to demonstrate that A is with C from its being present with B, and this last with C, but the other is negative, having one proposition (to the effect) that one certain thing is in another, but the other proposition (to the effect) that it is not with it. Now it is clear, that the same are principles, and what are called hypotheses, since it is necessary to demonstrate by thus assuming these,1 e. g. that A is present with C through B, and again, that A is with B through another medium, and that B is with C in like manner. By those then who syllogize according to opinion only, and dialectically, this alone it is clear must be

is the separation of one portion of the attributes co-existing in any object from the rest; hence, in this sense, Aristotle applies the expression here, τὰ ἐξ ἀφαιρέσεως, to geometrical magnitudes, because the geometer considers only the properties of the figure, separating them from those of the material in which it is found. (Cf. An. Post. i. ch. 5.) “Induction,” says Taylor, “is so far subservient to the acquisitions of science, as it evocates into energy in the soul, those universals from which demonstration consists. For the universal, which is the proper object of science, is not derived from particulars, since these are infinite, and every induction of them must be limited to a finite number. Hence the perception of the all and the every is only excited, and not produced, by induction.” Cf. Trendelen. de An. p. 478. Biese 1. Sententia nostri loci hæc est. Universales propositiones omnes inductione comparantur, quum etiam in iis quæ a sensibus maxime aliena videntur et quæ ut mathematica (τὰ ἐξ ἀφαιρέσεως) cogitatione separantur a materiâ quâcum conjuncta sunt, inductione probentur ea quæ de genere, ad quod demonstratio pertineat prædicentur καθ’ αὐτά et cum ejus naturâ conjuncta sint. Inductio autem iis nititur quæ sensibus percipiuntur; nam res singulares sentiuntur, scientia vero rerum singularium, non datur sine inductione, non datur inductio, sine sensu. Waitz. Cf. Metap. b. ii. and vi.; De Animâ, b. iii. iv. considered, viz. whether the syllogism is produced from propositions as probable as possible, so that if there is in reality a medium between A and B, but it does not appear, he who syllogizes through this, will have syllogized dialectically. But as to truth, it behoves us to make our observations from things inherent:2 it happens thus. Since there is that, which is itself predicated of something else, not according to accident, but I mean by according to accident, as we say sometimes, that that white thing is a man, not similarly saying, that a man is a white thing, for man not being any thing else is white, but it is a white thing, because it happens to a man to be white:3 there are then some such things as are predicated per se. Let C be a thing of this kind which is not itself present with any thing else, but let B be primarily4 present with this, without any thing else between. Again, also let E be present in like manner with F, and this with B, is it then necessary that this should stop, or is it possible to proceed to infinity?5 Once more, if nothing is predicated of A per se, but A is primarily present with H, nothing prior intervening, and H with G, and this with B, is it necessary also that this should stop, or can this likewise go on to infinity?6 Now this so much differs from the former, that the one is, whether it is possible by beginning from a thing of that kind, which is present with nothing else, but something else present with it, to proceed upward to infinity; but the other is, beginning from that which is itself predicated of another, but nothing predicated of it, whether it is possible to proceed to infinity downward. Besides, when the extremes are finite, is it possible that the media may be infinite? I mean, for instance, if A is present with C, but the medium of them is B, and of B and A there are other media, and of these again others, whether it is possible or impossible for these also to proceed to infinity? To consider this however is the same as to consider whether demonstrations proceed to infinity, and whether there is demonstration of every thing, or whether there is a termination (of the extremes) relatively to each other.7 I say also the same in respect of negative syllogisms and propositions, for instance, whether A is primarily present with no B, or there will be a certain medium with which it was not before present, as if G (is a medium), which is present with every B; and again, with something else prior to this, as whether (the medium is) H, which is present with every G; for in these also, either those are infinite with which first they are8 present, or the progression stops.

The same thing however does not occur in things which are convertible, since in those which are mutually predicated of each other, there is nothing of which first or last a thing is predicated;9 for in this respect all things subsist similarly with respect to all, whether those are infinite, which are predicated of the same, or whether both § subjects of doubt are infinite, except that the conversion cannot be similarly made; but the one is as accident, but the other as predication.10

Note del traduttore
  1. 1 So that both prop. affirm, or one affirms and the other denies.
  2. 2 Whether the propositions are really immediate.
  3. 3 I read this sentence with Buhle, Bekker, and Waitz.
  4. 4 Immediately.
  5. 5 So that a first predicate may not be found.
  6. 6 So that a last subject may not be found.
  7. 7 i. e. whether there may be found a last subject, which is the boundary of the progression downward from the first attribute ; and also whether there may be found a first attribute, by which the progression from the last subject upward will be terminated. Πρὸς ἀλληλα περαίνεσθαι, dicuntur quorum termini medii non infiniti sunt, ut sive uno sive pluribus terminis mediis interjectis major cum minore continuâ ratiocinatione connectatur in conclusione. Waitz.
  8. 8 So Waitz and Bekker ; but Taylor and Buhle read “not present.”
  9. 9 In circular proofs, as in the circle itself, there is not a first nor last.
  10. 10 Whether the attributes are infinite, in terms convertible, they may become subjects, or whether both attributes and subjects are infinite, the effect is the same, and Aristotle shows that these investigations may be adapted to reciprocals, when one is per se predicated of the other, and the other from accident. Excluding the last, the inquiry is whether the subjects and predicates which are so per se, are finite or infinite. A thing is attributed from accident, as man to a white thing ; but per se as risibility to a man. Predication therefore is now assumed for attribute per se, as will be shown in chap. 22.

San Tommaso: Libro I, lezione XXXI

Libro I, capitolo 20 Of Finite Media.82a21–35

Inglese

That media cannot be infinite, if the predications, both downward and upward, stop, is evident: I call indeed the predication upward, which tends to the more universal, but the downward that which proceeds to the particular. For if when A is predicated of F, the media are infinite, that is B, it evidently may be possible that from A in a descending series, one thing may be predicated of another to infinity, (for before we arrive at F, there are infinite media,) and from F in an ascending series, there are infinite (attributes) before we arrive at A. Hence, if these things are impossible, it is also impossible that there should be infinite media between A and F; for it does not signify if a man should say that some things of A B F1 so mutually adhere, as that there is nothing intermediate, but that others cannot be assumed. For whatever I may assume of B,2 the media with reference to A or to F,|| will either be infinite or not, and it is of no consequence from what the infinites first begin,3 whether directly or not directly, for those which are posterior to them are infinite.

Note del traduttore
  1. 1 So Waitz; Taylor and Bekker, A B; Buhle, A B C.
  2. 2 i. e. whatever medium is assumed between A and F; for the infinite media between A and F are signified by the letter B.
  3. 3 Whether from either (A or F) of the extremes, or from some me- dium. Infinites are directly or immediately placed from A or from F, but not directly when they are from some medium.

San Tommaso: Libro I, lezione XXXII

Libro I, capitolo 21 It is shown that there are no Infinite Media in Negative Demonstration.82a36–82b36

Inglese

It is apparent also, that in negative demonstration the progression will stop, if indeed in affirmative it is stopped in both (series), for let it be impossible to proceed to infinity upward from the last,1 (I call the last that which is itself not present with any thing else, but something else with it, for instance, F,) or from the first2 to the last, (I call the first that which is indeed itself predicated of something else, but nothing else of it). If then these things are so, the progression must stop in negation, for the not being present is demonstrated triply, since either B is present with every individual with which C is, but A is present with none with which B is. In B C therefore, and always in the other proposition, it is necessary to proceed to immediates, for this proposition is affirmative.3 With regard to the other however it is clear, that if it is not present with something else prior, for instance, with D, it will be requisite that this (D) should be present with every B. Also if again it[||] is not present with something else prior to D, it will require that to be present with every D, so that since the upward progression stops, the downward progression will also stop, and there will be something first with which it is not present. Moreover if B is with every A, but with no C, A will be with no C; again, if it is required to show this,4 it is evident, that it may be demonstrated either through the superior mode,5 or through this, or through the third, now the first has been spoken of, but the second shall be shown. Thus indeed it may demonstrate it,6 as, for instance, that D is present with every B, but with no C, if it is necessary that any thing[||] should be with B,7 and, again, if this8 is not present with C,9 something else10 is present with D, which is not present with C, wherefore since the perpetually being present with something superior stops, the not being present will also stop. But the third mode was if A indeed is present with every B, but C is not present, C will not be present with every A; again, this will be demonstrated either through the above-mentioned modes, or in a similar manner, in those modes the progression stops, but if thus, it will again be assumed that B is present with E, with every individual of which C is not pre-sent. This § again, also, will be similarly demon-strated,|| but since it is supposed that the down-ward progression stops, C also, which is not present with, will evidently stop.

Nevertheless, it appears plain, that if it should not be de-monstrated in one way, but in all, at one time from the first figure, at another from the second or the third, that thus also the progression will stop, for the ways are finite, but it is necessary that finite things being finitely assumed should be all of them finite.

That in negation then the progression stops, if it does so in affirmation, is clear, but that it must stop in them is thus manifest to those who consider logically.11

Note del traduttore
  1. 1 That is, in affirmative syllogisms, upward from the last subject.
  2. 2 A is the high- est predicate, F the last sub- ject, B the me- dia.
  3. 3 It is assumed that there is no infinite progression in affirmative prop., because this will be proved in the following chapter.
  4. 4 A ; the predicate of the major.
  5. 5 Because in 1st figure the middle is predicate of the minor.
  6. 6 The syllogism in the 2nd fig. will prove B to be predicated of no C.
  7. 7 In order that a syllogism may be formed in Camestres ; if, on the other hand, D is predicated of every C, and of no B, it would be in Cesare. This is a particular prop., in order to effect a syllogism in Bokardo, as Aristotle will shortly prove it in the third figure ; if it were universal in Felapton, it could not be proved in this figure.
  8. 8 As with E.
  9. 9 In the three figures.
  10. 10 In the proof of the minor. Taylor.
  11. 11 Aristotle calls those arguments logical which are not derived from the nature of a thing, but analytical are opposed to them, because they re-solve things into their principles; the one method is, as Waitz says, an accurate demonstration, which depends upon the true principles of the thing itself; the other, that which is satisfied with a certain probable ratiocination. Cf. Philop.; also Biese i. p. 261; Waitz in loc. Cicero (de Finib. i. 7) calls the “logical” that part of philosophy, “quæ sit quæ-rendi ac disserendi.”

San Tommaso: Libro I, lezione XXXII

Libro I, capitolo 22 That there are no Infinite Media in Affirmative Demonstration.82b37–84b2

Inglese

In things predicated therefore as to what a thing is, this is clear, for if it is possible to define, or if the very nature of a thing may be known, but infinites cannot be passed through, it is necessary that those things should be finite which are pre-dicated with respect to what a thing is. We must however speak universally thus: a white thing we may truly say walks, also that that great thing is wood; more-over, that the wood is great, and that the man walks, yet there is a difference between speaking in this way and in that. For when I say that that white thing is wood, then I say that what happens to be white is wood, but what is white is not, as it were, a subject to wood, since neither being white, nor what is a certain white thing, became wood, so that it is not (wood) except from accident. But when I say that the wood is white, I do not say that something else is white, but it happens to that1 to be wood, (as when I say that a musician is white, for then I mean that the man is white, to whom it happens to be a musician,) but wood is the subject which became (white), not being any thing else than what is wood, or a certain piece of wood. If indeed it is necessary to assign names, let speaking in this way2 be to predicate, but in that way be either by no means to predicate, or to predicate indeed, not simply, but according to accident. That which is predicated is as white, but that of which it is predicated as wood; now let it be supposed that the predicate is always spoken of what it is predicated of simply, and not according to accident, for thus demonstrations demonstrate. Therefore when one thing is predicated of one, it will be predicated either in respect of what a thing is, or that it is a quality, or a quantity, or a relative, or an agent, or a patient, or that it is some where, or at some time.

Moreover, those which signify substance, signify that the thing of which they are predicated, is that which it is, or something belonging to it, but whatever do not signify substance, but are predicated of another subject, which is neither the thing itself, nor something belonging to it, are accidents, as white is predicated of man, since man is neither white, nor any thing which belongs to white, but is perhaps animal, for man is that which is a certain animal. Such as do not signify substance it is necessary should be predicated of a certain subject, and not be something white, which is white, not being any thing else. For, farewell to ideas, for they are mere prattlings, and if they exist, are nothing to the subject, since demonstrations are not about such things.3 Again, if this is not a quality of this, and that 2. of this, neither a quality of a quality, it is impossible that they should be thus mutually predicated of each other, still they may possibly be truly said, but cannot truly be mutually predicated. For will they be predicated as substance, as being either the genus or the difference of what is predicated? It has been shown that these will not be infinite, neither in a descending nor in an ascending progression, as for instance, man is a biped, this an animal, this something else; neither can animal be predicated of man, this of Callias, this of something else, in respect to what a thing is. For we may define the whole of this to be substance, but we cannot penetrate infinites by perception, wherefore neither are there infinites upwards or downwards, for we cannot define that of which infinites are predicated. They will not indeed be mutually predicated of each other as genera, for genus would be a part itself, neither will quality nor any of the other categories be (mutually) predicated, except by accident, for all these are accidents, and are predicated of substances. But neither will there be infinites in ascending series, for of each thing, that is predicated, which signifies either a certain quality, or a certain quantity, or something of this kind, or those which are in the substance, but these are finite, and the genera of the categories are finite, since (a category) is either quality, or quantity, or relation, or action, or passion, or where, or when. One thing is however supposed to be predicated of one, but those not to be mutually predicated which do not signify what a thing is, since all these are accidents, but some are per se, others after a different manner, and we say all these are predicated of a certain subject, but that accident is not a certain subject, for we do not assume any thing of this kind to be, which not being any thing else, is said to be what it is said to be, but we say that it is predicated of something else, and certain other things of another thing.4 Neither then can one thing be predicated of one (infinitely) upwards, nor downwards, for those of which accidents are predicated, are such as are contained in the substance of each thing, but these are not infinite. Both these indeed and accidents are ascending, and both are not infinite, wherefore it is necessary that there should be something5 of which primarily something6 is predicated, and something else of this, also that this should stop, and that there should be something|| which is neither predicated of another prior thing, nor another prior thing of it. This then is said to be one mode of demonstration, but there is another besides, if there is a demonstration of those of which certain things are previously predicated, but of what there is demonstration, it is not possible to be better affected towards them than to know them, nor can we know without demonstration.7 Still if this8 becomes known through these, but these we do not know, nor are better affected towards them than if we knew them, neither shall we obtain scientific knowledge of that which becomes known through these. If then it is possible to know any thing simply through demonstration, and not from certain things, nor from hypothesis, it is necessary that the intermediate predications should stop; for if they do not stop, but there is always something above what is assumed, there will be a demonstration of all things, so that if we cannot pass through infinites, we shall not know by demonstration those things of which there is demonstration. If then we are not better affected towards them than if we knew them, it will be impossible to know any thing by demonstration simply, but by hypothesis. Logically then from these things a person may believe about what has been said, but analytically9 it is more concisely manifest thus, that there cannot be infinite predicates in demonstrative sciences, the subject of the present treatise, either in an ascending or descending series. For demonstration is of such things as are essentially present with things, essentially in two ways, both such as are in them in respect of what a thing is, and those in which the things themselves are inherent in respect of what a thing is, thus the odd in number which indeed is inherent in number, but number itself is inherent in the definition of it, again also, multitude or the divisible is inherent in the definition of number. Still neither of these can be infinites, nor as the odd is predicated of number, for again there will be something else in the odd, in which § being inherent,|| (the odd) would be inherent, and if this be so, number will be first inherent in those things which are inherent in it. If then such infinites cannot be inherent in the one, neither will there be infinites in ascending series. Still it is necessary that all should be inherent in the first, for example, in number, and number in them, so that they will reciprocate, but not be more widely extensive. Neither are those infinite which are inherent in the definition of a thing, for if they were, we could not define, so that if all predicates are predicated per se, and these are not infinite, things in an upward progression will stop, wherefore also those which descend.

If then this be so, those also which are between the two terms will be always finite, but if this be the case, it is clear now that there must necessarily be principles of demonstrations, and that there is no demonstration of all things, as we observed in the beginning, certain persons assert. For if there be principles, neither are all things demonstrable, nor can we progress to infinity, since that either of these should be, is nothing else than that there is no proposition immediate and indivisible, but that all things are divisible, since what is demonstrated is demonstrated from the term10 being inwardly introduced, and not from its being (outwardly) assumed. Wherefore if this § may possibly proceed to infinity, the media between two terms|| might also possibly be infinite, but this is impossible, if predications upwards and downwards stop, and that they do stop, has been logically shown before, and analytically now.

Note del traduttore
  1. 1 To that something else.
  2. 2 As the wood is white. As that which is white is wood. Cf. Met. lib. v. Phy. lib. ii.
  3. 3 Taylor tells us quaintly, “that Aristotle is not serious in the objections which he urges against Plato’s theory of ideas; for that demonstration cannot exist (from the testimony of Aristotle himself) unless the existence of ideas be admitted conformably to the doctrine of Plato,” in total opposition to what is stated in the 11th chap. What Aristotle means is, that ideas, even if they exist, are of little use to effect demonstration, because the latter cannot subsist unless there be ἓν κατὰ πολλν; but since ideas subsist per se, (χωριστά ἐστιν,) they cannot be predicated of others. Vide also Metap. lib. ix. (x.) and lib. xii (xiii.) ed. Leipsic.
  4. 4 As whiteness of a swan, blackness of a crow.
  5. 5 A last subject, e. g. D.
  6. 6 As C.
  7. 7 To first principles (indemonstrable) we are better affected than if we knew them through demonstration, as was shown in ch. 2.
  8. 8 i. e. immediately.
  9. 9 From the principles and essence of demonstration. Vide supra.
  10. Jam si vera scientia demonstratione comparari potest, quæ neces- sario vera sit, ut non pendeat ex aliis conditionibus quibuscunque, quæ et esse possint, et non esse, terminorum mediorum, quibus demonstratio utitur, numerus non erit infinitus: nam si esset, et omnia demonstrari possent, et, quia infinitam demonstrationem perficere non liceret, quædam demonstrari non possent, ut demonstratio non efficeret veram scientiam, sed hypotheticam, h. e. non cogeretur quod demonstratur ex proposition- ibus certis, sed ex propositionibus quæ, quamquam ipsæ demonstrari de- berent, tamen pro certis sumtæ essent. Waitz. By hypothesis, he alludes to what is not self-evidently certain, but is assumed to be so.
  11. 10 The middle.

San Tommaso: Libro I, lezione XXXIII · Libro I, lezione XXXIV · Libro I, lezione XXXV

Libro I, capitolo 23 Certain Corollaries.84b3–85a12

Inglese

From what has been shown it appears plain that if one and the same thing is inherent in two, for instance, A in C and in D, when one is not predicated of the other, either not at all or not universally, then it is not always inherent according to something common. Thus to the isosceles and to the scalene triangle, the possession of angles equal to two right, is inherent according to something common, for it is inherent so far as each is a certain figure, and not so far as it is something else. This however is not always the case, for let B be that according to which A is inherent in C D, then it is evident1 that B is also inherent in C, and in D, according to something else common, and that also2 according to something else, so that between two terms, infinite terms may be inserted, but this is impossible.|| It is not then necessary that the same thing should always be inherent in many, according to something common, since indeed there will be immediate propositions; it is moreover requisite that the terms should be in the same genus, and from the same individuals, since that which is common will be of those which are essentially inherent, for it is impossible to transfer things which are demonstrated from one genus to another. But it is also manifest that when A is with B, if there is a certain middle, we may show that B is with A, and the elements of this3 are these and whatever are media, for immediate propositions, either all of them, or those which are universal, are elements.4 Yet if there is not (a medium) there is no longer demonstration, but this is the way to principles. In like manner, if A is not with B, if there is either a middle, or something prior to which it is not present, there is a demonstration,5 but if not, there is no demonstration, but a principle, and there are as many elements as terms,|| for the propositions of these are the principles of demonstration. As also there are certain indemonstrable principles, that this is that, and that this is present with that, so there are also that this is not that, and that this is not present with that, so that there will be some principles that a thing is, but others that it is not. Still when it is required to demonstrate, that which is first predicated of B must be assumed; let this be C, and let A, in like manner, (be predicated) of this; by always proceeding thus,6 there is never a proposition externally, nor is that7 which is present with A assumed in the demonstration, but the middle is always condensed till they become indivisible and one.8 They are one indeed when the immediate is produced, and one proposition simply, an immediate one, and as in other things the principle is simple, but this is not the same every where, but in weight it is a minor, in melody a demi-semi-quaver,9 and something else in another thing, thus in syllogism, “the one” is an immediate proposition, but in demonstration and science it is intuition.§10 In syllogisms then, which demonstrate the being inherent, nothing falls beyond (the middle), but in negatives here,|| nothing falls external of that which ought to be inherent,11¶ as if A is not present with B through C. For if C is present with every B, but A with no C, and if, again, it should be requisite to show that A is with no C, we must assume the medium of A and C, and thus we must always proceed. If however it should be required to show12 that D is not with E, because C is with every D, but with no, or not with every E, the medium will never fall external to E, and this § is with what it need not be present.13 As to the third mode,|| it will never proceed external to that from which, nor which it is necessary to deny.14

Note del traduttore
  1. Being assumed between the subject and attribute of the prop. to be proved. Thus the middle term is assumed in the first figure, in which it is subjected to the attribute, i. e. to the greater extreme, and is attributed to the subject, i. e. to the less extreme. Taylor. By the middle being inwardly introduced, he means that in order to demonstrate A B, A must be predicated of C, and C of B, but A of B, and B of C. Upon the above chap., compare Metap. lib. iii. iv. vi. ix. xiii.; Eth. book i. ch. 6; De Anim. b. iii. Vide also Hill’s Logic, de Definitione, and Whately’s Logic, b. ii. ch 5, and b. iii. sec. 10.
  2. 1 Because if a thing is inherent in two things, it is inherent mediately. Taylor.
  3. 2 E is in C and D.
  4. 3 As E.
  5. 4 Immediate particular propositions are not the principles of demonstrations, but of inductions. Upon the use of the word στοιχεῖα, by Aristotle, cf. Ammonius upon Catego. ch. 12; also Biese i. p. 381, note 5, Trendelenburg Platonis de Ideis. In the Topics, as Waitz observes, he uses στοιχεα as synonymous with τόποι, for certain universal arguments, from which, with some appearance of truth, a thing may be either proved or refuted. Top. lib. iv. ch. 1, etc. The sense here, of elements, seems most suggestive of their meaning, viz. that of certain principles of disputation, which when provided, enable us rightly to conduct an argument.
  6. 5 If there is a certain middle (C) through which A is proved not present with B, A will first be denied of C in the major premise, and afterwards of B in the conclusion ; thus a syllogism will result in Celarent : No C is A, every B is C ; therefore no B is A.
  7. 6 By assuming a new term, as predicate of the minor, and subject of the major.
  8. 7 The conclusion.
  9. 8 Until we arrive at an indemonstrable and immediate proposition.
  10. 9 Δίεσις. The least perceptible sound we have therefore expressed it; by its closest representative in music.
  11. 10 For we know principles by “νος.” Cf. de Anim. iii. ch. 4—6, ubi cf. Trende., Biese, and Rassow. I have translated the word “intuition,” agreeing as I do with Professor Browne, (vide Ethics, b. vi. ch. 6, Bohn’s edition,) that no other word conveys with the same exactitude Aristotle’s own definition of it in the Magnâ Moralia (i. 35), Ὁ νοῦς ἐστὶ περὶ τὰς ἀρχὰς τῶν νοητῶν καὶ τῶν ὄντων, μὲν γὰρ ἐπιστήμη τῶν μετ’ ἀποδείξεως ὄντων ἐστίν, ἄρα δ’ ἀρχαὶ ἀναπόδεικτοι.
  12. 11 Thus Waitz, Buhle, and Bekker. Taylor evidently reads, ὃ, δεῖ, μὴ ὑπάρχειν, an amendment which Waitz approves in his note, and so do I, for the conclusion of the syllogism is of course negative; the meaning is, that a middle term is never assumed, which is predicated of the major extreme, since the major is that in which the conclusion is negatively predicated of the minor. Assume a middle term which does not fall externally to the major extreme, in order to demonstrate the negative proposition.
  13. 12 In Camestres.
  14. 13 It is the subject of the negative conclusion, of which D is denied.
  15. 14 A middle will never be assumed above the greater or less extreme, nor be predicated of either, because in the 3rd figure the middle term is always the subject of both premises. As Taylor remarks, in the whole of this chapter, the middle is said to fall external to the extreme, when it changes its situation; so that if it was before the subject of the major extreme, afterwards in the pro-syllogism, it becomes the predicate of the major.

San Tommaso: Libro I, lezione XXXVI

Libro I, capitolo 24 The superiority of Universal to Particular Demonstration proved.85a13–86a30

Inglese

As one demonstration is universal, but another particular, one also affirmative, but the other negative, it is questioned which is preferable, likewise also about what is called direct demonstration, and that which leads to the impossible. Let us first then consider the universal and the particular, and having explained this, speak of what is called direct demonstration, and that to the impossible.

Perhaps then to some considering the matter in this way, the particular may appear the better, for if that demonstration is preferable, by which we obtain better knowledge, for this is the excellence of demonstration, but we know each thing better when we know it per se, than when through something else, (as we know Coriscus is a musician, when we know that Coriscus is a musician rather than when we know that a man is a musician, and likewise in other things,) but the universal demonstrates because a thing is something else, not because it is that which it is, as that an isosceles triangle (has two right angles), not because it is isosceles, but because it is a triangle,) but the particular demonstrates because a thing is what it is, if then the demonstration per se is preferable, and the particular is such rather than the universal, particular demonstration would be the better. Besides, if the universal is nothing else than particulars, but demonstration produces opinion that this thing is something according to which it demonstrates, and that a certain nature of this kind is in things which subsist, (as of triangle besides particular (triangles), and of figure besides particular (figures), and of number besides particular (numbers), but the demonstration about being is better than that about non-being, and that through which there is no deception than that through which there is, but universal demonstration is of this sort, (since men proceeding demonstrate as about the analogous,1 as that a thing which is of such a kind as to be neither line nor number, nor solid nor superficies, but something besides these, is analogous,) if then this is more universal, but is less conversant with being than particular, and produces false opinion, universal will be inferior to particular demonstration.

First then may we not remark that one of these arguments2 does not apply more to universal than to particular demonstration? For if the possession of angles equal to two right angles is inherent, not in respect of isosceles, but of triangle, whoever knows that it is isosceles knows less essentially3 than he who knows that it is triangle. In short, if not so far as it is triangle, he then shows it, there will not be demonstration, but if it is, whoever knows a thing so far as it is what it is, knows that thing more.4 If then triangle is of wider extension (than isosceles), and there is the same definition, and triangle is not equivocal, and the possession of two angles equal to two right angles is inherent in every triangle, triangle will have such angles, not so far as it is isosceles, but the isosceles will have them, so far as it is triangle. Hence he who knows the universal, knows more in regard to the being inherent than he who knows particularly, hence too the universal is better than the particular demonstration. Moreover if there is one certain definition, and no equivocation, the universal will not subsist less, but rather more than certain particulars, inasmuch as in the former there are things incorruptible, but particulars are more corruptible.5 Besides, there is no necessity that we should apprehend this (universal) to be something besides these (particulars), because it shows one thing, no more than in others which do not signify substance, but quality, or relation, or action, but if a person thinks thus, it is the hearer, and not demonstration, which is to blame.6 Again, if demonstration is a syllogism, showing the cause and the why, the universal indeed is rather causal, for that with which any thing is essentially present, is itself a cause to itself, but the universal is the first, therefore the universal is cause. Wherefore the (universal) demonstration is better, since it rather partakes of the cause and the why, besides up to this we investigate the why, and we think that then we know it, when this is becoming, or is, not because something else (is), for thus there is the end and the last boundary. For example, on what account did he come ? that he might receive money, but this that he might pay his debts, this that he might not act unjustly, and thus proceeding, when it is no longer on account of something else, nor for the sake of another thing, then we say that he came, and that it is, and that it becomes on account of this as the end, and that then we especially know why he came. If then the same occurs, as to all causes and inquiries into the why, but as to things which are so causes as that for the sake of which, we thus especially know, in other things also we then chiefly know, when this no longer subsists because another thing does.7 When therefore we know that the external angles are equal to four right angles, because it is isosceles, the inquiry yet remains, why because isosceles, because it is a triangle, and this because it is a rectilinear figure. But if it is this no longer on account of something else, then we pre-eminently know, then also universally, wherefore the universal is better.

Again, by how much more things are according to the particular, do they fall into infinites, but the universal tends to the simple and the finite, so far indeed as they are infinite, they are not subjects of science, but so far as they are finite they may be known, wherefore so far as they are universal, are they more objects of scientific knowledge, than so far as they are particular. Universals however are more demonstrable, and of things more demonstrable is there pre-eminent demonstration, for relatives are at one and the same time more, whence the universal is better, since it is demonstration pre-eminently. Besides, that demonstration is preferable, according to which this and something else are known, to that, by which this alone is known, now he who has the universal knows also the particular, but the latter does not know the universal, wherefore even thus the universal will be more eligible. Again, as follows: it is possible rather to demonstrate the universal, because a person demonstrates through a medium which is nearer to the principle, but what is immediate is the nearest and this is the principle; if then that demonstration which is from the principle is more accurate than that which is not from the principle, the demonstration which is in a greater degree from the principle, is more accurate than that which is from it in a less degree. Now the more universal is of this kind, wherefore the universal will be the better, as if it were required to demonstrate A of D, and the media should be B C, but B the higher, wherefore the demonstration through this is more universal.

Some of the above arguments are logical, it is chiefly clear however that the universal is more excellent, because when of two propositions we have that which is the prior, we also in a certain degree know and possess in capacity that which is posterior; thus if a man knows that every triangle has angles equal to two right, he also in a certain respect knows in capacity that an isosceles triangle has angles equal to two right, even if he does not know that the isosceles is a triangle, but he who has this proposition by no means knows the universal, neither in capacity nor in energy. The universal proposition also is intuitively intelligible, but the particular ends in sense.18

Note del traduttore
  1. 1 They who employ universal demonstration do not keep within the exact limits of demonstration, but appear to go beyond them in the same way as those who reason ἐκ τοῦ ἀνὰ λόγον, for if they have demonstrated any thing of lines, body, etc., they apply the proof as equally conclusive to every thing similar, and thus extend the demonstration unfairly.
  2. 2 i. e. the first. 3. Reply to the above.
  3. 3 Minus scit quatenus ipsum (tale est ut habere duos rectos angulos illi insit). Buhle.
  4. 4 As Mansel observes, (Appendix, note B,) the office of logic is to contribute to the distinctness of a conception, by an analysis and separate exposition of the different parts contained within it. The mind, like the sky, has its nebulæ, which the telescope of logic may resolve into their component stars.
  5. 5 So Waitz, who has this note, “Notiones universales, si unitatem quandam exprimunt et si alius earum est usus quam ut orationem ambiguam faciant, quum singula quæ illis subjecta sint pereant, illæ vero non corrumpantur, etiam rectius ipsæ existere dicentur quam τὰ ἄτομα.” Cf. Metap. lib. ii. (iii.), v. (vi.), vi. (vii.), ix. (x.), and xi. (xii.), Leipsic ; Phys. lib. iii. and viii. ; also Crakanthorpe’s Logic, lib. ii., and upon this chapter generally, Aquinas in Periherm. sect. i.
  6. 6 That is, if a man thinks that universal is something besides particulars. By universal here, he means, that which is “co-ordinated” with the many, and which when abstracted out of the many by the mind, produces the universal, which is of posterior origin. Taylor.
  7. 7 A verbose exemplification of the terse truism of Swift, that “we unravel sciences, as we do old stockings, by beginning at the foot.”
  8. 8 An. Post. ii. ch. 19.

San Tommaso: Libro I, lezione XXXVII · Libro I, lezione XXXVIII

Libro I, capitolo 25 The Superiority of Affirmative to Negative Demonstration proved.86a31–86b39

Inglese

That universal is better than particular demonstration, let so much be alleged, but that the affirmative is preferable to the negative, will be evident from this. Let that demonstration be better, cæteris paribus, which consists of fewer postulates, or hypotheses, or propositions. For if they1 are similarly known, quicker knowledge will be obtained through these, which is more eligible. The reason however of this proposition, that that which consists of fewer is better, universally is this; for if the media are similarly known, but things prior are more known, let the demonstration be through the media of B C D, that A is present with E, but through F G, that A is present with E.2 That A is present with D, and that A is present with E subsists similarly,|| but that A is with D, is prior and more known than that A is with E, for that is demonstrated ¶ Viz. A E. through this, and that is more credible through which (a thing is demonstrated). Also the demonstration which is through fewer things is therefore better, cæteris paribus; both3 then are demonstrated through three terms, and two propositions, but the one assumes that something is, and the other, that something is and is not,4 hence through a greater number of things (the demonstration is made) so that it is the worse.

Moreover since it has been shown impossible for a syllogism to be produced with both propositions negative, but that one must of necessity be such (negative), and the other that a thing is present with, (that is affirmative,) we must in addition to this assume this,|| for it is necessary that affirmative (propositions) when the demonstration is increased, should become more, but it is impossible that the negatives should be more than one in every syllogism. For let A be present with nothing of those with which B is, but B be present with every C, if indeed, again, it should be necessary to increase both propositions, a middle must be introduced.5 Of A B then let the middle be D, but of B C let the middle be E, E then is evidently affirmative, but D is affirmative indeed of B, yet is placed negatively as regards A, since it is necessary that D should be present with every B, but A with no D; there is then one negative proposition, viz. A D. The same mode also subsists in other syllogisms, for the middle of affirmative terms is always affirmative in respect of both (extremes), but in the case of a negative (syllogism), the middle must be necessarily negative in respect to one of the two,|| so there is one proposition of this kind, but the others are affirmative. If then that is more known and credible through which a thing is demonstrated, but the negative is shown through the affirmative, and the latter not through the former, this, since it is prior, more known, and more credible, will be better. Again, since the principle of syllogism is an universal immediate proposition, but the universal proposition in an ostensive (demonstration) is affirmative, but in a negative is negative, and since the affirmative is prior to, and more known than, the negative, for negation is known through affirmation, and affirmation is prior, just as being is prior to not being, therefore the principle of affirmative is better than that of negative demonstration, but that which uses better principles is better. Moreover it partakes more of the nature of principle, since without affirmative there is no negative demonstration.6

Note del traduttore
  1. 1 Viz. the propositions of both demonstrations.
  2. 2 B C and F G are the same, but they are called B C, so far as they form parts of the syllogism concluding A E ; and they are called F G, so far as they belong to the syllogism A D.
  3. Cf. de An. iii. 6 ; Metaph. ix. 1 ; and upon the conception of universal notions, Reid’s Works, Hamilton’s ed. ; Mill’s Logic ; Whately’s Rhet. ; Trende. Biese i. p. 327, note 4 ; Rassow, p. 72.
  4. 3 i. e. both affirmatives and negatives.
  5. 4 Because of negative demonstration, one premise affirms, but the other denies.
  6. 5 This is done when a pro-syllogism is constructed in the 1st figure, because here alone the middle term occupies the middle place.
  7. 6 An affirmative partakes more of the nature of principle than a negative demonstration, because the minor prem. of a negat. is proved through an affirmative.

San Tommaso: Libro I, lezione XXXVIII · Libro I, lezione XXXIX

Libro I, capitolo 26 The Superiority of the same to Demonstration ad impossibile proved.87a1–30

Inglese

Since affirmative is better than negative demonstration, it is evidently also better than that which leads to the impossible, it is necessary however to know what the difference between them is. Let A then be present with no B, but let B be with every C, wherefore it is necessary that A should be with no C, (the terms) then being thus assumed, the negative proposition proving that A is not present with C will be ostensive. The demonstration however to the impossible is as follows: if it is required to show that A is not present with B it must be assumed present, also that B is with C so that it will happen that A is with C. Let this however be known and acknowledged impossible, then it is impossible that A should be with B; if then B is acknowledged present with C, it is impossible that A should be with B. The terms then indeed are similarly arranged, but it makes a difference which negative proposition is more known, viz. whether that A is not present with B, or that A is not present with C. When then the conclusion is more known that it is not, there is a demonstration to the impossible produced, but when that which2 is in the syllogism (is more known) the demonstration is ostensive. Naturally, however, that A is not present with B is prior to A is not present with C, for those things are prior to the conclusion, from which the conclusion (is collected), and that A is not with C is the conclusion, but that A is not with B is that from which the conclusion is derived. For neither if a certain thing happens to be subverted, is this the conclusion, but those (the premises) from which (the conclusion is derived). That indeed from which (it is inferred) is a syllogism, which may so subsist as either3 a whole to a part, or as a part to a whole, but the propositions A C and A B do not thus subsist with regard to each other. If then that demonstration which is from things more known and prior be superior, but both are credible from something not existing, yet the one from the prior, the other from what is posterior, negative demonstration will in short be better, than that to the impossible, so that as affirmative demonstration is better than this,|| it is also evidently better than that leading to the impossible.

Note del traduttore
  1. 1 Vide Hill’s and Mansel’s Logic, article Demonstration; also Whately, App. I. xi., upon “Impossibility,” and Rhetoric, part i. ch. 3, sec. 7. The ες τὸ ἀδύνατον γουσα ἀπόδειξις here, seems to correspond with the ἐλεγκτικὸν ἐνθύμημα of the Rhetoric, upon which see Dr. Hessey’s Schem. Rhet. Table 4. Cf. also Anal. Pr. i. 22 and 38; Rhet. ii. 22—24 and 30; iii. 17, 13.
  2. 2 The negation that A is not in C.
  3. 3 One proposi-tion is to the other as a whole to a part, i. e. the major as to the minor.

San Tommaso: Libro I, lezione XL

Libro I, capitolo 27 Upon the Nature of more Accurate Science.87a31–37

Inglese

One science is more accurate than, and prior to, another, both the science that a thing is, and the same why it is, but not separately that it is, than the science of why it is, also that which is not of a subject2 than that which is of a subject, for instance, arithmetic then harmonic science, and that which consists of fewer things than that which is from addition, as arithmetic than geometry. I mean by “from addition,” as unity is a substance without position, but a point is substance with position,3 this is from addition.

Note del traduttore
  1. 1 Cf. ch. 13; Plato, Phileb.; Rhet. b. i. ch. 7. In the last place, he says that the precedence of one science over another is dependent upon the higher elevation of its subject matter. Met. lib. i. and x.
  2. 2 Not conversant with a material subject, as arithmetic, which is con-versant with number. Taylor.
  3. 3 A point was defined by the Pythagoreans, unity with position : cf. Categ. ch. 6 ; Procl. in Euc. Elem. lib. ii. Θέσιν ἔχειν dicuntur ea quorum partes simul intuemur ac si oculis subjectæ essent ; quæ dum fluunt, manent et quorum quasi imagines ita animo representantur, ut quæ præterierint mente repeti possint simul cum iis, quæ præsto sint. Waitz, in Cat. cap. 6.

San Tommaso: Libro I, lezione XLI

Libro I, capitolo 28 What constitutes one, and what different Sciences.87a38–87b4

Inglese

One science is that which is of one genus of those things which are composed of first (principles), and are the parts or affections of these per se;1 but a science is different from another, whose principles are neither from the same things, nor one from the other.2 A token of this is when any one arrives at things indemonstrable, for it is necessary3 that they should be in the same genus with those that are demonstrated; it is also a sign of this when things demonstrated through them are in the same genus and are cognate.

Note del traduttore
  1. 1 Thus natural productions, though they possess their own proper principles, are ultimately composed of the first and common principles, matter and form : these last constitute the parts of body, but body and soul the parts of animal. Also in the sciences we must consider the subjects of them, their parts, and their proper affections.
  2. 2 That is, their principles neither issue from a common source, nor are so intermingled that the one may be derived from the other : thus physics and arithmetic are different sciences, but the science of motion and of the heavens are not entirely different. Vide Physics.
  3. 3 If it is one science.

San Tommaso: Libro I, lezione XLI

Libro I, capitolo 29 That there may be several Demonstrations of the same thing.87b5–18

Inglese

There may possibly be many demonstrations of the same thing, not only when one assumes an un-continued medium from the same class, as if C D and F (were assumed) of A B, but also from another (series).1 Thus, let A be to be changed, D to be moved, B to be delighted, and again G to be tranquillized. It is true then to predicate D of B and A of D, for whoever is delighted is moved, and what is moved is changed: again, it is true to predicate A of G, and G of B, for every one who is delighted is tranquillized, and he who is tranquillized is changed. Wherefore there is a syllogism through different media,2 and not from the same class, yet not so that neither is predicated of neither medium, since it is necessary that both3 should be present with something which is the same. We must also consider in how many ways|| there may be a syllogism of the same thing through the other figures.

Note del traduttore
  1. 1 That is, it is possible to effect this when the one is not subaltern to the other, as it may be shown that man is an essence if we take biped as a medium, or walking, or disputing, for these are not from the same class as the former.
  2. 2 That is, D and G, media, the same conclusion A B is proved.
  3. 3 D and G.

San Tommaso: Libro I, lezione XLI

Libro I, capitolo 30 That there is no Science of the Fortuitous.87b19–27

Inglese

There is no science through demonstration of that which is fortuitous, since the fortuitous is neither as necessary nor as for the most part, but that which is produced besides these, and demonstration is of one of these. For every syllogism is through premises, either necessary, or through those which are for the most part (true), and if indeed the propositions are necessary, the conclusion also is necessary; but if for the most part (true), the conclusion also is of the same character. Hence if the fortuitous is neither as for the most part nor necessary, there cannot be demonstration of it.

Note del traduttore
  1. 1 Cf. Metap. lib. v. (vi.).

San Tommaso: Libro I, lezione XLII

Libro I, capitolo 31 That we do not possess Scientific Knowledge through Sensation.¶.87b28–88a17

Inglese

Neither is it possible to have scientific knowledge through sensation, for although there is sensible perception of such a thing as this, and not of this particular thing, yet it is necessary to have a sensible perception of this particular thing, and some where and now.1 But it is impossible sensibly to perceive the universal and in all things, for it is not this particular thing, nor now, otherwise it would not be universal, since we call the universal that which is always and every where. Since then demonstrations are universal, but these cannot be perceived by sense, it is plain that neither can scientific be possessed through sense. In fact, it is clear, that even if we could perceive by sense that a triangle has angles equal to two right, we should require demonstration, and not, as some say, know this scientifically, for it is necessary sensibly to perceive the singular, but science is from the knowledge of the universal. Wherefore also if we were above the moon, and saw the earth opposite, we should not know the cause of an eclipse (of the moon). For we should perceive that it is eclipsed, but in short should not perceive why, since there would not be a sensible perception of the universal. Nevertheless, from observing this frequently to happen, by investigation of the universal, we should obtain demonstration, for the universal is manifest from many singulars, but is valuable, because it discloses the cause, wherefore the universal (knowledge) about such things, of which there is another cause, is more honourable than the senses and apprehension: about first principles however there is another reason. It is clearly then impossible to possess scientific knowledge of any thing demonstrable by sensible perception, unless some one should affirm that sensible perception is this, to possess science through demonstration. There are indeed certain problems which are referred to the deficiency of our sensible perception,2 for some if we should see them we should not investigate, not as knowing from seeing, but as possessing the universal from seeing. For instance, if we saw glass perforated, and the light passed through it, it would be also manifest why it illuminates in consequence of our seeing separately in each, and at the same time perceiving that it is thus with all.

Note del traduttore
  1. 1 Aristotle intends to show that sense is not science; otherwise since sense apprehends qualities, as sounds, etc., it may seem that sense and science are the same; but the fact is, that though they are employed about the same things, yet they are not so after the same manner, for sense apprehends particularly, but science universally. Moreover the perception of the senses is limited by time and place, but science, or universal knowledge, is not so restricted, so that the ascertainment of the universal is beyond the scope of sensuous perception. Cf. Physics; De Animâ, lib. ii. and iii.; Metap. lib. i. ch. 1; Magna Moral. lib. i. 34, and Moral. Eud. lib. v. c. 3.
  2. The nearest approach to simple apprehension is ἡ τῶν ἀδιαιρέτων νοήσις, but νοήσις is variously used, and in its widest sense will embrace all the logical operations. Mansel. See also Reid’s Works, pp. 242, 692. Waitz observes upon the passage, “Quare in iis quorum causa aliunde suspensa est, cognitio quam maxime universalis potior est omni alia, quæ vel ex sensuum affectione gignatur vel ex cognitione solâ originem habeat: eorum vero quæ non aliunde probantur, quippe quibus nitatur
  3. 2 Philoponus observes that Aristotle added this observation lest any discrepancy should appear to exist between what he has stated here and at chapter 18. Philop. Schol.

San Tommaso: Libro I, lezione XLII

Citato nell'enciclopedia: INDUZIONE

Libro I, capitolo 32 On the Difference of Principles according to the Diversity of Syllogisms.88a18–88b29

Inglese

That there should be the same principles of all syllogisms is impossible, first (this will be seen) by those who consider logically. For some syllogisms are true, others false, since it is possible to conclude the true from the false, yet this but rarely happens, for instance, if A is truly predicated of C, but the middle B is false, for neither is A present with B nor B with C. If however the media of these propositions are assumed, they will be false,1 because every false conclusion is from false principles, but the true from true principles, and the false and the true are different. Next, neither are the false (deduced) from the same (principles) with themselves, for they are false and contrary to each omnis ratiocinatio, alia ratio est: hæc enim mente ipsâ intuemur et quasi amplectimur.

B A Ex. 1. Every stone is an animal C B Every man is a stone C A ∴ Every man is an animal. other, and cannot be simultaneous, for instance, it is impossible that justice should be injustice or timidity, that man should be a horse or an ox, or that the equal should be greater or less. From these positions indeed (we may prove it) thus, since neither are there the same principles of all the true (conclusions), for the principles of many are different in genus, and are not suitable, as units do not suit points, for the former have not position, but the latter have it. At least it is necessary to adapt (either) to media or from above or below, or to have some terms within but others without.2† Nor can there possibly be certain common principles from which all things may be demonstrated: I mean by common as to affirm or to deny every thing, for the genera of beings are different, and some are present with quantities, but others with qualities alone, with which there is demonstration through the common. Again, principles are not much fewer than conclusions, for the propositions are principles, but the propositions subsist when a term is either assumed or introduced. Moreover, conclusions are infinite, but terms finite; besides, some principles are from necessity, but others contingent.

To those therefore who thus consider, it will be impossible that there should be the same finite principles when the conclusions are infinite, but if any one should reason in some other way, for instance, that these are the principles of geometry, but these of reckoning, and these of medicine, what is this statement other than that there are principles of the sciences?§ but to say that there are the same principles because they are the same with themselves is ridiculous,|| for thus all things become the same. Still neither is to demonstrate any thing from all things to investigate whether there are the same principles of all, since this would be very silly. For neither does this happen in evident disciplines, nor is it possible in analysis,3 since immediate propositions are principles, and another conclusion arises, when an immediate proposition is assumed. If however any one should say that the first immediate propositions are the same principles, there is one in each genus, but if it is neither possible that any thing can be demonstrated as it ought to be from all (principles), nor that they should be so different, as that there should be different ones of each science, it remains that the principles of all are the same in genus, but that from different principles different sciences (are demonstrated). Now this is evidently impossible, for it has been shown that the principles are different in genus of those things which are generically different, for principles are two-fold, viz. from which and about which, those indeed from which are common,4 but those about which are peculiar, for instance, number and magnitude.

Note del traduttore
  1. 1 i. e. the propositions of the prosyllogisms, if the former are to be proved by the latter.
  2. piece of glass.
  3. pieces.
  4. Example (1.)
  5. 2 That is, if principles are to be accommodated to another science, we must so arrange the terms as that the demonstrations may be formed either in the 1st figure, wherein the middle term holds the middle place; or in the 2nd figure, where it occupies the first place, and is above both the extremes; or in the 3rd figure, where it holds the last place under each extreme. Moreover, some must be formed in the first, but others in the second or third figure.
  6. 3 If any one were to analyze the different sciences into their principles, he would not be able to analyze them into the same, but into different principles.
  7. 4 As axioms, see ch. 10 ; also table of the principles of science. Cf. Sanderson's Logic, b. iii. ch. 11 ; Mill's Logic, vol. i. p. 197 ; Metap. v. and vi.

San Tommaso: Libro I, lezione XLIII

Libro I, capitolo 33 Upon the Difference between Science and Opinion.∥.88b30–89b9

Inglese

The object of scientific knowledge and science (itself) differs from the object of opinion, and from opinion, because science is universal, and subsists through things necessary, and what is necessary cannot subsist otherwise than it does: some things however are true, and subsist, yet may possibly subsist otherwise. It is evident then that science is not conversant with these, (for else things which are capable of subsisting otherwise, could not possibly subsist otherwise). Yet neither is intellect conversant with such, (for I call intellect the principle of science,1) nor indemonstrable science, and this is the notion2 of an immediate proposition. But intellect, science, and opinion, and what is asserted through these, are true, wherefore it remains that opinion is conversant with the true or false, which yet may have a various subsistence, but this is the notion of an immediate and not necessary proposition. This also agrees with what appears, for both opinion is unstable, and its nature is of this kind,3 besides, no one thinks that he opines, but that he knows, when he thinks it impossible for a thing to subsist otherwise than it does, but when he thinks that it is indeed thus, yet that nothing hinders4 it being otherwise, then he thinks that he opines; opinion as it were being conversant with a thing of this kind, but science with what is necessary.

How then is it possible5 to opine and know the same thing, and why will opinion not be science, if a person admits that every thing which he knows he may opine? for both he who knows and he who opines will follow through media till they come to things immediate, so that if the former knows, he also who opines knows. For as it is possible to opine that a thing is, so likewise why it is, and this is the medium. Or6 if he so conceives things which cannot subsist otherwise, as if he had the definitions through which the demonstrations are framed, he will not opine, but know; but if that they are true, yet that these are not present with them essentially, and according to form, he will opine and not know truly both the that and the why, if indeed he should opine through things immediate; but if not through the immediate, he will only opine that they are. Still opinion and science are not altogether conversant with the same thing, but as both the true and the false opinion are in a manner about the same thing, thus also science and opinion are conversant with the same.7 For as some say that true and false opinion are of the same; absurd consequences follow both in other respects, and also that he who opines falsely does not opine.8* Now since the same thing is stated in several ways, in one way there may be, and in another there cannot be (a true and false opinion of the same). For to opine truly that the diameter of a square is commensurate with its side, is absurd, but because the diameter about which there are (contrary) opinions is the same thing, thus also they are of the same thing, but the essence of each according to the definition is not the same.9 In like manner also knowledge and opinion are conversant with the same thing, for the former is so conversant with animal as that it is impossible animal should not exist, but the latter so as that it may possibly not exist, as if the one should be conversant with that which is man essentially, but the other with man indeed, yet not with what is man essentially; for it is the same thing, that is, man, but not the same as to the manner.

From these then it is clearly impossible to opine and know the same thing at the same time, for otherwise at one and the same time a man might have a notion that the same thing could and could not subsist otherwise, which is impossible. In different (men) indeed each (of these) may be possible about the same thing, as we have said,10 but in the same (man) it is impossible even thus, since he would have a notion at the same time, for instance, that man is essentially animal, (for this it is to be impossible not to be an animal,) and is not essentially an animal, for this it is to be possible not to be an animal.

For the rest, how it is necessary to distinguish between discourse and intellect, and science and art, and prudence and wisdom, belongs rather partly to the physical, and partly to the ethical theory.11

Note del traduttore
  1. 1 Because of our cognizance of axioms by it
  2. 2 i. e. Mathe- matics.
  3. 3 In fact, as Aldrich observes, “ei (opinioni) nulla competit certitudo sed in ipsa sui ratione includit formidinem oppositi: sunt opinioni tamen gradus quidam ad certitudinem.” For the most admirable example of all the vacillation of opinion from surmise to certainty, and of the desire for that full knowledge and assurance which after all will crush the heart, “the doom it dreads, yet dwells upon,” see Shakspeare’s Othello, passim, but especially act iii. scene 3: “OTH. By the world, I think my wife be honest; and think she is not; I think that thou art just; and think thou art not; I’ll have some proof.” See also Butler’s Analogy, Introduction on Probable Evidence. Cf. Top. i. 1; Aldrich, Whately, Sanderson’s and Hill’s Logic, in verb.
  4. 4 So Waitz, κωλυεῖν. Taylor and Buhle, κωλυεῖ.
  5. 5 Taylor and Buhle insert οὐκ—“non licet,” “it is not possible.” Waitz and Bekker omit it.
  6. 6 Supply, “shall we say.” Taylor. Waitz omits, but Bekker retains the question.
  7. 7 Science is however distinguished from opinion, by the certainty of its subject: error also consists with certainty of the subject, but opinion cannot consist with it. Vide Mansel's note, p. 102; Sanderson's definitions. Cf. also Anal. Post. i. 6. The whole subject is well discussed by Hill (Logic, p. 275, et seq.), and upon the distinction of the dialectic and demonstrative syllogism, as enunciative of opinion and science, the reader will find some valuable remarks in Mansel, and Crakanthorpe's Logic. Cf. Top. i. 1.
  8. 8 He here glances at the opinion entertained by Protagoras and the sophists, who asserted that truth and falsehood were only in opinion, and that if every opinion is true, false opinion is not opinion.
  9. 9 From the thing being considered in two ways, there are two essences of the thing, and the diameter is assumed in true opinion in one way, and in false opinion in another. Taylor.
  10. 10 Vide Aldrich in verb. “ opinio.” Top. i. 1.
  11. 11 Cf. Biese, vol. i. p. 89, 327 ; Hamilton’s Reid, p. 768. Διάνοια is the progress of the intuitive intellect (νος) in investigating truth, and is perhaps best rendered here “discourse,” though the latter applies both to it and to λογισμος. Upon these terms, cf. Mansel’s note, pp. 4—6, and upon the powers or energies themselves, see Ethics, b. vi., Bohn’s edition, and De Animâ.

San Tommaso: Libro I, lezione XLIV

Libro I, capitolo 34 Of Sagacity.†.89b10–20

Inglese

Sagacity is a certain happy extempore conjecture of the middle term, as if a man perceiving that the moon always has that part lustrous which is towards the sun, should straightway understand why this occurs, viz. because it is illuminated by the sun, or seeing a man talking to a rich person, should know that it is in order to borrow money of him, or that persons are friends, because they are enemies of the same man; for he who perceives the extremes1 knows all the middle causes. Let to be lustrous in the part toward the sun be A, to be illuminated by the sun B, the moon C. Wherefore B to be illuminated by the sun is present with the moon C, but A to be lustrous in the part turned towards that by which it is illuminated is present with B, hence also A is present with C through B.

Note del traduttore
  1. 1 i. e. conclusions.

Citato nell'enciclopedia: SILLOGISMO

Il latino letto da san Tommaso: translatio antiqua: James of Venice, revised by William of Moerbeke, as printed with his commentary in the Leonine edition, t. I (Rome 1882) (archive.org, University of Toronto scan). Public domain (1882). Our transcription of the scan.
Inglese (Owen, 1853): Octavius Freire Owen, London: George Bell & Sons, 1889 (Bohn's Classical Library), vol. I, from the plates of the first edition (London: H. G. Bohn, 1853), same pagination (archive.org). Public domain. Our transcription of the scan.

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