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.
Chapter 25 Chapter 25 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 they 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. 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 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; both 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, 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. 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.
Chapter 26 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 possible 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 which 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 either 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.
Chapter 27 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 subject than that which is of a subject, for instance, metic 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, this is from addition.
Chapter 28 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; but a science is different from another, whose principles are neither from the same things, nor one from the other. A token of this is when any one arrives at things indemonstrable, for it is necessary 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.
Chapter 29 Chapter 29 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). 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, and not from the same class, yet not so that neither is predicated of neither medium, since it is necessary that both 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.
Chapter 30 Chapter 30 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.
Chapter 31 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. 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, 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.
Chapter 32 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, 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 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. 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, 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, but those about which are peculiar, for instance, number and magnitude.
Chapter 33 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,) nor indemonstrable science, and this is the notion 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, 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 hinders 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 possible 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. Or 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. 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. 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. 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, 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.
Chapter 34 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 extremes 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.