Treatise V. On the comparison of demonstration to demonstration. Chapter I.

TREATISE V. On the comparison of demonstration to demonstration. CHAPTER I. On the intention of the treatise concerning the comparison of particular demonstration to universal demonstration. When the principles of demonstration taken absolutely have been determined in what has gone before, since after demonstration in itself and taken absolutely the parts of demonstration and the comparisons of the parts must be considered, and since concerning the parts into which demonstration is divided it has already been determined in what has been set forth before together with demonstration itself, namely universal and particular, affirmative and negative, ostensive and to the impossible, it follows here to treat of the comparison of the parts to one another. But first the comparison of the particular and the universal, and of the affirmative and the negative, must be touched on, because these are differences of demonstration on the part of the principles of demonstration, which are propositions, rather than the ostensive and the demonstration to the impossible, which are differences of demonstration on the part of the demonstrative syllogism. Moreover, since universal and particular are differences of demonstration on the part of the subject of the proposition, but affirmative and negative are differences taken from the part of the predicate or of composition, it is manifest that the comparison of particular demonstration to universal is reasonably placed first. <marginal-label>How the preferable, the worthier, and the more certain differ in the demonstration of the universal and the particular.</marginal-label> Therefore let us say that, since one demonstration is particular and another universal according to the division of the subject of the demonstration, and again since this one is categorical or predicative, that is, affirmative, but that other one is privative, that is, negative, according to the diversity of the quality of composition, it is doubted, or can be doubted by some, which is preferable if any is compared with the demonstration that divides opposite to it. But we call something preferable either in dignity, or in goodness, or in certainty, so that goodness is referred to a power compared to a better act, because those things are better whose power, that is, whose ultimate capacity, is for a better act. But dignity is referred to the goodness of that same act, as that which better reaches the end which is that act or operation. Certainty, however, is referred to us or to the thing which by inferring gives greater certainty. For the power of a human being, which is to reason, is better than the power of a donkey, which is for the substantial operation of a donkey; and a house is worthier when it protects more from rains, and a demonstrative syllogism is more certain than a dialectical one, because it gives greater certainty. Therefore according to these three things we will make the comparison of the species and parts of demonstration. Similarly, however, we will make a comparison concerning that demonstration which is said to demonstrate ostensively, because that demonstration truly demonstrates which shows, and concerning demonstration leading to the impossible. Therefore first let us direct our intention concerning the universal and the particular, which of them is preferable in goodness, dignity, and certainty. <marginal-label>What is to be understood by universal and particular demonstration.</marginal-label> Therefore, by plausible reasons of some, perhaps it seems to some persons intending thus through such reasons that particular demonstration is worthier than universal demonstration. But it must be noted beforehand that we do not call particular and universal demonstrations those which are determined by a particular sign or a universal sign in order that they be particular or universal demonstrations. Rather, we call particular the one which universally concerns a thing considered in its proper nature, as when we say, every isosceles has three angles equal to two right angles. But we call universal that which considers a property related to a subject which is a universal considered according to itself, as when we say that a triangle has three angles equal to two right angles. Therefore, comparing the universal to the particular in this way, certain people bring forward three plausible reasons from which they try to prove that particular demonstration is preferable to universal demonstration. <marginal-label>The first reason, that particular demonstration is preferable to universal.</marginal-label> Of these the first is this: they suppose that that demonstration is preferable according to which we know most of all, because the first effect of demonstration is to make one know, and this is the ultimate power of demonstration. But we know each thing more when we know it in its proper nature according to itself, that is, according as it is in itself in its own proper nature, than when we know it according to something that is not its proper nature, but is common, in which it itself exists only in potency. For the sake of example, let us say that we know musical Coriscus under the accident by which Coriscus is and under his nature more, and more distinctly and more determinately, than when we know him under this common thing, that he is a musical human being. And it is similar in other things which can also be known in their proper nature and not in a common nature. Having supposed this, they assume that universal demonstration, that is, demonstration showing a property concerning the universal according to itself, demonstrates a certain other thing and does not demonstrate that the property itself happens in the proper nature. For it does indeed demonstrate that this property, to have three angles equal to two right angles, belongs to equal-sided three-sided figures, because otherwise there would not be demonstration of every instance; and it does not demonstrate that this property belongs to equal-sided three-sided figures according as they are equal-sided, but that it belongs to equal-sided figures according as equal-sided figures are some other thing that is common, and this is triangle, in which equal-sided figures agree univocally as in a universal with other three-sided figures. But the particular demonstration demonstrates the property of a particular subject, since the subject itself is taken in its proper nature. Therefore, if, as those so intending say, that demonstration is preferable which demonstrates concerning the thing according to itself, that is, the proper nature of the thing according as it is of this kind, it seems that particular demonstration is more a demonstration and is certainly preferable, because it is according to the part, that is, according to the proper nature, than universal demonstration. Therefore this is the first reason. <marginal-label>Second reason for the same.</marginal-label> Moreover, the second reason. If the universal is not something besides singulars having actual being in them, but universal demonstration demonstrates concerning the universal not according as it is in singulars but according as it is in itself, by this very thing, namely that what has thus been demonstrated about it, it makes the opinion that it is something other in itself on account of the singulars according as they demonstrate about it, and not as it itself is in the singulars; and thus such a demonstration produces the opinion that there is some nature separated in the number of things that are, which is in actual being besides the singulars. Thus, for the sake of example, let us say that it produces the opinion that there is some nature of triangle which is separate besides certain particular triangles, and it produces the opinion that there is some common nature of figure which is besides some particular figures; and thus it produces the opinion that there is some nature of number which is besides certain numbers, that is, besides particular numbers. And this indeed is not so, because such a nature does not exist. Therefore the universal seems to be about that which is not, but the particular about that which is and truly is in nature. But demonstration that is about being and about that which is is preferable to that which is about non-being or about that which is not. For the universal is not apart from the many things in which it is. Therefore particular demonstration seems to be preferable to universal demonstration. Therefore this is the second reason. <marginal-label>Third reason.</marginal-label> But the third reason is that the demonstration on account of which one will not err concerning that of which demonstration is made, that is, on account of which one will not doubt concerning that of which demonstration is made, is preferable to that on account of which one will err and doubt concerning that of which demonstration is made. But universal demonstration, according as it is most universal, is of this sort, one which causes one to err and to doubt concerning that of which demonstration is made. The proof of this is that demonstrators proceeding to a more universal thing, which is analogous or common to many according to analogy, such as the proportional, which is interchangeably in number, time, line, solid, and plane, demonstrate about it according as it is something in itself besides these. Hence it is neither in line according as line, nor in number according as number, nor is it solid according as solid, nor plane according as plane, but according as it is something besides these. Therefore, if this demonstration is more universal among demonstrations, and is about that which is less than the particular, and thus makes the false opinion that this, namely what is less, is more than that which is more, then universal demonstration will certainly be less worthy than particular. For that which is truly singular in nature, and that which is nearer to it, is more than that which is more remote from it; and therefore the thing taken in its proper nature, which is nearer to the singular, seems more to be, and that which is considered in the most universal thing seems less to be, because it is more remote from the singular. Therefore these are the reasons by which some try to prove that particular demonstration is preferable to universal. <marginal-label>Reply to the first reason.</marginal-label> But before we set down the reasons to the opposite, replying to these we say that, if it is so as those people say, then the first thing that they bring forward for the first reason is not more a reason proving that universal demonstration is preferable than it is in particular demonstration, because it has more force for the opposite of their intention than it has for the proposal of their intention. For if this property, to have three angles equal to two right angles, does indeed belong, but does not belong to triangle according as it is a triangle of equal-sided figures, but belongs to it according as triangle is the proper nature according to which the property is present, then the property is universal and not particular. Therefore the one knowing this property to belong to the equal-sided insofar as it is equal-sided has known less according to the proper nature according to which the property is present than one knowing that such a property belongs to it according as it is a triangle, because in the particular demonstration the knower has not known according to the thing itself, but in the universal demonstration the knower has known according to the thing itself. But one knowing according to the thing itself has known more than one knowing not according to the thing itself. And altogether, that is, universally, if the stated property has not been demonstrated of triangle according to itself according as it is triangle, and afterward it is demonstrated of inferiors, it will certainly not be demonstration, because it falls short of the principle of demonstration, which is according to itself. But if he has known each thing according as the thing itself is, as they say and confess, he has known more. Therefore, if triangle, which is more extensive, that is, more common than equal-sided, and whose account is the same in all particular or special triangles, and this name triangle is not common according to equivocation by which triangle is predicated of many things considered in their proper nature, and if the property which is to have three angles equal to two right angles belongs to every triangle, then it surely follows that triangle, according as it belongs to equal-sided figures, does not have three angles equal to two right angles, but rather conversely the equal-sided has angles of this kind, namely three equal to two right angles, not according as it is equal-sided, but according as it is a triangle. For this reason, the one knowing universally in this way through universal demonstration knows more, and by a preferable demonstration, according as the thing is according to itself and as itself, than he does according to particular demonstration. Therefore what they said was false, that one knowing in the particular always knows more truly than one knowing in the universal. The universal is certainly preferable to the particular even by its own reason, which the caviller introduces. <marginal-label>Objection.</marginal-label> But what has been said in this solution seems contrary to what is determined in the second book of the Prior Analytics, namely that cognition in proper nature is preferable to science in the universal, and each is preferable to that which is in action. <marginal-label>Solution.</marginal-label> But one must know that there is cognition of a thing in itself, and this is not demonstrative, and by this cognition the thing is known better in its proper nature than in the universal. And there is cognition of the thing according to the power by which its natural and convertible properties flow from it; and thus the thing is known most powerfully when it is known according to that by which, in it, there is the principle of those properties. And these people, who by the stated reason preferred particular demonstration to universal demonstration, were ignorant of this distinction. And in this way Aristotle says in the first book On the Soul that cognition of accidents is most useful for knowing what a thing is. Therefore this is the solution of the first reason. Moreover, the solution of the second reason is that the universal is a certain one account, not an equivocal account, of that which is in several according to one and the same account. For that account will be of some nature or formal substance, as Aristotle says in the Predicaments, that in univocals the account of substance is the same; and this could not be, unless the very thing whose account it is were one. But it is one through one undivided relation to many; and the many are one in it through one and undifferentiated relation of many things to that nature or substance. For neither the equivocal nor the analogical has this unity. But if such a being is said to be had in singulars, without doubt the universal will be nothing less and will have being in singulars, that is, than singulars; and thus it will not be less than certain things, that is, than particulars existing according to a part, that is, particularly. Rather, universals will even be more and will have being more than singulars, insofar as universals are incorruptible, and the being of universals, as universals, is incorruptible in comparison with those things which are singular, whose being is corruptible. But you should know that the unity of the universal is the unity of the account of that which is in many ¹, and that the cause of that unity is neither the first intelligence nor any one of the second intelligences, as some say, but its cause is the undifferentiated relation to many, which has been stated, and the undifferentiated relation of many things, namely of supposits, to it; and the cause of its incorruptibility is that, taken as universal, it is removed in potency from matter and accidents. For according to the being that it has in them it is corruptible and variable, and according to this being it is not universal. But concerning this we have said more at the beginning of the book On Universals; however, in first philosophy these matters must be determined with study. It must also be known that Aristotle calls certain singulars corruptible, and not all, on account of the sun and the moon and things of this kind which are incorruptible, because they are from their whole matter, and none of them has in itself a universal which is actually predicated of many or is in many. And he does not say this on account of the intelligences, as some say. But concerning these things attention must be given in first philosophy, in the tenth book, because from the principles of that science these things cannot be determined. But here it must be noted that, unless universals were incorruptible in this way in which it has been said, there would not be one account of past, present, and future human beings, because there would not be one substance and nature; nor because of this is it necessary that the being-human be singularly a subject when being-human is spoken of. <marginal-label>That universals are incorruptible.</marginal-label> Moreover, the solution of the third reason is that there is not even one, that is, no necessity that someone should think this universal to be something actually distinct in actual being in nature apart from these singulars, in which it is and of which, as Boethius says, there is a substantial likeness, because demonstrations show it to be one, to which a property belongs according to itself. For it is not, on account of this, one thing separated from others according to being; and nothing on account of this is more one thing separated from others according to actual being, as in the other predicaments of accidents, whatever they are, which do not signify this something as substance does, but signify either quality, or quantity, or relation, or action. For concerning them many things are proved which do not belong to them according to the being that they have in a subject, and nevertheless on account of this they are not understood to have being separated from the subject. Therefore similarly the universal is not, on account of this, understood to be separated according to being from the singular because certain things are demonstrated to belong to it which do not belong to it according to the being that it has in singulars; and that it should thus be understood to have actual being apart from singulars is not caused by demonstration as the cause of that error, but by the one who hears the demonstration badly and does not understand what it concludes, and about what, and in what way. From all these things, therefore, it is clear that particular demonstration is not preferable on account of the stated reasons.