Treatise II. Chapter I-Chapter II.

TREATISE II. On the cognition of the demonstrative middle and of what things there is definition. CHAPTER I. On the middle according as it is what. But after it has been determined concerning knowable things through demonstration, through the number and reduction of questions, it follows to treat of the middle of demonstration, as it is to be known and also found, because it cannot be found unless in some way it is known. Therefore first we will speak about the cognition of the middle. And since the middle is what it is and on account of what it is, and what it is is simpler than on account of what, therefore first we will make known the middle according as it is what it is. Therefore intending about this, we set forth four questions, the setting forth of which is necessary for cognition of that which is what it is. Therefore by the first question we ask how that which is what it is is demonstrated, that is, whether it is known by demonstration or not. The second question by which we ask is what the mode of introducing knowledge into cognition of definition is, or of definition into knowledge. But the third question is what definition is. But the fourth is of what things there is definition. Treating these things, we will proceed by opposing and disputing first about these. But in such a process let the beginning, from which we begin, be that which is more proper to the things had, that is, to the things to be said consequently, because what is had is the same as what is consequent; from that one begins more suitably, and according to this one must begin from disputation. For someone will doubt or will be able to doubt whether the same thing and according to the same thing is known by definition and known by demonstration, or whether this is impossible, that the same thing and according to the same thing be known by definition and demonstration. Through this is known what is finally asked, namely of what things there is definition and of what things demonstration. The first reason indeed is that definition seems to know and declare that which is what it is. But a definition saying what it is to be such is universal concerning the defined thing and is predicated essentially. But of syllogisms concluding their conclusions in demonstration, some indeed are privative, but others are not universal, just as in the second figure all syllogisms are privative, but in the third they are non-universal. Then from this I argue: every definition is universal and affirmative concerning the defined thing; sometimes demonstration is neither universal nor predicative; therefore some demonstration is not about those things about which there is definition. And from that reason no more can be inferred than what has been said. Afterward, for the same point, the second reason: because not of all those things which are concluded or demonstrated in the first figure universally and affirmatively is there definition. For that every triangle has three angles equal to two right angles is demonstrated in the first figure; and this is not defined. The reason for this is that to know demonstratively is to have demonstration and to receive science through demonstration. For this reason, if in such matters there is demonstration in which a property is demonstrated of a subject, then it is manifest that there will not be a definition of them saying what they are, because definition does not gather accidents but only substance. For this reason it is said in the first book On the Soul ¹ that cognition of accidents indeed contributes to knowing what a thing is, but they do not enter into definition, nor are they definition. For someone certainly knows something as a subject according to definition through substantial things, while not having demonstration about the same thing, because he does not know per se accidents. For nothing prevents one from not having definition and demonstration at once, or through the same things. And to prove this, the faith made through the reason brought in suffices; and it suffices that it be proved from induction, because in singular cases it is thus, that true definition gathers none of the demonstrable things, which are per se accidents. For we who truly define something do not ever, that is, never, know anything from the number of those accidents which are per se; and expounding this, we say that we do not know any of those things which are per accidens by gathering the definition. Therefore there is not definition of all those things of which there is demonstration. Further, for the same point, the third reason is that if definition is a certain cognition of the substance and quiddity of the defined thing, because definition makes substance and quiddity known. But what is of this kind, such as demonstration is, is manifestly not of substance, and it does not make substance known, but a property concerning a subject. Through this reason it is concluded that definition is not demonstration, and that demonstration is not of the same thing of which definition is. Therefore by epilogizing we say that, since therefore there is not definition of everything of which there is demonstration, this is manifest from what has been said. Therefore let us ask conversely, saying whether, either from this that there is demonstration of something, there is not definition of it, and speaking properly, whether everything of which there is definition has demonstration, or not. One and similar reason concerning this too is the same as the preceding, because that to which we will dispute is the converse of the previously held conclusion, namely this, whether everything of which there is demonstration has definition; and its converse is whether everything of which there is definition has demonstration, or not. And the first reason indeed for this, that there is demonstration of none of those things of which there is definition, is this, which leads to the impossible. Of one thing insofar as it is one, there is one science and one mode of knowing. For this reason, if it is supposed that truly knowing is possible concerning that which is demonstrable or demonstrated, as was proved at the beginning of the first book, then a certain impossibility occurs, namely this, that one having definition will know without demonstration through definition alone, and thus he will have true science without the cause of true science. Therefore there is not demonstration of those things of which there is definition. Further, the second reason for the same point is that among the principles of demonstrations and the principal principles there are definitions which are middles, which principally are principles; but it has been demonstrated before in the first book of this science that there are not demonstrations of principles, because if it were said that there were demonstrations of principles, since those demonstrations would be from principles and those again from other principles, there would be other demonstrative principles, and again principles of those principles, and this will go on to infinity; or one must say that the first definitions of first things will be indemonstrable. And this is true; and from this indeed it is concluded that there is not demonstration of that of which there is definition. But when it has been shown that not everything of which there is definition has demonstration, there still remains to be asked, if it is granted that there is not demonstration of everything of the same thing of which there is definition, whether of some same thing there is definition and demonstration, or whether of no same thing there is definition and demonstration. Therefore for this reasons must be brought in, that of no same thing are there demonstration and definition. For concerning this, that it is impossible that of what there is definition there should be demonstration, the first reason is this: because every definition is what it is, that is, significative of quiddity; for the quiddity of the thing exists, and the definition is significative of that quiddity. And on account of this definition and quiddity differ as sign and signified. Therefore definition indeed is of the very what it is, and is indicative of substance and through substantial things; but all demonstrations seem to suppose their definitions, that is, the definitions of their subjects, and not to demonstrate them. And similarly mathematical sciences suppose definitions of their subjects, as what unity is, and definitions of their properties, as what odd is; and other demonstrative sciences similarly do this and do not demonstrate their definitions. Therefore it seems that there is demonstration of none of those things of which there is definition in any demonstrative science. <marginal-label>Definition and quiddity differ as sign and signified.</marginal-label> Further, another reason for the same point is that every demonstration demonstrates something, that is, some property, about some subject, just as it is also demonstrated that this is affirmatively, or that this is not negatively. But in a definition, concerning all things that are placed in the definition, nothing is predicated of another through the mode of affirmation or negation, but they are gathered in it as powers are referred to the ultimate act. But this is clear through induction, because when in defining it is said, a human being is a two-footed animal, neither is animal predicated affirmatively of two-footed, nor conversely two-footed of animal. And in mathematical matters, when it is said that triangle is a plane figure contained by three straight lines, figure is not predicated of plane, for plane is not a figure; nor is plane predicated of figure, because it is not said affirmatively that plane is figure. Therefore there is demonstration of none of those things of which there is definition. Further, for the same point there is a third reason. It belongs to one thing to demonstrate, or show and display, what it is, and to another to demonstrate that it is. But definition shows by signifying what it is, while demonstration shows by demonstrating that it is, that is, the predicate about this subject affirmatively, or that this is not, that is, negatively. But what it is and that it is are diverse. And of one thing from another, or of the diverse from the diverse, there is another and diverse demonstration, that is, display and science, unless one is related to the other as a subjective part to it as to a universal whole. But I say this by explaining, because it has been shown in a certain way, as in its universal whole, that the isosceles has three angles equal to two right angles, if it has been shown that every triangle has three angles equal to two right angles. For a subjective part is this which is isosceles. But this which I call triangle is the universal whole to the isosceles. But these, which are science what and science that, are not related to one another, that is, one to the other, in such a way that one is the universal whole and the other is its subjective part. Therefore it follows that of that of which there is definition, in no way is there demonstration. Therefore by concluding further universally it is manifest that neither is there demonstration of every thing of which there is definition, nor is there definition of every thing of which there is demonstration. For this reason also the third conclusion follows universally: wherefore altogether, that is, universally, it happens to no same thing to have both, that is, definition and demonstration; and thus there is demonstration of nothing of which there is definition. Therefore, by concluding further, it is manifest that neither is definition demonstration. For these will not be the same, nor is either of these in the other as a subjective part in its universal whole. The reason for this is that, if definition were demonstration or a subjective part of it, then the defined substance would be related similarly, because if definition were demonstration, then the definable would be demonstrable, which was shown to be false. Therefore these things have been opposed up to here concerning these two questions, namely what definition is and of what things there is definition. CHAPTER II. Whether the syllogistic way is the way of coming into cognition of definition. But it remains to be asked what is the way into the introduction and cognition of definition; and first it must be asked whether there is syllogism or demonstration of that which is what it is, or of definition, that is, whether one comes into cognition of the definition itself in such a way that it is concluded through syllogism or demonstration, or not, just as in the preceding chapter the reason supposes, which proved that not everything of which there is definition has demonstration. For this reason supposes that the demonstrative syllogistical way is not the mode of coming into knowledge of definition. But that the syllogistic or demonstrative way is not to arrive into cognition of that which is what it is is proved thus. A syllogism indeed demonstrates something about something through a middle, but what it is or definition is proper and convertible and immediate, because between definition and the defined there is no middle by which definition is concluded of the defined. For definition is predicated in what it is, namely in such a way that definition is predicated of the defined with this reduplication in that which is what it is, through which reduplication the mode of definition is distinguished from other modes of substantial predicates. But what is predicated in this way must be converted and reduplicated to each extreme ². For let us posit general terms in which this may be manifested, which are A B C, so that B is the middle by which A is concluded of C, which is the minor extreme. Then A must be the definition, and B the middle between definition and the defined; and this cannot be unless B is another definition, through which the definition first taken is concluded of the defined. And then the major extreme is predicated of the middle in that which is what it is, as definition of the defined; and the middle B will be predicated of C the minor extreme in that which is what it is, as definition of the defined; and thus A will be proper to B, and B will be proper to C itself, and thus all three are convertible and proper to one another. And there will be such a syllogism: every B is A in that which is what it is, and every C is B in that which is what it is; therefore every C is A in that which is what it is. But truly also if A is in that which is what it is in all things which are B, and B is predicated universally of every C in that which is what it is in the minor proposition, then it follows that A too must necessarily be said or predicated of C in the conclusion in that which is what it is, as was clear in the syllogism brought in, in which the reduplication of the middle is placed both in the major proposition and in the minor; and thus it is necessary that it also be placed in the conclusion. For every B is A in that which is what it is, and every C is B in that which is what it is; therefore every C is A in that which is what it is. And in this the Arabic commentary considers it unsuitable if the middle is between definition and the defined, because then of that definition which is the middle there will again be as middle another definition, and this will go on to infinity; and these are the words of the Arabic commentary which Alfarabi made. Therefore if such reduplication of the middle is placed toward each of the extremes, there will be a conclusion with reduplication. But if someone does not in this way accept a middle doubling or reduplicating in each of the premises toward the major and minor extremes, then it will not be necessary in the conclusion for A to be predicated of C with reduplication in that which is what it is; nor then, moreover, is it necessary in the major proposition