Questions on the Posterior Analytics: First Set

By Simon of Faversham.

Translated by John Longeway

Question 11

            Since the Philosopher says that demonstration is from what is first and true etc., we ask whether first axioms enter into demonstration.

            And it is argued that they do, since those things from which all knowledge is demonstrated enter into demonstration, but first principles are of this sort, as the Philosopher says later in this book; therefore etc.

            Again, the Commentator says on Metaphysics IV that every demonstrator resolves his demonstrations into the first principle, “concerning each thing, it is or it is not.” But each is composed from those into which it is resolved. Therefore all demonstrations are composed from these first principles. Therefore first axioms enter into demonstration.

            On the other hand, every demonstration must proceed from properties of the genus of the subject. But first axioms are not appropriate to anything, but arise in the most common terms. Therefore a demonstration cannot arise from first axioms.

            It must be replied that in demonstration there are three things, subject, passion, and axiom. The passion is demonstrated, and the subject is that of which it is demonstrated. The axiom, however, is the principle through which the passion is demonstrated of the subject. So when it is asked whether first axioms enter into demonstration, I hold that a principle’s entering into a demonstration can be understood in two ways, either according to its substance, or virtually. First axioms enter into no demonstration according to their substance--and I am speaking here of principles in the most general terms--since, as is said below, demonstration takes its rise from what is appropriate to the genus of the subject of the demonstration. And the reason for this is that the middle in demonstration is the definition of the subject, or the definition of the passion, or something put together from both, saying what it is of the subject and why it is of the passion. But definition must be appropriate to what is defined. From this it is argued that the middle term that enters into a demonstration must be an appropriate middle. But first axioms are not composed of anything that can be an appropriate middle, therefore they do not enter into any demonstration according to their substance. They do, however, enter into demonstration virtually, since the cause is virtually in its effect in every case, and because of this Proclus says that all things are in all things, effects in causes, and causes in effects. Now first axioms are causes of every later principle, and therefore are contained virtually in later principles; but later principles enter into demonstration according to their substance, and therefore the first enter into demonstration virtually.

            Again, this is obvious, since it must be held that there is one operation of the intellect by which it grasps simples concerning which there is neither true nor false, and another by which it grasps the composition and division of these [simple] principles, and in both operations it is necessary that something be known first, for otherwise there would be an infinite regress. Now that which is known first in the intellectual grasp of simples is being, and therefore that which must be first in the composing and dividing intellect should be what is formed by making a complex from being, for instance, “being is being,” “concerning each thing it either is or is not.” Therefore that is first in the genus of complex things. Now the first cognizable is the cause of the cognition of later things. If, therefore, this is first, as was shown, it will be the cause of the cognition of every other. If, then, later principles make known some conclusion, this does not occur except in virtue of this principle. Now that in virtue of which knowledge is had of every conclusion enters into demonstration virtually. But in virtue of this first principle, “concerning each thing it either is or is not,” cognition is had of every conclusion. Therefore this first principle enters into every demonstration virtually.

            The response to the arguments is apparent, since each takes the question in its own sense.

Question 12

            We ask concerning that part in which the Philosopher proves that demonstration is from what is true. But the Philosopher there, in order to prove that demonstration is from what is true, accepts this proposition, “what is not cannot be known.” Therefore it is asked whether one can know non-beings.

            And it is argued that one can, for one can know eclipses of the sun and moon, which are not. But this would not be unless one could know non-beings, and therefore one certainly can know non-beings.

            Again, we can certainly have knowledge of the infinite and the of the vacuum, as is obvious from the Philosopher in Physics III and IV, but the infinite and the vacuum are non-beings; therefore etc.

            Again, the Philosopher contends in De Interpretatione 1 that one can say that it is not of that which is not, and this truly. But every truth can be known, therefore we can know that it is not of that which is not, but we cannot know that it is not [non esse] of that which is not unless we know that it is not [non esse], since a complex cannot be known except through the cognition of its terms. Therefore one can know not-being [non esse].

            On the other hand, it is argued that “being” and “truth” are convertible, but one cannot know what is not true; therefore one cannot know a non-being.

            It must be said regarding this that one cannot know that which is not, and the reason for this, as is clear from Philosopher in De Anima III, is that the soul is in a certain way all things. For all things that are are either sensibles or intelligibles. The soul, through the senses, is all sensibles, and through the intellect it is all intelligibles, but all things that are are sensibles or intelligibles; therefore the soul is in a certain way all things. And he says “in a certain way” since it is not all things according to their nature and substance. For if it were all things according to their nature and substance, since its operation follows upon the substance, in understanding all things the soul would have all their operations, and in understanding a donkey it would have the operations of a donkey, and in understanding the good it would have the operations of the good, and so on. And therefore what is left is that the soul in a certain way is all things, since species and likenesses of all things are in the soul. And therefore the Philosopher says, further on in that place, that the stone is not in the soul, but a species of the stone, on this basis, therefore, the intellect is in a certain way all intelligibles, and it is not all intelligibles except through their species. Nothing will be intelligible to the intellect except what is suited to be in the soul through its species. Therefore what has no species in the soul cannot be understood by the intellect, but a non-being has no species; therefore etc. Nor, consequently, is it something knowable; therefore one cannot know what is not.

            Again, this is explained since according to Avicenna what is nothing in itself is nothing in another, for each thing is something in itself before it is in another, but a non-being is nothing in itself; therefore etc. But everything intelligible to the intellect is something in another, since it is what perfects and informs the soul. Therefore a non-being cannot be intelligible to the intellect.

            Again, this is explained in a third way, since, when something is a first object of some capacity, nothing is grasped by that capacity except insofar as it participates in the formula of that first object. For instance, since color is the first object of the visual capacity, nothing is grasped by vision except insofar as it is colored. Now being is the first object of the intellect. For this is the order of intellectual cognition of natures, that those that are more confused are bettern known in themselves, as is obvious from Physics I. But that which is the most confused of all things is being, since nothing is wider than being, according to Avicenna. Therefore being is the first object of the intellect, and therefore whatever is grasped by the intellect participates in the formula of being. But non-being does not participate in the formula of being, but removes it. Therefore etc. But just as each is known insofar as it is a being, so one is ignorant of each insofar as it is non-being, and therefore the Philosopher says in Physics I that the infinite as such is unknown, since the infinite as such is non-being. And therefore one cannot know what is not.

            But it must be understood that “being” is said in two ways, namely being of essence and being of actual existence. Being of essence is that being outside the soul that is said in the ten figures of the categories, and through that being one knows concerning each what it is. Now speaking of such being one cannot know what is not, since what is not, speaking of this sort of being, has no essence, and one cannot know what has no essence. Therefore, speaking about what is not the sort of being that is divided into the ten figures of the categories, one cannot know it, that is, one cannot know what it is. But one might well know what it is not. And I hold this because of the vacuum and the infinite, for such are non-beings, and so one cannot know of them what they are, since they have no quiddity. But one can know what they are not, and the Philosopher discusses them in this way. Speaking, then, of being of essence, one cannot know what is not in this way. But speaking of being in the second way, one can know something that is not, since one can know about rain and such. For even though they are not actual beings, it is still possible for them to be, and in this way they are in their causes and principles. Thus, when their causes and principles are assumed they are of necessity assumed. Nor does it follow that if such a thing is not actual, then it cannot be know what it is according to its essence. For Al Ghazalli says in his Logic that you can understand man without qualification without understanding man to be or not to be outside the soul, and if, perhaps, you are in doubt whether man has being anywhere in the world or not, this does not prevent your intellect’s understanding the essence of man. It is apparent from this that being of essence differs from being of existence. The Philosopher says the same thing in Posterior Analytics II, though it is more obviously apparent in another translation [than that by James?], for he says the discovery of the definition of a reality and that it exists, are two realities, and not one, since whoever cognizes what a reality is and its definition does not thereby grasp that the reality exists. And afterwards it is obvious that they differ in this way, because one certainly can have knowledge in respect of being of essence about that which is not actual in this way, but one cannot know about that which is not in respect of being of essence, so that it is not in its causes and principles.

            In response to the arguments, in response to the first, I grant that one can know eclipses of the sun and moon which nevertheless are not as regards actual being, but they are possible things in their causes and principles, and thus there is knowledge of them.

            In response to the second, I maintain that we cannot have knowledge of the infinite and the vacuum by which we know what these are, but only that in which we know what they are not. So there is no knowledge of these through assertion, but only knowledge through denial.

            In response to the third, this must be understood as Avicenna says: statements have being through what is in respect of the soul, and therefore everything that is stated about another, or about which another is stated, must immediately be in respect of the soul. And therefore when non-being is stated of a non-being, that non-being is in a certain way a being, namely in respect of the soul. But one cannot know what is not either in actual existence or the being of essence, or in respect of the soul. But if something is not as regards actual existence while it is a being in respect of the soul, that one can in some way know.

Question 13

            We inquire concerning that part in which the Philosopher proves that demonstration is from what is prior and better known, and we ask whether demonstration is from what is prior and better known.

            And it is argued that it is not, for if demonstration were from what is prior and better known, since demonstration produces knowing, then knowing would be from what is prior and better known. And since it is possible to know those things that are prior and better known, therefore they are know from what is prior and better known, and since one can know those prior things, therefore they are known from what is prior and better known, and one can know them, therefore from what is prior and better known; and so, given that demonstration is from what is prior and better known, it will proceed to infinity in knowables. But this is absurd, therefore etc.

            Again, demonstration that it is so is demonstration, and yet it is not from what is prior and better known, but from what is posterior, for it demonstrates the cause through the effect; therefore it is not true in every case that demonstration is from what is prior and better known.

            On the other hand, it is argued that demonstration is either from what is better known, or from what is equally known, or from what is less known. It cannot be said that it is from what is equally known or from what is less known, since then the demonstration would beg the question. To beg the question is to demonstrate something through what is less known or equally known. But in demonstration we do not beg the question. Therefore it will be from what is better known.

            It must be held that demonstration is from what is prior and better known. This is explained from the fact that demonstration without qualification produces knowing without qualification. But it is not possible to know without qualification except through what is first and indemonstrable, since it is not possible to know through what is demonstrable except from supposition, that is, unless is be supposed that those demonstrables are known and demonstrated through other, prior propositions. Therefore it is necessary, given that demonstration without qualification produce knowledge without qualification, that it be from what is first and indemonstrable. But what is first and indemonstrable is prior to everything that is demonstrated, since what is first and indemonstrable is cognized immediately through itself, and what is demonstrated is cognized through others. Therefore what is first and indemonstrable is prior to and better known than whatever is demonstrated. But a demonstration without qualification proceeds from what is first and indemonstrable; therefore demonstration without qualification is from what is prior and better known without qualification.

            Again, it is explained thus: demonstration without qualification produces knowing without qualification. But knowing without qualification does not occur except through the cause. Therefore demonstration that makes one know without qualification proceeds from causes. But every cause is prior to and better known than what it causes. Therefore every demonstration proceeds from what is prior and better known than that which is demonstrated. But it is necessary that what is prior and better known, from which the demonstration proceeds, be prior to and better known than the conclusion without qualification. And the reason for this is that according to nature that is prior to and better known than other things which is cognized in itself, and is the cause of cognition of all the others. Now the principles of demonstration are cognized in themselves. For just as we see, according to what Albert says, that regarding those external things that are seen, some are visible in their own light, others only by another’s light, so we see on the part of the intellect that some are seen, that is, are understood, by their own light, and such are principles of demonstration, and some by another’s light, and such are the conclusions that follow from these. The principles, therefore, are causes of the cognition of the others, and consequently demonstration proceeds from what is prior and better known. And from this it is apparent that demonstration that proceeds from what is prior and better known only insofar as we are concerned is not demonstration without qualification, but such are natural demonstrations, which, for the most part, proceed from to causes from their effects, which, although they are better known as far as we are concerned, are not better known without qualification. And therefore they are not demonstrations without qualification. But where the same things are better known without qualification, and better known as far as we are concerned, and according to nature, there are the most powerful demonstrations, and such are mathematical demonstrations. For these are the best proportioned to our intellect, since, as our intellect is in a certain way joined, and in a certain way separate, so also are mathematical objects. For just as our intellect is joined to matter in itself, so also mathematical objects, and just as it is separated according to reason or capacity, so also mathematical objects. And because of this the most powerful demonstrations occur in mathematics. And noting this, the Commentator, remarking on Metaphysics II, says that mathematical demonstrations are of the first degree of certitude, and natural demonstrations follow these.

            In response to the arguments, in response to the first, when it is argued, “if demonstration were from what is prior and better known” etc., I grant this. And when it is said next, “and when those prior and better known” etc., I hold that it is not necessary to cognize those prior and better known things from the conclusions are known in this way, for this way of knowing is proper to conclusions, and those prior and better known things are not known in this way, but through themselves, or through by reason of their terms.

            As for the other, the reply is obvious, since when it is said that demonstration proceeds from what is prior and better known, we understand this of demonstration without qualification, demonstration why it is so, and not of demonstration that it is so, which your objection is concerned with.

Question 14

            We inquire concerning the part, “but prior and better known things.” The Philosopher there, assuming a difference between what is prior and better known as far as we are concerned and what is prior and better known by nature, says that universals are better known by nature, but singulars are better known to us. Therefore it is asked whether the universal is prior by nature, or the singular.

            And it is argued that a singular is, in this way: that is prior to another by nature which is such that when it does not exist the other does not exist, but when it does exist it is not necessary that the other exist. Now when the singular does not exist the universal does not exist, since, as is said in the Categories