Questions on the Posterior Analytics: First Set
By Simon of Faversham.
Translated by John Longeway
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.
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.
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.
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 , when first things are destroyed it is impossible for anything else to remain. And when the singular exists the universal does not necessarily exist, since, as is obvious from Themistius on De Anima I, the universal is not unless a certain concept of the reality is understood from the similarity of many singulars. Now when the singular exists it is not necessary that such a concept remain in the soul. Therefore when the singular exists it is not necessary that the universal exist. Therefore etc.
Again, what proceeds from another is posterior to it by nature, for everything produced is posterior by nature to what produces it. But a universal is produced from singulars, for every community proceeds from singularity according to the author the Six Principles, therefore the singular is prior by nature to the universal.
On the other hand, it is argued that the incorruptible is prior according to nature to the corruptible, but the universal is incorruptible, the singular corruptible; therefore etc.
It must be understood here that “universal” can be taken in three ways, since it is either a universal in the reality, or in the intellect, or a separated universal. A universal in the reality can be taken in two ways. In one way an essence and nature considered absolutely and according to itself can be called a universal in the reality, of which, as well as being cognized or signified, is an accident, and this universal is called a potential universal. In another way, this same nature considered as existing in particulars, as having being confused and mixed with these particulars, can be called a universal in the reality. And speaking of this mixture the Commentator on Metaphysics II says that universals are well mixed with particulars, for they inhere in particulars more strongly than accidents in subjects, more strongly, indeed, since they indicate the essences of singulars, but accidents do not. But that same nature as it is understood in act, abstracted in act from particulars, predicable of these by the action of the composing and dividing intellect, is called a universal in the intellect. And this universal is called a universal in act. In the third way, a separated universal is called universal, and this is the universal which Plato assumed, the separated idea that he assumed to the cause of the being and cognition of singulars.
Speaking of the universal according to its essence and nature considered absolutely, to which actual being and being understood belong, I hold that in this way the universal is prior to and better known than the singular. And the reason for this is because the Philosopher accepts here that one cannot know what is not, and that one can know nothing unless it is true—the Philosopher accepts these propositions here —if this is so, then that is prior and better known by nature which is more true and more a being. Now a universal taken as it names an essence and nature absolutely so considered, is more true and more a being than a singular, so it is more true since it is more intelligible, for the true is an object of the intellect. It is more a being since there is no coming to be or destruction of the nature of a thing considered in this way, as the Philosopher proves in Metaphysics VII, but a singular comes to be and is destroyed. Therefore a universal is more true and more a being than a singular, and that which is more true and more a being is prior and better known by nature. The universal, taken in this way, is prior to the singular.
But if the universal is considered as what is confused and mixed with particulars, in this way the universal comes to be and is destroyed by the coming to be and destruction of singulars, and so the universal is not prior to and better known than these singulars, since the same thing is not better known than itself. But the universal existing in particulars, as it exists in them, is the same as singulars. It is neither as such distinct from them in being nor in substance. Therefore etc.
In another way, the universal in the intellect can be considered as it is a nature abstracted from singulars, and in this way the universal is posterior to singulars in the order of production, but it is prior in the order of perfection. That it is thus posterior in the order of production is apparent, since it is true of the universal considered in this way that the intellect is of universals as an object, and the senses of singulars. And because of this, just as intellective cognition is related to sensitive cognition, so is the universal, taken in this way, related to the singular. But intellective cognition is posterior to sensitive cognition in the order of production. Therefore the universal taken in this way is posterior in the order of production to the singular, I say posterior inasmuch as it presupposes a cognition of singulars, and the Philosopher says of this universal in De Anima I that the universal is either nothing or posterior. It is nothing if such an Idea as Plato assumed is assumed, it is posterior if something abstracted from singulars is assumed. And the saying of the author of Six Principles , that every community proceeds from singularity, is true of this sort of universal. Nevertheless, the universal taken in this way is prior to the singular according to substance and perfection, and the reason for this is that intellective cognition is of the universal, but sensitive cognition is of the singular. Now intellective cognition is prior to sensitive cognition according to substance and perfection, therefore the universal taken in this way is prior to the singular.
Again, this is obvious from the argument of the Philosopher by which he proves here that the universal is better known according to nature than the singular. That which is more distant from the senses is better known by the intellect, since the more distant it is from the senses the more immaterial it is, and the more immaterial it is, the more intelligible it is; therefore the more distant it is from the senses the more intelligible it is. But a universal taken in this way, namely as it is actually abstracted and understood, is distant from the senses, but a singular is not; therefore etc.
But if we speak of the separated universal that Plato assumed, if such a universal were assumed, it would be prior to and better known than singulars, for that which is a cause of the being and of the coming to be of another is prior to it, but such a universal, if it is assumed, is a cause of the coming to be and the being of singulars, according to Plato, and therefore it is prior to and better known by nature than singular. But although the universal is prior by nature to the singular, still the singular is prior for us to the universal, for since every cognition of ours takes its rise from the senses, that which is prior with respect to sensitive cognition is in a way prior for us. But the singular is prior and better known with respect to sensitive cognition, for what is grasped per se by a power is grasped by it prior to that which it grasps accidentally. But the singular is grasped per se by the senses, and the universal is not grasped except accidentally. Therefore the singular is prior to and better known than the universal with respect to sensitive cognition, so that the singular is said to be prior to and better known than the universal for us. And the Philosopher touches on this briefly in the text, for he says that singulars are prior for us since they are closer to the senses.
And if someone should say the Philosopher says in Physics I that singulars are prior by nature, but universals for us, and he says here the opposite of this, and so there seems to be a contradiction among the sayings of the Philosopher, it is apparent what must be said. For the Commentator distinguishes in the Physics between two singulars, for there is the singular without qualification, and the singular in a certain respect. The singular without qualification is an individual, of which other things may be said, and which is not said of any other. But a singular in a certain respect is an atomic species. So the Philosopher compares the universal to the singular in the Physics, that is, the more universal to the less universal, since the more universal is prior to and better known than the less universal for us. But here in the Posterior Analytics the Philosopher compares the universal to the singular without qualification, and in this way the singular is prior for us, but the universal is prior by nature, and we have seen the reason for this.
In response to the arguments. In response to the first, when it is argued “that which is such that when it does not exist, the other does not” etc., I hold that whatever is such that when it does not exist the other does not exist, without qualification, is prior to the other by nature. But it is not necessary that whatever is such that when it does not exist the other does not exist, according to some accidental being belonging to it, should be prior to the other by nature. For when whiteness does not exist a white man does not exist, but when whiteness does not exist it is false to say that a man does not exist without qualification, and therefore it is not to be concluded from this that whiteness is prior to man by nature. And as for the minor, I hold that, as we have said elsewhere, being is of two sorts, namely the being of actual existence, which is being outside the soul in the reality, and being of the intellect, which is being in the soul. So I hold that when singulars are destroyed the universal does not actually exist outside the soul, since whatever actually exists is singular, so that if all singulars are destroyed the universal does not exist actually, but the universal remains in its being in the soul. From this it must be noted that these two sorts of being are accidents of the essence of a reality, so that the essence of a reality is not in itself determined to this or to that. Nevertheless, the essence of a thing cannot be unless under this or that, for everything that is is either singular or universal. If it is universal, then in this way it has being in the soul, and if singular, it has being in the reality outside the soul. So even though it is destroyed as regards the being of actual existence it is not as yet destroyed in itself, since when singulars are destroyed the essence of the reality then remains in the concept of the mind alone, according to Avicenna. For from this, that the essence of a reality is not in itself determined to this being or to that, and because the singular is actually existing, if then the essence of a reality is not in itself determined to actually existing, because actually existing is only suited to singulars, we must not say that if a reality does not actually exist outside the soul then the reality is totally destroyed, since it remains in respect of its other being, that is, in the soul. So it is not necessary that, the first being destroyed, that is, singulars, to which actually existing is suited, then the essence of the thing must be totally destroyed.
In response to the other argument, when it is argued, “what proceeds from another” etc., I hold that what proceeds from another as from a perfecting and completing principle is posterior to it by nature. And as for the minor, I hold that the universal does not proceed from the singular as from a completing principle, but as from an initiating principle. But it proceeds from singulars as from an initiating principle, since unless singulars exist in actual reality or in possibles, the intellect can never abstract the intention of universality. So the universal proceeds from singulars as from an initiating principle, but it does not proceed to completion from these, but from the intellect. For singulars never move the intellect in themselves and by their own power, since the material never acts on the immaterial, for the agent is more noble than the patient. Because of this singulars do not act on the intellect by their own power, and therefore it is the possible intellect which, with the help of the active intellect, brings about the completed formula of universality. And noting this, the Commentator says on De Anima III that actual universals are actually understood (actu intellecta), and are not thus beings but are thus understood. So just as we see concerning health that health is initiated by nature, but perfected and completed by the art, so the universal is initiated by nature, but is perfected and completed by the intellect. Universality, therefore, does not proceed from singulars as from a perfecting or completing principle, but as from an initiating principle, and therefore it is not necessary that the singular be prior according to nature to the universal.
We ask concerning the part, “but since it is necessary to believe and to know the reality,” in which the Philosopher settles issues about the cognition of principles through comparison to the cognition of conclusion. And he proves three conclusions there. First in order is that we know the premises in a demonstrative syllogism better than the conclusions. The second is that one cannot know conclusions better than principles. The third is that nothing is better known than these first principles. Therefore it is asked whether there is scientific knowledge of first principles. And it is argued that there is, since each thing because of which is also more. But we know conclusions because of principles, therefore we know principles better. Therefore there will be scientific knowledge of principles, and more strictly so than of conclusions.
Again, every firm habit of a complex [i.e. a proposition] seems to be knowledge. Now a habit of a principle is a firm habit of a complex. Therefore a habit of a first principle seems to be knowledge.
On the other hand, it is argued that there is no knowledge of what is immediate, as the Philosopher says in the text. But first principles are immediate. Therefore etc.
It must be understood that although there are two sorts of cognition in us, namely sensitive cognition and intellective cognition, sensitive cognition is not scientific knowledge, since all scientific knowledge is possessed by a certain relating of one thing to another, namely a relating of the cause to the effect. But the sensitive power is not a relating power, since every relating power proceeds from one cognized thing to the cognition of another cognized thing. Therefore every such power grasps something under the formula of cause and something under the formula of effect, but the senses do not grasp the formula of cause and effect, since the senses grasp nothing except what is in itself determined to matter, and to this matter. But the formula of cause and effect is not in itself determined to matter, or to this matter, for they are found most powerfully in what is separated from matter. Therefore scientific knowledge is not sensitive cognition, but intellective cognition.
Next, some intellective cognition is of complexes [i.e. propositions], some of the incomplex [i.e., terms]. Scientific knowledge is not intellective cognition of an incomplex, since knowledge is obtained by way of reasoning. But what is obtained in this way is a complex, and there is no reasoning unless it is from something either composed or divided by the operation of the intellect. So the first operation of the intellect is to grasp something, the second is to compose and divide what is grasped, and the third is to compare the composed or divided to one another, and this last is called reasoning. Scientific knowledge, therefore, is not cognition of an incomplex, but of a complex.
Next, scientific knowledge is either a cognition of a complex through some cause other than itself, or not. If knowledge is the cognition of a complex, then it is cognition of a complex which is through some cause other than itself. And the reason for this is that scientific knowledge is strictly speaking of those things that are learned, but learning does not occur unless it is of those that have some cause other than themselves. And this is what Grosseteste says here --we, strictly speaking, learn what appears false or doubtful to us beforehand, and afterwards the contrary opinion is made obvious to us. Its truth, however, is not made obvious except through what is prior, and therefore knowledge of a complex occurs through certain prior things, and is of those which have some cause other than themselves. Scientific knowledge, therefore, is cognition of a complex that occurs through some cause other than the complex, and therefore the Philosopher says that to know is to receive something through demonstration. But demonstration occurs through a cause, therefore there is no knowledge of those that do not have some cause other then themselves. But there is no cause of principles other than themselves. Therefore there is no scientific knowledge either.
But it must be noted that although there is no knowledge of first principles, there is still a cognition of first principles that is truer and more certain than scientific cognition, for it is such cognition of first principles that is the beginning of knowledge, and the Philosopher says this in the text. But the cognition that is the beginning of scientific knowledge is truer than the cognition of what it establishes, since the principle is truer and more certain than what it establishes; therefore etc.
Again, this is obvious since it has been seen that among beings what is of itself has truer being than what has being from another. For since the disposition of a thing in truth and being is the same, those are more truly cognized that are cognized through themselves than those that are cognized through others. But first principles are cognized through themselves, and conclusions through others. Therefore etc.
And if you argue that the cognition that occurs through a cause is more certain than that which does not occur through a cause, but cognition of first principles does not occur through a cause, and cognition of conclusions do occur through a cause; therefore etc.--I hold that “something not cognized through a cause” can be understood in two ways. It can either be understood that it does not have something other than itself as the cause of its cognition, or “not through a cause” can be said of something because it is suited to be cognized through a cause other than itself, but it is not thus cognized. No I hold that, speaking of the cognition that is not through a cause in the first way, a cognition that is not through a cuase is more certain [exact] than that which is through a cause, since that which does not have a cause of its cognition other than itself is know more certainly [exactly?] than that which has such a cause. Now first principles are said to be cognized not through a cause since they have no cause of their cognition other than themselves, but conclusions are said to be cognized through a cause since they have some cause of their cognition other than themselves, so that the cognition of first principles is more certain than the cognition of conclusions. As regards the major premise, then, when it is said, “a cognition through a cause” etc., I hold that cognition of something through a cause is more certain [exact?] than cognition of the same thing not through a cause, and this if it is suited to be known through a cause other than itself. And in this way the proposition has truth when restricted to those which are suited to be known through causes other than themselves. But principles are not like this. Therefore etc.
And if you say that first principles are cognized by the way of experience, but experience is subject to error; therefore first principles are cognized in a way in which error and deception can occur, but conclusions are known in a way in which error cannot occur; therefore etc.--I hold that what is experienced is said in two ways, one from which the universal is received in the course of practical affairs, and the other from which the universal is received in the course of speculation. What is experienced in the first way is subject to error, but what is experienced in the second way is not. But the experience by which we arrive at the cognition of first principles occurs in the second way, and therefore first principles are not received in such a way that error or deception can occur.
In response to the argument. In response to the first argument, when it is argued that “each because of which” etc., I hold that this is true either formally or virtually. And when it is said, “we know conclusions” etc., I grant it. And therefore we know principles better either formally or virtually, and we cognize principles better virtually, for by cognizing principles we have a virtual cognition of more than when we have knowledge of a conclusion, and so we know principles better virtually. Again, we know principles better virtually since when we have knowledge or cognition of principles we have virtual knowledge of the conclusion, but when we have knowledge of the conclusion we have knowledge of no other thing virtually, since the conclusion in this way leads to a cognition of nothing else.
In response to the other, it is apparent through what has been said by imposition, since not every cognition of a complex is scientific knowledge, but only cognition of a complex that is acquired through the cause. But the cognition of principles is not of this sort, and therefore it is not strictly speaking knowledge.
We ask concerning the part up to “but it is not necessary to believe” etc. And let us inquire concerning the conclusion the Philosopher proves, whether principles are more certain and truer than conclusions.
And it is argued that they are not, since truth according to Avicenna is the adequation of realities and concepts. Now adequation is a certain equality, but equality is not susceptible of more and less, therefore truth is similarly not susceptible of more or less; therefore nothing is more true and more certain than any other. Principles, then, will not be more certain and more true than conclusions.
Again, those things of which there is the same formula of acting on the intellect act on the intellect and move it equally. But there is the same formula of acting on the intellect for both principles and conclusions, for both principles and conclusions move and act on the intellect under the formula of the true, for everything that moves the intellect moves it under the formula of the true; therefore principles and conclusions act on the intellect equally; therefore principles and conclusions are equally known to the intellect.
The opposed view is obvious from the Philosopher in Ethics I, where he contends that one should not desire equal certainty in all things. The Philosopher also says this in Metaphysics II. Therefore some things are more certain and better known than others. Principles are therefore better known than conclusions.
It must be replied that principles are better known and more certain than conclusions. And the reason for this is that everyone who knows believes those things that are known through themselves more than those that are known through another. For those that are known through another are unknown taken by themselves, and they receive cognition from another, but those what are known through themselves receive cognition from themselves, and they don’t need a cognition other than that of themselves. Therefore everyone who knows etc. Principles, therefore, are better known than conclusions. So Albert, speaking of axioms, says that an axiom is that which a learner does not get from a teacher, but acquires by a natural habit of the intellect, and nothing is required for knowledge of it but the cognition of its own terms according to the Philosopher —we cognize principles insofar as we cognize terms. And because of this Grosseteste says that just as when someone who has come upon something visible nothing is required for it to be seen but that vision actually turns itself to that visible thing, so nothing is required for a first principle to be cognized other than that the intellect actually turn itself to it. Therefore every knower believes principles more than conclusions; therefore etc. But in this way nothing seems to be better known than first principles, since those through which someone becomes a knower simply are best known in their truth, since a knower without qualification cannot fail to believe what he knows when he knows that which he knows through the best known. Now one becomes a knower, taken without qualification, through first principles, and from the cognition of first principles the knowledge of conclusions is divined, therefore etc.
Again, if there were something better known than first principles, then there would be something better known than that, and similarly for that, and so on to infinity. But there is no first in an infinite, and if there is no first there is nothing posterior; and so there would be no first cognized. And if there were no first cognized, there would be no posterior cognized; therefore nothing would be cognized but everything would be unknown, which is absurd. Therefore etc.
In reply to the arguments opposed to this view. In reply to the first, when it is argued, “truth is adequation” etc., I hold that although truth on its own part depends on an indivisible and is not susceptible of more and less, nevertheless, as regards the one who grasps truth, and on the part of those in which truth is found, truth is susceptible of more and less. That it is like this as regards the one who grasps truth is obvious, for just as not everyone is equally disposed [to cognition] by the senses, so neither according to the intellect, but some are better disposed [to cognition] by the senses, so that they see better and more sharply than others, and so some are better disposed [to cognition] by the intellect, and these see the truth better and those worse, and these more but those less, for souls follow the bodies to which they belong. Again, it is obvious on the part of those in which truth is found, since there is not so much truth or certitude in those that are subject to motion and change as there is in things separated from matter, and because of this truth is also susceptible to more or less on the part of things in which it is found. And therefore truth is not equally to be found in principles and conclusions, but there is more truth in the principles, but less in the conclusion, because truth in the conclusion depends on truth in the principles.
In response to the other, when it is argued, “those of which there is the same formula of acting” etc., this is granted. And as regards the minor premise, when it is said, “of principles and conclusions” etc., I hold that it is true that principles and conclusions move and act on the intellect under the formula of the true, but the true is not found equally here and there, but principles act on and move the intellect under the formula of the more true, and the other under the formula of the less true, for the truth of conclusions depends on the truth of principles.
We ask concerning the part in which the Philosopher excludes certain errors. There are two errors which he removes, for some had asserted that it was possible to know nothing, and others asserted that it was possible to know but that there is knowledge of all things through demonstration. Let us ask then about the first, whether it is possible to know something.
And it is argued that it is not, for all knowledge is of something fixed and permanent. So Boëthius says in the first book of his Arithmetic that knowledge is of those things that are in themselves unchangeable and are assigned to substance. Now among sensible things, from which we have our every cognition, nothing fixed or permanent is found. Therefore etc.
Again, whoever has come to know nothing learns nothing, for it is necessary that everyone who learns should already know something, but no man has come to know anything at all in the beginning, for the intellect of a man before it receives species is like a blank tablet upon which nothing has been written. So we argue in this way: whoever has come to know nothing learns nothing, but no man has come to know anything in the beginning; therefore neither does any man learn anything; therefore it is not possible to learn anything, at least through teaching.
Again, one who does not perceive the essence and quiddity of a reality, but only a similitude of it, cannot know the reality. Now our intellect does not grasp the quiddity of a reality, but only its similitude, for only the similitude of the reality is received into the soul. For a stone is not in the soul, but a species of the stone. Therefore etc.
On the other hand, it is argued that whoever denies there is knowledge says this because he is certain that there is no knowledge, but one is not certain of anything unless it be of what he knows. Therefore whoever denies that there is knowledge knows that there is no knowledge, but he does not know that there is no knowledge unless he has knowledge. Therefore whoever denies that there is knowledge grants that there is knowledge. If, then, the assertion of a contradiction is impossible, it is obvious that it is possible to know something. And I argue in the same way as the Philosopher argues in Metaphysics IV, when he says that whoever denies discourse grants discourse.
It must be said in reply to the question that it is possible for a man to know something, and this is apparent in sensitive cognition, and also in intellective cognition--in sensitive cognition, since that sense truly perceives a reality as it is, and no truer act of sensation offers contradiction to it in this act of sensing, nor does any superior power, such as the intellect. Now it is obvious that there is such an act of sensation to which neither any truer act of sensation nor any superior power offers contradiction in the act of sensing, and an act of sensation for which no impediment exists in the medium, nor in the organ, nor in its object, grasps its proper object. And therefore it is obvious that there is some act of sensation that truly perceives a reality as it is, and that act of sensation does not err in what it indicates. But from an act of sensation that does not err, knowledge is received, or cognition that is the way to knowledge, and so it is apparent in sensitive cognition that it is possible for a man to acquire knowledge.
Again, this is explained in intellective cognition, since, according to the Philosopher, the first principle “concerning each thing it either is or is not” is the most obvious principle, inasmuch as if anyone were to contradict this principle with his mouth, still he would not contradict it in his mind. And the Philosopher proves that no one contradicts it in his mind in Metaphysics IV, from men’s actions. For if some were to say that it is possible for something to be and not to be at the same time, and they believed it to be as they say, then, the Philosopher argues, if someone were to say that something at the same time both is and is not, and were to believe that it is as he says, why then, if he is travelling on a road leading into a pit, why does he flee the pit if he believes that the same thing both falls into the pit and does not fall into the pit? And Avicenna argues in this way: if someone were to believe the same thing both to be and not to be, why then would he, if he were afraid of being thrown into a fire, flee the fire if he believed the same thing both is thrown into the fire and is not thrown into the fire? From men’s actions, then, it is obvious that they do not believe the same thing to be and not to be at the same time, and so they believe this principle with the mind. And if this is so, this principle is the most certain in truth and its truth is determined and cannot be changed, but in this first principle all posterior principles and conclusions are included, so that by natural reason (naturali deductione) beginning from this first principle a man can arrive at the cognition of conclusions. And so one can know, and it is obvious that in intellective cognition it is possible to know something.
Again, each reality can attain to its end through the operation to which it is naturally ordered. Now knowing and understanding is the operation to which man is naturally ordered, since man is naturally ordered to happiness. But happiness depends on the operation of the soul according to its best power with respect to the best and most noble object. But the best power in man is the intellective power, and the noblest object of this power is the first principle. Now it is not possible to arrive at the final end unless it is possible to know about something, and therefore it is obvious from the end of man to which man is ultimately ordered that it is necessary that man know something.
Again, happiness is a common good that is suited to flourish in all who are not deprived of power (orbatis ab virtute), since there are then many men who are not deprived of power, and it is not possible to arrive at this happiness unless it is possible to know something; therefore etc.
But there are two signs, according the Commentator, by which one can tell if someone is a scientific knower. One is if he can thus reduce that which he knows to what is known per se, and if those things he knows agree with realities that are sensed, for the experience of the words of one’s speech is as they agree with realities that are sensed. The second sign is if he can produce that which he knows in another through teaching, since, according to the Philosopher in Metaphysics I, the sign of knowledge is being able to teach. And when these occur together it is obvious that a man has certain (exact?) scientific knowledge.
In response to the arguments. In response to the first, when it is said “all knowledge is of something fixed and permanent” etc., because all sensibles are thus in continuous motion and change, Heraclitus and those who followed him asserted that there cannot be knowledge of sensibles, and as it is related elsewhere, this error lasted until the time of Pythagoras. Afterwards Pythagoras, in a way agreeing with his predecessors, asserted that there is no knowledge of sensible things just as they did, but nevertheless, in order that we might in some way have knowledge of natural things he posited mathematicals to be joined with natural things in being, and since mathematical entities are, because of their abstraction from matter, unchangeable, therefore he supposed that knowledge of natural things is had through mathematicals. So he assumed mathematical entities to be causes and principles of natural things in being and cognizing. But Plato, after Pythagoras, seeing that mathematicals are joined in being with these natural things, also saw that it is not possible for natural things to be changed unless mathematical entities are changed, and because there cannot be knowledge of these through mathematicals, he posited certain separated ideas through which we have knowledge of natural things. And so Plato introduced ideas as much because of the understanding of natural things as because of their destruction and coming to be. For he supposed them to be the same in nature with sensibles, so that just as he assumed a separated man to be the cause of the being and cognition of particulars, he also posited the separated man so that it would not come to be or be destroyed. But the Philosopher, seeing that nothing is, or is cognized, in its essence through what is separated from it, posited something in existing sensibles through which knowledge is had of them, not under the formula by which it is in sensibles, since in this way it is particular, but as it is abstracted according to consideration and understanding. But these, abstracted in this way according to consideration and the understanding, are said to be universals, for instance genera and species. And therefore he asserted that knowledge is per se of universals, but of particulars accidentally, so that just as he posited knowledge to be both of those that are and those that can be, so the intellect grasps that there is in particular men one nature in which particular men have no differences. Of this nature thus abstractly considered according to the intellect properties and passions are demonstrated that coincide in it with the absolute nature, and knowledge of particulars is obtained through man not as they are particulars but as they are men. And so he assumed that knowledge is had of particulars in such a way that this nature of which we have knowledge is one according to consideration in particular men, but is made diverse according to real being in them. For man in Plato is another than in Socrates according to real being, and so on for the rest. But man considered abstractly is one in all of those many, and noting this, the Philosopher said that the universal is one in many and of many, and knowledge is had of this per se.
Then, as to the form of the argument, when it is said “all knowledge is of something fixed” etc., this is true. And you say that “in sensible things” etc. This is true. I hold that nothing is found fixed and permanent in them that is the same in number, but something permanent and fixed is found that is the same according to species. And therefore I grant that knowledge can be had of no sensible remaining one and the same in number, but knowledge can be had of sensibles as they remain the same in species or genus. For knowledge is had of all men in the way that has been said, and just as with men, so with the others.
In response to the other argument, when it is argued, “whoever has come to know nothing learns nothing,” I hold that “learning” can be taken in two ways. In one way it names every acquisition of knowledge, extending the name of knowledge to the cognition of conclusions as well as to the cognition of principles, and in this way this major premise is false, that “whoever knows” etc. For a man acquires cognition of first principles immediately from incomplex things when no cognition precedes, and so, extending the name of knowledge to the cognition of principles immediately from incomplex things, the major premise is false. But if “learning” names the cognition of conclusions, he who has come to know nothing learns nothing, for it is necessary that he who learns the cognition of a conclusion know something beforehand, since it is necessary that he cognize the conclusion beforehand in the universal. But then, in response to the minor premise, it is true that man then learns nothing from scratch, for from scratch, before he has the cognition of first principles, he does not learn the cognition of conclusions.
In response to the other argument, when it is argued “he does not learn” etc., I hold that “perceiving something” can be understood in two ways, either objectively or informatively. For something is perceived by the intellect under the formula of an object of the intellect, and something under the formula of what informs the intellect. The nature and quiddity of a reality is perceived by the intellect under the formula of an object, since that which is an object of a capacity is that the cognition of which perfects that capacity. Now the cognition of a reality as far as its quiddity and essence is concerned is what perfects the intellect, for this is not within the power of the species informing it. But through the species it is carried into cognition of the reality as far as what is interior to it is concerned, for instance, as far as its quiddity and nature are concerned. Therefore the essence and quiddity of the reality is contained in the formula of object of the intellect, but species and similitude is contained in the formula of what informs the intellect, and the intellect, informed in this way by the species, is carried to the reality. In this way, therefore, the intellect perceives the reality under the formula of an object of the intellect, and the similitude under the formula of what informs the intellect, and therefore when it is said, “he cannot know the reality” etc., it is true of one who does not perceive the reality under the formula of object. And you will say etc., and I hold that he perceives the quiddity of a reality under the formula of object of the intellect, but a similitude of the reality under the formula of what informs proximately, and since he perceives in this way the reality under the formula of object, therefore he can cognize it, but in such a way that when he perceives the species he is led to cognition of the reality. But in a way this similitude, which is a certain accident of the reality, can lead to cognition. There is a difficulty here, and elsewhere it will have to be looked into, but this much suffices for now. I hold that unless the intellect were a discursive power which from one cognized thing arrives at the cognition of another, it would never arrive by similitude at cognition of the reality, but the intellect is of its nature discursive, and therefore by natural discourse, when a sensible thing is represented to it it cognizes insensibles such as whatnesses and substances. So, just as everyone by natural instinct grasps non-sensed intentions under sensed species, since under the species of the wolf which one sees one grasps the original species of its nature, which is a non-sensed species, so next the intellect, through a sensible species represented to it, forming for itself from this species an intelligible species, also arrives through discursus at the cognition of the nature and quiddity of the reality of which the species is a similitude.
We ask whether knowledge can come to be in someone through discovery alone without any teacher.
And it is argued that it cannot, since a potential being does not come to be actual except through something that is actual, as is clear from the Philosopher in Metaphysics VIII. But every man has potentiality for actual knowledge in the beginning. Therefore, one does not come to be actual except through something that is actual, but an actual knower seems to be none other than a teacher; therefore etc.
Again, the Philosopher in Sophistici Elenchi I contends that it is necessary for a learner to believe. But one cannot believe unless it is on the authority of one who teaches. Therefore every learner must have someone who teaches him. One cannot, therefore, acquire knowledge without a teacher.
On the other hand, it is argued that the Philosopher in Metaphysics I says that experience makes art, inasmuch as Polus said rightly that experience makes art, but inexperience luck. But a man can acquire experience of sensible things by himself, therefore a man can acquire knowledge of sensible things by himself.
it must be said in reply to this that one can acquire knowledge for himself through discovery alone, for there are two ways in which knowledge is brought to be in us, namely, through discovery and through teaching, as the Philosopher suggests in the Sophistici Elenchi when he says that everyone who has come to know has come to know either in discovery or in learning, suggesting by this that knowledge can come to be in us in both ways. Proof that knowledge can come to be in us through discovery: If the causes leading to some effect are possible, the effect is also possible, but the causes through which a man can acquire knowledge for himself through discovery alone are possible; therefore etc. Proof of the minor premise: For there are two principles in us through which a man can acquire knowledge from discovery alone, namely the possible intellect and the active intellect. The possible intellect is related to intelligibles as senses to sensibles, for as the senses are potentially every sensible so the possible intellect is potentially every intelligible. So the possible intellect has only this of itself, that it is potentially every intelligible, just as prime matter has only this of itself, that it is potentially every sensible form. And since the intellect is thus potentially every intelligible form, and has none innate in itself, therefore besides the possible intellect it is necessary to assume the active intellect, through which the possible intellect comes actually to understand. But the active intellect does this since it brings potential intelligibles to be understood actually. So it reduces the possible intellect from potentiality to actuality, and hence, just as light brings colors to actuality, so that they move the vision, thus the active intellect brings intelligibles to actuality, so that they move the intellect. Therefore the Philosopher says in De Anima III that the active intellect is a habit like light.
And from this, that these two principles are in a man, it is immediately apparent how it is possible for a man to acquire knowledge by himself, since the possible intellect is first informed by some intelligible species by the power of the active intellect, and then the intellect, informed in this way, grasps the formula of the first incomplex things, namely of being and one. Afterwards the intellect naturally, as it were, and without any process of reasoning, by composing and dividing conceives the first complex intelligibles, “of everything either an affirmative or a denial” etc., and “every whole is greater than its part,” “a being is a being,” and the like. Next, since the knowledge of conclusions is included in these first principles potentially, a man, through application and hard work, can reduce these conclusions to actuality, so that these conclusions are known actually, and in their own form, for since they are, as it were, in proper first principles, a man can abstract those conclusions in actuality. In this way, then, the way is apparent in which a man can, by the light of the active intellect, elicit proximate conclusions from first principles and other conclusions from these proximate conclusions, so that a man by his own ability can acquire knowledge without a teacher. And noting this way of proceeding, the Philosopher said “we think we know each thing when we cognize its causes, both that it is is the cause of it and that it is impossible for it to be otherwise.” And arts and sciences were discovered from scratch in this way. Nevertheless, this way of acquiring knowledge is extremely difficult for a man, so through discovery alone no man can bring anything to perfection.
Knowledge can also be had through teaching, and knowledge is acquired correctly through teaching in the same way it would be obtained through discovery. For first the teacher set out first incomplex principles for the cognition of the pupil, then true first complex principles, and from the cognition of first principles he brings about the cognition of first posterior things in the pupil, and so on right up to the conclusions of a particular science. And in this way he will bring about knowledge in him, but nevertheless, in this bringing about of knowledge the teacher is no more than an instrumental agent, and the interior reason existing within the pupil is the principal agent, for it belongs to the interior reason of the pupil to judge what the teacher says when he has been informed, and if what he says is true and he believes its, knowledge will come to be in him. But it it is false and he believes it, then deception will come to be in him, and because of this Boethius says in On the Teaching of Students that it is stupid to believe wholly what the teacher says. But at first it is necessary to believe.
In response to the arguments. In response to the first, I grant the whole argument. For I hold that where there is something actual, one is led from potential to actual understanding by that. And I reply that what is actual is the active intellect, for it belongs to it actually, for unless, along with the possible intellect in man, an active intellect is assumed, to which it belongs to form intelligible species through which knowledge is gained of a reality, knowledge will never be gained by a man. But since intelligible species are abstracted by the power of the active intellect, the possible intellect is made to know and understand.
In response to the other argument, when it is argued that “it is necessary for one who learns” etc.—there is someone who learns strictly speaking, and this is the one who receives knowledge from a teacher and through teaching, through which it is necessary to believe, and this is what the Philosopher understands when he says it is necessary for a learner to believe. But he who receives knowledge through discovery need not believe, for he is not a learner strictly speaking.
We ask at this point concerning knowing, it being accepted that one can know through discovery as well as teaching. We ask whether knowing is in human beings by nature.
And it is argued that it is, since nature is not lacking in what is necessary, just as it does not abound in superfluities. But knowledge is necessary to a human being. Therefore nature is not lacking in actual knowing for a human being. But a human being is naturally capable in that in which nature is not lacking for him. Therefore a human being is naturally capable in actual knowing.
Again, the intellect is more perfect than the senses, but the senses naturally tend to the act of sensing; therefore etc. Therefore understanding and knowing are in man by nature.
On the other hand, it is argued, the Philosopher says in De Anima III that our intellect before learning or discovering is none of those which are, since it understands nothing actually. But if understanding were in a man by nature, a man would understand before learning or discovery. Therefore understanding and knowing are not in man by nature.
And as regards this, it must be held that an aptitude to knowledge is in a man by nature, but the act of knowing is not in a man by nature, but is in a man from acquisition. The first is obvious, because of the similarity of the coming to be of knowledge in the soul and the coming to be of the substantial form in matter. For in this way, according to the Commentator on De Anima III, our intellect is related to intelligible forms as prime matter is to sensible forms. But in matter only an aptitude to substantial forms is found, and the actuality of those forms is from the agent that alters and changes the matter. Therefore it must be held that, so far as that power of the soul that is the possible intellect is concerned, only an aptitude to knowledge is found in the soul, but the actuality of knowing is in it from outside, that is, from a teacher, or from within, that is, from the active intellect. In as much as intelligible species, by which the possible intellect is informed, are abstracted from images through the active intellect, it receives knowledge of a reality, and so the aptitude for knowing is in man by nature, but the actuality from something else.
Again, a man does not need application and deliberation for that which is in a man by nature, for nature does not deliberate, as is said in the Physics II. But a man needs application and deliberation for knowing and understanding, for, as the Philosopher says in Ethics II, the intellectual power has its coming to be and augmentation for the most part from teaching. Therefore, since it needs experience and time, the act of knowing and understanding is not in man by nature, but from acquisition.
Again, this is explained because what is in a species by nature is found equally in every individual of that species, as is apparent from the ability to laugh, which is shared equally by every individual man. For as a substantial form is not susceptible of more or less, so neither is a proper passion that is immediately consequent on a substantial form. But knowing is not in all man equally, but some are more knowers, some less. Therefore etc.
In response to the arguments. In response to the first, when it is said “nature is not lacking in what is necessary” etc., I hold that some things are necessary for being, some things for well being, so that nature is not lacking in what is necessary as far as being is concerned, but immediately confers everything necessary for being, and speaking also of what is necessary as far as well being is concerned, nature is not wholly lacking in what is necessary, but it is lacking in this way in what is necessary for well being, since it does not immediately confer what pertains to well being, but confers something by which they can be acquired. In response to the minor premise, I hold that knowledge pertains to the well being of man, and therefore it does not confer on him the act of knowing immediately, but something through which he can acquire it, for instance, senses and reason. Similarly, nature does not immediately offer man clothing and weapons, which pertain to well being, but it confers some thing or things by which such things can be acquired and made ready, like the intellect and the hand. And thus nature is not lacking in what is necessary either to being or to well being, but it provides for these differently, and therefore it is suited for knowledge by nature, but has it actually through acquisition.
In response to the other argument, when it is said, “the intellect is more perfect than the senses,” I hold that this is true. And in response to the minor premise, I maintain that they do not tend naturally to the operation of sensing in such a way that the act of sensing is in them wholly by nature, and in such a way that they immediately tend by themselves to the act of sensing, but they tend to the act of sensing from sensibles that are present. In the same way, I hold of the intellect that it does not naturally tend to the operation of understanding so that the act of understanding is in it wholly by nature, but it tends to the act of understanding from intelligibles that are present, when these are abstracted by the active intellect.
We inquire about the part, “but in a circle,” where it is asked whether it is possible to demonstrate in a circle.
And it is argued that it is, since what is in a superior is in everything inferior to it. Now syllogism is something superior to dialectical and demonstrative syllogism, but it is possible to syllogize in a circle; therefore it is possible to demonstrate in a circle.
Again, the Philosopher says in Prior Analytics II that it is possible to show in a circle in those things that are convertible. Now demonstration arises in convertible terms, therefore it is possible to demonstrate in a circle in demonstration.
On the other hand, it is argued that if it were possible to demonstrate in a circle etc., then there would be knowledge of all things through demonstration, for principles would be demonstrated from conclusions and vice versa, but there is not knowledge of all things through demonstration; therefore etc.
As is obvious from the Philosopher in Prior Analytics II, syllogizing in a circle is from the conclusion, and conversely, so that assuming one predication one concludes the other predication which had been assumed in the original syllogism. That is, syllogizing in a circle is syllogizing from the conclusion with the converse of one of the premises to the other premise, so that in a circular syllogism the conclusion is demonstrated from the premises, and conversely. And so there is a return from something back into the same thing. When, therefore, it is asked whether it is possible to demonstrate in a circle, I hold that demonstration is of two sorts, one that brings about knowing without qualification, and another that brings about knowing in a certain respect. The first is demonstration why, and proceeds from what is better known without qualification. The second is demonstration in a certain respect, and proceeds from what is better known as far as we are concerned. When, therefore, it is asked whether it is possible to demonstrate in a circle, I hold that speaking of demonstration without qualification it is not possible to demonstrate in a circle. And the reason for this is that a demonstration without qualification proceeds from what is prior and better known without qualification. If, then, a conclusion is demonstrated without qualification through premises, and the premises are demonstrated without qualification through the conclusion, then the conclusion is something better known without qualification with respect to the premises, inasmuch as it demonstrates the premises, and something less known without qualification, inasmuch as it is demonstrated through them. The same thing, then, would be both better known and less known in respect of the same thing, which is absurd. Therefore it is absurd to say that there is demonstrating in a circle in such a way that in both directions there is a demonstration without qualification.
Speaking of demonstration in a certain respect, demonstrating in a circle is possible in such a way that the conclusion is demonstrated without qualification through the premises, and the premises are demonstrated in a certain respect through the conclusion. For from this nothing follows except that the same thing in respect of the same is prior and better known in one way, and posterior and less known in another way, and this is not absurd, but rather, it is reasonable that the same thing should be better known without qualification, and less known in a certain respect, in respect of the same.
Next, it must be known that in mathematics, according to the truth, it is not possible to demonstrate in a circle, but in natural things it is necessary to demonstrated in a circle. The explanation of the first is that in mathematics the premises of a demonstration are prior to and better known than the conclusion both without qualification and as far as we are concerned. And therefore, since every demonstration must proceed either from prior things without qualification or from prior things as far as we are concerned, and the conclusion of the demonstration in mathematics is neither prior and better known without qualification nor as far as we are concerned, it is obvious that in mathematics it is not possible according to the truth to demonstrate in a circle.
The explanation of the second is that in natural things the effects are better known than their causes as far as we are concerned. Now teaching must always begin from what is better known as far as we are concerned, for the way from what is better known and prior to us is innate to us, from what is unknown by nature to what is prior and certain by nature, as is said in Physics I, and therefore the way of teaching in natural things must proceed at first from effect to cause. But then, in order that perfect cognition may be obtained, one must proceed from causes to effects; and therefore in natural things it is thus necessary to demonstrate in a circle, and before a man makes such a circle in natural things he will never have a perfect cognition of them. So just as from the cognition of accidents we arrive at the cognition of substances, since accidents contribute in large part to knowing what a thing is, and then we go back again in order to attain to the complete cognition of accidents, and this process is truly demonstrative, since from the cognition of substances we arrive lat the cognition of their per se passions, so in natural things, through the cognition of the effects we arrive at the cognition of the causes, and then we go back again in order to obtain a complete cognition of the effects. And this process is truly demonstrative. Thus it is apparent that there is demonstrating in a circle, and this is necessary in some sciences.
In response to the arguments, in response to the first, when it is argued that “the superior agrees” etc., so it does, and you hold, “syllogism is superior,” but I hold that it is not something superior, strictly speaking. For it is not the genus to dialectical and demonstrative syllogism, but is related to these as a whole to parts. In this way it is granted, but you say “it is possible to syllogize in a circle,” and this is true. And therefore I grant that it is possible to demonstrate in a circle in such a way that in demonstrative syllogisms it is possible to proceed from premises to conclusion, and vice versa, but it is not possible to have a demonstration without qualification in both ways.
In response to the other argument, when it is argued “in those things that are convertible” etc., I grant that in demonstrative syllogisms it is possible to demonstrate in a circle, but this is not the same manner of demonstration in both directions.
As to the argument on the other hand, I grant that it is possible to have knowledge of all things through demonstration, since it is possible to have knowledge and demonstration as much of principles as of the conclusion. But it is possible to have demonstration without qualification of conclusions, and in a certain respect of principles, and also in this way it is possible to have a demonstration without qualification of first principles. For the Philosopher in Metaphysics IV proves a first principle by refutation, and therefore the argument does not conclude an absurdity.