The Problem of Principles

 

Dr. Anthony Andres
Tutor Talk
November 6, 2024
Audio

 

The Problem of Principles

 

In the Seventh Book of Plato’s Republic, Socrates asks Glaucon:

Do you agree, then, that we have set dialectic above all other studies to be as it were the coping stone – and that no other highest kind of study could be rightly place above it, but that our discussion of studies is now complete?[1]

Aristotle, it turns out, does not agree that dialectic is the highest of studies. He contends that the highest kind of knowledge, wisdom, consists in the grasp of a discipline which he calls first philosophy, and that this discipline constitutes a science. And he points out that scientific knowledge is not gained by the use of the dialectical method, the ability to ask and answer questions; rather, he thinks that it is gained by the use of the demonstrative syllogism, a logical method that Aristotle sets out at great length in his Posterior Analytics. Just as Aristotle makes his treatise on first philosophy, the Metaphysics, the coping stone of his treatises on the philosophical disciplines, so he makes the Posterior Analytics the coping stone for his Organon, the collection of his writings on the logical method.

It often comes as a surprise, then, to those first taking up the Organon to find that its longest book is not the Posterior Analytics, but the Topics, a book on Plato’s dialectical method. Why would Aristotle write in such great detail on a philosophical method which he so clearly has rejected? Some commentators have conjectured that Aristotle wrote the Topics very early in his philosophical career when he was still a student of Plato and before he had worked out the superior method of the demonstrative syllogism. But cross-references between the Topics and his other logical works make this conjecture unlikely. In fact, after having made clear at the very beginning of the Topics that he is indeed discussing the Platonic method in contrast to the method of the demonstrative syllogism, Aristotle himself explains why he nevertheless is writing about dialectic:

Moreover, [this treatise] is useful for the first principles of each science. For it is impossible to say something about them from the principles proper to the proposed science, because the principles are the first of all. But it is necessary to discuss them through the probable opinions about each one. And this is peculiar, or most proper, to dialectic for, because it is scrutinizing, it builds a road to the principles of all the sciences.

Aristotle seems here to give this explanation of why philosophy still needs the dialectical method. The first principles of each of the philosophical sciences need to be discussed so that they can be examined, scrutinized, tested in some way. But the basis of that discussion cannot be principles proper to that science; that would imply that there were principles prior to the first principles. The principles can be tested, however, against commonly held opinions, and this task, to test a statement against common opinion, most properly belongs to the dialectical method. Therefore, Aristotle concludes that dialectic is the road to the first principles of the philosophical sciences, and thus implies that the demonstrative method must be supplemented by the dialectical one.

My ultimate purpose in this investigation is to understand in detail how dialectic builds a road to the principles, but my goal in this tutor talk is more modest. Here I just want to see why the principles need such a road in the first place. To do that I will look back at the Posterior Analytics, not only to see what a first principle is, but also to see the questions that arise about the first principles in the course of its discussion. I see that at least two problems arise there. The first concerns the very possibility of first principles, while the second concerns their usefulness for acquiring scientific knowledge.

 

The Existence of First Principles

Since these principles are the principles of demonstrations, our first task is to briefly review Aristotle’s doctrine on the syllogism and the demonstrative syllogism. In the Prior Analytics he defines the syllogism as “speech in which, somethings having been posited, something else than these necessarily follows by this, that these are.”[2] For example, if I propose that:

Every plane figure susceptible to a particular kind of construction has angles adding up to two rights.

And that:

Every triangle is susceptible to just such a construction.

It follows by necessity that:

Every triangle has angles adding up to two rights.

The first two statements laid down are called premises, while the third which follows is called the conclusion. Although Aristotle’s formulation of his definition is ambiguous about whether the conclusion is part of the syllogism or not, his practice in the treatise that follows makes it clear that only the premises are parts of the syllogism; the conclusion is a separate statement produced by the syllogism.

Aristotle begins the Posterior Analytics, by saying, “All rational teaching and learning comes to be from preceding knowledge.”[3] Since scientific knowledge, a knowledge in which we know “the cause through which the thing is, that it is the cause of that thing, and that it does not happen that this thing stands otherwise”[4], is acquired through rational teaching and learning, it only makes sense to say that it also comes to be from preceding knowledge. The most obvious candidate for this preceding knowledge is scientific knowledge of the premises of the demonstration syllogism: for example, it seems likely that our scientific knowledge that every triangle has angles adding up to two rights comes to be from the preceding scientific knowledge of the two premises which tells us the kind of construction the triangle is susceptible to.

But such a solution only puts off the evil day of reckoning: if we have scientific knowledge of these premises, they also are the conclusions of syllogisms, and they also rely on our having knowledge of the premises preceding them. Consequently, we can ask the same question about these prior premises as well. Aristotle notes that previous thinkers, considering this question, have come to two different conclusions about scientific knowledge. Aristotle tells us:

Through it being necessary to have scientific knowledge of the first things, to some it does not appear that scientific knowledge even exists; to others [scientific knowledge] does exist, but they think that there are demonstrations of all things.[5]

The first group contends that, since there must be scientific knowledge of the premises, the premises themselves also need to be demonstrated; similarly, the premises of these prior premises would themselves need to be demonstrated. For example, the premise that a triangle is susceptible of such a construction would need to be proved through prior premises, which themselves need to be proved, etc. Thus, either demonstration involves an impossible infinite regress, or the process comes to a stand by arbitrarily assuming primary premises, premises which we do not know to be true. In either case, the first group contends, the quest for scientific knowledge has failed.

The second group agrees that there must always be scientific knowledge of the premises, but disputes the conclusion that there is no scientific knowledge. Rather, they think that all things can be demonstrated because they allow demonstration to be circular; that is, under the right conditions a conclusion can be used as a premise in the argument that supports its own premises. For example, the premise that the triangle is susceptible to such a construction would be supported by prior premises, one of which is the conclusion that the triangle has angles adding up to two rights. By assenting to circular demonstration, this group hopes to consistently affirm both that scientific knowledge is real and that all knowledge is scientific knowledge.

Aristotle also wishes to affirm the reality of scientific knowledge, but he cannot accept that circular demonstration. He points out that, if we allow demonstration to be circular, then we are accepting that one and the same proposition can be related to another proposition both as premise and conclusion; that it, circular demonstration implies that the same can be both prior and posterior to the same, and that is an obvious absurdity.

In answer to this problem which touches on the very existence of scientific knowledge, Aristotle offers a third, unconsidered option: “We say that not all knowledge is demonstrative, but that [knowledge] of the immediates is not demonstrative.”[6] Let us recall what Aristotle said right at the beginning of the Posterior Analytics: “All rational teaching and learning comes to be from preceding knowledge.” The assumption of these two groups is that all rational knowledge is scientific knowledge. Aristotle denies this. He asserts that some rational knowledge is not scientific. Specifically, he asserts that rational knowledge of the first premises, the premises not proved from other premises, the premises lacking a middle term (hence the name “immediates”), is not scientific. In this way Aristotle solves for us a problem which threatens the very possibility of scientific knowledge.

Aristotle, then, in solving this problem has argued for the existence of first principles of demonstration. In fact, the necessity of positing first principles of demonstration is even suggested by the doctrine of the Prior Analytics, and so Aristotle has already, in the second chapter of the Posterior Analytics, given a brief account of these principles: “If to know scientifically is such as we posit, it is also necessary that demonstrative knowledge be from true, first, immediate, more known, prior to and cause of the conclusion.”[7] The first principles must be true because, while we can syllogize to the true conclusion from false premises, we cannot know that the conclusion is true from false premises. The first principles must be immediate in this sense, that their subject and predicates are not joined through the middle terms of demonstrative syllogisms, as conclusions are. Let’s ignore, for the moment, the rest of the account; it will become important later in my talk. But let’s note at least this. In the second chapter of the Posterior Analytics Aristotle gives us a logical account of the first principles of any demonstrative science. In the third chapter he solves the problem which threatens the very possibility of scientific knowledge by positing the existence of first principles. But that solution forces him to assert that there is some other kind of rational knowledge besides scientific knowledge, and that the first principles are grasped according to this other kind of rational knowledge. And this suggests to us a further question, a question that leads us directly to the first problem about first principles: how do we have rational knowledge of them?

 

The First Problem with the First Principles

Before I examine Aristotle’s solution to the first problem about first principles, I want to note that, while the problem is raised in logic, it is not up to the science of logic to solve it. Towards the end of the first book Aristotle points out that the question of distinguishing the various kinds of rational knowledge belongs to either to the study of the soul in natural philosophy or to ethics. That he does at least begin to solve the problem in logic is attributable, not to it belonging to the science but, as St. Thomas points out, to the excellence of Aristotle’s mode of teaching.

In Chapter 19 of Book II of the Posterior Analytics Aristotle lays out two possibilities for how we have rational knowledge of the first principles. One possibility is that we are born with knowledge of them; the other is that we acquire that knowledge, that the first principles in some way are learned. But there are strong arguments against either option. Aristotle writes:

 

It is improbable if we have [knowledge of the principles]; for then it would happen that, while possessing a knowledge more certain than demonstration would be hidden from us. But if we receive [knowledge], not having it before, how do we know and learn not from preceding knowledge?

 

I take Aristotle to be making the following argument. It is clearly not the case that, from the moment of our birth, we are aware of knowing the first principles of the philosophical sciences. On the one hand, then, if we claim that we are born knowing those principles, it follows that we possess a kind of knowledge, more certain than scientific knowledge, and yet we do not know that we possess it. This seems highly implausible. On the other hand, if we claim that we have to acquire knowledge of the first principles after we are born, it follows that we acquire new knowledge, but not from any preceding knowledge. This contradicts the very first sentence of the treatise which states that all teaching and learning come to be through preceding knowledge. Both options being closed off, it looks like it is impossible to know the first principles.

The reason, perhaps, why the problem above arises is that we assume that the preceding knowledge from which we come to learn the first principles must itself be rational knowledge. The solution is to say that the preceding knowledge is not rational, but instead is sensitive. That is, we learn the first principles of the sciences through sense perception. This solves the problem because sense perception is a kind of knowledge insofar as it is a power of judgment, and because it exists in us, and in all the animals, from birth, and because it is obvious to us, not hidden, that we know things by our senses.

A question remains: how can knowledge of the first principles, which is more certain, come from sensation, which is less certain? The answer is that sense knowledge rises to the level of rational knowledge by a series of steps. The first step is the sense awareness arising from the immediate presence of the object of sensation; for example, right now I might see a dog. The second step is the retention of that sense awareness even when its object is no longer present; after the dog runs away, I remember him. Should I encounter dogs many times, I will have many memories, but should I gather those many memories together, what arises is one experience of dog.

We should note two orders in this process, an order of dependence and an order of perfection. Later stages of the process depend on the former’s stages; no one has a memory of a dog without having first sensed a dog; similarly, no one has experience of dogs without having many memories of them. But the later stages of the process are more perfect than the former stages because they approach more closely the character of rational knowledge, which is permanent and one. That is, memory is more perfect than mere sensation because, like rational knowledge, memory does not require that the object be present in order to be known. And experience is more like rational knowledge than memory because memories are many, but the experience that arises from them is a unified knowledge of its objects. So the sense knowledge that precedes rational knowledge of the universal is not one in kind, but a series of acts of knowing that tend to be more and more like rational knowledge.

But, as in clear from the parallel passage in his Metaphysics, experience does not go beyond the level of sense; it is not yet rational knowledge. He writes:

Experience seems similar to art and scientific knowledge, but art and scientific knowledge come to be made in man through experience. . . . Art comes to be when from many notions of experience arises one universal estimation about similar things.

Rational knowledge, the arts, and sciences, only arise when the universal is attained. Experience does not yet attain to the universal, so it is not yet rational knowledge. A sign of this, as he further down points out, is that, while there is not necessarily a difference between the artist and the man of experience with respect to action, there is a difference with respect to teaching. Action deals with individuals; by experience a man can deal with individuals just as well as by art, perhaps even better. For example, by experience a man might know that a certain kind of diet helped Bill, Fred and Joe regain their health, and so he can recommend the same diet to Bob, who seems to be having similar problems. But that man cannot teach anyone else to heal other people. But a medical doctor, knowing that Bill, Fred, Joe and Bob are all sufferers from the same kind of disease knows the universal, that such a disease is always cured by such a diet. He has learned that as a result of teaching and he can teach others as well. We can see, then, that experience, although a more excellent kind of knowledge that memory or mere sensation, does not yet rise to the level of rational knowledge.

And so Aristotle likens the process to a mob of soldiers running away in battler. The soldiers correspond to the multitude of similar sensations that flow past the attention of the soul. One soldier coming to a halt, taking a stand in the face of the attacks of the enemy corresponds to one sensation remaining in the soul as a memory. And just as the one brave soldier rallies the rest of the soldiers around him as a unit to take a fresh stand against the attack, so the one memory marshals others around itself to form one experience or universal conception. The soul, he says, is the kind of thing to which this can happen.

But two questions arise about this account. First, sensations and memories are about singulars, about individuals, not about universals; they are about Fido, Spot and Rover, not about the universal nature of dog. Even experience, as we have seen, does not rise to the level of the universal. But our rational knowledge of the first principles is universal; it is not about Fido, Spot or Rover, but about the nature of dogs. How can our rational knowledge of the universal arise out of our knowledge of things which are individuals, not universals?

Aristotle answers that question by noting that, not only does the individual possess a nature which is in some sense universal, but even sense perception in some way possesses the universal. He writes (rather obscurely), “For the singular is sensed, but sensing is of the universal, as of man, but not of the man Callias.” St. Thomas explains what he says as follows:

What is sensed properly and per se is clearly singular. Nevertheless, the sense power knows the universal in some way, since it knows Callias, not only insofar as he is Callias, but also insofar as he is this man, and similarly, it knows Socrates insofar as Socrates is this man. Because of this pre-existing knowledge in the senses, the intellectual soul is able to consider man in both indvidiuals. But if the sense powers were able to grasp only what pertains to particularity and were in no way able to grasp, together with this, the universal nature in the particular, it would not be possible for universal knowledge to be caused in us by sense perception.

The universal nature is contained in the singular. Sensation is per se a knowledge of that singular, but in grasping the singular, it in some way also take in the universal. Per se grasping Callias, sense in some way also grasps man. This makes it possible for reason to take in a knowledge of the universal as such. In this way sensation is the source of our rational knowledge of the universal.

The second question is the following. The above account of how rational knowledge arises from sensation terminates in an account of how the universal nature is present in the individual, how the universal man is present in the man Callias, and how reasons takes in this universal through sensation. But the universal nature, for example, the nature of man, is not a first principle of a demonstration science. Our grasp of the universal nature belongs to the first act of the intellect, the grasps of the indivisible nature, which is expressed in speech by words and phrases. But the first principles of demonstrative science concern the true and the false, which imply a combination of ideas and which are signified by statements containing subject and predicates. How can an account of how our first grasp of the indivisibiles comes to be explain how our first grasp of the combinations of indivisibles comes to be?

In the Posterior Analytics Aristotle does not offer an answer to that question, but in his Disputed Questions on Truth St. Thomas points us towards such an answer. There St. Thomas writes:

We must say something similar about the acquisition of science, that there preexist in us certain “seeds” of the sciences, namely, the first conceptions of the intellect, which are known instantly by the light of the agent intellect through species abstracted from sensible things. These might be complex, such as the axioms, or incomplex, such as the ratio of being and one and other such things, which the intellect instantly apprehends.

St. Thomas here is telling us that the grasp of the first complex conceptions, that is, axioms or first principles, hardly differs from the grasp of first simple conceptions, such as those of being and one. The reason is that both are known as soon as, by the light of the agent intellect, the intelligible species are abstracted from the objects of sensation. And in fact rational knowledge of the simple conceptions and that of the axioms has the same name; in English we call both “understanding”, in Latin “intellectus”, and in Greek, “nous”. The common names are signs that there’s no need to give separate accounts for coming to the first conceptions and coming to the know the first principles.

But I think that we can understand this more clearly if we consider another name we use to point out the first principles: in English we often refer to them as “self-evident” and in Latin as “per se nota”. In the Summa St. Thomas gives this account of the per se nota: “Some proposition is per se nota from this, that the predicate is included in the ratio of the subject, as man is an animal.” Here St. Thomas offers “man is an animal” as an example of a per se nota proposition. He is pointing out that when we give a distinct account of the subject of that proposition, man, we find out that its very ratio includes the conception of animal. Therefore, it is clear that man is an animal, not through some middle term connecting them, but through the terms of the proposition by itself. Therefore, grasping what the subject is, we instantly see that the predicate must belong to it and thus that the proposition is true. This is what it means for the first principles to be self-evident, and thus it helps us to see why an explanation of how our knowledge of the terms of a proposition come to be from sensation is tantamount to an explanation of how our knowledge of the first principles comes to be through sensation.

Let me summarize the first problem concerning the first principles, and its solution. The first principles are immediate; that is, they are not known through a demonstrative middle term. Thus, they cannot be learned from some previous rational knowledge. But neither are they innate; and yet, Aristotle takes as a principle that all learning comes to be from preceding knowledge. He solves the problem by noting that sense knowledge precedes even our grasp of the first principles of the sciences. Further, although sensation has the individual as its proper and per se object, nevertheless, because the individual possesses the universal nature, sense knowledge also in some way contains the universal. And since the first principles can be known as soon as the natures of their terms are grasped, then the explanation of how the universal simple conceptions come to be will also be an explanation of how we come to know the first principles from sensation.

 

The Second Problem of the First Principles

I know what man is and what animal is, and thus I know that every man is an animal. Likewise, I know what a whole is and what a part is, and thus I know that every whole is greater than its parts. That is what we concluded above. The process seems so simple that it is hard to understand why Aristotle insists in the Topics that we need to use dialectic to discuss the first principles. Aren’t the first principles obvious? Why would we need a method for discussing the obvious?

It is the second problem about the first principles that, I think, makes the need for discussing them much more manifest. To see that problem, we are going to go back to the beginning of the Posterior Analytics and look again at his first discussion of the first premises of demonstration. What we will see is that the solution to the first problem is what brings up the second problem, and that it will be much more difficult to grasp the solution to the second. In fact, in this talk I’m not even going to try to solve that problem. I will be content to lay that problem out and point out that this problem explains why dialectic is necessary for knowing well the first principles.

Recall that Aristotle lists several features that necessarily belong to the first principles of a demonstrative science: they must be true, true, first, immediate, better known than and prior to the conclusion, which is further related to them as effect to cause. They must be causes of the conclusions because scientific knowledge is not just knowledge that a conclusion is true, but a knowledge of the cause, of the reason why it is true. Because they are causes, the premises must be prior to the conclusion. And the premises must be better known than the conclusion.

It is this last feature that brings about a difficulty. The phrase “better known” can be understood in two ways, either as referring to what is more known simply or what is more known with respect to us. These two are different because what is more known with respect to us is, as we just saw in the last section, what is closer to sense. After all, we have just seen Aristotle explain how all rational knowledge has its ultimate source in sensation. But here Aristotle tells us that the things which are more known simply are the universal causes, and these are farthest from sense. So the question becomes, which meaning of “more known” do the first principles have to conform to?

On the one hand, it seems that the principles must be more known in themselves. In true demonstration, the premises tell us the reason why the conclusion is true; that is, they give us the cause. But Aristotle points out that the cause, while more known in itself, is not more known to us because it is farther from sensation. But what is close to sensation is more known to us. Therefore, the first premises must be more known in themselves.

But later in the same chapter, Aristotle makes it clear that the principles must also be more known to us. He writes:

It is always the case that that through which something is such is more such. . . . Therefore, if indeed we know and believe through first principles, these we also know and believe more, since through them we know and believe what comes after.

Aristotle first asserts here a general principle, that the cause is always greater than the effect. Therefore, if something is the cause of another having some attribute, then the cause itself has that attribute in an even greater way. For example, the reason that we love another is even more loved than that other. Therefore, if the principles are the reason that we know that the conclusion is true, the principles must themselves be even more known to us than the conclusion. From this it follows that, at least in some way, the first principles of demonstration are more known, not in themselves, but to us.

And this is our second problem. From examining one characteristic, that the principles express the reason why the conclusion is true, Aristotle deduces that the principles are more known in themselves. From examining another, that the principles are the cause of our knowing the conclusion, Aristotle deduces that the principles are more known to us. But he has already stated that what is more known in itself and what is more known to us are opposed to each other. So the solution to the first problem about how we know the first principles seems to lead us to a second problem, how the principles can be better known both in themselves and to us.

 

Conclusion

Near the beginning of this tutor talk we saw how the idea of first principles solved a problem that threatened to render scientific knowledge impossible, the problem concerning circularity or infinite regress in demonstration. Aristotle had to posit that the first principles were known by a different kind of rational knowledge, understanding, than the conclusions of demonstrations. We then encountered a problem concerning the principles themselves, how they could arise from some preceding knowledge. The solution was that they arose from sensation, and we saw how Aristotle solved the various difficulties that arise when we try to describe how such a process is possible. And then we saw that another major problem concerning the principles flowed from our previous solution: the principles have to be both better known in themselves, but because they arise from sensation, they seem only to be better known to us. This latter problem we are for the moment leaving unsolved.

But I can’t help giving a hint about how it might be solved, and that hint comes from Aristotle’s book on dialectic, the Topics. There, in Book VI, Chapter IV he writes:

Different things are more intelligible to different people. . .. Moreover, to the same person different things are more intelligible at different times, first of all, the objects of sense, and then, as they become more sharp-witted, the converse.

So, in the Topics Aristotle proposes the beginning of a possible solution. Could it be that what is more known to us is not fixed, that in some way what is more known in itself can, through some process, become more known to us? Might that process be dialectical? I’m afraid that, for the moment, we will have to be content with these tantalizing suggestions.