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Dr. Anthony Andres: Probability and Likelihood in the Dialectical Proposition

Posted: October 1, 2018

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Probability and Likelihood in the Dialectical Proposition

By Dr. Anthony Andres
Thomas Aquinas College
Tutor Talk (prepared text)
September 19, 2018

 

In the beginning of Parts of Animals, Aristotle teaches us that each of the various sciences has its own proper method, and that it is the mark of the educated man to  know the method of each science. But besides their proper methods, all of the sciences share a common method, a method of proceeding from the known to the unknown which the human mind must follow in any subject if it is to achieve certain knowledge. But the nature of that method has often been a matter of dispute.

Plato called that common method “dialectic” and displayed its use in his dialogues. Their main character is Socrates, who taught that method to Plato in real life. The Socrates of the dialogues proceeds philosophically by engaging someone in conversation and then asking that person a series of questions, drawing out the consequences of their answers. His interlocutors are almost always surprised at the ultimate conclusion because it almost always contradicts their original opinion on the matter in question.

Aristotle was the student of Plato for 20 years, but ultimately he did not think that dialectic by itself was the common method of the philosophical sciences. He seems to explains why in this passage from his book, Sophistical Refutations:

Accordingly, no art that is a method of showing the nature of anything proceeds by asking questions; for it does not permit a man to grant whichever he likes of two alternatives in the question. (l72al5)

Clearly Aristotle does not think that dialectic is a sufficient method for reaching the truth in a philosophical science. He searched for and discovered a more certain method, a method which we now call logic and which Aristotle teaches in the collection of books called the Organon. The principal book of that collection, that to which the previous books are ordered, is his Analytics, Prior and Posterior. At the beginning of the former, Aristotle contrasts the method taught by Plato, dialectic, with his own method, which he names demonstration. He writes:

The demonstrator does not ask for his premiss, but lays it down, whereas the dialectical premiss depends upon the interlocutors choice between two contradictories. But this will make no difference to the production of the syllogism in either case.

So, in Aristotle’s view, dialectic and demonstration are opposed to each other by a crucial difference. Although they share the use of the syllogism, which Aristotle defines as discourse in which, certain things being stated, something else necessarily follows because of them, dialectic and demonstration differ in how they obtain those “things stated.” The demonstrator lays them down as the true first principles of his science and as sources of sure knowledge; the dialectician asks a question, called the dialectical proposition, and then accepts the answer of his interlocutor as the premiss of his syllogism.

We would expect, then, that Aristotle, having discovered and taught the better method of demonstration, would have left dialectic entirely aside. After all, as he said before, no art which aims at truth would permit the student to choose whichever he likes of two contradictory statements as its first principles. But in fact, Aristotle is full of surprises. He writes a whole book called the Topics which teaches the dialectical method, a book almost as long as the Prior and Posterior Analytics put together. And in that book he justifies himself  by arguing that the study of the dialectical method is useful to the philosophical sciences.

St. Thomas Aquinas  places a high value on this method as well. He asserts that the dialectical syllogism produces an op-inion that its conclusion is true, although not the certain knowledge produced by demonstration. St. Thomas believes that it is reasonable to agree to the conclusion of the dialectical syllogism because it follows necessarily from its premisses, and the premisses are themselves probable.

But if the premisses of the dialectical syllogism really are just  answers to questions, why would he think that they are probable? And if the conclusion depends upon those answers, how can we reasonably agree to it as true, even if our agreement is not certain but is accompanied by hesitation? In defending dialectic, Aristotle and St. Thomas seem to be defending a parlour trick whereby the quick-witted gain the unwitting agreement of the less clever. Dialectic seems unworthy of being called a philosophical method, despite its acceptance by Aristotle and St. Thomas.

What I want to argue today, first, is that St. Thomas, following Aristotle and the philosophical tradition, including St. Albert, was right to call the premisses of the dialectical syllogism probable. I want to show that, although these premisses are not known with certainty, and are answers to questions, they are nevertheless likely to be true. Then I want to dig a little deeper and investigate why we come to agree to these premisses whose truth we do not see. In doing so we will see why St. Thomas says that the premisses of dialectical syllogisms are in some way taken from logical relations.

But before we can defend the value of dialectic in this way, we need to see how Aristotle distinguishes two kinds of questions in dialectic, the dialectical problem and the dialectical proposition.

That Dialectical Premisses are Probable and Likely to be True

Aristotle begins by pointing out that both dialectical problems and dialectical propositions are questions. But they are questions of different sorts and are asked in different ways. The dialectical proposition is asked in this way: “Isn’t it good to do good for one’s friends?”; but the dialectical problem is asked in this way: “Is pleasure worthy of choice or not?” The former question is asked in such a way that it invites a particular answer, an affiliation that it is good to do good for one’s friends. The latter question is asked in such a way that invites either side of the contradiction, namely either that pleasure is worthy of choice or that pleasure is not worthy of choice. That is, the very form of the first questions invites just one answer, while the form of the other is open to opposite responses.

Aristotle’s account of the dialectical problem and dialectical proposition keeps this difference in mind. The dialectical problem is the subject of the dialectical inquiry; that is, it is the subject of disagreement, or at least it is a subject about which there is no settled opinion. The dialectical problem is the question which the series of dialectical syllogisms hopes to answer.

In contrast, the dialectical proposition expects a particular answer because it asks for something that is held by all or most men, or at least by the wise; and of the wise, all or most of them, or the most endoxos of the wise, those held in highest repute. We should note immediately that, if the common man disagrees with the wise, the question concerning this subject is not a dialectical proposition, but a dialectical problem. So what we see here is that dialectician asks the dialectical proposition, that is asks a question in order to secure a premiss, not because he wants to elicit the hidden opinions of his particular interlocutor, but because he wants to secure his assent to a statement that just about everyone agrees to. It is the answer to this question that St. Thomas calls the probable premiss.

Now we are going to have a slight difficulty about the word “probable.” In English the word first means “likely to be true” or “more likely than not to happen.” We say that statistics deals with probabilities: If you flip a coin, the probability of its coming up heads is 50 percent. No immediate connection between the word “probable” and our notion of the answer to the dialectical proposition is apparent to us.

But the case is different with the first meaning of the corresponding Latin word probabilis. This word is rooted in the verb probare, to approve or commend. Thus for the Latin speaker the first meaning of the word “probable” would be the approvable or acceptable. And the Greek word translated by the Latins as “probable” bears this out. The word that Aristotle used to describe the premisses of the dialectical syllogism in their distinction from the premisses of demonstration is endoxon, of high repute or held in esteem. The Oxford translation of the Topics renders this word as “generally accepted.”

I think this makes it easier to see the connection between the answer to the dialectical proposition and the probable. The dialectical proposition, in contrast to the dialectical problem, is a question which expects a particular answer. It is able to expect this answer because it asks for an answer that the dialectician already sees is held by all or most men, or the wise. Since the answer is already approved by or acceptable to all or most or the wise, it deserves the Latin name probable  and the Greek name  endoxon.

And when Aristotle distinguishes dialectic from demonstration, he uses the word endoxon  or probable to separate the dialectical premiss from the demonstrative premiss. The premisses of demonstration are true and primary, and are believed, Aristotle says, “not on the strength of anything else, but of themselves.” That is, they are self-evident. In contrast, the dialectical premiss is only probable, endoxon, and that means that it is accepted, not in virtue of being self-evident, but in virtue of being held by all, most, or the wise. Aristotle has not yet made a connection between “accepted” and “likely to be true.”

But Ivan Pelletier, the author of La Dialectique Aristotelicienne, provides us with a middle term. He points out that things which are so always or for the most part are in accord with natural inclination. For example, that most men live in villages or cities shows political life is not entirely artificial, but arises from a strong natural inclination in man. Likewise, the assent that most men give to the probable statements must arise from the natural inclination of the human intellect. But the intellect has truth for its object. And so the fact that all or most men affirm these statements is a strong, though not infallible, sign that these statements are true. Thus, the probable statements that are the answers to dialectical propositions and are the premisses of dialectical syllogisms are statements that are not known to be true, but are likely to be true. And St. Albert affirms this in his Commentary on the Topics. He says, “The probable things, from which the dialectical syllogism is made, are likely things.”

So the dialectician is not playing a parlour game. He is not trying to elicit the peculiar opinions of his chance interlocutor; rather, he is securing his interlocutor’s assent to what is held by all or most because it is likely to be true. Truth and probability do have a connection.

Dialectical Premisses are from Logical Intentions

We have already seen that probable statements function in dialectic as the self-evident first principles function in demonstration. Both are acceptable to the mind immediately, without a middle term. But how can a statement be immediately acceptable when it is not self-evident? To answer this question, it will be helpful to first examine what makes a statement self-evident.

St. Thomas in many places describes the various properties of the self-evident statement: It is known immediately, without the agency of a middle term; it is assented to as soon as its terms are understood; it is assented to by necessity. But behind these properties is the cause of self-evidence: a statement is self-evident when its predicate belongs to the very ratio of its subject. For example, it is self-evident that all right angles are equal because being equal to other right angles belongs to the very nature of the right angle. Similarly it belongs to the very nature of a whole that it is greater than its part.

The probable statement, however, is not self-evident; its predicate does not belong to the very ratio of its subject. But since they are accepted immediately, there must be something about the conceptions of the predicate and subject that inclines the mind to join them. That something is what St. Thomas is pointing to when he says that the probable statement is taken, in some way, from logical intentions.

In his Commentary on the Posterior Analytics, St. Thomas notes that logic, first philosophy and dialectic, all proceed from common principles, but in different ways. First philosophy proceeds from common principles because its subject matter is being in common; logic and dialectic, however, proceed from common principles because both proceed from the intentions of reason, that is, logical intentions, which are common to all being insofar as all being is knowable. About dialectic in particular he writes:

Dialectic does this because the dialectician proceeds by arguing from common intentions toward those things which belong to the other sciences, whether those things are proper or common, although most to the common.

The common intentions from which the dialectician proceeds are logical intentions, while the proper or common things toward which he proceeds are the matters of the sciences, particular or metaphysical.

In a passage from the Commentary on the Physics, however, St. Thomas makes it clear that logic and dialectic proceed from logical intentions in different ways. Logic is about logical intentions, and so the names of the logical intentions are themselves the terms in the syllogisms that the logician makes in his own science. That is, logic not only proceeds from the notions of genus and species, it uses those names as terms in its premisses and conclusions. In contrast dialectic usually does not use those names as terms in its syllogisms; rather, the terms that it uses belong to the subject matters of the particular sciences or metaphysics. And that fact leads to the following question: How can dialectic be said to proceed from logical intentions if it does not use the terms of logic in its reasonings?

St. Thomas provides us with an example of how this works. The following, he says, is a dialectical syllogism:

Love is in the concupiscible appetite.
Hate is in what love is in.
Therefore, hate is in the concupiscible appetite.

What reason does St. Thomas think underlies the assertion that love and hate are in the same thing? He tells us:

From this, that contraries are about the same thing.

We should notice that neither is the statement about contraries a premiss in the argument, nor is the term “contrary” a term in the argument. Nor is the premiss that hate is in what love is in the conclusion of a previous syllogism which has the statement about contraries as one of its premisses. Rather, the statement about contraries is a more universal statement, of which the statement about love and hate is a particular application. It has, in dialectic, the character of a Common Notion or Axiom: the statement about love and hate is affirmed in the light of the statement about contraries because love and hate are corresponding contraries.

And this analysis invites me to take a further step, a step that I have  not found explicitly in Aristotle or St. Thomas, but a step which I think fits with what they are saying. The intellect is moved to affirm probable statements, not because it sees that the predicate belongs to the very ratio of the subject, but because the logical relation of the predicate with the subject strongly suggests their truth. The subject and predicate of a statement names two natures, and logical intentions belong to such natures. But the logical intentions do not belong to the natures as such; rather, they belong to them only insofar as they are known. For example, being the genus of man belongs to the nature animal, but not as such; rather, it belongs to animal insofar as animal is known. Similarly, being the contrary of hate does not belong to love as such, but results from our way of understanding love, in which we conceive of love as belonging to a genus and being related to another member of that genus in a particular way. And because we conceive of love and hate as contraries, we conceive of them as belonging to the same subject. And because we conceive of them as being in the same subject, we incline to affirm that, in reality also, they are in the same subject.

And perhaps they really are in the same subject. After all, the logical relation does not arise only from the way of understanding, but from the way of understanding these real natures. Thus, the logical relation is a sign, not always infallible, of some truth about the natures. In sum, because the logical relation arises partly from the nature of the thing, the statement to which it inclines us is likely to be true. But because it also arises from the mode of understanding, we cannot affirm it with certainty. These opinions, which are like first principles in dialectical discourse, are both probable and likely.

So let me gather together again the strands of this inquiry. Our problem was that dialectic receives the premisses from which it reasons as answers to questions, rather than laying them down as true. It seemed before that this implied that dialectical discourse was

rooted in the peculiar opinions of the chance interlocutor. This in turn seemed to imply that dialectic bad no relation to truth. What we found, however, was that the questions that the dialectician asks are ordered to eliciting from the interlocutor, not his peculiar opinions, but the opinions that he shares with all or most men. This is what makes them answers  to the questions probable. And we further saw that, through their source in logical relations, those statements are not only probable, but also likely to be true. And so both probability and truth are, in some way, found in the dialectical proposition.

 

 

Dr. Anthony Andres: Probability and Likelihood in the Dialectical Proposition

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