Chapter I: Containing the Preface of the Book
Although in his Prior Analytics, Aristotle firmly established and relied on solid foundations to set forth only three figures of syllogisms, there were, however, those who believed that he had either overlooked or omitted the fourth figure, which Galen discovered and attributed to Averroes in Chapter 8 of Book 1 of the Prior Analytics. In the extant works of Galen, we find no mention of this figure. Still, in other works by him, which are missing and which Averroes read, Galen spoke on this matter. Since it is either believed that no one, without a strong reason, dared to assert such a viewpoint against Aristotle, it is not surprising that very learned men who took up the task of defending Galen and his doctrine against Aristotle sought to support it with very powerful arguments and to defend it from Averroes' reasons. Therefore, since this controversy among great men appeared to us to be worthy of attention, we thought it would be wise to consider it with diligence, especially since it will provide us an opportunity to clarify many matters related to all figures, which are most worthy of understanding but known to only a few. Without knowledge of these, we would not be able to speak well about the fourth figure. In this discussion, we shall follow this order: first, we will explain what this fourth figure is; then, we will present all the arguments that can be put forth to confirm it according to Galen. Next, we will approach the explanation of the truth and clarify Averroes' arguments against Galen. At the same time, we will examine the responses of the physicians to ascertain whether Galen's defenses are sufficient against Averroes' arguments. Finally, we will resolve the arguments put forth by the physicians against Aristotle.
Chapter II. In which it is explained where the number of figures originates
Before we explain the fourth figure, it's essential to understand where the diversity of figures originated. It's important to note, as stated by Averroes in his Commentary on Aristotle's Prior Analytics, chapters 5 and 8, and in the epitome at the beginning of the second figure, as well as acknowledged by the defenders of Galen, that a syllogism, as considered by Aristotle in his Prior Analytics, is constituted upon a specific problem—a conclusion proposed for gathering through a syllogism. What the Greeks call "problem" is referred to by Averroes as "quaesitum," which, after reasoning, becomes a conclusion. The idea is that before we take propositions, we have a specific problem, a conclusion that we intend to deduce through the syllogism. Averroes calls this "quaesitum," and Alexander also uses similar terminology.Giacomo Zabarella
So, before we even consider propositions, we first have a definite problem—a conclusion composed of two terms: the subject and the predicate. The subject is usually the less extreme, while the predicate is the more extreme. These are called by Averroes "subjectum quaesiti" and "praedicatum quaesiti."
After this, we seek a third term called the middle term. We connect this middle term with each of the extremes of the problem. This creates two propositions, from which we deduce the original problem. When the middle term is connected in any way with the predicate of the problem, we get the major proposition. When it is connected with the subject of the problem, we get the minor proposition. From these two propositions, we deduce the problem. When we change the name, it's called the conclusion.
This explains why the earlier books are titled "Resolutive." They teach how to resolve the propositions into the principles of their reasoning. To resolve means to find two propositions for those conclusions because it is moving from the later to the prior, and in a way, it's moving from the effect to finding the cause.
To determine the number of figures, Aristotle found that the middle term is combined with two extremes in various ways in different propositions. The way in which the middle term is related to the extremes gives rise to the number of figures. If the middle term is connected with both extremes in the same way in the propositions, it becomes the major proposition and gives rise to the second figure. If the middle term is connected with both extremes inversely in the propositions, it becomes the minor proposition and gives rise to the third figure. If, however, in the proposition, the middle term is connected to the minor extreme, and it is connected inversely to the major extreme, it becomes the major term and gives rise to the first figure.
Chapter 3: Where the fourth figure is explained
Galen, however, seems to have discovered the fourth position of the middle term and, therefore, the fourth figure. The fourth position occurs when the middle term is placed under the subject of the minor premise and is predicated of the major premise. To illustrate this, let's consider some examples:
Suppose we want to conclude "some body is a human." We take the middle term "animal." The major premise is "every human is an animal," and the minor premise is "every animal is a body." Using the fourth figure, we deduce that "some body is a human."
Now, if we switch the premises, with "every animal is a body" as the major premise and "every human is an animal" as the minor premise, we would conclude "every human is a body," which belongs to the first figure, not the fourth.
If we aim to derive a negative conclusion, such as "some body is not a human," we can follow a similar process. Let's assume the major premise is "no animal is a human," and the minor premise is "every animal is a body." Through the fourth figure, we can conclude "some body is not a human." This mode of reasoning consistently leads to negative conclusions in the fourth figure.
We can demonstrate with several arguments that this is the fourth figure useful and should be counted as the first. First, from what has been said previously, it follows argumentatively that the fourth figure is given when the seat of the middle term is with respect to the extremes. Therefore, let the fourth figure be granted as you wish; the antecedent has already been declared: the consequent is also manifest because Aristotle found the number of figures by no other reason except from the different position of the middle term with respect to the extremes.
Furthermore, a good syllogism is one that fits the definition of a syllogism given by Aristotle. Now, the definition of a syllogism in the fourth figure applies to it. Therefore, syllogisms of the fourth figure are good. The minor is proven because syllogisms of the fourth figure are syllogisms in which the conclusion follows necessarily from the premises themselves, as was evident in the examples. Furthermore, all syllogisms of the fourth figure are good because they are perfected and proven by reduction to the first figure.
Moreover, it is Aristotle's opinion that syllogisms of the second and third figures are good only when reduced to the first figure. Therefore, they are good. The major is Aristotle's because he seems to show by no other reason that syllogisms of the second and third figures are good than by reducing them to the first figure. The minor is proven because the affirmative mode of the fourth figure, which we have posited, is confirmed by reduction to Barbara by the mere transposition of propositions and the conversion of the universal conclusion into a particular one. From the major premise "All animals are bodies," which was the minor premise in the fourth figure, and from this minor premise, "Every man is an animal," we obtain by reduction a conclusion in Barbara: "Every man is a body." So the fourth figure is proven to be good.
We can also argue as follows: Aristotle considered no other reason for deeming the modes of the figures useless except that they do not always lead to certain conclusions. In the fourth figure, conclusions are sometimes affirmative, sometimes negative. Therefore, we cannot say of those two modes of the fourth figure that either of them always and universally draws a certain conclusion. However, any syllogism of the fourth figure consistently and always produces a certain conclusion. The affirmative mode always yields a particular affirmative conclusion, and never a negative one, while the negative mode consistently results in a particular negative conclusion and never an affirmative one.
Thus, we can conclude that these modes are not useless but good and useful. Therefore, a place should be assigned to them among the figures of syllogisms. However, no distinction can be made among the three other figures based on the different positions of the middle term. Therefore, the fourth figure should be recognized as distinct from the other three. These are the arguments that doctors adduce or can adduce to support Galen's viewpoint.
Chapter 5: On Dual Logic and the Dual Syllogism, Natural and Artificial
Against this fourth figure, Averroes argues most effectively. But for his arguments to be understood, many things need to be known first concerning all the figures, without which the truth of this matter and Averroes' arguments will not be well understood.
First and foremost, it must be understood (and Aristotle himself affirms this in the end of his second book of "Elenchi Sophistici") that Aristotle was the first inventor and constructor of the art of syllogism, which no one had written or taught before him. Alexander also testifies to this in his "Prior Analytics," stating that Aristotle was the first to discover the method of syllogism, which no one had known before him. Thus, he can be called the inventor of the whole art of logic, for this is the common form of all methods and the instrument of all logic, as we have explained in our book on methods.
However, the way in which Aristotle discovered and constructed the art of logic is evident from what we have said elsewhere about the nature of logic. Since logic is dual, one being natural and the other artificial, Aristotle found and composed the artificial logic from the natural logic. The natural logic, which other people used by instinct and by nature, was guided only by nature. Aristotle, on the other hand, brought forth artificial logic from the natural one by observing methods and progressions which others followed naturally. He reduced them all to the rules and precepts of art, as we have set forth in the place mentioned.
Therefore, since Aristotle constructed the art of syllogism from natural logic and the natural syllogism, he was unwilling to consider any syllogism that did not proceed by the natural route, namely, through those syllogisms which men, being led by natural instinct, follow naturally and necessarily. He also wanted to reduce all syllogisms that conclude by necessity to the natural ones, and to declare what necessity is, a necessity known naturally to all men. For how could these others be generated from the natural ones, or how could these be confirmed and corroborated by the others unless the former were similar to the latter and conformed to them? Therefore, it should be noted, for the sake of clarity when reading Averroes, that by the ambiguity of words, we do not stray. For when we say "artificial syllogism," we can mean two things. Either we mean a syllogism following artifice and derived from the natural one, as we have said, and which is similar to it, such as all the syllogisms which Aristotle treats of in the three figures. For they are called "artificial" because they are taken from the natural ones. Or we mean artificial syllogism as opposed to the natural one and as its contrary because it does not conclude in the natural way, but by artifice and the device of some man. In this way, Averroes calls all syllogisms of the fourth figure, namely, the contrary of the natural ones.
Chapter 6. That the dictum de omni and the dictum de nullo are the natural foundations of all concluding syllogisms
Since Aristotle decided to deduce all syllogisms constructed by art from natural syllogisms, in the first chapter of the Prior Analytics, he proposed the dictum de omni and dictum de nullo as natural syllogisms themselves and the roots of all artificial syllogisms he was going to discuss in that book. Therefore, Averroes rightly said in the Epitome of those books, chapter 1: "The dictum de omni is the root and principle of all concluding syllogisms." In reality, all syllogisms that affirm are derived from the dictum de omni, just as all syllogisms that deny are derived from the dictum de nullo, as these phrases indicate: "omnis" (every) and "nullus" (none). The second term is predicated of the third in the conclusion, which is the last of all and is predicated as a subject part. Therefore, this second term is called "totum" (whole) with respect to the lowest term and is the middle term in the syllogism. However, the highest term, which is predicated of the whole, is called the major extreme, and the lowest, of which the whole is predicated, is called the minor extreme. Thus, when we state the dictum de omni or the dictum de nullo, and explain their meaning, we are stating a complete syllogism. For we present two propositions and draw a conclusion from them. When we affirm the first term universally predicated of the second, which is said to be the whole, we make a major proposition that is always universal, but sometimes affirmative and sometimes negative. When we take a part as the subject in the minor proposition, we form a minor proposition, which is always affirmative. For it wouldn't be a part if it were negative; the whole is always predicated affirmatively of the subject part. Hence, Averroes rightly recognized these aspects, stating in Chapter 1, Book 1 of the Prior Analytics that the dictum de omni and dictum de nullo necessarily require two conditions: one, that the major proposition is always universal, and the other, that the minor is always affirmative. Averroes thus means to emphasize that these two dicta signify complete syllogisms and not simple propositions. In Chapter 10 and 24 of the same book, Averroes also speaks of the consideration of the whole and part in a syllogism through the dictum de omni or dictum de nullo. However, this should be understood in a broad sense, not confined to specific individuals or species but rather in a broad sense referring to a part and the whole. This is to ensure that we don't mistakenly think that a species always subsumes an individual or that an individual should be understood as a part under a species. We take "whole" and "part" in a broad and extensive sense, not obliging ourselves to the conditions of materials, so whatever is affirmed of another in any way is considered to have the same relation that a whole has to a part. Therefore, in every affirmative proposition, we say that the subject is predicated as a part of the predicate, for example, if we say "every human is visible," "visible" is taken as the whole and "human" as a part. If we say, "some animal is human," "human" is taken as the whole and "animal" as a part. In the Prior Analytics, we do not consider the matter, but only the form and mode of enunciation. We abstract from all conditions of matter to focus only on the form of propositions. We abstract to such an extent that we do not consider the truth or falsehood of the propositions, but only how the propositions are structured, as they are stated and connected. We do not consider whether a true or false conclusion is drawn, but only that the conclusion follows from the given propositions by necessity.
To consider only the form without any matter: truth and falsehood are conditions related to the matter.
From this, it is evident that the dictum de omni and dictum de nullo both contain only the first figure. In both of them, it is necessary for there to be a middle term. When the whole is affirmed of a part, the mood Barbara arises; if it is affirmed particularly, AII results. In the case of the dictum de nullo, if a part is taken universally from the whole, EAE arises; if it is taken particularly, EIO results. Other moods are not given in the first figure due to the reasons we mentioned.
However, other figures can be reduced to the first figure. This is because in those cases, the middle term is placed outside of the other two terms, where the power and effectiveness of these two principles are not evident. Therefore, Averroes says in the first book of the Prior Analytics, chapter 24, that the dictum de omni is actually in the first figure, but in the others, it is potentially. Aristotle used the dictum de omni to confirm the usefulness of the modes in the first figure, as it demonstrates the effectiveness of two affirmative modes. Through the dictum de nullo, he explains, as if declaring that syllogisms constructed by art are naturally rooted in us, the force of syllogisms built by art. Because Aristotle wanted to admit no syllogism constructed by art except if its effectiveness could be confirmed by these two natural roots, he sought to confirm all other syllogisms in the second and third figures through reduction to the first figure. In this way, the efficacy of these two natural principles, which was not apparent before, becomes evident in other figures as well.
Chapter 7: Reduction of Other Syllogisms to the First Figure
Certitude, and even the evidence of necessity, distinguish two things through the perfect idea of necessity, but not through the appearance of necessity. They take this through reduction to the first. Now, this reduction happens in two ways: One through the conversion of propositions when they are turned to the first; the other through the reduction to the impossible when the form of conversion cannot be achieved. Indeed, in the first way, we convert two propositions, putting the middle term, which is outside the other two terms, in the middle. Therefore, in the unsound figure, we convert that proposition which is going to be the major in the first figure because we want the middle to be predicated in the major, which was predicated in the second figure. In the third figure, however, we convert that proposition which is going to be the minor in the first figure because we want the middle to be predicated in the minor, which was put in the third figure. We use this reduction in all modes of the second and third figures, with two exceptions called Baroco and Brocardo, in which, since we cannot use conversion in proposition, we resort to reduction to the impossible. In this way, through the first mode of the first figure, we declare the effectiveness of these two modes. For when the conclusion is denied by the opponent, and both propositions are granted, we take the universal affirmative opposite to the conclusion. We affirm one of the granted propositions universally, and from these, through Baroco, we infer the opposite of the other granted proposition. So, we lead the opponent to assert that either both opposites are true simultaneously, or that there are no useful modes of reasoning, and no power of drawing conclusions, which was the point to be demonstrated.
However, this reduction to inconvenience is not allowed only in these two ways but also in others of the second and third figures. Nevertheless, when in other cases, we can perform this reduction better and more easily through the conversion of propositions, we reject the reduction to the impossible. This is because it is more oblique and difficult. For when we can proceed directly to a certain end by the straight path, there is no need to go through the oblique and longer route.
A third method was also used by Aristotle for proving syllogisms proper to the third figure, which he called exposition in the third figure. Averroes and Alexander, however, called it sensible exposition. For the third figure is entirely specific and collects a sensible conclusion and has a middle subject for both extremes. Therefore, we take some particular sensible thing under the middle term, in which the conclusion can be sensed. For example, if we argue in this way: 'Every human is a biped, every human is laughable; therefore, some laughable thing is biped.' We can demonstrate the effectiveness of this inference through sensible exposition by taking some well-known singular under the term 'human,' such as Socrates, who is seen to be both laughable and a biped. Hence, it is evident that some laughable thing is a biped.
From this, a doubt arises, which is easily resolved by us. It seems that a syllogism is formed in the third figure from both singular propositions, perpetually concluding a particular affirmative. For if Socrates is a biped, and Socrates is laughable, it necessarily follows that some laughable thing is a biped. This mode of reasoning is effective in every subject matter and can also be confirmed by reduction to the first figure or by reduction to the impossible. For, by taking the contradictory of the conclusion, assuming that nothing laughable is a biped, and adding the other granted singular proposition, 'Socrates is laughable,' it follows that Socrates is not a biped, which is contradictory to the other granted proposition. For there is a contradictory opposition between singulars that does not exist among particulars. Therefore, Aristotle was right in stating that nothing is concluded from two singulars. However, it seems that, in practice and useful discussions of the third figure, he should have counted this one, which concludes from two singulars when there is a contradiction between them, and another in particulars. For the term 'particular' has different meanings.
In the manner of the part and the vague, there is ambiguity in proposition A. This is because an affirmative proposition can be true of one thing, and a negative proposition can be true of another. Hence, there is no opposition between them, and a syllogism from such propositions would conclude nothing because of the ambiguity of the middle term, which has four terms.
However, the singular signifies in the manner of the whole and is designated. Therefore, it does not admit any ambiguity and has contradictory opposition. Hence, reasoning from singulars is effective. For when two predicates are attributed to a certain subject, it always follows that one is affirmed of the other particularly, whether the subject is universal or singular. Therefore, the syllogistic power is the same in the mode that arises from both singulars, which is also found in Darapti, as is evident to anyone considering it.
In response to this doubt, I think it should be said that the argumentative method from both singulars is not impossible and is indeed effective. Anyone who denies this would be lacking in understanding. However, Aristotle did not consider it worthy of the name syllogism, nor did he include it among syllogisms. For where the consideration is entirely singular and sensible, where nothing is universal, there is no use of reason by which a syllogism gets its name. Therefore, it does not deserve the name of reasoning, as it is a conclusion known by sense rather than collected by reason. It is also unrelated to statements about every and no, in which each proposition is universal, as is evident.
Aristotle did not ignore this kind of argumentation, as he used it for confirming the modes of the third figure. Recognizing that it involves more sensory knowledge than reasoning, he did not include it among syllogisms but preferred to use it as a testimony of sense to declare the power and efficacy of syllogisms of the third figure.
Chapter 8: In which the first argument of Averroes against the fourth figure is explained, demonstrating that it is not natural
With these considerations related to the three figures of syllogisms, let us now turn to the fourth, for which we have set out the discussion. We shall examine Averroes' arguments against it and see how others, like Galen, respond to Averroes and raise objections. Firstly, in chapter 8, book 1, Prior Analytics, Averroes argues against Galen as follows: Syllogisms considered in Logic should be such that our natural thought falls upon them when a definite question is asked. However, our natural thought does not fall upon syllogisms of the fourth figure; therefore, they should not be considered in Logic, nor should they be counted among other syllogisms. In this manner, Averroes refutes Galen's fourth figure and presents the reason why Aristotle ignored it and chose not to consider it. He argues against our natural thought process, which is why he also goes against Aristotle's intention in treating syllogisms. We have already said that Aristotle intended to discuss those syllogisms in Prior Analytics that are in harmony with nature, not those that go against nature. However, it should not be assumed that Averroes meant to say that the fourth figure is contrary to nature, for it concludes a predication that is not unnatural to nature, such as species from genus or subject from accident. For instance, we can say that some animal is a human, or everything laughable is a human. Such unnaturalness, so to speak, arises due to the nature of the subject matter, not due to the form. Hence, it is considered by both Averroes and Aristotle in Posterior Analytics. There, it is the matter that is considered, not the form. Therefore, this predication, though seemingly unnatural, like 'an animal is a human' or 'laughable is a human,' is examined in terms of matter and not form. In the Prior Analytics, no consideration of matter is made, and no defect of matter is examined. Only the pure and separate form is looked at, still unaffected by any conditions of matter. Therefore, supporters of Galen rightly argue that if Averroes interprets unnaturalness in this way, his argument carries no weight, and it would not stand more against Galen than against Aristotle. For conclusions like 'everything laughable is a human' and 'some animal is a human' can be drawn in the first figure.
So, by declaring this, we might similarly conclude that the first figure is not natural. Moreover, Aristotle taught the conversion of propositions for reducing syllogisms of other figures to the first. However, it is certain that every proposition, whether affirmative or negative, becomes non-natural when converted. For when this proposition is natural, 'A human is laughable,' when converted, it becomes non-natural, 'Laughable is a human.' Therefore, we must conclude that either no proposition can be converted, or Aristotle opposes nature in the other three figures as well, which we should not say. Thus, Averroes did not mean to refer to the unnaturalness of matter. In Prior Analytics, this is neither rejected nor considered, for every granted proposition is admitted there. Neither true nor false is considered there. I wonder how many logic professors have attributed to Averroes this foolish interpretation and considered his argument, thus understood, effective and strong, although it could be said that nothing is more absurd if understood in this way.
Therefore, we say that Averroes had a different intention. When speaking of syllogisms as natural or unnatural in their deviations, he meant naturalness or unnaturalness in terms of form, not matter. He did not understand natural or unnatural predication in propositions as related to matter. Instead, he understood natural or unnatural inferential conclusion drawn from propositions, whether it is made naturally or unnaturally according to the order of inference. For the power of inference resides in the form, not in the matter. Therefore, the naturalness or unnaturalness of the conclusion is the naturalness or unnaturalness of the form, and without a doubt, this is what Averroes meant.
Now, the naturalness of the form entirely depends on the dictum de omni and the dictum de nullo. We say that an inference is natural when what is predicated in propositions remains predicated in the conclusion, and what is the subject in propositions remains the subject in the conclusion. Such an inference is made through the dictum de omni and the dictum de nullo. We have already said that three terms are involved here. In this, the highest term is called the major extreme, below which stands the middle term, and below the middle term stands the lowest term, which is considered as a part of the whole. Now, when the major extreme is only predicated in propositions, not the subject, and the minor extreme is only the subject, not the predicated, the rule of dictum de omni requires that the same two terms maintain the same relationship in the conclusion. That is, what is predicated in the upper proposition is inferred to be predicated of what is subject in the lower proposition, so that the predication of the upper is inferred into the lower. This means that the same two terms are involved in the conclusion as were involved in the propositions.
Therefore, it is not the case that 'above' and 'below' are understood as they are in the Categories and in reality, where we are compelled to predicate 'body' of 'animal' but cannot predicate 'animal' of 'body.' Rather, we understand 'above' and 'below' according to our usage in propositions, so that what was 'above' in them remains similarly 'above' in the conclusion, and what was 'below' remains 'below.' This is the natural inference that is clearly signified by the dictum de omni. We do not say that something is predicated 'of every' with respect to some subject and is predicated of a part of that subject. Instead, we say that if something is predicated 'of every,' it is also predicated 'of every part' of that subject. Hence, by the dictum de omni, we mean that what is predicated remains predicated in propositions in the conclusion, and what is the subject remains the subject. This is the natural inference, which is perverted in the fourth figure, and the nature of the dictum de omni is not preserved; this inference is contrary to the dictum de omni.
So, Averroes says that our natural thought does not fall upon that conclusion. Any person hearing the complication of those propositions would expect, due to the inherent force of the dictum de omni, a natural conclusion: 'Every human is a body.' However, the syllogism that they say exists in the fourth figure is actually in the first mode of the first figure, with the minor proposition placed before the major. For what they call the major is, in fact, the minor, and what they call the minor is, in fact, the major. As for the conclusion 'Some body is a human,' we do not deny it, but we say that this consequence is indirect and remote and, as Averroes puts it, artificially and with manipulation. First and immediately, the universal affirmative conclusion 'Every human is a body' follows. Then, from this universal affirmative, its particular converse follows, 'Some body is a human.' These do not follow directly from those two propositions but through a universal conclusion. Aristotle was not unaware of this mode of argumentation, which they call the fourth figure. He made mention of it in the first chapter of the second book of the Prior Analytics, showing that some syllogisms in the figures gather more conclusions than a single one primarily and immediately but others mediately and secondarily, like AAA, which gathers three conclusions, primarily the universal affirmative, and secondarily two particular affirmatives, one being a part of the universal and the other its converse. For if someone demonstrates that 'Every human is an animal,' they also demonstrate that 'Some human is an animal' and 'Some animal is a human,' because these two follow necessarily from the universal. However, this diversity of conclusions drawn from the same propositions gives rise to the diversity of figures or modes. Yet, there is one mode that primarily gathers one through the dictum de omni, while others are gathered secondarily and artificially. Similarly, in EAE, four negative conclusions are derived from the same propositions. However, one is universal primarily and naturally through the dictum de nullo, and the other is universal secondarily and artificially negative converse and two particular negatives, which are parts of those two universals, are gathered in the affirmative mode that they call the fourth figure. Aristotle places it as the first figure because if we look at the order of terms in propositions, it is the first figure. This is because the middle term is in the middle position in terms of assertion but indirectly, artificially concluding. This mode is called by the Latins 'Baralipton,' which they put in the first figure and call it an indirect conclusion. Those who say this are far less mistaken than those who claim it to be the fourth figure. Therefore, Averroes' first argument is very strong, proving that the fourth figure is not natural. And his statement is very true when he says, 'For if such a syllogism is proposed in the fourth figure, that some body is a human, and we take these two propositions: every human is an animal, and every animal is a body, then we find ourselves in between, and we hesitate whether to dismiss that proposition and infer only the natural conclusion, every human is a body, which is drawn by our innate understanding of the dictum de omni. And thus, we do not conclude the proposed question from the beginning. Or do we rather infer both at once, namely, the natural conclusion and the other proposition from the beginning?' As if Averroes is saying that it is not possible for our mind not to infer the natural conclusion, which is derived from those propositions by the dictum de omni. For our nature compels us to think that way upon hearing those propositions. Therefore, we either infer only the natural one or both it and the other proposition together with it.
Chapter 9: The Response of Galen's Followers to Averroes' First Argument
Responders to Galen's arguments often reply to this argument as follows: if the two affirmative propositions are arranged in such a way that they follow the order of the first figure, namely, that the one stating "every animal is a body" is placed before the one stating "every human is an animal" as the major premise, and the latter is placed as the minor premise, then the conclusion, "some body is a human," only follows secondarily and artificially. On the other hand, if these same two propositions are arranged in reverse order according to the fourth figure, where the major premise states, "every human is an animal," and the minor premise states, "every animal is a body," then the situation changes. In this case, the conclusion, "some body is a human," follows immediately and naturally through the fourth figure. The argument proponents assert that this change in arrangement of the same two propositions alters the syllogism's mode. Therefore, they argue that the conclusions reached are determined by the arrangement of these two propositions.
They assert that this argument rests on the foundation that the transposition of these two propositions changes the syllogism's mode. This, they claim, necessitates adopting a different mode and consequently arriving at a converse conclusion naturally. When the middle term's position is altered, a new figure emerges, which may require a different mode. They argue that this principle is confirmed by Aristotle himself, who, in the second figure, introduced two modes: EAE and AEE, which are considered different but fundamentally have no distinction other than the reversed order of the same propositions, resulting in a reversed conclusion. In Cesare, when the affirmative proposition is placed first, as in "every human is an animal," and the second proposition negates, as in "no stone is an animal," the conclusion "no stone is a human" follows naturally. On the other hand, when you reverse the order of the same propositions to create AEE, with "no stone is an animal" as the affirmative proposition and "every human is an animal" as the negation, the conclusion "no human is a stone" follows naturally. Therefore, they argue that both conclusions are considered natural in their respective contexts, despite being different from one another.
The same principle applies to the third figure, with its two modes, AII and EIO, and it results in the same conclusion: that transposing the propositions leads to different modes and consequently to different conclusions, which can be either natural or artificial, depending on the context. In summary, they argue that the arrangement of propositions plays a significant role in determining the syllogism's mode, which affects the nature of the conclusion reached. Nevertheless, they do not always mention what is emphasized by Aristotle and Averroes, namely, that from the same propositions, a conclusion is more easily and clearly derived in the first and fourth figures, as is evident.
However, those who defend Averroes' argument neither resolve it nor can they effectively turn it against Aristotle, as it holds considerable weight only against the fourth figure, not the others devised by Aristotle. We will easily demonstrate this if we clarify how natural inference is made in each figure and how it is not natural. Natural inference, as we have previously explained, depends on the expression "de omni" (concerning all) and consists of making the predicate in the conclusions remain also a predicate in the premises. This means that the two extreme terms in the conclusion retain the same relationship to each other as they did in the premises. This type of natural inference occurs most clearly in the first figure, where the actual "de omni" can be found, as we have already explained. Now, let's consider the other figures.
We claim that in the second and third figures, it is not apparent how the predicate in the conclusion can remain a predicate concerning the minor extreme term in the premises. This is because, in these figures, the two extreme terms in the premises are not assigned different roles. They are either both subjects of the middle term (as in the second figure) or both predicates of the middle term (as in the third figure). Therefore, since there is no clear reason in the premises to make one of the extreme terms greater or smaller than the other, we maintain at least the order of our pronunciation, designating the term and proposition that come first as major and the ones that come later as minor. This is the source of the difference between the two modes of the second figure, EAE and AEE, as well as between AII and IAI in the third figure. For in both cases, we can choose to place one proposition before the other. In doing so, we specify which of the two extreme terms we want to make the predicate in the conclusion. This does not contradict nature. For example, if the extreme terms are "stone" and "man," and we can equally place the middle term "animal" under both terms, we can choose which extreme term will become the predicate in the conclusion. Thus, no contradiction arises concerning nature. If we select the extreme term "stone" before "man," the conclusion will state, "No man is a stone." If we reverse the order, it will state, "No stone is a man." This applies to both EAE and AEE modes. In neither of these modes do we make the predicate in the conclusion anything other than what was established in the premises when "man" and "stone" held an equal position. Therefore, when transposing the propositions, no other order of conclusion is inferred except that of our proposition's enunciation.
Moreover, it can be argued that the distinction between these two modes primarily concerns the proposition initially proposed. For instance, if the conclusion to be drawn is "No man is a stone," and the middle term "animal" is provided, we will necessarily argue in EAE mode because the greater extreme term, "stone," negates the minor term, "man." However, in AEE mode, which is used when the conclusion is initially proposed as "No stone is a man," the argument proceeds accordingly. In both of these modes, we make the predicate in the conclusion match our proposition's enunciation. Hence, the transposition of propositions alters the modes of inference.
We can also say that the distinction between these two modes is based on the initial proposition's focus. If the conclusion to be established is "No man is a stone," and the middle term "animal" is provided, we will argue in EAE mode because the focus is on negating the greater extreme term, "stone." Conversely, in the AEE mode, which is used when the initial proposition is framed as "No stone is a man," the argument is conducted accordingly. In both modes, the predicate in the conclusion aligns with the primary proposition's focus.
This clarification shows that the nature of inference differs between these two modes, and they do not contradict each other. In the second and third figures, we do not have the same situation. In the second figure, the predicate "animal" is affirmed concerning the greater extreme term, and the minor extreme term "man" is subsumed affirmatively. This figure is referred to as minor because "man" is subsumed in the conclusion. In contrast, the term "stone" in the conclusion is predicated affirmatively, and this figure is called major. This distinction is based on the position or relationship of the extreme terms in the initial proposition and is reflected in the naming of the major and minor propositions.
Now, if the converse of the proposition is presented, such as "No stone is a man," and the same middle term "animal" is provided, the argument necessarily proceeds in the AEE mode. In this case, the negative proposition is minor, and the affirmative proposition is major. It is evident that both converse conclusions can be drawn from the same propositions. However, the one that was initially proposed is considered primary. Neither of these two modes is more natural or evident than the other. Both conclusions are naturally inferred from their respective modes, and each mode leads to a different conclusion. In the propositions themselves, there is no clear difference between this mode and that. Therefore, neither mode involves a violation of nature or contradicts the "de omni" dictum.
The same applies to the two modes of the third figure, AIIand IAI. The second and third figures are considered natural because many people naturally reason in them, just as they do in the first figure. Although these figures do not have the "de omni" dictum in their propositions, as they lack a middle term in the middle position, they have the potential, as we previously explained. They are not entirely natural, nor are they contrary to nature, as they do not oppose the "de omni" dictum but rather deal with the middle term in a specific way.
In summary, the second and third figures can be considered natural in terms of potentiality, as they can be reduced to the first figure. Therefore, they are not entirely unnatural, nor do they contradict the "de omni" dictum. These figures serve as guidelines and rules for even ordinary people, although they do not always adhere to them perfectly. Due to the influence of the materials from which practical works are constructed, deviations from strict adherence to these rules may occur. These figures still function as norms for practical reasoning, even if they are occasionally applied somewhat obliquely, albeit not perverted or destroyed than others, if they need to be reduced to the first figure. We prefer the first figure because it is superior to others, clearer, and more natural. Therefore, the other figures, except the first, should not be used. I believe it should be noted that the rule of the "de omni" dictum, which is naturally inherent in us, always leads us to reason in the first figure. The first figure is the root of all syllogisms, and it properly generates the first figure. However, practical considerations and material constraints may sometimes lead us to apply this rule somewhat obliquely, similar to the leaden rule used to bend stones. We want to consider what is most pressing and achievable, and the way it is done must be explained briefly. It is certain that the common goal of all reasoners is to infer and prove something from known and accepted propositions that are usually provided. Aristotle seems to testify to this natural instinct in humans in the preface of Book 1 of Physics when he says that this path, moving from the known to the unknown, is innate in us. Aristotle signifies this in the very definition of a syllogism when he says, "Assuming certain things." It is certain that what is granted is not denied. No one will dispute that Aristotle meant this in the very definition of a syllogism when he said, "Assuming certain things." Since this pertains to what we are discussing, it is not denied that Aristotle meant this in the very definition of a syllogism when he said, "Assuming certain things." For this reason, we always try to take known propositions and those that can be readily conceded, from which we can later infer a controversial conclusion. This sometimes leads us to prefer certain propositions for reasoning in the second or third figure rather than their converse, or the first figure. This is because the former is more readily available and more suitable. For example, if we need to prove "No man is a horse," and we have the middle term "laughable," it is more expedient and appropriate to use the major premise "No horse is laughable" for a syllogism in AEE mode rather than its converse "No laughable thing is a horse," which is less known. We tend to use the former proposition more than the latter. This custom arises from the very nature of things, as we attribute properties to substances rather than substances to properties. This is why we are more inclined to say "No crow is white" rather than "No white thing is a crow." However, in those modes that are more difficult to reduce to the first figure, such as through the transposition of propositions or the reduction to the impossible, there is still a stronger reason why we do not argue in the first figure. If we are presented with a syllogism, "No stone is a man," and the middle term "animal" is given to us, we immediately make the argument in the second figure in AEE mode because a syllogism cannot be formed in the first figure for the given proposition. In the first figure, we would conclude, "No man is a stone," but we were not looking for this conclusion; we were looking for the converse, "No stone is a man." This is what was proposed to us. This argument is highly valid, and we draw it from Aristotle, who, in many places, observed that the use of syllogism from both affirmative propositions, although a corrupt and imperfect way of reasoning, is valid in itself due to the nature of the matter. This is because the major proposition can be easily converted, making the reasoning similar to that in the first figure. However, Aristotle preferred to use what was more immediate and clearer than its converse, which was more obscure and disregarded form due to the matter, as the former seemed to be more pressing.
Therefore, nature leads us to deviate somewhat from the rule of the "de omni" dictum and to incline away from its straightness due to the material to which this rule must be adapted. Propositions are the material we want to use for reasoning; hence, it often happens that we argue in the second and third figures rather than the first. However, they do not deviate so far from the first that they are not closely related to it and can't be reduced to it with evidence. Therefore, the whole difficulty in resolving this lies in the fact that all reasoners naturally seek evidence. This evidence is twofold one is related to the material, i.e., the known and accepted propositions; the other is related to the form, where reasoning through the dictum de omni makes it most evident. Therefore, if both forms of evidence can be attained simultaneously, they unquestionably reason in the first figure, not in the others. However, if they cannot attain both forms of evidence simultaneously, they prioritize the evidence that seems to be more pressing, as we have explained. For this reason, due to the material, we deviate somewhat from the evidence of the form, but then we also attain this through the reduction of syllogisms to the dictum de omni and to the first figure. Therefore, it is evident how and why the second and third figures are natural, and it is clear why Averroes' argument against them has been poorly refuted in various ways.
Chapter 11: Averroes' argument against the fourth figure is the most effective
Now let us demonstrate that Averroes' argument against the fourth figure is the most robust and that the solution devised by the physicians, who did not see the fourth figure as comparable to the first or the other two, is futile. The fourth figure is rightly called "artificial" by Averroes because it does not manifest a natural inference as convincingly as the first figure, nor does it have the evident power of the other two. Instead, it is situated at the far end of the spectrum, opposed to nature. Therefore, it is justly characterized by Averroes as artificial, originating from contrived reasoning and devoid of the natural clarity of the other figures.
The first figure clearly has the manifest dictum de omni in its propositions and, according to its law, derives the conclusion. On the other hand, the second and third figures, although lacking the disposition of terms in their propositions following the dictum de omni, at least do not contradict it. The fourth figure, however, places the middle term between the extremes, and thus, it does have the dictum de omni explicitly and clearly in its propositions. However, it draws an inference in the opposite direction, contrary to our natural expectation. Instead of concluding that the predicate of the highest term applies to the lowest, it asserts the opposite, which goes against our natural reasoning.
In conclusion, it is evident that the instance given by Averroes regarding EAE and AEE in the second figure, as well as AII and IAI in the third, is baseless. This is because the comparison does not hold. We have already explained that there are two reasons why the larger term can be applied to either of the extremes. The first reason is the disposition of the terms in the propositions according to the dictum de omni, where the highest term of all is called the "major," and the lowest, the "minor." The second reason is the order of the propositions themselves, derived from the initial order of the two terms posed in the original proposition. As the natural order of terms cannot be ascertained from the mere predication of terms in propositions, we cannot determine which term should be called major or minor, or which proposition should be considered major or minor. Therefore, we designate them as major or minor based on the nature of the original proposition from the outset.
However, the prior of these two reasons is by far more efficacious and compelling, and when we possess it, we do not consider the other. For when the terms in propositions are arranged according to the dictum de omni, we do not contemplate which proposition was posited first to designate it as the major. Instead, we call as major the one in which the term of higher predication is contained, even if the other proposition was posited earlier. This is frequently found in Aristotle's works where the minor proposition is presented before the major. Therefore, the syllogism made from two universal affirmatives, which is said to belong to the fourth figure, Aristotle would not judge to have a different mode of arrangement in propositions and figure from the first mode of the first figure, which is called Barbara. This is because the presence of the dictum de omni leads to the term always being called major, the one predicated about the highest, and the proposition in which it is contained is always called major, even if the minor proposition has been uttered before it. Thus, the objection devised by Averroes that transposing propositions changes both the mode and figure is entirely unfounded. The same figure and mode remain intact. The reason is that the same major and minor terms remain in place. Thus, the dictum de omni is impressed upon our minds in such a way that, no matter how propositions are arranged, we always consider the one predicated about the higher term to be the major and the one predicated about the middle term to be the minor. This is in line with the natural instinct present in every human being of sound mind. Therefore, the notion that the term predicated about the highest should be called minor, and the term at the bottom should be called major, is a contrived invention by some individuals, not everyone, without any natural order. Indeed, it is contrary to nature.
As for EAE, AEE, and similarly AII and IAI, they present a different situation. When the first reason no longer applies, we resort to the second reason, and we can designate whichever term we wish as major, just as they do, without contradicting nature or the dictum de omni. Consequently, the argument concerning the negative mode of the fourth figure is empty and fallacious. For that mode is such as "No horse is a man; every man is an animal, therefore some animal is not a horse." They claim that the Aristotelians did not object because it fits the first figure, and the minor proposition comes before the major. They argued that if it is called the minor when it is placed first and it constitutes a syllogism in the first figure, then in the first figure, a negative minor proposition would follow, which is indeed impossible since nothing can be concluded from a negative minor proposition in the first figure. However, the mode we presented is a concluding syllogism. Therefore, since it cannot belong to the first figure, much less to the second or third, it remains that it must be the proper mode of the fourth figure.
However, even though they may have some appearance of truth, they possess none. For we have a perpetual and universal law that whenever a middle term is placed between extremes, whether done well or poorly, it is judged to be in the first figure. This designation of the first figure does not come from the usefulness of the mode but from the position of the middle term. Aristotle, therefore, names not only the four useful modes but also various others, completely different ones. It must be noted that the negative syllogism they propose for the fourth figure is actually in the first figure. Nevertheless, it is useless and inconclusive when the minor proposition is negative. It rightly and naturally concludes nothing, although it sometimes, artfully and obliquely, arrives at a certain conclusion. However, it is not a natural inference, as anyone with a sincere and sound mind can recognize through careful consideration. For a middle term is always placed between extremes. The proposition in which the term is predicated about the highest is considered the major, while the one in which it is predicated about the lowest is considered the minor. Therefore, the natural thought of all humans would falter upon encountering the converse conclusion. For anyone would expect from these propositions a conclusion in which "animal" is predicated about "equus," even though the mode is inconclusive and useless. Thus, the conclusion "some animal is not a horse" goes against all our natural expectations and thoughts.
Aristotle was not unaware of this negative mode to which they seem to turn. He discussed it in Chapter 8 of Book 1 of the Prior Analytics, and this mode, which the Latins call "Sapelmo" or "Frilesomorum," if it has a particular major term. The Latins rightly place these two modes in the first figure but call them oblique and against nature when they conclude. This is why Aristotle did not mention them in the first figure since he only considered syllogisms that naturally conclude in the figures. He excluded all others from the figures. However, he mentioned them outside the figures, as we can see in Chapter 8, where he stated that these kinds of syllogisms could be made to belong to the first figure, even though they conclude obliquely. He also added that similar syllogisms that conclude obliquely could be formed in other figures, which leaves us something to consider. However, since they are not syllogisms that naturally conclude, and they are not worthy of mention in the figures, we, who defend Aristotle, are moved by reason, not by custom or love of the master, to follow his opinion that there are only three figures that naturally conclude. No educated and sincere judge would think otherwise, as Averroes' argument, which we have discussed so far, relies on such solid foundations that it cannot be refuted
Chapter 12: Averroes' argument is presented and defended against the physicians
Averroes used another argument against the fourth figure, which goes as follows: "In the fourth figure, a predication of the same as identical with itself is concluded, therefore, it is an absurd, useless, and meaningless figure." The first part of the argument is proven by the following example: when one uses the fourth figure to reason, such as "every man is an animal, every animal is a body," anyone would naturally expect the conclusion to be "every man is a body." However, in the fourth figure, they conclude the converse, which is "some body is a man." Consequently, by attaching this to the first figure, it is concluded that some body is a body, which is a meaningless predication.
In response, the physicians seem to provide a triple defense. Firstly, they deny that our natural thought falls upon the conclusion "every man is a body" when these propositions are set up as required in the fourth figure. They argue that it is not naturally inferred, and hence, it does not follow that a predication of the same as identical with itself. Secondly, they claim that even if it is granted that a predication of the same as identical with itself is made, it should not be seen as absurd. Instead, it should be seen as referring to something different rather than the same. Therefore, they argue that the absurdity can be avoided. Lastly, they argue that even if such a predication is considered problematic in terms of content, it is not an issue in terms of form and structure, which should be the main focus, as Aristotle himself considered in the Prior Analytics when discussing forms. For instance, even in the first figure, if we say "everything visible is a man, every man is laughable," it follows that "every man is laughable." This syllogism, with its proper form, is something that we cannot condemn when we focus solely on its form.
The defenders of Galen mainly rely on the following response to support their argument against Averroes and deny the absurdity of the consequent: First, they argue that the same can be concluded from itself in other figures as well, such as in the first figure when "man is laughable." Second, they contend that this argument is also contrary to Aristotle's teachings because when converting propositions for reduction to the first figure, as Aristotle instructs, a similar absurdity arises. For example, Aristotle teaches to convert the proposition "every man is an animal" to "some animal is a man," which, when subjected to conversion, leads to the conclusion "some animal is an animal." Therefore, if Averroes' argument holds against Galen, it also holds against Aristotle.
However, I would like to emphasize that while I do not give as much weight to this latter Averroes' argument as to the former, which was more effective, I still argue that the initial response from Galen's defenders does not stand. This is because we have thoroughly refuted it, demonstrating that our natural thought does not naturally fall upon the conclusion in the fourth figure but rather on its converse, which is naturally inferred through the first figure. We have clarified that the natural inference is when the conclusion is above in the propositions, and the converse is below in the conclusion, just as it is when we consider the naturalness of the matter. Natural predication occurs when something is predicated about what exists outside the mind, and it is subsumed under what is external to another mind. For example, when we predicate genus or difference about species and accidents, it is subsumed under the species. Similarly, the naturalness of the form, which is the natural inference, occurs when what is predicated in the conclusion is what was predicated in the propositions, and what is subsumed in the conclusion is what was the subject in the propositions. Just as in natural predication, which is termed naturalness according to matter, we consider the agreement of the proposition with the thing, so the agreement of the conclusion with the propositions is what determines naturalness in inference. If this agreement is overturned, it leads to an inference against nature.
Therefore, they cannot deny that from the complication of these propositions, the conclusion "every man is a body" naturally follows. This has been thoroughly demonstrated through Averroes' second argument. Hence, if the first argument remains strong, it strengthens this second one. Therefore, if the former argument stands, this consequent deduced by Averroes from the fourth figure is justified.
Concerning the defenders of Galen, they primarily rely on this second argument by Averroes to oppose him, asserting that it also contradicts Aristotle. They argue that in other figures, similar absurd conclusions can be drawn, such as in the first figure, as previously explained. Moreover, they claim that when Aristotle advises converting propositions for reduction to the first figure, the same kind of absurdity arises. For instance, Aristotle suggests converting the proposition "every man is an animal" to "some animal is a man," which, when further converted, leads to the conclusion "some animal is an animal." Therefore, if Averroes' argument is valid against Galen, it is equally valid against Aristotle.
However, despite acknowledging the second Averroes argument, I would like to point out that it does not hold as much weight as the first one, which was more effective. Nonetheless, even in this case, the initial response from Galen's defenders is not solid. This is because, as we have thoroughly argued, the same can be concluded from itself in this context. If something else were inferred, it would make the syllogism complex, not simple. Therefore, when concluding that "a body is predicated of a body," it is necessary to understand that the body in the conclusion is the same as that in the propositions and that it is both predicated and subjected to predication. A syllogism with a different consideration for the same terms would be faulty. Considering this, it is not enough to rely solely on differences in consideration to reject the argument, as Averroes' argument still holds.
The last attempt to counter Averroes' argument, claiming that it is not a problem in terms of form but rather in matter, is also easily refuted. While Aristotle primarily focuses on form without considering matter in his earlier Analytics, he does so with the intention of applying it to matter afterward. Aristotle's intention is not to exploit form inappropriately, but rather to apply it correctly. However, in the case of the fourth figure, the problem is intrinsic to the form itself, not its misuse by those who employ it. Thus, Averroes' argument against the fourth figure remains valid. Moreover, it does not contradict Aristotle's teaching on the conversion of propositions because the context is different. In Averroes' argument, we consider that the same is predicated of itself, leading to an absurdity that always occurs in the fourth figure, making it inherently flawed. In contrast, when converting propositions in Aristotle's method, the absurdity does not necessarily arise and is instead contingent on improper usage. Therefore, Averroes' argument stands, and the attempt to use Aristotle's teachings against it is not valid.
In summary, Averroes' second argument is indeed supported by the first one, and even though it is not as strong, it remains a valid corollary to the first argument.
Chapter 13: The Arguments of the Adversaries are addressed.
Having declared and established the truth of this matter, it remains for us to address the arguments in favor of Galen at the beginning of this contemplation. The first argument was: "If there is a fourth seat of the middle, then there is a fourth figure." To deny this, the antecedent must be denied. For we have shown that it is not the fourth seat but the same as the first figure. However, if opponents say that it is the fourth seat because the middle is not between the extremes but rather outside of both, being above the greater and below the lesser, this is a vain contrivance that opposes nature. It can barely be conceived because the greater is predicated of the lesser, and it is above, and they posit the middle as below the lesser. Therefore, the same is simultaneously above and below in one and the same syllogism. Hence, Aristotle should not have considered this fourth seat, assuming it is indeed the fourth seat, which is fabricated and opposed to nature, and involves a contradiction. Therefore, even given, but not conceded, the antecedent, the consequent can be denied: given that it is the fourth seat, it does not necessarily follow that it is the fourth figure because such a seat, contradictory to nature and artificial, should not constitute any figure. As for the second argument, the minor premise must be denied, namely that the definition of syllogism given by Aristotle applies to syllogisms of the fourth figure. For when he said that a syllogism is an argument in which, some things being posited, something else necessarily follows from them, he meant a natural conclusion, that is, one which follows according to the order of nature and by the dictum de omni, as is clear to those who consider the words carefully. It is one thing for a conclusion to be derived by us from propositions suitably composed, and another for a conclusion to be, as it were, deduced by itself from propositions, flowing as an effect, necessarily following, and being compelled by the force of the cause without any artifice of ours. This is the sense Aristotle wanted to convey in that definition. For a conclusion naturally follows from well-composed propositions due to the nature of the propositions themselves and the arrangement of the terms, not from some artificial contrivance of ours, such as the inference in the fourth figure is said to be, which is, in fact, not a straightforward and natural course of terms but rather runs counter to the natural order. Therefore, in his definition of syllogism, Aristotle did not say that we can deduce any conclusion we wish from posited propositions but rather that, because of the propositions being posited, a conclusion necessarily follows. He meant that the conclusion immediately follows in a certain natural order, beyond any human artifice, and even against our will. Regarding the third argument, the major premise must be denied, namely that every concluding syllogism that can be reduced to the first figure deserves to be placed in the figures. For we have said that Aristotle in the beginning of the second book of the Prior Analytics and in the eighth chapter of the first book mentions syllogisms that conclude obliquely and shows how they can be reduced to the first figure. Nevertheless, he did not deign to place them in the figures. It is certain that any concluding syllogism, whether it concludes correctly and naturally or obliquely and against nature, concludes if there is a dictum de omni, and therefore, it can be reduced to the first figure. However, Aristotle decided to place only those syllogisms in the figures that conclude naturally, not those that conclude against nature and against the dictum de omni, and which are not used by people who naturally reason.
Therefore, when they say that every syllogism that can be reduced to the first figure should be placed in some figure, this should be denied if stated without qualification. However, if this condition is added, that it makes a natural inference, it should be admitted. But then, we will deny the minor premise. For syllogisms of the fourth figure are not such. We can also respond differently by conceding the whole argument. We have already shown that all the syllogisms that these argue belong to the fourth figure are, in fact, in the first figure. Aristotle said that they belong to the first figure but conclude obliquely. Therefore, he mentioned them outside the figures, as has been said. Thus, any syllogism that concludes and can be reduced to the first figure should be placed in some figure, either directly or obliquely. Those that opponents refer to the fourth figure can be reduced to the first figure either directly or obliquely. Lastly, regarding the third argument, we say that a syllogism can be called useless for two reasons. First, because it does not yield any certain conclusion, as sometimes it leads to an affirmative conclusion and at other times to a negative one. Aristotle considered such syllogisms in each figure and rejected them as useless. For it seems to have the dictum de omni, like other useful syllogisms, but in reality, it does not have it unless superficially. Others are called useless for another reason, namely that they are not used by most people who naturally reason. Although they do lead to a certain conclusion, it is oblique and against nature, and they do not truly or apparently observe the rule of the dictum de omni. Aristotle did not even want to mention these in the figures, neither admitting them nor rejecting them, because they do not proceed by the natural way, nor do they appear to proceed that way. Such are the syllogisms of the fourth figure, which, according to the first reason, are not useless, for we admit that they draw a certain conclusion. However, according to the second reason, they are useless because they are oblique and contrary to nature, and they are not used by most people. For this reason, they were not mentioned by Aristotle in the figures but only outside the figures, as mentioned. We can also concede that these syllogisms are useful in the sense that they are opposed to the useless in the first meaning mentioned above, and therefore, they should be placed in some figure, but not directly, rather obliquely. It is reasonable since they securely draw oblique conclusions, they should also be placed obliquely and secondarily in a figure. Therefore, it is not necessary to add the fourth figure because all of these syllogisms belong to the first figure as oblique conclusions.
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