SOURCE: Manekin, Charles H. “Logic, Science, and Philosophy in Gersonides.” In Studies on Gersonides, edited by Gad Freudenthal, pp. 285-303. Leiden, The Netherlands: E. J. Brill, 1992.

[In the following essay, Manekin explains Gersonides's views on logic, particularly those ideas which run counter to Aristotle's understanding of the subject.]

I. INTRODUCTION: GERSONIDES’ LOGICAL WRITINGS

The contributions of Levi ben Gershom (Gersonides) to the fields of science and philosophy are well-known, but his logical writings, though of some influence in the Middle Ages, have only begun to be studied. To these writings belong two major works: the Commentary on Logic (1322-1323), which is a supercommentary on the Middle Commentary of Averroes on the Aristotelian Organon,¹ and the Book of the Correct Syllogism (1319), an independent treatise on inference and modal logic.² With the exception of the first book of the Commentary on Logic, all these writings are extant in Hebrew only in manuscript.³ The first three books of the Commentary on Logic, and all of the Correct Syllogism, were translated into Latin, the former being available in the Venice edition of Averroes' commentaries on Aristotle (1562-1577),⁴ and the latter in manuscript.⁵

The Correct Syllogism appears to have had less influence on subsequent Jewish logicians than the Commentary on Logic, perhaps because of its difficulty and originality. Yet it is a fascinating book because Gersonides intended it as an “improvement” upon Aristotle's syllogistic. The title is indicative of the work's boldness: whereas Aristotle had written the Book of the Syllogism (the medieval Arabic and Hebrew name for the Prior Analytics), the thirty-one year-old Gersonides would now write the Book of the Correct Syllogism. As he writes in his brief introduction:

Inasmuch as we saw some things in Aristotle's Book of the Syllogism, as understood by the philosopher Averroes, that appear to us to be incorrect—namely, in the conversion of modal sentences and the mode of the conclusion of modal syllogisms, simple and mixed—we have seen fit to investigate the truth of these matters in this book. And since everything that we shall bring in this book is manifestly verified, we have entitled it The Book of the Correct Syllogism …⁶

From the statement above we learn that Gersonides' main motivation for writing the Correct Syllogism was his dissatisfaction with Aristotle's system of modal logic. The work in fact also contains other discussions that are of interest to the historian of logic. One finds such novelties as an analysis of syllogisms in terms of class-relations, an investigation of inferences with relational terms, and a spirited defence of the controversial fourth syllogistic figure. Together with the modal syllogistic, these discussions earn Gersonides a worthy place in the history of logic.

II. LOGIC AS AN ORGANON FOR SCIENCE ACCORDING TO GERSONIDES

In view of Gersonides' expertise in both science and logic, I wish to raise the question whether Gersonides saw any connection between the two. In other words, what were Gersonides' views on the age-old question of the relationship of logic to science, or to philosophy?⁷ Unfortunately, although Gersonides wrote very extensively on scientific and logical topics, he never treats the question I have raised in any detail. Indeed, Gersonides makes few theoretical statements in his logical treatises. The Correct Syllogism, for example, focuses on the very specialized task of constructing a system of inferences whose validity is demonstrable. To use the modern idiom, the Correct Syllogism is an exercise in “doing logic” and not in talking about it; philosophy of logic finds no place therein. The book's interest lies chiefly in the almost mathematical rigor of the discussion and less in any new conception of logic itself. Nor do the supercommentaries lend themselves naturally to broad interpretation. The Commentary on Logic is an exegetical work that follows closely the text of Averroes. In places where one would hope to find some theoretical discussions on the relationship of logic and science, such as in the supercommentary on the Posterior Analytics, Gersonides confines himself to the text at hand.

Moreover, the supercommentaries present us with a problem of interpretation that has not been sufficiently appreciated in the scholarly literature, namely, that it is often difficult to determine which comments represent Gersonides' own opinions and which express his interpretation of Averroes. It is standard to assume that the phrase “Levi said” introduces Gersonides' own views on a given matter, as opposed to one of his explanations of Averroes. But while this phrase generally introduces an independent observation, that observation may be made “according to the principles of Averroes”, and not according to Gersonides' own views. In other words, while the interpretation is genuine Gersonidean, it remains an interpretation of someone else's doctrine. For example, Averroes often makes reference to a syllogistic condition known in traditional logic as the dici de omni, “whatever is said of the whole is said of the part.” He holds that all concludent premise-pairs yield their conclusion by virtue of the dici, which, according to him, is used by Aristotle as the ultimate principle of the syllogism.⁸ So much importance does he attach to the condition that he gives discussions to it in all of his works on the syllogism.⁹ Now, Gersonides comments upon the dici in the Commentary on Logic¹⁰ and at greater length in his commentary on the fifth of the Logical Questions.¹¹ Yet he does not even mention the dici in the Correct Syllogism, preferring instead to develop his theory of the syllogism differently. So one must be very cautious in attributing to Gersonides broad theories on the basis of his scattered remarks in the Commentary on Logic.

But with this warning in mind, I believe that we are able to reduce the risk in our case. For one thing, Gersonides informs us in his introduction to the Commentary on Logic that he is not interested in writing a commentary for its own sake for, in his opinion, the contents of Aristotle's logical works need no explanation. His main purpose is to draw attention to those places where his opinion differs from that of Aristotle and to explore areas which should have been investigated by Aristotle but were not. Original composition (hḥibbur) and not commentary (be'ur) is his primary aim.¹² This is particularly true in his supercommentary on the Prior Analytics, where the commentary becomes a series of critical notes. Page after page, Gersonides speaks critically of Averroes' arguments, beginning his comments with remarks like “This is incorrect” or “This argument is necessarily defective,” or “[Averroes'] solution here merits derision.” From these remarks one can safely learn about Gersonides' own views.

The passage coming closest to a general statement of the relationship of logic and science occurs near the beginning of the Commentary on Logic:

We say that this art qua being prior does not require that which is posterior to it.¹³

Like most medieval philosophers, Gersonides holds that logic differs from science insofar as it does not investigate the true essences of things, which is the aim of science: logic is not a science, that is, an inquiry with a particular domain of objects. Yet logic bears a special relationship to science because through logic the intellect learns to distinguish between the true and the false in things. Gersonides here follows the Aristotelian view of logic as an organon for science, an instrument for the acquisition of knowledge.¹⁴ Logic is hence prior to science, though in precisely what manner of priority we shall consider below.

The view of logic as an organon is standard for a medieval Aristotelian, often implying little more than the truisms that right thinking will advance scientific inquiry, or that the theory of proof underlying science has to conform to the canons of (Aristotle's) logic. But for Gersonides the instrumental nature of logic is not a mere methodological declaration of faith. He occasionally appeals to logic to settle issues of metaphysical import. For example, in Wars of the Lord I:10 he tackles the difficult question of the ontological status of our mental concepts, or “intelligibles” (muskalot), to use the technical term.¹⁵ When we think of triangle, are we thinking of a particular triangle, a class of triangles, or what? What is the ontological status of the triangle intellected? To answer these questions Gersonides appeals to the logic of definitions and propositions, because, he claims, thoughts themselves can be divided into definitions and propositions. His analysis leads him to conclude that in a sentence like “Every triangle possesses angles that equal the sum of two right angles” the subject “triangle” signifies any arbitrary triangle, which implies that the objects of our thoughts are neither entirely particular nor entirely universal. Considerations of logic are paramount in the argument for his position on this key question.

It would be mistaken to claim that Gersonides was unique, or even unusual, in appealing to logic in his philosophical writings. On the contrary, since many medieval Aristotelians believed that the structure of language (the logical structure that is common to all languages) represents the structure of the world, they were of the opinion that it is possible to employ arguments from logic to settle questions of metaphysics. For example, from an analysis of the structure of predicative sentences one can learn something about the underlying structure of substance and accidents to which these sentences refer. This idea had formed the basis of Maimonides' discussion of divine attributes and of Gersonides' critique thereupon. When Maimonides argues on the basis of Aristotelian logic that essential attributes are inadmissable because they entail multiplicity, Gersonides counters—on what he considered to be a better reading of Aristotle—that essential attributes, when predicated “by priority and by posteriority”, are admissable.¹⁶ Still, Gersonides' utilization of logical analyses in his metaphysical writings gains an added dimension if we see it as part of his general conception of logic as distinguishing “the true from the false in things.”

What does it mean to distinguish “the true from the false in things”? The phrase appears awkward; in modern philosophical parlance, truth and falsity are said to apply to sentences and not to things, i.e., extramental reality. But even if it is proper to speak of things being true, does this mean that Gersonides includes existents (nimz'aot) within the domain of logic, in addition to intelligibles and utterances (millot)? While there is no explicit statement of his showing that he did, one can infer it indirectly on the basis of a highly unorthodox doctrine that he holds in the C. Categories. According to Gersonides, the ten Aristotelian categories classify existents in themselves and not insofar as they are spoken about. But this doctrine presupposes a conception of the nature of logic according to which extramental existents are included within its domain:

Since this art explains the intentions of speech and what follows from it and directs a man so that his external speech will correspond to, and be equal to, what is represented in the soul … while the representations in the soul are taken from the matters (ha-'inyanim) outside the soul, i.e., the existents, it is proper that 17

Gersonides' view seems to be that if the art of logic is to enable its practitioners to understand the meanings and logical implications of discourse and to achieve a correspondance between thought and linguistic expression, then it must consider the things that are the sources and causes of our thoughts. This does not mean that logic is concerned with the causal process by which the intelligibles arise in our mind; that is a topic for psychology and not for logic. Rather, it means that for us to understand even in a preliminary fashion such concepts as “species,” “opposite,” or “substance,” we must be acquainted with what such concepts classify, namely, extramental existents. This theme indeed runs throughout Gersonides' supercommentary on the Categories. For example, to explain the concept of opposition, he points out that every existent is either a “same” or an “other.” Since whatever is a “same” is clearly not an “other,” we must distinguish the various kinds of oppositions between entities, namely, contrariety, negation, and privation. For logic to investigate the different types of opposition it must know something about the existents to which the relation of opposition applies. To generalize, the art of logic must assume some knowledge about extramental reality.

Gersonides' position on the subject-matter of the Categories is most unusual for his period. The inclusion of the Categories in the Organon had always been considered problematic by the Aristotelians. On the one hand, it was held that extramental existents should be excluded from the domain of logic because they were the object of scientific inquiry. On the other, the Categories deals with the classification of reality, an eminently metaphysical topic. To solve this problem the commentators generally took one of two ways out: some simply held that the Categories deal with existents not per se, but only as they are conceived or talked about; others held that it deals with existents and for this reason indeed excluded it from the logical writings altogether. Most commentators chose the first avenue. Among the Greeks, Porphyry claimed that the work treated utterances (phonai) as signifying things, while Ammonius, followed by Philoponus, thought that the subject was “utterances which signify things through concepts.” Among the Arabs, Alfarabi treated the subject matter of the Categories in line with his general position on the subject matter of logic: according to him, the work bears on “intelligibles as they are signified by utterances and utterances as they signify intelligibles.” Avicenna, by contrast, held that the work is concerned with existents and for this reason did not consider it in his logical writings.¹⁸ Averroes' position, lastly, shows the influence both of Alfarabi and Avicenna. Like Alfarabi, Averroes considers the subject matter of the Categories to fall within the domain of logic: “The science of logic investigates 19

Gersonides' three major Arab predecessors, and virtually all medieval philosophers, thus share the major assumption that the subject matter of the Categories does not include extramental existents. As we have seen, Gersonides is of the opposite view: the Categories treats existents in themselves and not insofar as they are spoken of, and hence logic requires some sort of knowledge of existents.

But what sort of knowledge? Here we face the question of the relationship between logic and science with great urgency. Gersonides argues that logic must begin with an investigation of extramental reality, yet he accepts fully the view of the study of logic as prior to, and independent of, the study of science. How can we reconcile these two seemingly contradictory requirements: the one that logic treat extramental entities in themselves and the other that logic be prior to and independent of the sciences which also investigate these entities?

Gersonides' answer to our question can be inferred from the last-cited passage: While logic assumes knowledge about extramental reality, it must not make any assumptions that depend upon scientific investigation. Logic thus assumes knowledge of things not according to the way they really exist, but only according to the way that they are commonly believed to be. Gersonides here avails himself of a doctrine that appears repeatedly in Averroes,²⁰ namely, that the discussions in the Organon are from the standpoint of “generally accepted opinion,” and applies it to the question of the domain of logic: the entities assumed by logic to exist are those which are commonly held to exist.

With this interpretation, the question “What sort of knowledge of reality is required by the Categories?” becomes: “What sort of entities are subsumed under the Aristotelian categories?” The answer, according to Gersonides, is: solely perceptible objects (ha-debarim ha-murgashim, ha-murgashot).²¹ Imperceptible objects, even those whose existence is not at all metaphysically controversial according to Gersonides (e.g., separate intelligences), are excluded from the domain of logic. This view accords well with the previous requirement that logic be prior to the other sciences and that its discussions be from the vantage-point of commonly accepted opinions. For even if separate intelligences, for example, are universally taken to exist by philosophers, their existence is established through the sciences of physics and metaphysics. But since the logic of the Organon is geared to all men, the entities that logic assumes to exist are the ones with which all men are familiar.

To be sure, Gersonides does not hold that logic can justifiably apply to perceptible objects alone. In his own formal logic he never restricts the range of his term-variables to perceptible objects, and one imagines that he would reject any suggestion of that sort. Indeed, as I mentioned earlier, in the Wars of the Lord he employs logic to consider the metaphysical question of the ontological status of concepts. His logic is deeply loaded with ontological commitments.

To understand how, then, imperceptible entities can be included after all within the domain of the objects of logic, we must retun to Gersonides' view that the study of logic should be prior to the study of the other sciences. This view, we saw, entails a restriction on the type of entities admitted. But this restriction is only temporary. As the student advances in his philosophical studies, he acquires knowledge of things that were unknown to him previously, and is thus able to enlarge the scope of objects to which logic, via the doctrine of the Categories, applies. This extension does not call for any fundamental changes, because the new objects are subsumed under the previous categories. For example, the student learns what substances are with reference to perceptible objects; when he acquires knowledge about imperceptible objects such as separate intelligences, he will be able to classify them as substances and not as qualities.

Two examples from the Commentary on the Categories clarify these points, the first example illustrating the continuity between what we may call the pre-scientific and the scientific domains of logic, the second showing a discrepancy. At Categories 5, 2a11-19 Aristotle distinguishes between substances which are primary, e.g., the individual man or the individual horse, and those which are secondary, e.g., the species man and the genus animal. According to Averroes' interpretation in the Middle Commentary, primary substances “signify” a certain individual, whereas secondary substances “signify” an arbitrarily selected individual.²² Now since, according to Gersonides, the existents referred to in the Categories are all perceptible objects, which are by nature individual, it is clear that he will have to hold that secondary substances also refer to perceptible objects. So it is not surprising that he adopts Averroes' view that secondary substances “signify” arbitrarily selected individuals. Let us note that this is not an ad hoc move, forced on him by the restriction on the domain of objects of the Categories. Rather, it is an essential part of Gersonides' general view: we saw above that in his mature philosophical doctrine, Gersonides holds an intelligible like triangle to signify an arbitrarily selected triangle. The notion that an intelligible signifies an arbitrarily selected individual, rather than a form or a universal, forms a metaphysical thesis of the Wars of the Lord and is not just limited to his logic.

On the other hand, when we move from a pre-scientific classification of reality to a scientific one, there will have to be some adjustments. Thus, Aristotle claims in the Categories that substances, unlike accidents, lack contraries; no one substance is the contrary of another. This claim, comments Gersonides, is true of perceptible objects but not of all substances: imperceptible objects such as the four elements, earth, air, fire, and water in their pristine state, do indeed possess contraries.²³ The claims in the Categories that are based on the restricted domain of logic are sometimes revised in the light of a more accurate, scientific, description of reality. Nevertheless, these revisions do not alter fundamentally the classification of reality provided by Aristotle in the Categories.

Gersonides, then, defends his controversial interpretation of the subject matter of the Categories by appealing to the conception of logic as an organon for science. Since the art of logic enables one to distinguish between the true and the false in things, which is also the intention of science, logic has to investigate extramental entities. But it is proper that the art of logic not assume anything whose explanation requires one of the sciences since, to cite Gersonides, what is prior must not require that which is posterior to it.

Gersonides' affirmation of the priority of logic over science can be taken in two senses. In a temporal sense, logic is prior to science because knowledge of logic is a necessary condition for scientific inquiry. Indeed, students of philosophy in the Middle Ages, Moslem, Christian, and Jewish, began their studies with logic and only once that discipline had been mastered were they supposed to continue. In this sense there is nothing really new to Gersonides' claim.

But according to Gersonides, logic is prior to science not merely in the ordo cognescendi: the doctrines of logic, he holds, must also be independent of, and hence unaffected by, scientific research. We have seen this independence in Gersonides' interpretation of the Categories, where he affirms that logic treats extramental existents “from the standpoint of commonly accepted opinion” and not from that of science. It also comes to the fore, as we shall presently see, in his theory of the syllogism, where he holds that the validity of an inference-pattern is to be judged independently of its scientific utility. This is a highly unusual stance in medieval logic, in which appeals to extralogical considerations like “scientific utility” or “naturalness” were sometimes taken to determine the validity of an inference-pattern.

It would yet be wrong to view Gersonides' formal logic as science-neutral; on the contrary, according to Gersonides, logic remains an organon for science even in formal logic, and he holds that the scientific utility of an inference-pattern can bolster its acceptability. To understand these views we have to make a short detour into the byways of medieval syllogistic.

III. LOGICAL VALIDITY, PSYCHOLOGICAL NATURALNESS, AND SCIENTIFIC UTILITY

It is well known that the traditional Aristotelian syllogism consists of two premises and a conclusion. Each premise consists of two terms, one unique to that premise and the other common to both premises. The conclusion always consists of two unique terms, known as the minor and the major terms. Now, in the Arabic and Hebrew tradition of logic, syllogisms were constructed so as to prove a particular thesis that had the minor term as its subject and the major term as its predicate. This thesis was known as al-matlub in Arabic, ha-derush or ha-mebuqqash in Hebrew, and as the quaesitum in Latin. For example, if we know that every A is B and that every B is C, then through syllogistic reasoning we conclude that “Every A is C” which is the quaesitum.

Because the quaesitum of a syllogism is often the same as its conclusion, logicians sometimes identified the two. Algazali writes: “That which is derived from a syllogism is called the conclusion after it has been derived, and the quaesitum before it has been derived.”²⁴ But it was known that some premises yield a conclusion whose subject is the major term and whose predicate is the minor, which is the opposite of how these terms appear in the quaesitum. This arrangement of terms is called simply by the logicians “what is other than the quaesitum” (mah she-zulat ha-derush).

What is the logical status of a syllogism that yields a conclusion that is other than the quaesitum? Is it a valid syllogism or not? According to Averroes it is invalid because it represents an “unnatural” pattern of reasoning:

The cogitative faculty will not exert itself naturally with a syllogism that yields quaesitum, and will only formulate one metaphorically. For example, if we seek to know “Is A in C?” and we say that A is in C because A is in B and B is in C, then this syllogism will be natural and commonly found in people's speech …, but if we say A is in C because C is in B and B is in A, then this is something that no one thinks naturally …²⁵

Moreover, a syllogism that yields something other than the quaesitum is of no scientific utility because it does not yield what we sought to prove in the first place. Such a syllogism is, at best, incomplete, for in some cases it is possible to convert the conclusion to yield a sentence whose subject is the minor term and whose predicate is the major. Where the conclusion cannot be converted, it is, strictly speaking, not a valid syllogism at all.

Gersonides disputes this position with two arguments: since syllogisms that yield a conclusion other than the quaesitum fulfill the general conditions laid down by Aristotle for valid syllogisms they are themselves valid; although they would not usually be used in demonstrations, because they are of no scientific utility, they may be useful in dialectical debate.²⁶ His view seems to be that to hold that a syllogism is invalid because it yields a conclusion other than the quaesitum is to misunderstand the notion of logical validity. Although such a syllogism may be useless for furthering our knowledge, this does not mean that it is incomplete or defective. As long as the conclusion is derived necessarily from the two premises, the syllogism is valid. It also matters not whether the syllogism represents a natural pattern of reasoning or not; naturalness, according to Gersonides, is not a relevant consideration for determining the validity of an argument.

The question of “naturalness” brings us to Gersonides' defence of the controversial fourth syllogistic figure. In the fourth figure the middle term is the predicate in the minor premise and the subject in the major premises, which is precisely the opposite of the arrangement of terms in the first figure. For some reason Aristotle failed to posit the existence of a separate fourth figure, although he appears to have implicitly recognized some fourth-figure moods.²⁷ Galen is usually given the credit for the fourth figure, which, according to the text-books of the history of logic, lay undefended until the end of the Middle Ages.²⁸ Indeed, although the fourth figure became known in the Latin West beginning in the middle of the thirteenth century, when the new translations of Aristotle and the commentaries of Averroes became available, yet Averroes' energetic criticisms, especially his rejection of “unnatural” modes of inferences, impeded the acceptance of the figure for many generations.²⁹

Yet recent research into Jewish logical writings of the thirteenth and fourteenth centuries has uncovered two defences of the fourth figure against the attacks of Averroes. One of these defences, preserved in a work by the Spanish philosopher Isaac Albalag (end of thirteenth-, beginning of fourteenth-century), is by his contemporary Abner of Burgos.³⁰ The second, and most developed, is presented by Gersonides in the Correct Syllogism and in the C. Prior Analytics.³¹

What is most interesting about Gersonides' treatment of the fourth figure is his self-confident approach to what he knew to be a controversial issue. He begins by pointing out without much comment that two premises composed of three terms may be arranged in four different ways; these are the four figures. He then proves generally that premises that fail to yield the quaesitum in the first figure will do so when they have been transposed, and vice-versa. Now, it can be shown that there are first-figure premise-pairs that yield a conclusion other than the quaesitum. So by the aforementioned rule it follows that they will yield the quaesitum if the premises are transposed, i.e., if they are set out in the fourth figure.³²

Averroes had argued that it is not necessary to posit a fourth figure, for if one reverses the order of the premises one obtains the first-figure, the minor term becoming the major term and vice-versa.³³ Gersonides was, of course, familiar with the argument, yet he rejects it out of hand. It is this rejection which is of special interest to us because of the light it sheds on his view of the relationship of logic and science. Basically he argues that the fourth figure should be posited in order that all concludent premise-pairs yield the quaesitum. If the premises were arranged in the first figure, as Averroes had suggested, then the premises would yield a conclusion other than the quaesitum because the order of the terms of the conclusion would also be reversed. Not all of these conclusions could be converted so as to yield the quaesitum; there are two premise-pairs that will yield the quaesitum only in the fourth figure: “Every B is A/No C is B” and “Some B is A/No C is B”; these yield “Some A is not C” in the fourth figure alone. Since these premise-pairs may arise in one's investigations, and since they satisfy the general conditions of the syllogism, there is no reason why they should not be arranged as fourth-figure syllogisms.

In sum, the fourth figure must be posited not in order to yield a valid conclusion, but in order to yield certain types of the quaesitum that cannot be obtained otherwise. And yielding the quaesitum is what makes syllogisms important for scientific inquiry. We see, then, that while Gersonides appeals to scientific utility to argue for the importance of positing a separate figure, he proves the logical validity of fourth-figure syllogisms independently of extra-logical considerations.

At this point Gersonides has to confront head-on Averroes' contention that the fourth figure is not only unnecessary, but also represents an unnatural form of reasoning.³⁴ This, we will now see, leads Gersonides notably to distinguish the notion of the validity of an argument from that of its naturalness. Averroes does not say what makes the fourth figure unnatural, but this may be the point of his next objection: when the middle term is the subject of the minor premise and the predicate of the major premise (the arrangement of the fourth figure), then we predicate something of itself, which is strange. Consider, for example, the fourth-figure syllogism “Every B is A, Every C is B; hence, Some A is C” (Bramantip, according to the scholastics). Since A is predicated of B in the minor premise, and C is predicated of A in the conclusion, one can conclude that C is predicated of B. But the major premise tells us that B is predicated of C; it is as if something is predicated of itself.³⁵ In his commentary on this passage, Gersonides suggests that Averroes may also be concerned by the fact that one of the premises of a fourth-figure syllogism contains an unnatural predication in Aristotle's sense of the phrase, e.g., a predication in which a substance is affirmed of an accident.³⁶ Finally, Averroes notes that in order to reduce the fourth figure to the first we must perform two operations: transposition of the premises and conversion of the conclusion. This, too, he considers strange.³⁷

Gersonides addresses these objections at some length in the Correct Syllogism.³⁸ To the last one mentioned above he replies that the reduction of the second mood of the fourth figure is no stranger than the reduction of the second mood of the second figure (Camestres), which involves two conversions and one transposition. Furthermore, all of the fourth-figure syllogisms can be proved easily by the procedure of reductio per impossibile. As for the objection that the fourth figure involves self-predication, as well as other “unnatural” predications, Gersonides points out that this applies only to two moods of the fourth figure, namely, the ones in which both premises are affirmative; it hardly can serve as a reason for eliminating the other three. More importantly, it is obvious that unnatural predications are allowed in syllogisms, for the theory of the syllogism is based on the theory of conversion of premises, which assumes that the subject and predicate can be exchanged.

But what of the more fundamental charge that the fourth figure represents an unnatural pattern of reasoning? To this Gersonides responds as follows:

As for Averroes' statement that we do not possess this figure naturally—even if we concede this point it is no objection against us. For when we mistakenly consider two inconcludent premises to be concludent, as in the case of two affirmative premises in the second figure, this art corrects our error and provides us with knowledge of what we were ignorant of at the beginning of the inquiry. But if this art investigated only by means of what we know by nature, then our exertions in it would be an idle exercise. For it would not inform us of anything which we did not already know. This is completely evident.³⁹

Gersonides' response can be understood in two ways. He may mean simply that the “unnaturalness” of the fourth figure does not diminish its importance for logic because logic takes us beyond what we know by nature, i.e., originally, or in our natural state. On this interpretation, Gersonides' answer implies an understanding of “unnatural” as something like “developed,” “advanced.” But Gersonides is probably making the stronger point that the oddness or counterintuitiveness of certain valid patterns of inference are not insufficient grounds for rejecting them: on the contrary, since logic proceeds from what is known to what is unknown, it is likely that there will be strange patterns of inference; if our reasoning leads to these patterns then we cannot reject them because they are odd or unusual. This interpretation makes Gersonides sound strikingly modern in his disregard for a psychological criterion such as “naturalness” in the assessment of the validity of inferences. Such a disregard is in keeping with what we may describe as his rigorous, almost mathematical, approach to the theory of inference.

In Gersonides' syllogistic, then, we see an implicit distinction between the logical notion of validity, the psychological notion of naturalness, and the pragmatic notion of scientific utility. An inference-pattern may be valid, though psychologically “unnatural” and of no profit for science (e.g., the syllogisms that yield a conclusion other than the quaesitum). Or it may be valid and of possible value for scientific demonstration, yet unnatural (e.g., fourth-figure syllogisms). Since logic, according to Gersonides, is an organon for science, scientific utility will serve to bolster the acceptability of a given inference pattern, although it will not determine its validity.

Notes

1. Be'ur la-Higgayon. This title is found in only a few mss (e.g., MS. Bodley Mich. 209 (Ol. 71) [Neubauer 1383]), but as it is accepted by Steinschneider (Die Hebraeischen Übersetzungen des Mittelalters und die Juden als Dolmetscher [Berlin, 1893; rept. Graz, 1956], p. 68) I shall use it here. For most medievals, the Aristotelian Organon was composed of Porphyry's Isagoge and Aristotle's Categories, De Interpretatione, Prior and Posterior Analytics, Topics, Sophisticis Elenchis, Rhetoric, and Poetics. Henceforth, references to the individual books of the Commentary on Logic (C. Logic) will be of the form, “Commentary on the Isagoge” (“C. Isagoge”), etc.; the divisions of the work are according to the Hebrew version, and not the Latin translation.

2. Sefer ha-Heqqesh ha-Yashar. I am currently preparing a critical edition of this text. Gersonides also wrote a smaller work entitled, Commentary on Averroes' First and Second Treatises Concerning Some Points in the Prior Analytics (Be'ur ha-Ma'amar ha-Rishon ha-Nimza' la-Filosof' Ibn Rushd bi-Qezat 'Inyanei Sefer ha-Heqqesh … Be'ur ha-Ma'amar ha-Sheni …). This is a commentary on the fifth and ninth of Averroes' Logical Questions. See Steinschneider, Hebraeischen Übersetzungen, pp. 96-108. (Henceforth, Commentary on the Logical Questions (or C. Logical Questions).)

3. See S. Rosenberg, “Gersonides' Commentary on the Mavo” (Hebrew), Daat 22 (Winter, 1989): 85-99.

4. Levi Ghersonidis in Porphyrium, in Praedicamenta Arist., in Lib. de Interpretatione, et in Averoim Annotationes, in Aristotelis Opera Cum Averrois Cordubensis Commentaria, 14 vols. (Venice apud Junctas, 1552-1574; rept. Frankfurt am Main, 1962), vol. 1, pt., 1, pp. 1-106.

5. See Charles Manekin, “Preliminary Observations on Gersonides' Logical Writings,” Proceedings of the American Academy of Jewish Research 52 (1985): 86-113.

6. Correct Syllogism, Introduction. (All translations are taken from my book, The Logic of Gersonides: A Translation of “Sefer ha-Heqqesh ha-Yashar” [The Book of the Correct Syllogism] of Rabbi Levi ben Gershom, with Introduction, Commentary, and Analytical Glossary, New Synthèse Historical Library [Dordrecht: Kluwer, 1992].) Gersonides may also be alluding to the fact that his treatise considers the direct syllogism (ha-heqqesh ha-yashar), i.e., a syllogism in which the conclusion is drawn directly from the premises, as opposed to the per impossibile or apagogic syllogism (ha-heqqesh ha-ḥiluf). (For this distinction see Prior Analytics I:23, 41a23-4029a19; cf. the discussion in G. Patzig, Aristotle's Theory of the Syllogism [Dordrecht, 1968], p. 149. For the Hebrew phrase, cf. Jacob Klatzkin, Ozar ha-Munaḥim ha-Filosophiyim ve-'Antologiah Filosofit [rept. New York, 1968], I, pp. 207-8.) Gersonides does use the phrase heqqesh yashar in the sense of ‘direct syllogism’ in the C. Prior Analytics.

7. In what follows I shall follow the medievals who often used the terms ‘philosophy’ and ‘science’ interchangeably.

8. See the beginning of the fifth Logical Question (cited in the C. Logical Questions, Bodley Mich. MS. 219

   dici de omni became the dictum de omni in the Renaissance, and how it became famous as Aristotle's ‘principle’ of the syllogism, is a fascinating story in the history of logic that I hope to tell elsewhere.

9. I.e., the Middle Commentary on the Prior Analytics, the Epitome of the Organon, and the fifth of the Logical Questions.

10. C. Prior Analytics, Bodley Mich. MS. 219

11. C. Logical Questions, fols. 263v-264r.

12. Cited by Steinschneider, Hebraeischen Übersetzungen, p. 67. This passage is not in the edition of the C. Isagoge edited by Shalom Rosenberg, which is based on only several of the extant manuscripts. See S. Rosenberg, “Gersonides' Commentary on the Mavo,” p. 90.

13. C. Isagoge, Vatican MS. Urb. 35, fol. 1r.

14. On the historical discussion of the relationship of logic to science, see Christel Hein, Definition und Einteilung der Philosophie. Von der spätantiken Einleitungsliteratur zur arabischen Enzyklopädie (Frankfurt am Main, 1985), pp. 153-62.

15. See Milḥamot ha-Shem I:10 (Riva di Trento, 1560), pp. 11b-16a. For an interpretation of this chapter, see Charles H. Manekin, “Logic and Its Applications in the Philosophy of Gersonides,” in Gersonide en son temps. Science et philosophie médiévales, ed. G. Dahan (Louvain/Paris: E. Peeters, 1991), pp. 133-49. Earlier interpretations include Isaac Husik, “Studies in Gersonides,” Jewish Quarterly Review, n.s. 7 (1916-1917): 553-94, and 8 (1917-1918): 113-56 and 231-68; Julius Guttmann, “Levi ben Gersons Theorie des Begriffs,” in Festschrift zum 75-jährigen Bestehen des jüdisch-theologischen Seminars (Breslau, 1929), 2, pp. 131-49; and Charles Touati, La pensée philosophique et théologique de Gersonide (Paris, 1973), pp. 413-24.

16. This doctrine was itself not original to Gersonides; he could have learned of it from his reading of Averroes. See Harry A. Wolfson, “Avicenna, Algazali, and Averroes on Divine Attributes,” in Homaje a Millas-Vallicrosa (Barcelona, 1956), II, pp. 545-71; rept. in his Studies in the History of Philosophy and Religion I (Cambridge, Mass., 1973), pp. 143-69, esp. p. 169.

17. C. Categories, Vatican MS. Urb. 35, I: 1, fol. 26r.

18. Sources for the preceding paragraph are: Porphyry, In Aristotelis Categorias Commentarium, ed. A. Busse, Commentaria in Aristotelem Graeca, vol. 4, pt. 1 (Berlin, 1887), pp. 56-7; Ammonius, In Porphyrii Isagogen, ed. A. Busse, Commentaria in Aristotelem Graeca, vol. 4, pt. 3 (Berlin, 1891), p. 9; John Philoponus, In Aristotelis Categorias Commentarium, ed. A. Busse, Commentaria in Aristotelem Graeca, vol. 13, pt. 1 (Berlin, 1898), p. 8, line 27—p. 9, line 15. The above are all quoted in Herbert A. Davidson, ed., Ha-Be'ur ha-' Emza'i shel Ibn Rushd 'al Sefer ha-Mavo le-Porfirius ve-Sefer ha-Ma'amarot le-'Aristoteles, Corpus Commentariorum Averrois in Aristotelem, Versionum Hebraicarum, Vol. I, a (Medium) (Cambridge, Mass., 1969), p. 114, note to 33.24; idem., Averroes' Middle Commentary on Porphyry's “Isagoge” … and on Aristotle's “Categoriae”, Corpus Commentariorum Averrois in Aristotelem, Versio Anglica, Vol. I, a 1-2, (Cambridge, Mass., 1969), p. 99, n. 6. See D.M. Dunlop, ed. and trans., “Al-Farabi's Introductory ‘Risālah’ on Logic,” Islamic Quarterly 3 (1956): 224-35, on p. 229, trans. p. 232; A. Gonzalel Palencia, ed. and trans., Ihsā' al'Ulūm (Madrid, 1953), pp. 46-7, trans., p. 32. For Avicenna's exclusion of the categories in the Shifā, see I. Madkour, L'Organon dans le monde arabe, seconde édition (Paris, 1969), pp. 79-84. They are also missing from Avicenna's other major logical writings (e.g., al-Shifā, al-Najāt, al-Ishārāt, and the Danesh-Name Alai.): see A.I. Sabra, “Avicenna on the Subject Matter of Logic,” Journal of Philosophy 77 (1980): 746-64.

19. Averroes, Kol Melekhet Higgayon (Riva da Trento, 1527), p. 9a. The translation, by Jacob ben Makhir in 1189, is of the epitomes of the books of the Organon. For Gersonides' familiarity with the work, see Manekin, “Preliminary Observations,” p. 98.

20. See Davidson, Ha-Be'ur ha-'Emza'i, p. 31 and p. 113, note to 31.8; idem., Averroes' Middle Commentary, p. 31 and note 7, p. 98.

21. C. Categories, I:12, 29v: “It behooves us rather to say that this art

22. See Davidson, Ha-Be'ur ha-'Emza'i, 2:1, p. 45, and p. 119, note to 45.31; idem., Averroes' Middle Commentary, p. 42 and note, p. 98. The notion of a substance signifying something else sounds odd to modern ears, but that is what Aristotle says at Categories 5, 3b10. According to Ackrill, “it is careless of … [Aristotle] … to speak as if it were substances (and not names of substances) that signify.” See Aristotle's “Categories” and “De Interpretatione”, trans. with notes by J.L. Ackrill, Clarendon Aristotle Series (Oxford, 1963), p. 88.

23. C. Categories, II:11, fol. 30v. Cf. Ibid., II:12, fol. 31r, where Gersonides claims that the primary elements, like other substances, do not admit of a more or a less. He adds that he plans to consider this topic elsewhere, “for it is evident that this is not the place for such an investigation.” Gad Freudenthal writes (personal communication): “One place, at least, where he considers this topic, if briefly, is his Commentary on Averroes' epitome of the De generatione et corruptione, at the passage corresponding to II, 1, 328b26; cf. MS. Berlin, Staatsbibliothek preussicher Kulturbesitz, MS. Orient Fol. 1055 (catalogue number 110), fol. 91. His argument is essentially that since the elements act on, and are affected by, one another, they must be contraries (just as the qualities). His argument is not found in the corresponding passage of Averroes' epitome; see Samuel Kurland ed., Be'urei Ibn Rushd'al Sefer ha-Havayah ve-ha-Hefsed le-'Aristoteles, Corpus Commentariorum Averrois in Aristotelem, Versionum Hebraicum, Vol. IV, 1-2 (Cambridge, Mass., 1958), pp. 112-3; idem., Averroes on Aristotle's ‘De generatione et corruptione’: Middle Commentary and Epitome, Corpus Commentariorum Averrois in Aristotelem, Versio Anglica, Vol. IV, 1-2 (Cambridge, Mass., 1958), pp. 124-5.”

24. Opinions of the Philosophers, I:4, in The Logical Part of Al-Ghazali's “Maqāsid al-Falāsifah …, ed. and trans. G.B. Chertoff (Dissertation, Columbia University, 1952), II, p. 55.

25. Middle Commentary on the Prior Analytics, I:1, MS. Jewish Theological Seminary 2466, fol. 78r.

26. C. Prior Analytics MS. Leiden Warnero 42, fol. 129v.

27. See I.M. Bochenski, A History of Formal Logic, trans. Ivo Thomas (Notre Dame, 1975), p. 71; cf. Jan Lukasiewicz, Aristotle's Syllogistic From the Standpoint of Modern Formal Logic (Oxford, 1954), p. 27.

28. For characteristic statements see A.N. Prior, “Logic, Traditional,” Encyclopedia of Philosophy, ed. Paul Edwards (New York: Collier-Macmillan, 1967), vol. 5, p. 39, and William Kneale and Martha Kneale, The Development of Logic (Cambridge, 1962), p. 183, who write, “… we have no trace of anyone who defended the doctrines of four figures before the end of the Middle Ages.”

29. As late as the nineteenth-century an English logician would write about the fourth figure, “Ought we to retain it? If we do, it should be as a sort of syllogistic Helot, to show how low the syllogism can fall when it neglects the laws on which all reasoning is founded. … Where the First Figure draws its conclusion naturally … this perverted abortion forces the mind to an awkward and clumsy process which rightly deserves to be called ‘inordinate and violent.’.” From Father Clark's Logic (p. 337), quoted in J. N. Keynes, Studies and Exercises in Formal Logic (fourth ed., London, 1928), p. 284.

30. In Bochenski, A History of Formal Logic, pp. 217-8. Bochenski included a translation of the text by Georges Vajda. Following Vajda, Bochenski attributed the defense to Albalag in the original German edition of his history; he then corrected the attribution in the second German edition on the basis of Vajda's correction in Isaac Albalag: Averroïste juif, traducteur et annotateur d'al-Ghazâlî (Paris: J. Vrin, 1960), pp. 274-5. Unfortunately, the English translation is of the first German edition, and hence does not take into account Bochenski's correction in the second edition. For the Hebrew text cf. Georges Vajda (ed.), Isaac Albalag, Sefer Tiqqun ha-De'ot (Jerusalem: Israel Academy of Sciences and Humanities, 1973), pp. 9-12.

31. I consider these and other defences in a forthcoming study of the syllogism in medieval Hebrew logic.

32. Correct Syllogism II:4, fol. 114r.

33. This is precisely what Aristotle's student Theophrastus was said to have done, and it has been suggested that this was Aristotle's own view. See Kneale and Kneale Development, p. 100. On Aristotle's acceptance of the fourth figure moods, cf. Lukasiewicz, Aristotle's Syllogistic, 55-83; Bochenski History, pp. 70-72, and G. Patzig, Aristotle's Theory of the Syllogism, trans. Jonathan Barnes (Dordrecht, 1977), pp. 55-83.

34. Middle Commentary on Prior Analytics, I.1, fols. 67v, 78r-v. The charge of “unnaturalness” is found in the writings of Avicenna, although it is probably older. See Livre des directives et remarques (Kitab al-'Ishārāt wal-Tanbīhāt), trans. A.M. Goichon (Paris: J. Vrin, 1955), p. 198. Cf. I. Madkour, L'Organon dans le monde arabe, p. 206.

35. Middle Commentary on the Prior Analytics, I:1, MS. Jewish Theological Seminary 2466, fol. 78r-v.

36. C. Prior Analytics, fols. 192-193.

37. Middle Commentary on the Prior Analytics, I:1, fol. 73v.

38. In II:6.

39. Correct Syllogism, II:9.