This paper addresses a central metaphysical issue that has not been recognized: what kind of entity is a syllogism? I argue that the syllogism cannot be merely a mental entity. Some counterpart must exist in nature. A careful examination of the Posterior Analytics’s distinction between the syllogism of the fact and the syllogism of the reasoned fact shows that we must set aside contemporary logic to appreciate Aristotle’s logic, enables us to understand the validity of the scientific syllogism through its content rather than its form, and explains the priority of the scientific syllogism over other valid syllogisms. The opening chapters of Posterior Analytics II help us to distinguish the entities that scientific syllogism must include as its terms; namely, a genus, an essential nature, and essential attributes of the genus. Often, the attributes are found in closely linked sequences. By exploring why there are such sequences and how they are linked, the paper argues that sequences of genus, nature, and sequential attributes are the basis in nature for the process of reasoning that we call the syllogism: we come to grasp the syllogism over time but the sequences to which it refers exist together in things. So understood, the syllogism, like knowledge of forms and truths, exists in us and in the world.
Ancient philosophy has been so intensely studied for so long that it seems unlikely that any major issue remains unexplored. It will, therefore, come as something of a surprise to realize that the issue I will discuss here is not just unexplored by contemporary scholars but wholly unrecognized, even in passing. The issue can be stated simply: What is an Aristotelian syllogism? Of course, there has been a great deal of discussion of the syllogistic forms and especially of how to represent them in a formal deductive system. My question is ontological: what sort of entity is the syllogism?
Aristotle defines the syllogism as “a discourse (logos) in which certain things being stated, something other than what is stated follows of necessity, from their being so” (Prior Analytics I 1, 24b18–20, Jenkinson translation). Aristotle goes on to explain that what is “stated” are two premises that contain three terms and that what “follows of necessity” is a conclusion that contains two of these terms. (Although he uses “syllogism” to signify only valid syllogisms, the Prior Analytics considers all possible syllogistic forms in order to determine which are valid. Hence, it is more convenient to use “syllogism” to refer to the form, regardless of its validity.)
The Greek word that is here rendered “discourse,” logos, could as well be understood as “process of reasoning.” In any case, Aristotle’s definition is notably opaque on what the syllogism is, on why a conclusion would follow from what is posited, and on why the inference would be necessary.
Contrast Aristotle’s definition of a (valid) syllogism with his account of true propositions:
An affirmation is a positive assertion of something about something, a denial a negative assertion. It is possible to assert of what holds that it does not hold and of what does not hold that it does, as well as to assert of what holds that it does hold and of what does not hold that it does not. (De Interpretatione 6, 17a25-29, my translation)
Propositions are true when they express what holds in the world. A valid syllogism, that is, a “perfect syllogism” needs “nothing other than what has been stated to make plain what necessarily follows” (APr. 24b22–25, Jenkinson translation). Whereas something in the world makes a proposition true, a syllogism is recognized as valid from itself, independently of anything in the world.
Nonetheless, the syllogism is used to draw inferences about the world. Why does a valid syllogism whose premises are true yield a conclusion that is also true? Inasmuch as the syllogism is a tool for deriving or, at least, affirming some truths about the world on the basis of others, the assertions that constitute a sound syllogism must be linked together somehow not only in our minds, but also in the world. What is it in the world that allows a syllogism whose premises are true to yield a true conclusion? Again, a syllogism that was merely valid might, conceivably, lack a connection with the world, but it is impossible to suppose that a sound syllogism would not have something in the world that would somehow correspond to it. This something must be more than whatever it is that corresponds to the sound syllogism’s three propositions, for their very connection in the syllogism signifies something about the world: three true sentences need not be a syllogism. My concern here is what this could be. Thus, to ask “what is a syllogism?” in the way I am proposing here, is to ask, “what is it in the world that corresponds with and, thereby, legitimates a sound Aristotelian syllogism?” Why can we assume that a logos that we can recognize to be valid only from what it states also applies to the world? Inasmuch as the Posterior Anyalytics aims to show how to use the syllogism to arrive at scientific knowledge of the world, my question is crucial for understanding this work.
Again, a logos is either a series of sentences or a process of reasoning. Maybe it would not be too surprising if there were some pattern in the sentences or in the reasoning to which our human intellect must somehow give its assent. The primary rule of inference in contemporary logic, modus ponens, may be just such a pattern. What is difficult to understand is why such a pattern, process of reasoning, or discourse—or whatever else it might be—must also hold of the world. Why can reasoning about the world be a way to discover what is true of the world?
Someone might think this question could be answered by identifying “truthmakers” in the world that make each premise of a valid syllogism true and then by showing that they imply a third truthmaker that makes the conclusion true. The issue is what sort of thing in the world this implication would be. Since merely being true does not suffice for three sentences to constitute a syllogism, there must be something in the world besides the three truthmakers that somehow makes them into a syllogism. What could this be? To coin a term, what is the “soundness maker”? This is the question I am posing here.
In short, to ask, “what is a syllogism?” in the way I am proposing here is to ask, “what is it in the world that constitutes the peculiar process of inference that is an Aristotelian syllogism?” Can processes of inference exist in the world or is there, rather, something else in the world that allows there to be sound mental inference? So understood, the question is about the relation of logic to the world. This was once a central question for philosophers. In the Tractatus Wittgenstein understands the structure of logic as the structure of the world as well as the structure of language; in his later work, logic comes to be a collection of grammatical features of our language, features we often find useful—though not always, as Graham Priest likes to remind us.1 Even if we had no other reason to raise the question, it would be interesting to inquire into how Aristotle understands his logic to relate to the world.
In fact, though, we have good reasons from Aristotle’s philosophy to raise this question. In the De Anima Aristotle maintains that the form that is a thing’s essential nature exists both in the thing and in the mind, albeit in the former with matter and in the latter without (III 4, 429a13–18). In this respect, the intelligible form parallels the sensible form that exists in an object and in the pertinent sense organ of the sensing animal. In other words, the essential nature that we know also exists, albeit with matter, in the thing known. The existence of this nature in our minds is necessary if we are to know the object, Aristotle maintains. Were our minds to have an image or representation of the object, we would not have knowledge; nor would we have real knowledge if we grasped the object by somehow sending out a beam of light or something else, as bats grasp the world, and as Plato seems to think we sense (Timaeus 45c).
The paradigmatic essential natures that we know are the essential natures of substances. But there is no reason to suppose that only substances have essential natures: Aristotle speaks of knowledge of: mathematical entities (quantities) (Metaphysics K 3, 1061a28–b3), colors (Metaph. I 7, 1057a18–b34; De Sensu 3), and grammar (Categories 1a29–b3). Indeed, in the Metaphysics he claims that substances have essences most properly, but that instances of other categories have essences as well, albeit derivatively (Z 4, 1030a38–32). Importantly, for us, the Metaphysics makes clear that something’s essential attributes have their own essences, though, again, not in the primary way: “in one way there will not be definitions or essences of anything except substances, but in another way there will be” (Z 5, 1031a1–14).2 Aristotle claims here that the essential attributes have essences “by addition.” What this means becomes clear when the Posterior Analytics discusses essential attributes in chapter 4 of book I. Attributes are essential to some subject, first, when the subject is included in the formula that makes clear what the attribute is; thus, the definition of odd includes number (the example also appears in the passage just cited from Metaph. Z 5) and the definition of straight includes line (73a37–b3; Metaph. 1031a1–5). That is to say, the essential definition of straight does not express an independent, self-subsistent entity. Since straight does not exist without a line in which it inheres, the essential nature of straight includes the essential nature of line “by addition,” as the Metaphysics puts it. My point here is that these passages make clear that an essential attribute has an essential nature. Like the line in which straight inheres and the sensible substance in which the line inheres, straight is a form that can exist in the world and, when it is known, in our minds.
I 4 describes another kind of essential attribute that is important for demonstrative knowledge: the essential attributes that are included within the essential definition of some subject (I 4, 73a34–37). Once again, Aristotle’s examples of these attributes include the line, but now it is an attribute of the triangle because it is included within the definition of the triangle. Since we know that line has an essential nature because it is an essential attribute inhering in a substance (that is, since it is the first sort of essential attribute), it is clear that line and the other attributes that are essential because they are included in an essential definition (that is, since they are the second sort of essential attribute) must also have their own essential natures. It is important that the definitions of essential attributes are intrinsically linked to the natures to which they belong because it is these two types of essential attributes that can be demonstrated (I 22, 84a11–17). We will come back to this link later.
The essential natures of substances and their essential attributes are among the terms of scientific syllogisms. There is another thing that can appear as a term in a syllogism: a genus or a species (I 7, 75a42–b2). These usually serve as the subjects whose attributes are demonstrated, and they are universals. The last chapter of the Posterior Analytics claims that we can come to know a universal through repeated sensation. Eventually, the sensible’s features “take a stand” like soldiers who stem a rout in battle when they turn around and the battle lines reform around them, and we can identify a universal character that a group of sensibles share (II 19, 100a3–b5). The universal here seems to be an identifying character that enables us to say that something is, say, a man or a dog. Interestingly, some sensible feature common to a class of individuals somehow comes to exist in the mind as the character that is common to all instances of the genus. What makes a character that can be sensed into something that is grasped by reason? Apparently, it is just its being able to be used to mark off a class of things.
The generic character that we use to designate a class is just one of multiple characteristics that are common to the class. Presumably, we come to know these characters by the same sort of induction from sensible instances. Those universal characters we see first are “prior to us” but not “prior in nature” (I 2, 71b33–72a5). The essential nature of the class is prior in nature, and it accounts, somehow, for the other characters that are common to the class.
Aristotle’s point is that after the repeated sensations of similar objects, we somehow grasp a feature or features that mark off things as being of a single type, a genus. This same sort of repeated sensation allows us to recognize other features of the genus, such as “having two legs” or “the capacity to laugh.” Once we have identified a group of such characters that are common to the genus, we can ask which of them is the essential nature that defines it. One sign of the essential nature is that the other characters common to the genus can be understood to belong to the genus in respect of this nature. As I said, this essential nature exists both in the things included within the genus and in the mind that grasps this nature. Again, if the essential nature has this dual existence, then so, too, must those universals that initially come to be grasped through sensation; namely, the genus and all its essential attributes. If the form that is sensed exists in the thing and in a sense organ, then the universals that result when sensations “take a stand” must also exist in the things, somehow, and in the mind. In sum, all three terms of the syllogism exist in things and, equally, in the mind.
If the terms that are contained in the syllogism exist in things, must not the inference between them that constitutes the syllogism also exist in things? Can a syllogism be merely a mental addition to the physical counterparts of the individual terms? Surely, there must be something in the things corresponding to the inference, something in the things that corresponds to the syllogism as a whole, or possibly both. If a form that is known exists in the mind and in the thing and if a true proposition with this form exists in the mind and, somehow, in things, then the scientific knowledge, that is, the knowledge through the syllogism that demonstrates the proposition must also exist in the mind and, somehow, in things.
In order to pursue our problem, we need to appreciate Aristotle’s account of the scientific syllogism. Aristotle gives an account of the syllogism in general in the Prior Analytics. He is particularly concerned with setting out the three figures and showing which forms are valid. The Prior Analytics is Aristotle’s formal logic. (A number of readers have tried to put Aristotle’s account into the formal logic that is in wide use today.) In the Posterior Analytics Aristotle expounds the scientific syllogism. Two syllogistic forms could be scientific syllogisms, one positive and the other negative, but the more important of these is the positive form, and it is the form that Aristotle usually uses to express a scientific syllogism. This form was called by the medieval mnemonic, “Barbara”:
The other form of a scientific syllogism was called “Celarent”:
Both are clearly valid syllogistic forms, but it is not merely its form that makes a syllogism scientific. It must also meet various criteria that the Posterior Analytics specifies: Its premises must be true, primary, immediate, and the premises must also be more known than, prior to, and the causes of their conclusions (71b19–22). The assumption is that only what cannot be otherwise can be known (71b12). In order that the syllogism be able to convey scientific knowledge (ἐπιστήμη), that is, demonstrative knowledge, what its premises affirm or deny cannot be otherwise and so, consequently, what its conclusion affirms or denies cannot be otherwise. Hence, the scientific syllogism must have necessary premises and conclusion (71b12–16). Moreover, that “through which” some attribute C belongs (or does not belong) to the subject A must itself belong to the subject “more” (72a28–29). In other words, the cause of the subject’s having or not having an attribute, the attribution that the conclusion asserts or denies, is a middle term whose own attribution to the subject is prior to that of the attribute. Importantly, Aristotle calls such a middle term the “cause” (90a5–7). A syllogism that meets these criteria is “scientific” or, equivalently, it constitutes demonstrative knowledge. (Although they are often called “explanatory syllogisms,” this phrase captures neither the scientific syllogism’s demonstrative necessity nor the essential priority of its middle term.)
These criteria are widely understood to specify additional conditions that make a valid syllogism scientific. Thus, they are taken to be grafted on to syllogistic forms that are recognizably valid. I am going to challenge this view, but first we need to see why it seems plausible and, in the process, come to appreciate how these criteria actually work.
One place where they do seem, at least at first, to be grafted on to the syllogistic form is Aristotle’s important distinction between the “syllogism of the fact” (τὸν τοῦ ὅτι συλλογισμόν) and the “syllogism of the reasoned fact” (τὸν τοῦ διότι συλλογισμόν) in I 13 (see 78b32–34, 78a36–37). Both are valid syllogisms, but they differ “according to the position of the middle terms.” In the syllogism of the reasoned fact, the causal term appears as the middle term. In the syllogism of the fact, this causal term occupies another position, out of place, as it were. Aristotle’s illustrations are memorable:
Both syllogisms are formally valid, but the first, the syllogism of the fact, puts “not-twinkling” in the middle position. If this syllogism were a scientific syllogism, “not-twinkling” would belong to the planets “more” than being near and, thereby, be the cause of the planets’ being near. In other words, syllogism would claim that the planets are near because they are not-twinkling. The second syllogism is the syllogism of the reasoned fact because it rightly uses the nearness of the planets to explain their not-twinkling (78a36–38).
Aristotle does not explain how we know that it is the planets’ nearness that causes them not to twinkle, rather than their not-twinkling that causes them to be near. He relies on our ordinary experiences of objects that are relatively near: they do not twinkle (78a34–35). But this observation supports the first premises of both syllogisms equally. We also need to recognize that to say that the planets are near is to express how they are, whereas to say that they do not twinkle is to express how they appear. That the way things are accounts for their appearances, rather than the other way around, is assumed here as an axiom. Like the principle of non-contradiction, which is assumed in every syllogism, the priority of being to appearance is assumed without being stated (compare I 11, 77a10–12, 27–28). Recognizing the axiom, we can see that 2, rather than 1, is the syllogism of the reasoned fact. But Aristotle does not invoke this axiom even here; he simply asserts that twinkling is not the cause of nearness (78a36–38). Clearly, we would not be able to rely on this or, perhaps, any other axiom to distinguish every syllogism of the reasoned fact. Rather, Aristotle seems to suppose that we simply have an innately human ability to discern that one thing is a cause and another is not. This ability is necessary to have demonstrative knowledge.3
As I said, this I 13 passage seems to support the idea that the demonstrative syllogism is just a syllogism with extra conditions because the syllogism of the fact and the syllogism of the reasoned fact, 1 and 2, have the same syllogistic form and differ only in that the middle term of syllogism 2 is a cause, whereas the middle term of 1 is not. More precisely, the conditions of the priority of the premises to the conclusion for scientific knowledge (ἐπιστήμη), spelled out in I 2 (71b9–19) are met by syllogism 2, but not by syllogism 1.
The question I want to raise is whether the causal role of the middle term in the syllogism of the reasoned fact is an additional condition that can be readily grafted onto the account of the syllogism in the Prior Analytics or whether it fundamentally transforms the syllogism so that it can serve as the expression of demonstrative knowledge. In the latter case, the syllogism of the Prior Analytics would play a heuristic role in uncovering the scientific knowledge expressed only in a syllogism of the reasoned fact. In this way, scientific knowledge would emerge as the unifying goal of both Analytics.
We are in nearly uncharted territory here, and it is only fair to warn the reader that what follows will prove challenging; indeed, all the more so to readers familiar with contemporary logic. As Jonathan Barnes noted, both syllogisms “would count as explanatory on the orthodox modern account of explanation” because on the “Human notion of causation” that is “a presupposition of that account, … the major premises of both accounts are equally causal.”4 Barnes claims that Aristotle does not explain why non-twinkling can be “explained” by nearness, but not the other way around, until he discusses essence in Posterior Analytics II (16, 98b21-24). As we saw, I 13 treats the causal priority of nearness to twinkling as obvious; II 16 does not justify this priority, but does indicate the basis for any causal priority. We will consider it shortly. First, though, notice how deeply insightful Barnes’s words are, even if he himself does not always appreciate them.5 We can appreciate the distinction between the syllogism of the fact and the syllogism of the reasoned fact by reflecting further on contemporary notions of logic. It is customary to refer to logic as “formal logic” by which we mean that a deduction, such as p ⊃ q, p ├ q, holds whatever the values of p and q. Contemporary logicians rarely if ever consider the values of terms or whether there might be some values that would undermine or transform the inference. The conditional p ⊃ q is now universally taken to be the so-called “material conditional”: its truth value depends solely on the truth value of p and the truth value of q. No connection between p and q is assumed. So, no one objects to a conditional like “if 2+3=5, then π is the ratio of the circumference of a circle to its radius” or questions its truth. Nor is there much concern that a conditional in which the terms were intrinsically connected, like “if x>3 then x>2,” would not be a material conditional. Some logicians have spoken of the “strict conditional” to mark the connection, but it is not widely used because the material condition has seemed to serve adequately to express conditionals with connected components or, at least, to express their truth conditions. As Barnes sees, the metaphysics of the material conditional is rooted in Hume’s analysis of causality: Hume challenges his readers to find something in one sense perception that would necessarily connect it with a sense impression that succeeds it. Failing to find any such perception, he reduces causality to one type of perception’s regularly following another type, that is, to the relation expressed by the material conditional. The early Wittgenstein and Russell expounded a metaphysics of logical atomism based on what they took to be presuppositions of logic. This metaphysics faded long ago, and today’s logicians are apt to suppose that logic makes no metaphysical assumptions because it can be used to express everything or, at least, everything scientific.
These reflections on contemporary logic have no direct bearing on Aristotle’s understanding of the syllogism, but I think they help to explain why readers have tended to think of the syllogism of the reasoned fact as a syllogism of the fact with some added conditions. Formally, the syllogism of the fact and the syllogism of the reasoned fact are identical. Both are composed of three terms that are extensionally identical. It makes no difference formally which position any of the terms occupies. Both syllogisms are equally valid. If Aristotle prefers one set of positions to another, it can only be for reasons that are extraneous to the syllogism itself. Or so it has seemed.
We have only to set aside (1) Humean causality along with the notions that (2) inference must be only formal and that (3) inference is justified extensionally to let the Aristotelian picture emerge from I 13. (1) We have seen that in a scientific syllogism, Aristotle claims the middle term is a cause, specifically, the cause of some attribute’s necessarily belonging to a subject. This cause is not a Humean regular conjunction because mere conjunction could never be necessary. It should not be surprising that Aristotle’s causes are pre-Humean. Only one of the terms of the syllogism is properly causal because, as we have seen, this term belongs to the subject term “more” than the other and because this other term somehow belongs to the subject because it belongs to the middle term. Only one of the three terms is properly a subject: it either is a substance or can be treated as a substance (that is, as if it were separate, compare Metaph. M 3, 1078a17–21). (2) Whereas contemporary logic is formal insofar as the content of its propositions or its predicates is irrelevant to logical truth, Aristotle insists that the proper term must occupy the middle position if there is to be a scientific syllogism. Again, truths of contemporary logic do not depend on what the p’s and q’s signify, whereas the content of the B term in the Barbara syllogism is critical if the syllogism is to be scientific. (3) Inasmuch as the syllogism of the fact and the syllogism of the reasoned fact are both valid because their terms have the same extensions, the difference between them cannot arise from their extensions. If, then, the one syllogism constitutes scientific knowledge whereas the other does not, scientific knowledge cannot come from grasping that a syllogism is valid through its extension. Since the middle term is the cause and since it must occupy the B position to make clear that it is through it that C belongs to A, it is clear that we grasp the truth of the conclusion of a scientific syllogism through the one term that can exclusively serve as its cause. However, to say that the truth of the conclusion follows from a single, specific causal term is to deny that the conclusion follows merely from the extension of the terms! Whereas the truth of the conclusion of a syllogism of the fact follows from the common extensions of its three terms, the truth of the conclusion of a syllogism of the reasoned fact follows from the particular natures of those terms, that is, from their intensions or, more specifically, from the intension of the middle term. Equivalently, since the Prior Analytics catalogues a number of syllogistic forms that are valid when all three terms have the same extensions, we can say that the syllogism of the fact is valid because of its form, whereas the syllogism of the reasoned fact is valid because of its content. Of course, the syllogism of the reasoned fact is also valid because of its form, but this form, which it shares with the syllogism of the fact is not what makes it scientific knowledge. Rather, we have scientific knowledge when we know a conclusion through its cause, and the syllogism of the reasoned fact shows how that is possible. But the conclusion has to be known through its cause, not through its syllogistic form or through a shared extension, and to know it through its cause is to know the conclusion through the special nature or meaning of the syllogism’s B term. It is evident that to know a conclusion scientifically is the highest way it can be known (ἐπιστήμη), short of some sort of direct vision (νοῦς). Grasping a conclusion through a syllogism of the fact is a much weaker type of knowledge, barely deserving of being called knowledge at all.
Yet, I 13 suggests that if we can attain syllogism of the fact, we may be able to transform it into a syllogism of the reasoned fact by rearranging its terms. Thus, the elaborate account of valid syllogistic forms that occupies the Prior Analytics can be seen to serve a propaedeutic to the inquiry into the causes that is central to the Posterior Analytics. The syllogistic serves as a tool to help uncover terms that are properly causal and, thereby, the key constituents of scientific knowledge. However, it is only the scientific syllogism that counts as scientific knowledge because it alone is a way of knowing something through its cause (compare Metaph. A 3, 984a24–26). Since it is this cause rather than the syllogistic form that makes the conclusion of the scientific syllogism true, it is the basis of the validity of the scientific syllogism.
The notion that there are two possible sources of validity of a syllogism, its content or its form, has no counterpart in contemporary logic where content plays no role. Hence, it will not sit well with contemporary readers. Moreover, it is indeed puzzling how the same syllogism can be valid both because of its form and because of its content. I think that the root of the problem is the supposition that the syllogism of the fact and the syllogism of the reasoned fact are both syllogisms and that their differences must be somewhat superficial because both have the same syllogistic form. My strategy has been to show that their differences are significant, so significant, I now suggest, as to make them distinct entities. A syllogism of the fact can only rely on its form for its validity because the terms need share only common extension. To be sure, usually the terms in a valid syllogism of the fact will also share common content, but we do not need to use this content because we can draw the conclusion from its form alone. Indeed, since Aristotle assumes that whenever two characters are always present together, they must be essentially connected, there will always be common content among the terms of a syllogism of the fact. That makes the syllogism of the fact a useful step in the discovery of this connection. In contrast, a syllogism of the reasoned fact is valid because of the content of its terms, not because of its form. However, content that functions causally naturally takes the form of the Barbara syllogism because there the real cause is positioned so as to serve as the cause. Ironically, then, the syllogism of the reasoned fact takes on the same form as the Barbara syllogism of the fact, yet its validity does not stem from this form. It is clear that the meaning of validity differs in the two types of syllogism, for a syllogism of the fact is valid insofar as its conclusion follows from its premises by virtue of their common extension, whereas a syllogism of the reasoned fact is valid because its conclusion follows from the essential natures of the terms in its premises.
What difference could it make how or why a valid syllogism is valid? Is a syllogism more or less valid if it has a single source of validity or multiple sources of validity? Of course not. However, a syllogism whose validity depends on the nature of its terms has an intrinsic and necessary connection among these terms that the syllogism depending only on extension cannot have. In consequence, the conclusion of the syllogism of the reasoned fact is necessary and that of the syllogism of the fact is not. So, the source of validity makes a difference to the strength of the reasoning and the modality of the conclusion.
There is some small support for this interpretation in the next chapter, I 14. There Aristotle argues that the first figure is the most scientific. One reason is that it is the syllogism of the reasoned fact (79a17–24). He means, I think, that in the first figure the real cause of the thing stands in the causal position in the syllogism. That is to say, the cause is positioned in between the inner and outer terms, and it serves to link them together: in syllogism 2 above, the planets are non-twinkling because of their nearness. Here, the syllogistic form is perfectly suited to the content: it makes manifest the relation that the terms have in respect of their content. In contrast, the syllogism of the fact (1 above), has exactly the same syllogistic form, but its terms are not linked together by their content because there the middle term is not truly causal. The syllogism of the fact can only rely on its form for its validity.
A second reason that I 14 advances for the first syllogistic figure’s being most scientific is that it enables us to pursue knowledge of the essence (79a24–25). This essence (B) is the cause of an attribute (C) belonging to a subject (A). Of course, the syllogism in the first figure need not have the essence in the proper position to be valid, but its terms can be rearranged to help us discover the essence, as I said. I 14’s final reason for the first figure’s being most scientific is that it can stand alone whereas instances of the other figures are shown to be valid or invalid by converting them into the first figure (79a29–32). This is a good summary of the procedure of the Prior Analytics. Aristotle evaluates the validity of syllogisms in the second and third figures by reducing them to syllogisms in the first figure. Further, he evaluates the validity of syllogisms in the first figure by reducing them to one of the two primary syllogisms, Barbara or Celarent. These are the instances of the first figure that properly stand alone. Why can Aristotle simply assume that they are valid? Perhaps, we can intuit their validity. However, as I 14’s first reason suggests, in the syllogism of the reasoned fact, a syllogism that is always in the first figure, the middle term plays a causal role because it is located between the other two terms. As we saw, the syllogism of the reasoned fact is valid through its content, but that content properly takes on the form of a primary syllogism, Barbara. In this ideal case, the form of Barbara is a valid syllogistic form because of its content, but the form remains valid even when the content is not causal, albeit valid in a lesser way, as I have explained. Similarly, Celarent can be a valid syllogistic form because of its causal content inasmuch as the essence that occupies its middle position causes the subject not to have attributes that belong to an entirely distinct genus, and this syllogistic form remains valid, but only extensionally, when the middle term is not causal. My suggestion is that the properly causal roles of the content of Barbara and Celarent account for their strict, necessary validity and allow us to recognize the extensional validity of these forms even without their causal content. If, then, the Prior Analytics shows all the other syllogisms to depend on these, and these, in turn depend on scientific syllogisms that are valid through their content, then the entire syllogistic depends upon the causal essences necessary for scientific syllogisms.
From another point of view, we can say that this syllogistic leads us toward these essences. Early in the Posterior Analytics Aristotle distinguishes what is prior to us from what is prior in nature (I 2, 71b33–72a4). Although we must start with the former, we aim to arrive at the latter. This is what I think he did. The variety of syllogistic forms is what we notice first; it is prior to us. Some of these forms can be reduced to valid forms that are prior in nature, and these forms, in turn, reflect the material content of scientific syllogisms.6
In sum, my case for the priority of content validity rests on three arguments: (1) I 14’s claim that the first figure is more scientific because it is the form of the syllogism of the reasoned fact; (2) the same chapter’s claim that the first figure is more scientific because it can stand alone; and (3) Aristotle’s claim that what is “prior to us” is “posterior in nature” along with the recognition that the Prior Analytics’s exploration of extensional validity is prior to us.
There is a fourth reason for recognizing the priority of content validity. We saw at the beginning that the definition of a subject contains one type of essential attribute and that the definition of a second type of essential attribute contains its subject. Either definition can serve as the middle terms in a demonstration that essential attributes belong to a subject (II 16, 98b21–24). Such a syllogism links subject and attribute through their natures. It is, first and foremost, the essences of the terms that make the syllogism valid. As we saw, the syllogistic form can, at best, make this content validity apparent.
As I mentioned earlier, contemporary logic countenances only formal, extensional validity. To those schooled only in contemporary logic, the idea that logic might not be “formal logic” but rooted in the natures of things—what we could call, to make a contrast, “material logic”—is apt to seem entirely bizarre. My claim is that although Aristotle devotes the whole of the Prior Analytics to elucidating valid forms of inference, this entire account is “prior to us,” whereas the account of scientific syllogism is “prior in nature.” Scientific syllogisms have valid forms, but those forms are valid because of the nature of the terms and their relation to each other. That is why the Prior Analytics shows various syllogistic forms to be valid by reducing them to the Barbara syllogism of the first figure or to Celarent, the two syllogistic forms that reflect the material content of their terms. In the scientific syllogism, validity is a function of the content of the terms. Other syllogisms are valid, but only extensionally valid, because they have forms that are equivalent to the forms of syllogisms valid by their content. This extensional validity is, however, prior to us, and we can use it to discover the natures that are causes. If this is right, Aristotle’s logic is indeed, an organon, a tool for discovering causal essential natures.
This account differs radically from standard readings of the text, and a brief paper can hardly be convincing. What I can do here is introduce this account and, thereby, raise the possibility of an alternative to the standard readings. One virtue of my reading is that it enables us to see the otherwise difficult and dry Posterior Analytics to be engaged in an exciting project, namely, explaining what the world must be like if it is to be known through demonstration. Not surprisingly, this project is closely connected with the central question of this paper, how the syllogism exists in the world. Instead of arguing further for content validity, let us turn to its consequences for our question. The first step is to appreciate just what the terms of the scientific syllogism are.
Just what sort of thing is the causal middle term that plays so central a role in the scientific syllogism? In II 11, Aristotle insists that any of the four causes could be the middle term. However, his examples are not all scientific syllogisms. As usual in Aristotle, it is more important to look for the primary kind rather than the broad range of possibilities.
What the primary cause of the scientific syllogism is becomes clear at the beginning of book II. This book opens by distinguishing four types of things about which we inquire and, accordingly, four scientific questions: is it? (εἰ ἔστι), what is it? (τί ἔστιν), does P belong to S? (τὸ ὅτι), and why does P belong to S (τὸ διότι) (1, 89b23–25). These questions, he claims further, turn on two questions, is there a middle term in a syllogism? and what is this middle term? Scholars have wrestled with the question of how there could be a syllogism involved in either of the first two questions since they ask only about a single term, but I have argued elsewhere that Aristotle’s point must be that we cannot ask about a single term without supposing some other character.7 Hence, even if the question seems to be about a single term, it will be pursued along with some other term, and the inquiry will seek a middle term between them. It cannot be accidental that the Greek for “fact” and “reasoned fact” in the “syllogism of the fact” and the “syllogism of the reasoned fact” is ὅτι and διότι, the same terms that Aristotle uses to designate what are now two scientific questions and that these questions seek to know whether there is such a middle term in a syllogism and what it is.
This last question has a special resonance in the Aristotelian corpus. Often, when Aristotle wants to indicate a substance in contrast with the other categories, he refers to the “what is it?” (τὸ τί ἐστι) or, as it is also rendered, the “what it is” (Metaph. Z 1, 1028a13–18). He also uses this expression to refer to the substance (or essential nature) of instances of other categories (1028a36–b2). We might wonder whether the “what is it?” question of the Posterior Analytics must always refer to a substantial nature or the essence of something in another category. Can it be a less ontologically charged request simply to identify the middle term? There are passages that suggest that this is what Aristotle has in mind. One example in II 11 claims that when we ask why the Persians declared war on the Athenians, we are seeking to identify what the middle term is; it is, the Athenian raid on Sardis, Aristotle proposes (94a36–b8). But, as I said, this is not a scientific syllogism; its terms can be otherwise. In a scientific syllogism, the middle term belongs necessarily to the subject, and this condition is met canonically when the middle term is the subject’s essential nature or, alternatively, the essential nature of the major term. So, in general, the “what is it?” that is sought as the middle term of a scientific syllogism is some essential nature.
These opening chapters of Posterior Analytics II are very important for a number of reasons. In book I, the emphasis is on drawing a conclusion from necessary, causal premises. Here in book II, where the syllogism is being used for inquiry, the assumption is that we know the conclusion: it is prior to us. What we are seeking is the cause, which is prior in nature. There is absolutely no notion of pursuing inquiry by syllogistic demonstration.8 In inquiry the syllogism works in the opposite direction, from conclusion to middle term. The syllogism turns out to be a means of answering the “what is it?” question. It serves to direct our attention toward looking for a term that can serve in the middle, causal position so that there will be a syllogism, and when such a term is discovered, the syllogism provides evidence that this middle term is a cause.
It hardly makes sense to speak of discovering a real cause in the context of contemporary logic because inferences are derived by deductions in a closed system: a number of propositions or predicates are specified, and nothing new is introduced from the outside. In this type of system, it makes no difference whether the deduction proceeds from premises to conclusion or in the opposite direction. They are mathematically equivalent. Aristotle’s syllogistic demonstration is not properly called a “deduction” because his system is not closed. The syllogism does not arrive at a conclusion so much as provide inquiry with a direction: it is a way to determine what is needed, as I said. Once we recognize that a middle term is needed to justify a conclusion, it is easier to find it. Once found, we have scientific knowledge of the conclusion by recognizing the relationships of the terms. The lengthy discussion in II 3–10 of whether the definition can be demonstrated by a syllogism is justified because it shows that the terms of the syllogism cannot simply be rearranged so as to demonstrate the essential definition, the definition that answers the “what is it?” question.9 The scientific syllogism is uniquely directional. If the definition could be demonstrated, then it would not be a first principle. A scientific syllogism must begin (ultimately) from what is indemonstrable (I 3, 72b18–25).
What makes the question of demonstrating a definition interesting is that with a purely formal rearrangement, we can create a formally valid syllogism in which the essential definition appears in the conclusion. This is, of course, a syllogism of the fact. We would have circularity if the definition could equally well appear in premises or conclusion. This type of circularity is not a problem in a formal deductive system; rather, it is a requirement of the system. Aristotle is arguing that the syllogism cannot demonstrate a definition without giving up the priority of the definition and, thereby, the possibility of knowing something through the definition. It is because we know something when we know its cause and because the definition is the cause that we cannot demonstrate a definition.
Nonetheless, we can use the syllogism as a tool to help to discover the definition, as I said. The syllogism’s conclusion is known prior to inquiry. We are seeking to discover and, so, come to know the essential nature through which the conclusion is known. That the conclusion can be demonstrated from some definition counts as evidence that this is the definition of the essential nature, though that essence must still come to be known by nous apart from the demonstration.10 The Posterior Analytics says nothing about attaining noetic knowledge of essences, perhaps because each case is different. However, it does propose some techniques for arriving at definitions though here, too, there are no mechanical procedures. We will look at the techniques later. First, we need to consider the inner and outer terms of a scientific syllogism.
Book II’s discussion of inquiry makes clear that the middle term is, canonically, the essential definition of some nature, either the minor or major term, as I said. What are the two other terms? As I said earlier, they are a subject and an essential attribute of that subject, an attribute that belongs to the subject in respect of the nature the definition expresses. Inasmuch as an attribute belongs to the subject through some nature, it must be essential to the subject.
Aristotle provides more detail in I 28. He says there that one science treats one genus, and he includes with the genus its “primary constituents,” its species (μέρη), and its “essential attributes” (87a38–39). The “primary constituents” must be the essential attributes of which the essential nature of the genus is composed; that is, the first type of essential attribute that Aristotle distinguishes in I 4 (73a34–37). “Essential attributes” here must refer to the I 4’s second type of essential attributes, those whose definitions include the definitions of their subject. Aristotle’s justification for including all these in one science is that the indemonstrables are in the same genus as what is demonstrated from them (87b1–4). The indemonstrables are, as we have just seen, the essential definitions that are the causes of what is demonstrated. The latter are, in turn, the essential attributes of the genus as a whole or of one or more of its species. The essential definition is most plausibly the definition of the genus, and the demonstration shows that the essential attributes belong to each instance of the genus in respect of the genus’s essential nature. In short, the scientific syllogism demonstrates the essential attributes that belong to a genus in respect of the genus’s essential nature. To put it in the Barbara form:
Again, this syllogism is valid primarily because the essential nature is the cause of the genus’s having the attribute. The genus is X in respect of its essential nature. An important variation is the scientific syllogism that relies on the essential nature of the attribute rather than the nature of the genus. We will see that it is closely connected with the paradigmatic case.
So understood, the scientific syllogism meets all the criteria that Aristotle sets out in I 2. The genus itself is often relatively easy to identify by some character. We can presumably discover it through the procedure that Aristotle sketches in II 19 (compare I 18).11 After repeated observations of dogs, for example, some common feature “takes a stand” and we come to recognize that there are multiple things with this universal feature. In the same way that we come to recognize the genus of dogs, we recognize that instances of this genus bark. The task for inquiry is to determine why dogs bark. The reason should lie in the dog’s nature, that is, in what it is to be a dog. In seeking the nature of dog, we seek something that accounts for the dog’s barking. Just what this nature is remains unclear, but we do have a criterion through which to recognize it: the nature must somehow account for dogs barking.
Since the nature of dogs is obscure, we can consider a nature that is better known, our own. Human beings stand upright. What is the reason? We are rational animals. An upright posture enables us to look at the heavens, and their regular motions are objects of knowledge that we can grasp with reason. A condensed version of multiple syllogisms could go like this:
This reasoning process could also be expressed as a series of syllogisms, a sorites. That way each demonstration can be presented with a single middle term and seen to be true. But there are advantages to my presentation. First, it makes clear that the essential nature of human beings is a necessary term for the inference. Second, it makes clear that there are actually a number of “middle terms” between the genus, human being, and the attribute we are interested in demonstrating. The first of these middle terms is the essential nature of the subject.
The essential nature belongs to the genus immediately (I 15, 79a33–38). That is to say, there is nothing that stands between these two terms: if there were, what is between them would be a middle term, it would be more properly the nature of the genus. Hence, the middle term of the syllogism not only mediates the relation between the extreme terms, but it also stands between them in a sequence of attributes. Ideally, the connection between each adjacent term in the sequence is immediate or, as Aristotle says here, “indivisible” (ἀτόμος). If not, one or more additional terms should appear between them until every term in the sequence follows immediately and is followed immediately. The middle term is not merely a position in a syllogism; it is also a position in a sequence of terms or, equivalently, a sequence of attributes.12
Could there be an infinite number of middle terms between a subject and its attribute? If so, the connection between attribute and subject would not be indivisible. Aristotle addresses this question along with the parallel issues of whether there can be an infinite sequence of subjects or of predicates in a lengthy discussion (I 19, 81b–82a8). That all of these infinities are impossible is hardly surprising: since it is impossible to traverse an infinity, were terms infinite in any of these ways there could be no demonstrative knowledge (84a2–4). Still, it is surprising how much attention Aristotle devotes to the question (82a2–84a2). He argues against an infinity of middle terms between any two terms on the ground that, depending on which term one started from, it would imply either an infinity of predicates (that is, of attributes) or an infinity of subjects (I 20). An infinity of attributes of the first type of essential attributes would mean that the subject was unknowable (83b8; 84a25–26). Since there is no attribute of an attribute (83b36–37), a series of attributes of the second type of essential attribute would all be attributes of the subject and their definitions would include the subject along with all the intermediate terms; if a single subject does not admit of an infinite number of attributes of the second type, then there cannot be an infinity of predicates (84a17–25). In arguing against the various kinds of infinities, Aristotle assumes that there are sequences of attributes and that each attribute in the series is immediately connected with what precedes it all the way back to the subject. The assumption is not argued, but Aristotle seems to think that only such sequences could make possible demonstrative knowledge. Inasmuch as there is demonstrative knowledge, there must be such sequences of attributes.
It is, therefore, apparent that in explaining how an infinite sequence of attributes or subjects would undermine demonstrative knowledge, Aristotle is tacitly equating the series of attributes with a demonstrative syllogism or series of syllogisms. If we start from a subject, the first predicate is its essential nature. Then, some essential attribute is predicated of the essential nature. After this, comes another essential attribute, then comes a third essential attribute in the series, and so forth. The first essential attribute is known to belong to the subject through the essential nature. That is the first syllogism. The second essential attribute in the series belongs to the subject through the first essential attribute. That is to say, it can be ascribed to the subject by means of a syllogism that has the first essential attribute as its middle term. Since the first essential attribute belongs to the subject through the essential nature, the second one also belongs to the subject ultimately through the essential nature. A third syllogism ascribes the third essential attribute to the subject through the second essential attribute (as its middle term) and, so, ultimately through the essential nature (see II 18). If this sequence of syllogisms is infinite, then the subject would have an infinite number of attributes, but this is impossible. Again, the assumption here is that the sequence of attributes is tantamount to the sequence of syllogisms. This is a sequence of “indivisible” attributes, which is to say that there is no other attribute between any two attributes in the series. This immediacy is, presumably, the key to the possibility of a sequence. Because there is nothing between any two attributes in the series, we grasp their connection immediately. Just as we have a natural human ability to discern that nearness is the cause of non-twinkling, rather than the other way around, we have the ability to recognize that one attribute is immediately connected with another, as is clear from examples.
We have answered our central question: a syllogism exists in a subject as a sequence of immediately connected essential attributes. However, this answer does not really make the syllogism intelligible. An “indivisible” connection links the terms of the syllogism with each other, but it remains unclear whether what the terms refer to are so connected. Do the attributes of a subject genus really constitute a sequence in which each is immediately connected with the next? What about the genus and its attributes would make us think that they do?
We saw earlier that there is a definitional connection between the subject’s essential nature and the essential nature of the attributes: one or the other of these is contained in the essential definition of the other. So, the sequence is not a casual collection of attributes; there is an essential connection that is rooted somehow in the natures of the terms, but what is it?
Aristotle talks about arranging essential attributes properly in II 13. The context is his discussion of how to find definitions. He proposes collecting attributes together to define something that, uniquely, has all the characters, but he also suggests reaching a definition by division. In order to be sure nothing is omitted, the division must proceed step-wise and, it seems, include all the preceding differentiae. Not every animal is split-winged or whole-winged, but every winged-animal is. If, then, the genus animal is differentiated by differentiae that together include all animals, each of these differentiae can be further differentiated (96b35–97a8). Getting the right sequence of essential attributes (type 1) is crucial for the definition of the ultimate species, for the split-winged will include winged, as well as its genus, animal (as Aristotle argues in Metaph. Z 12). Conversely, while the science of zoology treats the genus of animal and its essential attributes, there is nothing that is simply animal. Every actual animal is an animal of some sort. That is to say, the genus is necessarily differentiated.
Let me explain. Consider the following sequential reasoning: An animal is a substance that is capable of moving itself. In order to move itself it must have an organ for motion. Organs of motion must propel the animal on land, water, or air. Propelling an animal on land, water, or air requires organs specifically fitted to each of these, that is, legs, fins, or wings, or comparable organs.
What’s striking about this particular sequence of attributes is the way each term follows what precedes it. We can say, abstractly, that all animals can move themselves; but no animal can actually move itself without organs fitted to the task, and the motion is always accomplished in a characteristic way that is suited to the medium. Thus, the essential nature of a genus-like animal is a kind of potentiality that can only be realized in something actual. The transition between this potentiality and the actual realization occurs through steps, that is, through species, until we arrive at the ultimate differentiae, characters that are sufficiently determinate to have a concrete existence. Again, the nature of an animal, “having the capacity to move,” does not cause motion nor does it issue in a specific motion. By referring to wings, legs, and fins, we are indicating particular modes of motion, distinct ways in which species make actual what it is to be an animal. That every animal must have some such organ follows from the nature of an animal. We can easily represent the sequence of thought with a series of syllogisms about the genus, animal. The point is that such syllogisms are possible because of the way that the attributes exist.
We can go further by looking at some of these species. Having wings specifies a mode of motion and, thereby, a species of the genus animal. Wings are of two types, split or whole. The wings of birds are split into feathers that are themselves divided, in contrast with the whole wings of insects (Parts of Animals IV 12, 692b12–15). With this last division, we have a definition that is more concrete and, thereby, closer to actual existence. The split-winged species is itself a genus, birds, and it has its own differentiae. Aristotle distinguishes birds whose large wings allow them to hold other animals as they fly, birds whose wings allow them to fly swiftly to escape danger, and birds whose wings are so small relative to their bodies that they cannot fly (693b26–694a7). The size of the wings indicates not just their mode of flight or their absence of flight but important details about their modes of life. These particular kinds of wings serve to allow the potentialities inherent in their genera to be realized. Since the abstract genera exist only in concrete instances, the genus must be differentiated. My claim is that differentiation occurs through a necessary succession of attributes that are immediately connected with each other and the initial genus.
If this interpretation of II 13 is correct, then we can see how a sequence of attributes can be constituted from “indivisible” connections and yet be propelled forward from the most general to the more specific. Since the more specific natures (split-winged animal) include within themselves the more general characters (animal), whatever belongs to animal must also belong to split-winged animals. Thus, we have the basis for one sort of scientific syllogism.
This account will do for the first type of essential attribute. The second type of essential attribute is more important for science. For these, it is the definition of the attribute that includes the definition of its subject. Number’s being odd or even is one example; the definitions of odd, for example, includes number. Using the definition of odd as the middle term, we can construct a syllogism whose conclusion is that some numbers are odd. However, this is not a scientific syllogism because odd does not belong to every instance of the genus. A scientific syllogism about number would require treating “odd or even” as a single predicate whose definition is, perhaps, “divisible by 2 or not divisible by 2.” The conclusion would be: number is odd or even.
The alternative is to use the essential attribute to delimit a species. Thus, Aristotle suggests that the shedding of leaves is the coagulation of sap at the junction of leaf-stalk and stem (II 17, 99a24–29). Hence, we have the following syllogism:
Aristotle’s challenge here is to characterize the genus of those trees that shed their leaves. We call such trees “deciduous trees,” but if this were the subject of the syllogism, the conclusion would be tantamount to “trees that shed their leaves shed their leaves.” Instead, Aristotle looks for what figs, vines, and other such trees have in common. They are all broad-leafed. Perhaps, he thinks that broad leaves, by virtue of their size, require a great deal of sap and, therefore, die when cooler temperatures cause that sap to coagulate at the narrow point where leaf meets stem. If so, then the three terms in the syllogism are indissolubly linked. Thus, we have a kind of sequence here: broad leaves, coagulation of sap, and shedding leaves. Each of these terms is a kind of an abbreviation of something larger: the broad leaves requiring much sap from the trunk to sustain them, the cool weather coagulating the sap at the narrow point where leaf stem meets branch, and leaves that are deprived of their nourishment dying and falling off. So understood, each term leads to the next.
There is another more famous example that depends on the definition of the attribute. Why does the moon suffer eclipse?13 The answer depends on noticing that the moon only suffers eclipse when it is full, and that the moon is only full when it is directly in line with the sun and the earth. In this configuration, the earth is between sun and moon and capable of cutting off the light from the sun and, thereby, casting a shadow on the moon. The syllogism that is most immediately apparent is the syllogism of the fact:
On this rendering the full moon’s being shadowed is, as the middle term, the cause of its being eclipsed. The syllogism of the reasoned fact results when we have an essential definition of the eclipse in the middle term:
This formulation of the syllogism omits the phase of the moon that is essential for understanding the eclipse. We need another syllogism or other premises:
What I have here expressed as one scientific syllogism could be expressed as multiple syllogisms. What is important to see is that there are series of essential attributes that stand between the moon and the eclipse, the last of which is the essential definition of the eclipse. Taken as a whole, the syllogism constitutes demonstrative knowledge of the eclipse. As is often the case in the Posterior Analytics, Aristotle does not fully elaborate all the terms necessary for a syllogism.
So far, I have mentioned three sorts of essential attributes of the second type that can be demonstrated by scientific syllogisms: attributes like “odd or even” that belong collectively to their subjects, attributes like “eclipsed” that do not always belong but must be able to belong to their subjects, and attributes like “the shedding of leaves” that are as closely connected with their subjects as having angles that sum to two right angles is connected with all triangles. In each case, we have seen a sequence of necessarily linked attributes.
Must subjects have attributes? If so, why? Let me suggest that the answer to these questions can be seen from an important argument in the Metaphysics. In Z 17 Aristotle asks why the composite of material parts is one substance. He reasons that the materials cannot be made one by some other material because we would, then, have to ask the same sort of question, what is it that makes this material and all the others one? Instead, the cause of unity must be some principle that is not material, a form. It becomes clear by the last chapter of book H that this form is an actuality, which is to say, the materials are one insofar as they are capable of acting together. The practical import of this conclusion is that animals are defined by their capacity to move themselves, as we have seen, and human beings by our capacity for thought. The Metaphysics is concerned with the unity of each substance; other theoretical sciences have the opposite concern: animals could not move themselves without their having bodies, nor could human thought occur without the sensible images of imagination, images that require organs capable of sensation. In these cases, the essential natures that define subjects require attributes because they exist not alone, but in some matter. It is the task of the particular sciences to spell out the relations of these essential natures to the sequences of attributes that they entail. At one point in the Posterior Analytics, Aristotle claims that the definition signifies something that is one and the demonstration also signifies something one because “what a man is” differs from man’s being (II 7, 92b9–11). The unity that the definition signifies is an essential nature, such as the essential nature of human being. The syllogism signifies the unity of an essential nature and the attributes that necessarily belong to it. These attributes are what make the nature a real being; the essence requires them for its real existence. The essence can only exist in some matter that is fitted to it, and from the perspective of the essence, these materials and their characteristics are essential attributes.
Some examples make clear how these attributes are connected with their essences. As I said, in order to think, we need sensation. Sensation, in turn, requires sense organs that can be affected by the elements without being destroyed by them. These organs require other organs that sustain them in such a way that they can fulfill their purpose. Thus, Aristotle supposes that our long and folding intestine helps us to think; for were our intestine not as long as it is, we would be constantly hungry and, therefore, unable to listen to long lectures (On the Generation of Animals I 4, 717a21–b4; compare PA III 14, 675b22–28 and Tim. 73a). Similarly, human beings stand upright in order to see the heavens and, thereby, to be able to realize our capacity to reason about what is eternal. The point is that the material bodily parts are structured so as to help promote the actual functioning that is our human nature (PA I 5, 645b14–20; 1, 640a33–b4). These parts and their dispositions are, I suggest, a fourth sort of essential attribute of the second type.
Starting from one of these attributes, we can find a sequence of attributes that extends to an essential nature through which it can be understood. However, it would be hard or impossible for us to start from the essence and derive the attributes.14 In other words, we can follow a sequence of attributes back to a nature, but we cannot generally start from a nature and derive specific attributes like upright posture or long intestines. There is, thus, a directionality to our knowledge. If the directionality were in the opposite direction, it would be possible to conceive of the syllogism as deriving conclusions. As it is, though, the syllogism serves, first, to direct us toward finding which, among the terms that we know in advance, is the causal middle term and, then, serves to tie together all these terms by expressing their sequential connections.
For us, the thought process proceeds in syllogisms formed by recognizing the sequence of the attributes. A superior mind could conceivably grasp this sequence all at once, through nous. As Augustine was later to say of an entirely different subject: time is the extension of God’s mind and exists for him all at once, whereas for us it unfolds bit by bit.15 So, too, we come to know the world gradually one attribute at a time through syllogisms even though these attributes exist as a unity, all together, all at once within the thing known.
Logic is sometimes thought to exist independently of things and, thereby, independently of metaphysics. It is clear that Aristotle does not agree. Not only is the principle of non-contradiction, upon which all demonstration depends (I 11) a subject for metaphysics (Metaph. Γ 3–8), but logic is pervaded by metaphysics, as we have seen. I conclude by mentioning two metaphysical issues with Aristotle’s account that, I suggest, remain problematic.
He himself broaches the first of them. After distinguishing the syllogism of the fact from the syllogism of the reasoned fact, Aristotle notes that it often falls to one science to use the results of another (78b34–79a16). His point is that while one science will properly demonstrate a conclusion, a different science merely uses this conclusion without demonstrating it or uses a syllogism of the fact. In some of his examples, there is a metaphysical connection between the two sciences: thus, the results of mathematics bear on nautical astronomy because the navigator is concerned generally with mathematics as it exists in the physical world. However, Aristotle also illustrates multiple sciences treating the same subject by claiming that it belongs to medicine to know that circular wounds heal more slowly than wounds of other shapes, though it belongs to mathematics to know why this is so. This case apparently relies on medicine’s being a pros hen science, as claimed in Metaphysics Γ (1003b1–4). Its subject matter is not a genus in the strict sense, health in a body, but a more broadly understood (pros hen) genus, healthy (1003b11–14). But this move is not always available, and there is good reason to think that many if not most demonstrations must rely on entities and attributes that belong to other genera. That the sum of the angles of a triangle is two right angles is one of Aristotle’s favorite examples of an essential attribute’s belonging to a genus. The genus is triangles, and the attribute belongs in respect of the nature of the triangle, but the demonstration also uses facts about parallel lines and the angles formed by lines that traverse them. These latter are not included within the genus triangle.16 Likewise the demonstration that a triangle inscribed in a semi-circle must be a right triangle relies on attributes of circles, but also on the attributes of triangles. What is its subject genus? Does one science treat one genus in such cases? We might suppose that in these examples the pertinent genus is not triangle or circle, but plane figures, for this is how we now understand the subject matter of geometry. However, this move cannot be applied to the syllogistic structure of demonstration: to demonstrate an essential attribute of triangles, we must begin with a subject genus and the essential nature that defines the genus. That we need to rely on features of parallel lines or circles to demonstrate attributes of triangles indicates the richness of relations between all geometric entities, a richness that does not readily fit into the Aristotelian scheme. The issue here is not about mathematics or about using syllogisms to make mathematical demonstrations but about whether these demonstrations can all be neatly fit into a single genus.
There is another metaphysical issue with Aristotle’s account of the syllogism. We saw that the syllogism exists in a mind as an inference and in the thing as a sequence of attributes. We have struggled to understand how these attributes are connected to each other and why attributes must exist in such sequences. By considering different kinds of attributes, I have proposed several different ways of answering these questions. As I understand the Posterior Analytics, it sets out a way in which demonstrative knowledge is possible. That we do indeed know some things through their causes seems obvious from Aristotle’s examples, especially the mathematical ones. The issue is how this is possible. It is possible, Aristotle seems to be saying, if the attributes exist in sequences because a sequence of attributes is the basis of a demonstration. Since no other configuration of nature allows for the possibility of demonstrative knowledge, the attributes must exist in sequences. Moreover, there are plenty of examples of sequences of attributes that we judge to be “indivisible” in their connection. Knowing that there must be such sequences does not really explain how their terms are connected. Yet, there is no further explanation of how to understand the connection of the attributes. There could not be, for if there were some relation that held between them, there would be something, another term, between them and thus the connection would not be indivisible. Further, if there were something else between the terms, we would need to ask the same question about it and each of them: what is it that connects this intermediate term with each of the extremes? To avoid regress, we must simply accept the existence of immediate terms. Sometimes the immediate term is an actualization of what precedes it, sometimes it is necessary for the thing’s actuality, and sometimes it is merely beneficial for this actuality. We can appreciate why there are various sorts of sequences and what these sequences are, but we cannot really understand what connects the attributes in the sequence because it is not anything over and above the attributes themselves. The attributes are connected by their own natures. The angles of a triangle sum to two right angles because they are angles of a triangle. In the strict sense, there is no way to understand why there are sequences of attributes and, thus, why demonstrative knowledge is possible because there is not, nor can there be, an overall formula for the sequence: the connections of the attributes are content or material connections rather than formal connections. Were there some common form of sequences of attributes, logic would indeed exist as an independent science with its own subject matter, and it could be thoroughly known. Instead, logic lies rooted in nature, and we come to be aware of it by coming to know nature. It is, as Aristotle’s editors called it, an organon, a tool to help uncover, bit by bit, essential natures and their attributes.
Bronstein 2016 claims that we recognize that syllogism 2 is the syllogism of the reasoned fact from some prior knowledge; in particular, (a) by knowing noetically that “all planets are near” is a first principle and, thus, that syllogism 1 cannot demonstrate it or (b) by having demonstrations of both premises of syllogism 2. However, so far from taking “all planets are near” to be known noetically, I 13 claims that “planets are not twinkling” is “more known” (78a26–32). Aristotle means, of course, “more known to us.” The point is that even though noetic knowledge is immediate in itself, we do not have it immediately and Aristotle does not assume it in I 13. In contrast, he does assume that “Whatever is not-twinkling is near” and “All the planets are not-twinkling” are both known immediately to perception (compare 78a34–35). As for Bronstein’s (b), we do have a demonstration of one premise of syllogism 2, “all planets are near”; namely, syllogism 1. (The other premise is true by induction from sense perception.) But this demonstration implies that syllogism 1 is prior to syllogism 2, just the opposite of what Aristotle is arguing. The point Aristotle makes is that if there are demonstrations of a syllogism’s premises, it cannot be the syllogism of the reasoned fact because it does not contain the first cause, which is a necessary requirement for being a syllogism of the reasoned fact (78a23–26). This is just the opposite of what Bronstein claims. Indeed, Bronstein seems to confuse Aristotle’s discussion of two ways in which a syllogism would be a syllogism of the fact (78a23–36) with an account of how a syllogism could be recognized as a syllogism of the reasoned fact. Significantly, though, Aristotle just declares 2 to be the latter “since it is not that they are near because they do not twinkle, but that they do not twinkle because they are near” (78a36–37). That is to say, Aristotle takes the causal role of the planets’ nearness to be obvious. Syllogism 2 is the syllogism of the reasoned fact because it has the cause in the causal, middle position.
Elsewhere he famously declares that the Posterior Analytics “attempt[s] to characterize and investigate an axiomatic deductive system,” Barnes 1975, 87. Later, Barnes 1981, 33–34, cf. 30, claims that the Posterior Analytics’s theory of demonstration does not rely on the theory of syllogistic in the Prior Analytics. He argues for the chronological priority of the account of demonstration, suggests that non-syllogistic demonstration is important for Aristotelian science (whereas syllogistic is not), and speculates (contrary to I 14 and most of book II) that Aristotle was “never in a position to assess” the application of syllogism to demonstration (59). Ultimately, though, he thinks an Aristotelian science is a “coherent sequence of propositions” deduced from primary propositions (27). Despite recognizing important differences between contemporary logic and Aristotle’s logic, he continued to represent the latter by means of the former.
Goldin 2009 proposes a similar relation between the two works, but he claims, rightly, that the Prior Analytics provides matter for the Posterior Analytics form. I have reversed form and matter in order to compare Aristotle’s syllogistic with contemporary logic.
When Owen 1968, 167 famously declares that Aristotle’s sciences do not follow the method he set out in the Posterior Analytics, he means that Aristotle’s sciences are not demonstrative. Likewise, apparently assuming that syllogism could only be useful to inquiry by demonstrating conclusions, Barnes denies that syllogisms play any role in demonstration, and he proposes that II 1–2 “contain … directions to the pedagogue on how to construct his lessons” (Barnes 1975, 83).
Aristotle recognizes multiple senses of definition, as he explains in II 10. For a good summary of them, see Byrne 1997, 162–63. The definition that expresses the essential nature of the subject term is one type of middle term. Another definition arises from ascribing this nature to the subject term; it is this definition that Aristotle argues cannot be demonstrated.
In Halper 2017, 71–96, I show how the opening books of the Physics lead the reader to a noetic knowledge of nature.
Identifying the genus seems to be what Charles 2000, 24, takes to be “stage 1” of philosophical inquiry. He is right, but I do not think this is Aristotle’s point in the opening lines of II 10. If stage 1 is attained through what II 19 describes, as I think it is, then it occurs together with Charles’s stage 2, the grasp of the existence of an individual instance of the universal.
See Barnes 1995, 49–50. The connection must be grasped with nous. There is no discussion of how we come to grasp it, but this connection is not rooted in sensation, as is the grasp of the universal that Aristotle discusses in II 19.
On this example, see Goldin 1996. The middle term in the syllogism of the fact is usually understood to be the moon’s inability to provide enough light for things on earth to cast shadows. As Goldin notes (122n) this is an “artificial” character. Bronstein 2016, 48, also distinguishes two types of syllogisms: those in which the middle term is the essential definition of the subject (his example is the nearness of the non-twinkling planets) and those in which the middle term is the essential definition of the essential attribute (his example is the deciduous tree).
Bronstein 2016, 32–35, argues that Aristotle thinks that the “expert scientist” can learn from demonstration on the ground that the expert has made the premises of the scientific syllogism, premises that are more known in nature, also be more known to himself. Hence, he thinks the expert can begin with the premises and derive the conclusion. This procedure looks like beginning with essence and deriving the attributes. However, any attribute that appears in the conclusion must also be present in the premises. So, the demonstration does not derive a new attribute. There may be some demonstrations in which someone who knows an essential nature comes to see that it must also have an attribute he had not observed because of its necessary association with one he had observed, though this is not deriving an attribute from a nature. In any case, the expert usually knows the conclusion because it is prior to us. What he learns from the demonstration is that this conclusion is a consequence of an essential nature. That is to say, learning by demonstration is not usually learning a new conclusion, but learning the demonstration, and this demonstration is itself scientific knowledge, as we have seen.