The Metaphysics Of The Syllogism 31 COLLOQUIUM 2 The Metaphysics of the Syllogism Edward C. Halper University of Georgia Abstract 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 syl- logism over time but the sequences to which it refers exist together in things. So under- stood, the syllogism, like knowledge of forms and truths, exists in us and in the world. Keywords syllogism – logic – validity – scientific syllogism – essential nature – essential attributes I Ancient philosophy has been so intensely studied for so long that it seems un- likely 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 pass- ing. The issue can be stated simply: What is an Aristotelian syllogism? Of © Koninklijke Brill NV, Leiden, 2018 | doi 10.1163/22134417-00331P05Downloaded from Brill.com09/25/2021 03:26:46PM via free access 32 Halper 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 nota- bly 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 syl- logism, 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 syl- logism 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 prem- ises 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 Downloaded from Brill.com09/25/2021 03:26:46PM via free access The Metaphysics Of The Syllogism 33 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 scien- tific 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 “truth- makers” 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 collec- tion 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. 1 In multiple books and articles. See, for example, Priest 2006. Downloaded from Brill.com09/25/2021 03:26:46PM via free access 34 Halper II 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 in- telligible 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 na- ture that we know also exists, albeit with matter, in the thing known. The exis- tence 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 es- sential natures: Aristotle speaks of knowledge of: mathematical entities (quan- tities) (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 cate- gories have essences as well, albeit derivatively (Z 4, 1030a38–32).