Edward Halper’s “The Metaphysics of the Syllogism” argues that the ontological ground of valid inference is found in the necessity of the predications that constitute the premises of the sort of syllogism central to Aristotle’s theory: demonstration. I further support his conclusion on the basis of a consideration of the title and structure of Aristotle’s Analytics, as well as some recent analysis of Aristotle’s modal logic. Halper however suggests that the logical form of inference is a result of how the mind sorts out the elements involved in a complex unity. I suggest that it is not primarily the mind that does this work, but language. What the mind does is primarily to be understood as a reflection of what language does, not vice versa.
In Posterior Analytics II 1 Aristotle tells us that every theoretical investigation begins with determining whether the subject matter in question exists; this is followed by investigating what it is. Once we know the “what it is” we can arrive at explanations of why something has certain characteristics (89b25–31). We should expect that this is so in regard to one of Aristotle’s own great discoveries: the syllogism. Presumably, if we have an adequate understanding of what a syllogism is, we will be in a position to say something about why it functions as it does. What is it about the essence of a syllogism that is responsible for the fact that true propositions whose terms have a particular formal relationship to one another must entail a third proposition? Halper points out that these are questions that have been rarely, if ever, asked of Aristotle. Surely it would be anachronistic to attribute to Aristotle a “formalist” metalogic, according to which logic is a series of rules for the manipulation of certain symbols, allowing for the generation of certain other symbols.1 Perhaps students of Aristotle may have assumed that his response to the metalogical question concerning the grounds of the indispensability of these rules for language and thought parallels that of most logicians—ignoring the question. But if this is so, Aristotle is most un-Aristotelian in regard to logic, his own innovation (Sophistical Refutations 34 184b1–3).
Halper presumes that Aristotle’s account of the syllogism meets Aristotle’s own requirements for scientific knowledge. He asks what it is it about the world that grounds what is responsible for how the sequence of related terms which constitute a syllogism is revelatory of how things are. As the mind2 works through a sequence of true propositions that have a certain formal character in relation to one another, it is led to affirm the truth of a further proposition. Because Aristotle accepts the isomorphism of the conceptual and the real, there must be something about the world that grounds the reliability of such reasoning. What can this be? Aristotle says nothing about logical space, and apart from taking the principle of non-contradiction to be a principle of first philosophy, he says little about the metaphysical basis of logic. However, Aristotle does talk at length about the metaphysical basis for demonstration. Demonstrations presuppose basic kinds, with essences that are responsible for other necessary features that belong to those kinds. Halper argues that this ontological commitment grounds the very validity of demonstrations, those inferences that show how these other features are logically entailed by essences. Other kinds of inferences (somehow) derive their validity from the same source.
Halper supports his view that the primary variety of syllogism is demonstration by appealing to Posterior Analytics I 14, which argues that the most scientific syllogism is that which is in first figure, for which the middle term occupies the central position in the sequence of terms. For any sound syllogism, the middle term is the cause of our knowing that the major term is truly predicated of the minor. Within a scientific demonstration (which is what Aristotle calls a syllogism of the reason why, as distinguished from a syllogism of the fact), the middle term does more than play this central role in justification: it expresses the cause of the conclusion. So although other syllogisms might be formally valid, it is only in the case of a scientific demonstration that the formal structure mirrors the metaphysical structure of the subject matter. As Halper writes, “Scientific syllogisms have valid forms, but those forms are valid because of the nature of the terms and their relation to each other.”
The root of the validity of demonstration then is to be found in that feature of demonstrative premises that allows them to ground the sort of syllogism that reveals the reason why the conclusion holds. This is what Aristotle calls καθ’ αὑτό predication. In such a predication one term is predicated of another κατά (on account of) what that other is. A science is concerned with καθ’ αὑτά predications alone (APo. I 22, 75a29–31). A science deals with a kind (whether substantial or nonsubstantial) that has a number of features that are closely linked in such a way that, given one, others are found together with it. Within a demonstration, a path is traced within the kind through its various linked features. It is the metaphysical bonds holding simultaneously among the terms that ground the validity of the syllogism. Hence, Halper argues, it is the nexus of καθ’ αὑτά bonds that hold among these features that are responsible for how demonstration, and, by extension, all syllogism reveal how things are.
But just because demonstrative inference must be grounded on how certain attributes are necessarily linked to the essence of a kind, why must we say this of all inference? Halper’s case would be strengthened if it can be shown that demonstration is the focal variety of syllogism. I offer two other considerations in support. First, the opening of the Prior Analytics identifies the object of his inquiry as “demonstration and demonstrative science,” and then says inquiry into demonstration must begin with identifying what a premise, a term, and a syllogism are (Prior Analytics I 1,24a10–13). Perhaps Aristotle proceeds in this way because an understanding of syllogistic is a precondition for understanding demonstration. Before one understands the species, one must understand the genus. The analysis with which the Prior Analytics is concerned is the analysis into perfect syllogisms.The Posterior Analytics simply applies this analysis to syllogisms that meet certain additional criteria, by which we consider them scientific. This was the interpretation offered by Alexander and Philoponus. The commentary on Posterior Analytics II attributed to Philoponus in the Berlin edition, of uncertain provenance, gives another, more convincing account. The analysis with which the Posterior Analytics (and especially its second book) is concerned is causal analysis. If the title “Analytics” is not equivocal for the two works, Aristotle has his eye on causal analysis throughout his account of the syllogism,3 which is precisely Halper’s point.
Halper’s thesis also derives some support from recent work on Aristotle’s modal logic. Aristotle’s account of modal syllogisms has often been regarded as hopelessly muddled, as he indicates that a first figure universal syllogism with a necessary major premise has a necessary conclusion, but one with a necessary minor premise does not have a necessary conclusion. Taking the necessity involved here to be either de re or de dicto allows for one of these results, but not both. Patterson, and improving on his innovations, Malink and Vecchio,4 have made great progress in solving the problem. The gist of this recent work is that the problem of the two Barbaras and other alleged inconsistencies in Aristotle’s modal logic are resolved if we take the modal operator of necessity to govern neither the whole proposition (as in de dicto necessity) nor the predicate alone (as in de re necessity) but to qualify the predicative bond itself. Recall that as Aristotle understands them, the sciences deal with predicative bonds that have the distinguishing feature of being καθ’ αὑτά. This is a feature of the predications as such, not of the term, and not of the whole propositions that serve as premises. So both demonstrations and syllogisms of necessity concern predications with a special bond of necessity between subject and predicate. This suggests that the syllogisms of necessity discussed in the Prior Analytics simply are demonstrations, and that the inquiry into the nature of syllogism pursued in the Prior Analytics simply is inquiry into the nature of demonstration. (It must however be admitted that it is unclear exactly how the modal syllogistic of the Prior Analytics is supposed to be applicable to demonstration. A demonstration has as its conclusion a universal predication “all S is P,” where the predication happens to be καθ’ αὑτό and necessary; the conclusion is not “all S is-necessarily P,” which is the form of the conclusion of a modal Barbara syllogism, as Aristotle understands it.)
Halper’s account faces an obvious objection: Aristotle recognizes the validity of syllogisms that are not demonstrative; they could, for example, be dialectical, rhetorical, or practical. In the latter two cases, at any rate, we are dealing with terms that do not have the requisite relations of necessity among one another. Consider the syllogism “all of my socks are in the top drawer; my athletic socks are socks; therefore my athletic socks are in the top drawer.” Here there is no tight metaphysical connection between being a pair of socks and being in the top drawer; yet the syllogism is valid. Prof. Halper says that it is the “formal resemblance” between this sort of inference and the syllogism in the strict sense, the demonstration, that ensures its validity. But why is formal resemblance enough to guarantee validity? For there to be formal resemblance, certain formal features must be shared, and it is these formal features (as opposed to other ones) that ensure validity. What is it about these formal features that gives them this epistemological significance? I worry that our problem about the grounds of logical form and how it relates to ontological truth has reemerged.
I propose the following admittedly speculative solution. Recall that syllogism in general is the genus of demonstration. Aristotle understands the genus of a kind as like its matter insofar as the genus has the potentiality for those differentiating characteristics that constitute that kind. This is why the conjunction of genus and differentia expressed in a definition does not signify a duality but a unity; the differentia is not a characteristic over and above the genus, but simply is the genus, considered as determined in a certain way (Metaphysics H 6 1045a21–b7). I have elsewhere5 suggested that this is the way to understand the relationship between syllogism and demonstration, and by extension, the relationship between the kind of (formal) analysis that is the goal of the Prior Analytics and the (causal) analysis that is the goal of the Posterior Analytics. Syllogism simply is demonstration, considered as indeterminate. And, just as matter can exist without form (though not vice versa), and has certain characteristics by virtue of being the kind of matter it is, so too, there can be syllogism that is not demonstration. And just as matter, properly understood, must be understood as matter for a certain kind of form, so too syllogism in general must be understood as a kind of logos that when fully actualized (that is, when completing its function of making the world intelligible) is demonstration, insofar as it discursively presents the causal connections that hold in the world. This solution is, I think, in the spirit of the innovations and insights that Halper has shared.
I close by considering another aspect of Halper’s account of syllogism. Halper points out that the terms of a demonstration refer to attributes that are always found together. They are not separated in either time or in space. It is the mind that distinguishes them in sorting them out by virtue of the order of causal priority. Halper writes:
For us, the thought process proceeds in syllogisms formed by recognizing the sequence of the attributes. A superior mind could conceivably grasp the 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. 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.
Aristotle however does not limit to a divine mind the simultaneous grasp of all of the terms in a demonstration, and the causal relations that hold among them. At Posterior Analytics I 34, we are told that those with the virtue of ἀγχίνοια are said to be able to grasp the middle term of a demonstration in an imperceptible time (ἐν ἀσκέπτῳ χρόνῳ). It is not clear whether Aristotle is saying that all three terms and the relations that they hold to each other are grasped instantly (where ἄσκεπτος means “not involving investigation” (σκέψις)), or that the passage through the syllogism is too quick to notice. The very notion of mental processes occurring so quickly that one is unaware of their passage would pose severe problems for Aristotle, for it would require attributing to him the anachronistic notion of subconscious thought. This puzzle can be avoided if, instead of taking syllogism to be a mental process, we attend to Aristotle’s own definition of syllogism, according to which it is a logos (APr. I 1, 24b18, Topics I 1, 100a25). A logos is neither a proposition nor an ordered sequence of propositions—there is no room for “propositions” in Aristotelian ontology. A logos is in the category of action,6 for it is by speaking (logos) that one human being communicates with another. To be sure, just as Parmenides insisted that what is for saying is also for thinking (fragments B3, B6.1), and Plato understood διάνοια (discursive thinking) as a kind of inner discourse (Theaetetus 189e4–90a7), so for Aristotle too, logos is isomorphic to thought (compare De Interpretatione 1 16a3–6). Even if Aristotle does not posit an inner language (“Mentalese”) he surely holds that linguistic communication is possible insofar as the structure of what is spoken somehow corresponds to the structure of what is thought.
Nonetheless, I do not think that it is nitpicking to emphasize that discursive speech is primarily linguistic, not mental. Aristotle posits only one kind of mental entity, a νοητόν (an intelligible). But a νοητόν is a monadic form. Aristotle is clear that it is a mistake to say that the νοητόν is a representation of the form in the world: it is the very form that is present in the world.7 This is what it means to say that the mind is identical with what it knows (De Anima III 5 429b26–430a9). Aristotle’s account of propositional knowledge is cloaked in obscure metaphor: when one entertains what (we would call) a proposition, this is a matter of the production of a new identity by the faculty of nous.8 A complex such as “the cat is black” is derived from an inner act of unification of the terms “cat” and “black.” At 430b26 we are told that the predicative complex (of the formτικατάτινος) is a φάσις, a kind of inner saying (or, as the Revised Oxford translation would have it, an “assertion”); this linguistic act, with discrete parts, is distinguished from the unity of objects of thought that Aristotle had just been discussing. Thought unifies; it is language that breaks the thought into parts, and then creates new unities: propositions and inferences with parts that can be distinguished according to the causal order of the states of affairs to which they refer. This suggests to me that what Halper is saying about inferential thought—that it breaks into a multiplicity the features of things that, in spite of their sequence of causal priority and posteriority, cohere as a unity in things—should rather be said of inferential discourse.
Such a formalist account of the rules of inference has been most famously offered by Carnap 1937, Section 17.
As will become clear, I hold that Aristotle’s syllogisms are not primarily mental processes but linguistic actions. For the time being, no harm will be done in tracing Halper’s account of the workings of syllogisms, considered as mental inferences.
Patterson 2002, Malink 2013, Vecchio, 2016. Vecchio’s main innovation is to show how the use of obversion is both consistent with Aristotelian semantics and metaphysics, and allows for the resolution of some problems remaining on Malink’s account.
This is the gist of Metaphysics Z 6: a substance (that which is) and the what is it (that which is the object of knowledge) are one and the same. Otherwise, what is known would be a conceptual entity, and not the thing known.
Ἡ μὲν οὖν τῶν ἀδιαιρέτων νόησις ἐν τούτοις περὶ ἃ οὐκ ἔστι τὸ ψεῦδος, ἐν οἷς δὲ καὶ τὸ ψεῦδος καὶ τὸ ἀληθές σύνθεσίς τις ἤδη νοημάτων ὥσπερ ἓν ὄντων ἀλλ’ οὖν ἔστι γε οὐ μόνον τὸ ψεῦδος ἢ ἀληθὲς ὅτι λευκὸς Κλέων ἐστίν, ἀλλὰ καὶ ὅτι ἦν ἢ ἔσται. τὸ δὲ ἓν ποιοῦν ἕκαστον, τοῦτο ὁ νοῦς. “The thinking of indivisibles is found in those cases where falsehood is impossible: where the alternative of true or false applies, there we always find a sort of combining of objects of thought in a quasi-unity… . However that may be, there is not only the true or false assertion that Cleon is white but also the true or false assertion that he was or will be white. In each and every case that which unifies is thought” (Revised Oxford Translation), DA 43026–8, b4–6. Note the it is nous that unifies the νοημάτα; a proposition does not itself subsist as a νόημα.