Ancient Logic, Language, and Metaphysics

Selected Essays by Mario Mignucci

Andrea Falcon, Pierdaniele Giaretta, Andrea Falcon, Pierdaniele Giaretta

• Publisher: Routledge
• Year: 2019
• eBook ISBN: 9781000022377
• Edition: 1
• Topic: History
• Subtopic: Ancient History
• Index: History

The late Mario Mignucci was one of the most authoritative, original, and influential scholars in the area of ancient philosophy, especially ancient logic. Collected here for the first time are sixteen of his most important essays on Ancient Logic, Language, and Metaphysics.

These essays show a perceptive historian and a skillful logician philosophically engaged with issues that are still at the very heart of history and philosophy of logic, such as the nature of predication, identity, and modality. As well as essays found in disparate publications, often not easily available online, the volume includes an article on Plato and the relatives translated into English for the first time and an unpublished paper on De interpretatione 7.

Mignucci thinks rigorously and writes clearly. He brings the deep knowledge of a scholar and the precision of a logician to bear on some of the trickiest topics in ancient philosophy. This collection deserves the close attention of anyone concerned with logic, language, and metaphysics, whether in ancient or contemporary philosophy.

Part I
Inference and syllogism

1
Syllogism and deduction in Aristotle’s logic

I

It is common among scholars nowadays to render the Greek “συλλογισμός” as “deduction” and to interpret the connected notion accordingly. To my knowledge, this usage originated in 1981 with Jonathan Barnes’s influential article “Proof and Syllogism”¹ and has been accepted by the majority of interpreters.²

Of course, I am not concerned here with a simple question of translation but with the logically more interesting question of whether Aristotle really tries to capture the notion of deduction with “συλλογισμός” in such a way that it would be misleading to render the Greek with “syllogism” – a term which, by itself, refers to the particular kind of deduction theorized in the Prior Analytics.

Let us examine the view of the defendants of the deduction-translation and start by quoting the official definition of συλλογισμός as it appears in the Prior Analytics:

(A) A syllogism (συλλογισμός)³ is a discourse in which, certain things having been posited, something other than the things laid down follows of necessity (ἕτερον τι τῶν κειμένων) in virtue of the fact that they are there (τῷ ταῦτα εἶναι). By “in virtue of the fact that they are there” I mean that it follows because of them (τὸ διὰ ταῦτα συμβαίνειν), and by it “follows because of them” that no external term is required for the production of the necessity.

(Aristotle, Prior Analytics 1.1, 24b18–22)

In order to interpret this definition Barnes distinguishes three different terms: “inference,” “deduction,” and “syllogism.” In his view, an inference is an ordered pair of items, with the first one being a set of premises, let us say Π and the second one a conclusion σ, such that σ follows necessarily from Π. A deduction is a similar pair in which two conditions must be satisfied, namely

• (i) σ follows necessarily from Π.

and

• (ii) σ holds (if it holds) because each element of Π holds.

Finally, a “syllogism” is a deduction in which Π has two members.⁴ It is easy to see that every syllogism is a deduction and every deduction an inference but not vice versa. Having given these definitions, Barnes claims, without any further delay, that

(B) Aristotle’s word for “Deduction” is “συλλογισμός”; for “Inference” he will sometimes use τὸ ἀναγκαῖον […]; he has no word for “Syllogism,” but he can express the notion periphrastically.⁵

Barnes does not explain in so many words why the definition given in text (A) should correspond to his characterization of “deduction.” We can fill the gap by supposing that, in his view, condition (i) corresponds to ἕτερον τι τῶν κειμένων ἐξ ἀνάγκης συμβαίνει, “something other than the things laid down follows of necessity,” whereas condition (ii) has τῷ ταῦτα εἶναι, “in virtue of the fact that they are there,” as its counterpart. Therefore, an Aristotelian συλλογισμός is a deduction and not a syllogism.

The problem with this interpretation is to understand what these distinctions mean. Let us begin by considering the definition of deduction according to clause (ii), which makes a deduction a special kind of inference. I take the term “holds” in this clause to mean, or at least to imply, “is true.”⁶ A possible paraphrase of (ii) is:

• (ii*) if Π is true, then σ is true because of the truth of each element of Π.

This way of putting things entails that in those cases in which σ, the conclusion, is false, the condition is automatically satisfied, and to get a deduction it would be sufficient for σ to follow necessarily from Π. This looks strange because, in Barnes’s view, condition (ii) is intended to distinguish deduction from a simple inference, whereas in fact it distinguishes only deductions with true premises and conclusions from the corresponding inferences. Consider, for instance, an argument such as

As we will see in a moment, according to Aristotle the conclusion of (1) does not follow from its premises “because they are there,” that is, in Barnes’s interpretation, (1) does not satisfy condition (ii*).⁷ Therefore, (1) can neither be classified as a deduction nor, alternatively, as a συλλογισμός. Take now:

Here the conclusion is clearly false. Therefore, condition (ii*) is vacuously satisfied so that (2) is a deduction and a συλλογισμός, although one should not find it too difficult to recognize that (1) and (2) are instances of the same type of argument.

More importantly, Aristotle clearly accepts some arguments in which the conclusions are true and their premises false as συλλογισμοί. For instance, a syllogism such as

is a first-figure syllogism and nobody could cast doubts on its validity.⁸ But are we allowed to say that its conclusion, “every horse is a quadruped,” is true because of the truth of its premises? No: They are plainly false.

Finally, the parenthetical “if it holds” in clause (ii) is not part of the Aristotelian definition in any of its versions.⁹ To be faithful to the Greek, one should omit the parenthetical, and so the clause becomes:

• (ii**) σ is true because the elements of Π are true.

But it is clear that in an Aristotelian syllogism it is not necessary for the conclusion to be true. Actually, this is why the parenthetical has been added by Barnes. So the only way to interpret (ii) without the parenthetical is as a conditional, namely

• (ii***) if the elements of Π are then σ is also true.

Condition (ii***) is weaker than the Tarskian definition of logical consequence, because no modal requirement is implied by it.¹⁰ But because of its weakness, it is difficult to believe that it expresses a requirement that is not already implied by condition (i). May we think that σ follows necessarily from Π and that there may be a case in which truth is not preserved, namely that all the elements of σ are true and Π is false? What sort of following is this, and how can we conceive of a sound inference that is not always truth preserving? If (ii***) is what is supposed to distinguish inference from deduction, one is led to conclude that there is no difference at all between the two.¹¹ As we will see in a moment, this is exactly Aristotle’s position, at least in my interpretation.

II

I do not think that it is very useful to continue to consider Barnes’s approach to the Aristotelian definition of συλλογισμός, and we must try to start afresh. Let us return to text (A). It is quite obvious that two distinct conditions play a role in the definition of a συλλογισμός. The first is Barnes’s condition (1), that is,

• (i) σ follows necessarily from Π

and however mysterious the notion of “following of necessity” may be, let us take it as primitive. The second condition needs more investigation. It is expressed by the clause:

• (iii) τῷ ταῦτα εἶναι.

What does Aristotle mean by (iii)? A first problem concerns its translation. It is clear that “ταῦτα” is acting as the subject of the sentence,¹² as is confirmed by Prior Analytics 1.4, 26a2–5, where (iii) appears. So the problem concerns the way in which “εἶναι” ought to be understood. Although it surely has an existential sense, we cannot take it to imply that in a συλλογισμός the conclusion follows from its premises because they express real states of affairs. What “εἶναι” probably means is “being there.” Therefore, a possible paraphrase of (iii) is:

• (iii*) because the elements of Π are there

where “are there” means nothing m...

Table of contents

• Cover
• Half Title
• Series Page
• Title
• Copyright
• Contents
• Foreword
• Acknowledgments
• List of abbreviations
• Conventions
• PART I Inference and syllogism
• PART II Identity, predication, and quantification
• PART III Modality, time, and future contingents
• PART IV Paradoxes
• PART V Relatives
• Bibliography
• Publications by Mario Mignucci
• Index
• Index of passages