Paul Thom
What is logic about? According to one familiar account logic tells us when arguments are valid; logic is thus about arguments. On another account logic tells us which propositions are (unconditionally) neces- sary; logic is thus about propositions (Smith 2012). Less familiar than either of these accounts is the Aristotelian tradition of thinking about logic. Aristotelians have standardly thought of logic as being about terms, as well as propositions and arguments. Let us call propositions and arguments, and whatever else logic has been supposed to be about, the objects of logic. The general question that interests me is: What are the metaphysical types to which the objects of logic belong? More specifically, I will look at the way this question has been addressed in the Aristotelian tradition. I will not be dealing with answers to our question proposed by Platonists or with the Stoic concept of lekta.
I use the expression ‘the Aristotelian tradition’ to cover the writings of Aristotle himself as well as those over time who have broadly sympathised with his views. The latter include the ancient Greek commentators, a multitude of medieval logicians writing in Arabic or Latin, and a smaller number of later thinkers (notably Bernard Bolzano). But my main focus will be on just one of these, the thirteenth-century philosophical logician Robert Kilwardby (d. 1279). Kilwardby dealt with our question at some length, and his discussion is also useful in that it considers several views other than his own. Let us begin with Aristotle’s own ideas on our question.
1. Aristotle
There is not much in Aristotle’s own writings that bears directly on our question. Four passages are noteworthy.
First, the Categories makes a remark about statements:
Statements and beliefs, on the other hand, themselves remain completely unchangeable in every way; it is because the actual thing changes that the contrary comes to belong to them. For the statement that somebody is sitting remains the same; it is because of a change in the actual thing that it comes to be true at one time and false at another. Similarly with beliefs. Hence at least the way in which it is able to receive contraries – through a change in itself – would be distinctive of substance, even if we were to grant that beliefs and statements are able to receive contraries. However, this is not true. For it is not because they themselves receive anything that statements and beliefs are said to be able to receive contraries, but because of what has happened to something else. For it is because the actual thing exists or does not exist that the statement is said to be true or false, not because it is able itself to receive contraries. No statement, in fact, or belief is changed at all by anything. So, since nothing happens in them, they are not able to receive contraries. (Aristotle 1963: 4a5)
Here Aristotle leaves two positions open: either statements do not change truth-value at all, or else any change in their truth-value is due to a change in something external to them, namely the things which the statements are about.
Second, in the De Interpretatione we find Aristotle apparently proposing a general semantic theory according to which the meaning of spoken and written utterances is to be found in the existence of mental items that somehow correspond to them:
Now spoken sounds are symbols of affections in the soul, and written marks symbols of spoken sounds.. . . Just as some thoughts in the soul are neither true nor false while some are necessarily one or the other, so also with spoken sounds. For falsity and truth have to do with combination and separation. (Aristotle 1963: 16a2)
Here, the meaning of spoken and written language is derived from ‘affec- tions in the soul’, and truth and falsity are seen as residing primarily in the combination or separation of mental items.
Third, there is a remark in the Posterior Analytics which, again, seems to point to the soul as the locus of truth and demonstration.
By contrast, it is always possible to find fault with ‘external’ arguments (i.e. spoken or written ones): For demonstration is not addressed to external argument – but to argument in the soul – since deduction is not either. For one can always object to external argument, but not always to internal argument. (Aristotle 1994: 76b23)
Finally, there is a remark in Metaphysics Book 6 which again locates truth and falsity in the soul rather than in external reality:
But since that which is in the sense of being true, or is not in the sense of being false, depends on combination and separation, and truth and false- hood together are concerned with the apportionment of a contradiction (for truth has the affirmation in the case of what is compounded and the negation in the case of what is divided, while falsity has the contradictory of this apportionment – it is another question, how it happens that we think things together or apart; by ‘together’ and ‘apart’ I mean thinking them so that there is no succession in the thoughts but they become a unity – ; for falsity and truth are not in things – it is not as if the good were true, and the bad were in itself false – but in thought; while with regard to simple things and essences falsity and truth do not exist even in thought): – we must consider later what has to be discussed with regard to that which is or is not in this sense; but since the combination and the separation are in thought and not in the things. (Aristotle 1993: 1027b30)
In sum, Aristotle thinks that
1. statements, as the bearers of truth and falsity, are in the soul and are either unchanging or any change in them is due to a change in something else;
2. the meaning of written and spoken language is to be explained by reference to what goes on in our minds;
3. truth and falsity belong in the first instance to combinations and separations that occur in our minds.
These are scattered remarks. Aristotle doesn’t show how they could be combined in a coherent theory of terms, propositions and arguments. We do not find such a theory in Aristotle; we find only some materials that seem to have the potential for theoretical development.
An interpreter of Aristotle, faced with this situation, might try to develop a theory in one of two ways. One option would be to enlist elements drawn from Aristotle’s metaphysics or his account of scientific knowledge. Another would be to import non-Aristotelian ideas. We will see that both approaches were used by later Aristotelians in their efforts to flesh out Aristotle’s sketchy remarks.
One obvious place to look for theoretical help in this enterprise is the Philosopher’s division of all beings into the ten categories (substances, quantities, relatives, qualities etc). From the standpoint of the theory of the categories, our question becomes: Do the objects of logic belong to any of the Aristotelian categories, and if they do, to which category or categories
do they belong? This question was explicitly posed by a number of thinkers in the twelfth and thirteenth centuries.
2. Robert Kilwardby
The thirteenth-century English philosopher and churchman Robert Kilwardby commented extensively on Aristotle’s logic, as well as compos- ing a treatise On the origin of the sciences and a set of questions on the four books of Peter Lombard’s Sentences. Over the course of his career he showed a continuing interest in the nature of the objects of logic, and indeed the nature of logic itself.
In his early question-commentary on the Prior Analytics Kilwardby takes the view that logic is one of the language-related sciences along with grammar and rhetoric. In the work’s first sentence he adopts Boethius’s characterisation of logic as an art of discoursing (Kilwardby 1516: 2ra).1
He goes on to consider the meaning of the words ‘proposition’ [propositio, Aristotle’s protasis] and ‘syllogism’ [syllogismus] as they occur in Boethius’s translation of Aristotle’s text, distinguishing propositions from statements [enuntiationes]. A statement is put forward on its own account, a propos- ition on account of the conclusion it is intended to support. A statement expresses what is in the speaker’s soul, and accordingly is defined as that which is either true or false since truth and falsity reside in the soul (Kilwardby 1516: 4rb).2 In his other writings Kilwardby will generally preserve this distinction, reserving the term ‘proposition’ for the premise of an argument.
He asks whether a syllogism should be defined as a kind of process, rather than a kind of discourse (following Aristotle’s definition). He agrees that there is a sense in which a syllogism is a mental process, but says that this is a metaphorical sense (Kilwardby 1516: 4vb).3And it must indeed be regarded as a transferred usage for someone whose starting-points are Aristotle’s usage of ‘syllogism’ to mean a kind of discourse and Boethius’s characterisation of logic as a science of language.
In his later work On the rise of the sciences logic is no longer characterised purely as a linguistic science, and the syllogism is no longer a purely linguistic phenomenon. Logic is there presented under two guises. It is a science of reason as well as being a language-related science:
1
Robert Kilwardby, Notule libri Priorum, Prologue.
2
Kilwardby, Notule libri Priorum Lectio 2 dubium 5.
3
It is called a science of reason not because it considers things belonging to reason as they occur in reason alone, since in that case it would not properly be called a science of discourse, but because it teaches the method of reasoning that applies not only within the mind but also in discourse, and because it considers the things belonging to reason as the reasons why things set forth in discourse can be reasoned about by the mind.. . .. It is, therefore, a ratiocinative science, or science of reason, because it teaches one how to use the process of reasoning systematically, and a science of discourse because it teaches one how to put it into discourse systematic- ally. (Kilwardby 1988: 265)
On this view, which places mental reasoning on a par with reasoning in words, it cannot be right to dismiss as merely metaphorical a conception of the syllogism as a mental process.
He raises the issue of the basis or foundation of logic, declaring that there are three different kinds of basis on which a body of scientific knowledge can be founded. The science might be based on things that actually exist. Or it might be based on potentialities, even when they are unactualised. Finally, a science might be based not on potentialities but on aptitudes of things. These are incomplete potentialities, such as the apti- tude for sight which exists even in a blind eye. Now, even though speech passes away as soon as it is uttered, something remains, namely certain natural principles wherein potentialities or aptitudes reside. Because of these, speech contains enough on which to found a science, even when no-one is speaking (Kilwardby 1976: 429).
Later in On the rise of the sciences he adds that an art of reasoning has a sufficient foundation in the natures of things through which they are susceptible to a rational account. Among these natures he mentions antecedents, consequents, incompatibles, universality, particularity, middles, extremes, figure and mood (Kilwardby 1976: 463).
This interest in the foundations of the art of logic is even more evident in a late theological work, Kilwardby’s questions on Peter Lombard’s four books of the Sentences. Question 90 on Book One of the Sentences contains a detailed exposition of the metaphysical status of the objects of logic. It seems that Kilwardby himself attached some importance to this exposition, for in the alphabetic index which he compiled of the matters covered in his questions, he refers on four occasions to question 90 on Book One.4It is therefore worth examining his exposition in detail.
4
Here is his question:
The next question is about divine knowledge in respect of things of reason, which namely are in the human reason and are brought about by reason – things such as propositions, syllogisms and the like, and all manner of complex and incomplex things insofar as they concern reason. And the first question about these is whether they are something, in such a way that they are things in one or more of the categories. (Kilwardby 1986: 1, q.90: 1)
Although he refers here to ‘propositions’, he proceeds to discuss instead what he calls ‘stateables’ (enuntiabilia). This is no doubt partly because of the distinction he had made earlier between propositions and statements; but this doesn’t explain why he talks about stateables rather than state- ments. Christopher Martin takes the expression enuntiabile in earlier authors to refer to a statement’s content rather than to the statement itself (C. Martin 2001: 79). But I will argue later that there is reason for doubting that this is Kilwardby’s meaning.
Concerning the nature of the objects of logic, Kilwardby mentions a view according to which stateables cannot be assigned to any of the Aristotelian categories. Among the arguments he mentions in favour of this view, two rest on Aristotelian texts. First, there is the chapter of the Categories where the ten categories are presented as a classification of ‘things said without any complexity’; stateables on the other hand, if they are things at all, are things possessing complexity. The second Aristotelian text is the one we noted above from Metaphysics book 6. Here, says Kilwardby, the ten categories are presented as being truly outside the mind or soul, whereas composition and division are said to belong to cognition, not to external things (Kilwardby 1986: 1, q.90: 57).
Views denying categorial status to stateables or similar quasi-entities were not uncommon in the twelfth and early thirteenth centuries. Peter Abelard, for one, in using the word dictum to refer to a that-clause, or an accusative and infinite construction in Latin, thought that the question of what sort of things these dicta are simply does not arise: they are not things at all (King 2010).5
5
King 2010: ‘Abelard describes this as signifying what the sentence says, calling what is said by the sentence its dictum (plural dicta). To the modern philosophical ear, Abelard’s dicta might sound like propositions, abstract entities that are the timeless bearers of truth and falsity. But Abelard will have nothing to do with any such entities. He declares repeatedly and emphatically that despite being more than and different from the sentences that express them, dicta have no ontological standing whatsoever. In the short space of a single paragraph he says that they are “no real things at all” and twice calls them “absolutely nothing.” They underwrite sentences, but they aren’t real things. For although a sentence says something, there is not some thing that it says. The semantic job of sentences is to say something, which is not to be confused with naming or denoting some thing. It is instead a matter of proposing how things are, provided this is not given a realist reading.’
Again, the twelfth-century Ars Burana denies that enuntiabilia belong to any of the Aristotelian categories.They exist, but belong to a category of their own (Ars Burana, 208).6
But Kilwardby doesn’t have these versions in mind when he refers to the view that the stateables are not to be found in any Aristotelian category. Rather, he is thinking of the version of the view advanced by the English theologian Alexander of Hales (Hales 1951–1957: 1 d.39 n.1). Alexander held that the ontological type to which a statement belongs depends on whether the statement expresses an essential or an accidental predication. In the former case the statement is nothing other than its subject, and thus belongs to the same Aristotelian category as its subject. Thus the statement ‘Fido is a dog’ is a substance, and is the very same substance as Fido. In the case of accidental predications, the statement can be reduced to the Aristotelian categories in one of two ways: either it reduces to the category in which its accidental predicate is located, or partly to that category and partly to the category of the subject. Thus ‘Fido is white’ turns out either to be a quality (and then it is the quality of whiteness) or partly a quality and partly a substance (and then it is partly Fido and partly whiteness) (Kilwardby 1986: 1 q.90: 70).
In opposition to this view, Kilwardby holds that compositions, state- ables and the other objects of logic can be assigned to the Aristotelian categories in their own right without having to be reduced to the categories to which their subjects and predicates belong. His view involves a complex reduction to the Aristotelian categories.
Every thing, he declares, is either divine or human. The products of nature he includes among the divine, along with things that issue from God by himself. Human things, in his parlance, do not include what issues from humans solely in virtue of their existence as natural beings, but only what comes about through human activity in the form of industry or skill. He classes the objects of logic, not among divine things, but among human things in this narrow sense (Kilwardby 1986: 1 q.90: 102).
Among such things he distinguishes those that are internal to a human and those that are external. The former include actions of combining, dividing or reasoning, as well as the corresponding acts which he calls
6 Anon 1967: ‘If you ask what kind of thing it is, whether it is a substance or an accident, it must be
said that the sayable [enuntiabile], like the predicable, is neither substance nor accident nor any kind of other category. For it has its own mode of existence [suum enim habet modum per se existendi]. And it is said to be extracategorial, not, of course, in that it is not of any category, but in that it is not of any of the ten categories identified by Aristotle. Such is the case with this category, which can be called the category of the sayable [praedicamentum enuntiabile].’
combinations, divisions, reasonings etc. The human things that are exter- nal include utterances, the making of works and the works made (e.g. the making of a house, and the house that is made). This distinction between what is internal to the human and what is external appears to rest on a distinction between doing and making. While making can be considered as a kind of doing, it can also be distinguished from other kinds of doing insofar as it involves the production of something, or at least a process aimed at the production of something. Thus when we mentally combine or separate concepts, or when we reason ‘in our heads’, we do not thereby produce anything external to ourselves: we have done something but we haven’t made anything. But when we utter something, or build a house, we do produce something external, we make something. If this is what