This paper was written as part of the program ‘Theories of Cognition in the Aristotelian Commentators’, funded by the Fonds National Suisse.
- 1 Theophrastus, Galen, and Alexander also wrote commentaries on this Aristotelian treatise, but only (...)
- 2 I retain the traditional translation of ἐπαγωγή but issue a warning : the reader should be careful (...)
- 3 For the sake of brevity, I will report them only indicating the corresponding pages and lines of W (...)
1Philoponus’ commentary on the Posterior Analytics is remarkable* for two reasons : it is the oldest surviving and one of the longest ever written.1 Its merits, however, certainly do not end there : some of the views it presents are quite interesting either as explanations of Aristotle’s doctrines or in their own right. In the present paper, I try to shed some light on one of these views, namely Philoponus’ interpretation of induction (ἐπαγωγή).2 Accordingly, I examine the most relevant passages in this work,3 also resorting to what he says in his other commentaries when this can be of some help for understanding them, and I also combine my findings into a unified account—or rather, into two unified accounts, since some of the views about induction that emerge from these passages turn out to be quite different. Through this examination, I hope to show the originality and historical interest of Philoponus’ account of induction with respect to Aristotle’s own account.
2The first occurrence of the term ἐπαγωγή in Philoponus’ commentary on the Posterior Analytics appears very early :
- 4 In APr. 5,4-6 : καὶ ἄλλως ‘διανοητική’ εἶπε καὶ οὐκ ‘ἀποδεικτική’ ἐπὶ τὸ καθολικώτερον ἀνιών, ἵνα (...)
[T1] And besides, in saying ‘intellectual’ and not ‘demonstrative’ he ascends to the more general in order to encompass every syllogism, including the dialectical and sophistical kinds, and induction and rhetorical means of persuasion.4
- 5 Translations of the Posterior Analytics are taken from Barnes 1994.
- 6 I note in passing that the second example of learning by perceiving offered by Philoponus in the t (...)
3Here Philoponus is commenting on the opening line of Aristotle’s treatise : ‘All teaching and all learning of an intellectual kind proceed from pre-existent knowledge’ (71a1-2).5 Earlier, he aptly noticed that the qualification ‘intellectual’ (διανοητική) is meant to distinguish the kind of teaching and learning under consideration from that based on sense perception. Indeed, the latter does not require any pre-existent knowledge ; for instance, to perceptually learn about something that it is white, one may just need to look at it.6 In [T1] Philoponus continues the analysis of this qualification. The passage can be read in different ways, but the most natural is to take it as pointing out that the dialectical and the sophistical are the only kinds of syllogism there are apart from the demonstrative (in accordance with the account of the kinds of syllogism given at 2,1-7), and that all three kinds of syllogism, together with induction and rhetorical means of persuasion, constitute the kinds of intellectual teaching and learning there are. From this passage, then, we may argue already that for Philoponus induction is not a syllogism but something – possibly, an argument-form, since the rest of the items he lists are clearly such – involved in the teaching and learning of an intellectual (i.e., non perceptual) kind.
- 7 At least, according to the traditional interpretation scholars give of this chapter. See, e.g., Ro (...)
- 8 Note that, although Philoponus fails to realise it, his analysis of induction in the commentary on (...)
4Although it may look trivial, the interpretation according to which induction is not a syllogism could not have been taken for granted. As a matter of fact, in APr. 2.23 Aristotle disposes of his usual distinction between the two,7 and commenting on this chapter Philoponus himself goes as far as to call induction a ‘rhetorical syllogism’ and proceeds to analyse it in syllogistic terms (in APr. 473,3-5).8 The non-syllogistic account of induction that we find in the commentary on the Posterior Analytics indeed constitutes a later departure from the syllogistic one given in the commentary on the Prior Analytics, if the latter work was written before the former. That this is the case is evident from the cross-reference in 2,3, which refers back to the commentary on the Prior Analytics, but also from the general prescription in 1,5-10 about the order in which Aristotle’s logical treatises should be studied (Categories, De Interpretatione, Prior Analytics, Posterior Analytics)—that should correspond, one would be inclined to assume, to the order in which Philoponus wrote his commentaries on them. Therefore one should wonder why he changed his mind on this issue. And yet, it is possible that he really never did : as we shall see in a moment, it is questionable whether the non-syllogistic account of induction truly reflects Philoponus’ view, even if only for his commentary on the Posterior Analytics.
5In the lines following [T1] Philoponus reports that Aristotle confirmed the claim that all teaching and learning proceeds from pre-existing knowledge from the arts, syllogisms, induction, and rhetorical arguments (i.e., enthymemes and examples). When he comes to comment specifically on induction, he says :
- 9 In APr. 5,23-7 : καὶ ἐξ ἐπαγωγῆς δὲ οὕτως ἔστι πιστώσασθαι· εἰ γὰρ βουληθείην μαθεῖν εἰ πᾶν ζῷον τ (...)
[T2] In this way [the claim] can be confirmed by induction : for if I wanted to learn whether every animal moves its lower jaw, I say that since human, horse, dog, and ox [do], the rest [of the animals] move their lower jaw too. For I knew at this point that the knowledge of each of the particulars is pre-existent, from which we then syllogise the universal.9
6Let us for the moment focus on the final statement that the universal conclusion is syllogised. If we take the word in the strict sense – as we probably should, since it is a key one in the context of the Analytics – then Philoponus does think that induction is a syllogism, contrary to what was previously argued. Or should we rather take him to be speaking loosely ? Note that just before this passage, when dealing with the pre-existent knowledge in syllogisms, he says that after we put together the premises as the art demands it is necessary to ἐπαγαγεῖν the conclusion (5,22), where the verb can mean either ‘to infer’ or, in a more restricted sense, ‘to infer by induction’. So, maybe he is playing with words. And yet, shortly below we find a revealing passage in which he says :
- 10 In APr. 6,12-16 : ὁμοίως δὲ τοῦτο καὶ ἐπὶ τῶν ἄλλων ἔστιν ἰδεῖν τεχνῶν καὶ περὶ τοὺς λόγους, ἀντὶ (...)
[T3] Likewise this [i.e. that all learning is based on pre-existing knowledge] can be seen also in the other arts and concerning arguments—by which he means syllogisms. For those who confirm both universals from particulars and particulars from universals through syllogisms confirm them from pre-existing knowledge.10
- 11 See [T3-4] and my comments, below. Cf. also the alternative account given in in APr. 34,20-1 : ‘th (...)
- 12 Most likely this is the familiar, deductive syllogism—which is then homonymous with the genus. In (...)
7The argument that confirms universals from particulars, which surely indicates induction,11 here is subsumed under the genus syllogism, along with the argument that confirms particulars from universals,12 since Philoponus says that by ‘arguments’ Aristotle means syllogisms. Thus, the use of ‘to syllogise’ to characterise induction in [T2]’s final statement is far from being unique or casual. And although this characterisation of induction as a syllogism is at odds with the standard Aristotelian account, it is consistent with what Philoponus explicitly says in the commentary on the Prior Analytics, as I have pointed out (in APr. 473,3-5 ; but see also 34,13-4 discussed in n. 14, below).
8If this interpretation is correct, then the list of argument-forms presented in [T1] cannot be regarded as drawing a distinction between the syllogistic and non-syllogistic ones, for there are indications that Philoponus might believe that the items in that list are all syllogistic in one way or another. We should thus wonder what could be the precise meaning of συλλογισμός and συλλογίζομαι in [T2]. It looks as if they generally indicate any kind of inference, or perhaps, more specifically, inferences that can ultimately be construed as having three terms arranged in a certain way as to form two premises and a following conclusion that is different from the premises. The fact that Philoponus could take induction to be an argument of this sort is shown, once again, by his comments on APr. 2.23. At any rate, his ease in using syllogistic terminology to characterise induction in several different texts is telling, and it distinguishes his approach from that of Aristotle, who is more cautious in this respect.
- 13 For instance, it appears in Alexander’s commentary on the Prior Analytics (43,26-44,2) For other r (...)
- 14 In this passage the comparison is made to the necessity by which a conclusion follows in a syllogi (...)
9Anyway, the example of induction given in [T2] is a stock one in late ancient philosophy.13 Usually its point is that induction is misleading, for not all animals move their lower jaw (e.g., crocodiles). Philoponus may be subtly conveying this idea when he says that a claim can be confirmed (πιστώσασθαι) by induction, that is, not necessarily proved. Still, he is not that explicit and in fact, when he presents this example again (49,20-22, see [T4] below), he says rather bluntly that, through induction, we show (δείκνυμεν) the conclusion. It is striking how much more clearly, in the commentary on the Prior Analytics, he stresses the non-necessity by which the induction’s conclusion follows from the premises (in APr. 34,13-4)14, to the point that he says that a universal cannot be established by induction even if one goes through countless examples (in APr. 34,28-9). However, later in the same commentary he rightly corrects himself again and says that an inductive syllogism carried out by going through all the particulars (διὰ πάντων τῶν κατὰ μέρος) must be logically valid (in APr. 474,3-4).
10More importantly, the illustration in [T2] allows us to determine what Philoponus thinks is the logical form of an induction. Notably, in an induction the premises are propositions whose subjects are the species (human, horse, etc.) of a genus (animal) that constitutes the subject of the conclusion. In every premise, the same predicate (moves its lower jaw) is applied to each species, and in the conclusion this predicate is applied to the common genus. In symbols : let g1, g2, …, gn be the species of γ, their common genus, and let P be a predicate. Then, an inductive argument has the following form :
Pg1
Pg2
…
Pgn
Pγ
- 15 On καθόλου meaning ‘universal proposition’, see, e.g., Chiaradonna, Rashed, and Sedley 2013, p. 18 (...)
11With this reconstruction we get a fairly accurate representation of Philoponus’ account. However there remains one point of detail to explain : at the end of [T2] he also states that in this kind of argument the universal is syllogised by way of (the previous knowledge of) the particular. What does this mean, exactly ? We have seen earlier that Philoponus uses the verb ‘to syllogise’ to mean something like ‘to infer’. Properly speaking, only propositions are inferred. So, when Philoponus says that in an inductive argument we syllogise a ‘universal’, he must mean a universal proposition.15 Correspondingly, by ‘particular’ he must mean a particular proposition. But then, how does his statement at the end of [T2] square with his illustration (and our reconstruction) ? For it seems that none of the propositions involved in it are particular (‘human moves its lower jaw’, ‘horse moves its lower jaw’ … therefore ‘all animals move their lower jaw’).
12The examination of another passage in which the example of an induction given in [T2] is recalled can help us understand more clearly Philoponus’ view. Let us take a quick look at it, too :
- 16 In APr. 49,18-22 :οἵα ἐστὶ καὶ ἡ δι’ ἐπαγωγῆς δεῖξις, ἐκ τῶν κατὰ μέρος τὰ καθόλου κατασκευάζουσα, (...)
[T4] Of this sort also is proof through induction, which establishes universals on the basis of particulars, i.e., prior things from posterior things. For from what source do we show that every animal moves its lower jaw ? We show [it] by enumerating the particular animals, and establishing the universal through the particular and the prior on the basis of the posterior.16
- 17 Aside from the lemma on which Philoponus is commenting (APo. 1.3, 72b 28-9), see APo. 1.2, 71b 33- (...)
13The universal here is identified with what is prior, and the particular with what is posterior. What underlies this analysis is the well known17 Aristotelian distinction between what is prior/posterior to us and in nature. In this passage, ‘prior’ and ‘posterior’ are employed in the latter sense. So understood, [T4]’s train of thought is straightforward : when one casts an induction, he establishes a proposition that is prior in nature on the basis of propositions that are posterior in nature. Thus, the idea is that the proposition ‘animal moves its lower jaw’ in itself is more primitive than, e.g., ‘human moves its lower jaw’. What justifies this idea, then ? It looks as if Philoponus believes that the species owe their common characteristics to the genus under which they fall ; that the species have, so to speak, these characteristics derivatively from the genus. Notably, he seems to believe that it is because moving its lower jaw belongs to animal that it belongs also to the particular species of animal such as human. If this is what is in the back of Philoponus’ mind, then what he means by ‘universal’ and ‘particular’ propositions, in contexts like that of [T2] and [T4], are propositions that involve a more or less general kind, respectively. In this sense, therefore, for him induction is the sort of argument in which a conclusion that involves a relatively more general kind (animal, in his preferred example), i.e. the genus, is inferred from premises that involve less general kinds, i.e. the species (human, horse, etc.)—consistently with the reconstruction we laid down before.
14It is also interesting to note that [T4] locates the source of the induction’s inferential power in the enumeration (ἀπαριθμούμενοι) of the particular species of animals. As we have previously shown, Philoponus wavers about the necessity by which the conclusion follows from the premises in an inductive argument. The observation he makes here might be intended as another point of view on this issue, namely that the plausibility by which an inductive conclusion follows is directly proportional to the number of reviewed particular species over the total number of particular species falling under the same genus. In other words, Philoponus might allude to a statistical-probabilistic aspect of induction : the wider the sample of species reviewed, the more likely it is that the conclusion about the whole genus follows. This is merely a speculation, but if this is indeed what he is suggesting, then it is something quite original, since it is absent from both Aristotle’s and Alexander’s treatments.
15Overall, [T2-4] confirm what we argued already when commenting on [T1], namely that for Philoponus induction is a logical argument-form. As he expressed it : it is an intellectual (i.e. non-perceptual) way of teaching and learning. For what concerns its structure, the premises are particular propositions, in which one attribute is applied to a species, and the conclusion is a universal proposition, in which the same attribute is applied to the relevant genus. As such, it is also characterised as a passage from the posterior to the prior. Finally, Philoponus often stresses the non-necessity by which the conclusion follows from the premises (but at times he presents more nuanced views).
16Later in the commentary on the Posterior Analytics we find a long section (214,5-216,8) that brings up induction again. Philoponus is there commenting on APo. 1.18, in which Aristotle commits himself to show that ‘if any perception is absent, some scientific knowledge must also be absent’ (81a39-40). Although Aristotle’s argument is convoluted, its gist is clear : the thesis is justified by pointing out that there can be no scientific knowledge without induction, and no induction without perception. Aristotle backs up the first claim suggesting that the universals – the knowledge of which is obviously fundamental to scientific knowledge – are reached through induction only ; and the second claim suggesting that induction has to do with particulars and that these are reached through perception only.
17In his comments Philoponus limits himself to paraphrasing what Aristotle says, and just adds a few examples. Nonetheless, the interpretation he gives of the thesis is peculiar :
- 18 In APr. 214,21-25 : καὶ οὐ δήπου διὰ τούτων τοῦτό φαμεν, ὅτι αἱ αἰσθήσεις αἴτιαί εἰσι τῶν ἐπιστημῶ (...)
[T5] And of course we do not say this [scil., e.g., that a blind person will not have scientific knowledge of colours] because the senses are the causes of scientific knowledge, for it is not right for what is inferior to be the cause of what is superior, but because our souls are possessed by the drowsiness or sleep of birth, as it were, and need the senses to waken them and rouse up the spark of knowledge hidden within us. (214,21-25)18
- 19 McKirahan 2012, n. 504 p. 138. See Damascius, in Phaedonem II, § 14 (Westerink 1977, II. Damascius (...)
18He subsequently illustrates his view by saying that just as we come to think of a long-forgotten friend as soon as we see an object that belongs to him, so too the ‘sense objects stimulate the soul to project the concepts of the Paradigms which [concepts] are joined essentially with it’ (214,29-31). This interpretation is steeped in Platonic and Neoplatonic philosophy. Besides the idea of one’s soul projecting the concepts of the Paradigms, this is evident from the choice of the ‘forgotten friend’ example, which tellingly also appears in the Phaedo (73d5-10) in the discussion of Platonic recollection. Moreover, just below (215,1ff.) Philoponus refers to : (i) to Plato and his explanation in the Timaeus (46e8-47e2) of the reason why the Demiurge has given us ears and eyes, namely to enable us to proceed in thought from bodies to the ‘incorporeal power’, through which philosophy was invented ; and (ii) to a commentary on the Phaedo, possibly the one written by Damascius,19 for a proof that the soul does not acquire knowledge of things from the sense objects.
- 20 This sketch of Aristotle’s account is based on APo. 2.19. A full discussion of that chapter would (...)
- 21 On the contrary, in the commentary on the second book (see esp. 432,24ff.) the hypothesis of inbor (...)
19What is more relevant to our present concerns, this interpretation has deep implications for the notion of induction that Philoponus seems to support. The sort of empiricist perspective that underlies the Aristotelian view is traded for another in which the universals – in this case understood as the concepts of the Paradigms – are present within our soul since before birth. As such they are no more, so to speak, to be cognitively built through a development that, starting from sense perception, unfolds through memory, experience, and a series of inductive processes ranging over ever-increasing cross-sections,20 but are already known and reconquered as soon as one perceives the appropriate sense object. In this picture there remains no clear role for induction to play ; in fact, it is bound to be flattened out on this sort of sense perception, thus ceasing to represent a cognitive process in its own right. In other words, in Philoponus’ interpretation, ‘induction’ ends up indicating the recovery of a universal already present in the soul that, as a matter of fact, needs only perception (and then recollection) to be accomplished.21
20That this is Philoponus’ view finds an indirect confirmation in two other passages included in the same section of his commentary :
- 22 In APr. 214,11-14 :τὰ δὲ καθόλου εἰδέναι ἢ λαβεῖν ἀποδεικνύντα μὴ δι’ ἐπαγωγῆς ἀδύνατον (ὅταν γὰρ (...)
[T6] it is impossible for a person who is demonstrating to know or grasp universals except through induction (for when you ask a student to grant you to draw a straight line from any point to any point, or any of the other postulates or axioms, you bring confirmation of these through induction).22
- 23 As McKirahan notes (2012, n. 500, p. 138) : ‘P. assumes that the way a teacher uses informal expla (...)
21In this passage he argues that a person who demonstrates (i.e. one who has scientific knowledge of a certain subject-genus) acquires through induction the relevant principles just as a student accepts the validity of, say, a geometrical principle after having considered a few cases presented by the teacher. This is not just a metaphor, for if it was, it would rest on a hefty assumption (i.e., that the two cases are similar)23 while failing to explain how the universals are grasped through induction, which is exactly the reason for which it would have been introduced. So, this is Philoponus’ actual explanation of how an expert inductively grasps the universals, namely just by considering some particular cases. The way in which a student gets to know a universal principle is explained in more detail in a passage appearing shortly below :
- 24 InAPr. 215,16-22 : ἀκούσας γὰρ ὁ ἄρτι τῇ γεωμετρίᾳ προσιών, ὅτι τὰ τῷ αὐτῷ ἴσα καὶ ἀλλήλοις εἰσὶν (...)
[T7] For a person who has recently approached geometry, upon hearing that things equal to the same thing are also equal to one another, even without understanding very well what is being said, will recognise it by induction, when we say, for example, that if there should be two magnitudes that are each two cubits long, and also a third which is equal to one of the ones mentioned, it will of course have to be equal to the other one too, and similarly for the claim that if equals are subtracted from equals the remainders are equal : he will recognise what is said through induction of particulars. Likewise too in all other cases.24
- 25 While it is unclear (at least to me—but see Barnes 1994, ad 81b3 p. 168, who quotes de An. 432a3-6 (...)
22A geometry novice inductively grasps a universal principle simply by, quite literally, being exposed to25 some of its instances. For Philoponus, therefore, what affords the universal knowledge is sense perception of the appropriate particular cases. In his explanation, there is nothing more to induction than this. Indeed, as we know from [T5], Philoponus thinks that sense perception of particulars is sufficient to ‘rouse up the spark of knowledge hidden within us’. Thus, [T5-7] jointly explain that both experts and novices grasp the universals in this way. Note that in these passages there is no one hint of a progressive, cognitive development taking place ; on the contrary, what is emphasised is the swift passage from particular to universal knowledge.
- 26 This reading has the further advantage of providing an easy explanation as to why Philoponus, some (...)
23The same view is also illustrated by the image of burning coals hidden in the ashes given in Philoponus’ in De an. 4,30-5,5 (cf. also De int. 20,72-88), with which [T5-7] can be proficiently compared. In this passage, Philoponus describes the suddenness (εὐθύ) by which the sparks again ignite as a result of a little (μικρό) poking that just (ἀλλὰ μόνον) removes what was smothering the coals. This image is meant to explain how opinion (i.e., one of the soul powers) is provoked by sense perception to project the formal principles of things. ‘In this way’, adds Philoponus, ‘it is also said that teachers do not put knowledge into us, but they bring to light the knowledge that is already in us and as it were hidden’. Once again, the perspective is very different from that adopted by Aristotle in APo. 2.19, where the emphasis is rather on the complexity and gradualness of the process by which we get to assemble the knowledge of the principles. In fact, this passage confirms that for Philoponus the universal knowledge really is not something that is assembled (‘it is not that the person who has done the poking has created the spark’). On the contrary, the emphasis is on the fact that the principles are already present within the soul, and that all one needs to do is to recover them by removing what obstructs their conscious grasp (that [T5] identifies as ‘the sleep of birth’, i.e. the descent of the soul in the material body). Somewhere else he even says that these inborn principles are the ‘traces and manifestations’ of the intellect, which can get them by direct apprehension (cf. in De an. 3,16-4,4). The fact that in these passages induction is never mentioned again confirms that its role indeed is deflated. As argued before, in Philoponus’ interpretation ‘induction’ just ends up denoting the kind of sense perception that prompts one to recover the knowledge of a universal already present within his soul, and nothing more.26
24But the flattening out of induction on sense perception also finds a straightforward confirmation in an early passage that we still have to discuss :
- 27 In APr. 17,11-14 :Τὸ ἐπαγόμενος ἀντὶ τοῦ ‘προσβάλλων αὐτῷ κατὰ τὴν αἴσθησιν’, ἐπειδὴ ἡ διὰ τῶν κατ (...)
[T8] By ‘performing the induction’ he means ‘noticing it in accordance with perception’, since knowledge of particulars is being called induction, and we know particulars through perception.27
- 28 This idea of a triangle being identified as such by induction may seem gratuitous. However, recall (...)
25This explanation is given while commenting on another difficult Aristotelian example, but its importance for our present concerns can be appreciated without going through its details : once again, and this time explicitly, Philoponus equates induction to some act of sense perception. Further below, he clarifies that this equation is without exception, for speaking about a situation in which a certain triangle is recognised to be such a thing by induction,28 he adds that all perceptual knowledge is of this kind—i.e., I take it, inductive (17,17-18). This view complements the one according to which inductive knowledge is perceptual, that is, the view we presented and discussed above.
- 29 Some of the texts that may have influenced Philoponus’ interpretation are presented and discussed (...)
26At this point, one should wonder what could have been the rationale behind such a transformation of the notion of induction. Most probably the answer lies in the sought-after harmony of Plato and Aristotle, a common concern of the Late Antique commentators. It is reasonable to suppose that Philoponus wanted to stick to the Aristotelian authoritative text, including the claim that ‘if any perception is absent, some scientific knowledge must also be absent’, but at the same time he did not want to give up other Platonic tenets that he embraced.29 This generated friction, for the sort of innatism-based framework on which he wanted to build his interpretation neither required nor admitted the knowledge of universals to be causally brought about by a kind of cognitive development ultimately based on the sense perception of particulars. To ease this friction he elaborated an interpretation of Aristotle’s claim in which the role of sense perception is maintained, but in a radically different way. More specifically, he understood the perception of particulars just as the extrinsic condition for getting to know the universals, inasmuch as it awakens the knowledge of universals that one otherwise has always present in himself—without any cognitive development needed. In this picture, there remained no obvious role for induction to play. It thus became a cumbersome presence that had to be deflated to the point it became indistinguishable from sense perception, and as much extrinsic as this to grasping universals. At most, induction could designate the very jump from the knowledge of particulars to the knowledge of universals—but not anymore an independent cognitive process that properly contributed to bringing this jump about.
27I would like to briefly point out one last thing. In [T5-8], insofar as induction is flattened out on sense perception, specifically that which triggers the awakening of the universal knowledge already present within the soul, it differs from the induction presented in [T1-4]. The basic characterisation of the latter, as we have seen, is that of an intellectual, i.e. non-perceptual, means of teaching and learning ; more precisely, it is a logical argument-form in which a universal conclusion is inferred from particular premises. The characterisation of the former, instead, is that of a mental process on which knowledge supervenes, based on the perception of the appropriate sense objects and innate knowledge : in this case there is no logical sequence of premises and conclusions, and the grasp of the universals is rather the result of a direct insight. However, these two different ways of understanding induction are united by one fundamental aspect : both hold it to be something that leads to knowledge of universals. Nevertheless, the contexts in which each kind of induction operates are different : one is logical, the other psychological.
28This two-fold account of induction takes the cue from the sparse remarks that Aristotle gives in his works, but it constitutes a peculiar and interesting elaboration of the notion of induction in the philosophy of Late Antiquity.