Apeiron Volume 42 issue 2 2009 [doi 10.1515%2FAPEIRON.2009.42.2.105] Hasper, Pieter Sjoerd -- Logic and Linguistics- Aristotleâs Account of the Fallacies of Combination and Division

Logic and Linguistics 105

APEIRON a journal for ancient philosophy and science003-6390/2009/4202 105-152 48.00 © Academic Printing and Publishing

Logic and Linguistics: Aristotle’s Account of the Fallacies of Combination and Division in the Sophistical Refutations*

Pieter Sjoerd Hasper

1 Introduction

In his Sophistical Refutations Aristotle introduces a list of thirteen falla-cies. Six of them he classifi es as ‘depending on the formulation’, falla-cies which rely on purely linguistic features of the statements involved in the reasoning. Two of these are the sophisms of combination and division. Aristotle does not characterize them abstractly in any way, but his introductory examples seem clear enough:

Depending on combination [is] ... for example [i] ‘being able to walk while sitting’ and [ii] ‘[being able] to write while not writing’ ( ). (SE 4, 166a23-5)

And:

Depending on division [are the arguments] [iii] that fi ve is two and three, and odd and even, and [iv] [that] the larger [is] equal, as it is

* Dedicated to Erik Krabbe on the occasion of his retirement as Professor of Argu-mentation Theory at the University of Groningen (February 2008) — with many thanks for comments and the most enjoyable cooperation in trying to understand Aristotle’s dialectic and theory of fallacy.

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106 Pieter Sjoerd Hasper

so-much and something in addition (). (SE 4, 166a33-5)

The two examples of combination (i and ii) exhibit the same pattern, as the phrase ‘being able to while not-ing’ can be interpreted in two ways:

(1a) while not-ing, being able to

(1b) being able to [ while not-ing]

The two examples of division (iii and iv) likewise are structurally simi-lar, as the phrase ‘a is b and c’ is interpretable in two ways:

(2a) a is [b and c]

(2b) a is b, and c

For if ‘fi ve is two and three’ is understood along (2b), then we may claim that fi ve is even, because it is two, and odd, because it is three. And if ‘what is larger than x is x and something in addition’ is simi-larly understood, then it follows that what is larger than x is something equal to x.

In terms of how they work these introductory examples may be suf-fi ciently perspicuous, but that is not the case with the two fallacies of combination and division in general. For one, quite a few of the further examples Aristotle gives are diffi cult to understand and have caused commentators trouble — as we shall see, some cases of combination or division have not even been identifi ed as such. More serious, however, is that what little Aristotle sets forth on a theoretical level about combi-nation and division seems incomplete and inconsistent. One point on which Aristotle’s account is incomplete is that he, on the one hand, tells us that the fallacies of combination and division arise ‘because of think-ing that a combined or divided does not differ at all’ (SE 7, 169a25-26), but, on the other hand, does not give any criterion for counting one reading as divided and another as combined. Of course, in the case of (i) and (ii) it is natural to suppose that (1b) constitutes the combined reading, as it is somehow linguistically intuitive, which is confi rmed by the fact that the fallaciously drawn conclusion, which is said to depend on combination, derives from reading (1b). (Similarly with (iii) and (iv) reading (2b) would be the divided reading.) But a clear criterion would have been useful with examples as the following:




All such arguments are dependent on combination or division: ‘Was he being hit with that with which you saw him being hit?’ And: ‘Did you see him being hit with that with which he was being hit?’ () (SE 20, 177a35-8)

These two questions, which are each other’s converse, can be analysed in two ways, depending on where ‘with which’ and ‘with that’ respec-tively are to be placed, but both these ways can be phrased in terms of combination as well as of division: combined with ‘you saw’/‘did you see’ or with ‘him being hit’, or, alternatively, divided from ‘him being hit’ or from ‘you saw’/‘did you see’.1

Aristotle is, secondly, also incomplete in so far as he fails to provide an explanation why there is in the one case a fallacy of combination and in another one of division. It is true that Aristotle does say of most examples of fallacies he gives whether they are dependent on combina-tion or on division, and sometimes, as with examples (i)-(iv), a natural explanation for their classifi cation suggests itself. However, with some of the examples where such a qualifi cation is lacking an explicit ex-planation would have been most helpful. In addition, it remains to be shown that whatever explanation we may want to ascribe to Aristotle on the basis of the examples explicitly called the one or the other, can be extended to all examples unproblematically.

Now incompleteness may perhaps be compensated for, but inconsis-tency is quite another matter. The fi rst point on which Aristotle seems to contradict himself derives from the fact that even though every fallacy of combination or division involves two readings of one sentence and thus underlying both fallacies is the same kind of what one may term ‘doubleness’, Aristotle counts them as two separate fallacies. For when Aristotle wants to establish that there are merely these six linguistic fal-lacies he has just listed, he seems to argue from types of doubleness:

Of this [i.e. that there are these six fallacies] there is a proof both [] by way of induction and [] as a deduction, [that is,] both [] when some other [case] is taken up () and [] that in so many ways we may indicate with the same words and sentences what is not

1 Cf. S.G. Schreiber, Aristotle on False Reasoning. Language and the World in the Sophis-tical Refutations (New York 2003), 91-2.




the same (). 2 (SE 4, 165b27-30)

How then are we going to end up with six rather than fi ve linguistic fallacies if those of combination and division involve the same way of indicating what is not the same?

A similar inconsistency seems to occur because Aristotle often likens the doubleness involved in the fallacies of combination and division to that in the fallacy of accent. Both, he states, do not concern one state-ment or one word with several meanings and are thus not based on am-biguity. Rather they involve two statements or words, corresponding to two readings of the same sentence (as a string of words) or written word, in the former case a combined and a divided reading, in the latter a reading with higher pitch and one with lower pitch. This doctrine he states most explicitly in the following passage:

Of the [apparent deductions and refutations] which reside in the formulation, some are dependent on something double, such as homonymy, amphiboly ( ) and similarity of formation () ..., whereas combination and division and accent [come about] because of the statement not being the same or [because of] the word [being] what is different (). (SE 6, 168a23-8)3

2 For alternative translations of this sentence, see e.g. L.-A.Dorion, Aristote: Les réfutations sophistiques (Paris and Laval 1995), 124; J. Barnes, ed., The Complete Works of Aristotle: The Revised Oxford Translation [CWA] (Princeton, NJ: 1984), 280; Schreiber, False Reasoning, 20; E. Poste, Aristotle on Fallacies or the Sophistici Elenchi (London 1866), 7; E.S. Forster, Aristotle: On Sophistical Refutations, On Coming-to-be and Passing-away [together with: D.J. Furley, Aristotle: On the Cosmos] (Cambridge, MA 1955), 17; and P. Fait transl. and comm, Aristotele: Le confutazioni sofi stiche. Organon VI (Rome and Bari 2007), 7, who at 107-9 offers an overview of all attempted interpretations. All these translations ignore the clearly parallel double ... ... structure. One should confer, moreover, Topica I 8, 103b3-8. It might be objected against my translation that I cannot supply any masculine word with from the context. However, in a classifi cation of fallacious arguments the word easily springs to mind (cf. a few lines further, at 165b31).

3 Cf. the remarks immediately following at SE 6, 168a28-31; cf. also SE 7, 169a25-9 and 21, 178a2-3.




He even goes on to claim that they are to be solved similarly:

In general in the case of arguments dependent on the formulation the solution will always be according to the opposite of that on which the argument is dependent. For example, if the argument is dependent on combination, there is a solution for someone who has divided it, while if the argument is dependent on division, there is one for someone who has combined it. Again, if it is dependent on a sharp accent, a low accent is the solution, while if it is dependent on a low accent, a sharp [accent is the solution]. (SE 23, 179a11-15)

But why then does Aristotle not distinguish likewise two fallacies of accent, one depending on a sharp accent and one depending on a low accent?4

To add to the confusion, sometimes Aristotle seems to forget about this claim that combination and division involve two readings or state-ments rather than one. For example, he states that a fallacy may oc-cur ‘when a divided and combined signifi es something else’ (SE 20, 177a34-5).5 Moreover, this inconsistency points to a further issue on which Aristotle’s account is not complete. For why do we have, rather than one ambiguous statement, two separate statements in the case of combination and division? We could ask the same question by compar-ing combination and division with the fallacy of amphiboly, which oc-curs when the same statement can be construed grammatically in two different ways. Aristotle himself seems to acknowledge that they are quite similar, for after giving the two examples of hitting someone with the same as that with which one saw him being hit, he continues:

It has, then, also something belonging to amphibolous questions (), though it is dependent on combination.6 (SE 20, 177a38-b1)

4 Cf. Dorion, Les réfutations, 79.

5 See also SE 4, 166a35-6 and 7, 169a25-6.

6 At a38 I hesitatingly read , with manuscripts D, u and V, and Boethius’ trans-lation, against the reading of A and B, which is adopted by W.D. Ross, ed., Aristotelis Topica et Sophistici Elenchi (Oxford 1958) (for the letters standing for the manuscripts, see J. Brunschwig, ed and trans, Aristote: Topiques I Livres I-IV [Paris 1967] — the reports about V, which has not yet been used in any edi-tion of the Sophistici Elenchi, are based on my own inspection of the manuscript).




What is the principle difference Aristotle has in mind? (And when we have answered that question, why does he think that in this particular case there is something smacking of amphiboly?7)

In this article I shall try to deal with all these issues, trying to show that Aristotle’s account may be completed in ways suggested by his own remarks and examples, and that it is certainly not inconsistent. I will only be able to do so, however, after having discussed all the ex-amples to be found in the Sophistical Refutations. These examples will provide part of the evidence on which my answers to the theoretical questions are to be based. Moreover, what is foremost required, as a fi rst step towards answering these questions, is a uniform account of all the examples. It is therefore to such a uniform account that I shall proceed fi rst.

2 Analysing Aristotle’s examples

2.1 Looking for a uniform account

In their attempts at analysing Aristotle’s examples, scholars have tra-ditionally gone about in a case by case way, trying for each example to come up with at least two readings in which lexical items are combined or divided. This has worked perfectly well for the easy examples, like those mentioned in the introduction. On the other hand, with the less perspicuous cases this has given rise, for lack of a common scheme to adhere to, to a large variety of proposals, without one of them obvi-ously or more plausibly being the correct analysis. It has, moreover, not given us anything to build on in answering the further theoretical worries listed above.

Dorion, Les réfutations, 340, argues that should here mean ‘ambig-uous’ rather than ‘amphibolous’, on the grounds that amphiboly only concerns statements in which terms can be assigned two different grammatical functions and that and retain their grammatical function, whether they belong to or . However, not only does this seem too strict an application of the concept of grammatical function, but it also leaves Aristotle with a case of ambiguity which he cannot accommodate in his scheme. For the only two cases of ambiguity Aristotle distinguishes in the Sophistical Refutations are homonymy (lexical ambiguity) and amphiboly (syntactical ambiguity), and these two exam-ples obviously do not involve any kind of lexical ambiguity.

7 Cf. Fait, Le confutazioni, 184.




Things have changed, however, with the proposal by Annamaria Schiaparelli to analyse the fallacies of combination and division con-sistently as involving an operator with wide and narrow scope respec-tively.8 Her starting point, of course, is provided by examples (i) and (ii), which lend themselves very easily to such an analysis, with ‘being able to’ as the operator which governs either just ‘’ (narrow scope) or ‘ while not-ing’ as a whole (wide scope). The obvious advantage of such a uniform account is that it would give us a clear criterion what to call the divided reading and what the combined reading. For example, in ‘Was he being hit with that with which you saw him being hit?’ the operator would be ‘saw’, which either governs ‘him being hit’ or ‘with which ... him being hit’, so that we have good reason to call only the sec-ond reading combined, despite the fact that on the fi rst reading ‘with which’ is in a sense also combined, namely with ‘you saw’.

Schiaparelli has diffi culties, however, with examples like (iii) and (iv), where there is no operator to be found. In such cases she takes re-course to what she calls analogues of operators, namely one- or many-place relations and elliptical expressions with several empty slots, of which then either one place or slot (combined reading) or two places or slots (divided reading) are fi lled. Thus example (iii) ‘fi ve is two and three’ becomes on her analysis either a conjunction of two one-place predicates ‘fi ve is ...’ with ‘two’ and ‘three’ as constants respectively, or a two-place predicate ‘fi ve is ... and ...’ with ‘two’ and ‘three’ as the two terms. Similarly she analyses the example ‘I made you free while being a slave’ () — to be discussed further below as example (viii) — in such a way that it consists of the elliptical expression with two empty slots ‘I made you (...) (...)’ and either the whole expression ‘free while being a slave’ fi lling only one of these slots (combined reading) or ‘free’ fi lling the one slot and ‘while being a slave’ fi lling the other (divided reading).

The very fact that Schiaparelli has to come up with such a way out of the diffi culties tells already against her proposal. For even though she insists that these analogues of operators are merely analogues, the unity of her account is thus seriously undermined. The two analogues

8 See A. Schiaparelli, ‘Aristotle on the Fallacies of Combination and Division in So-phistici Elenchi 4’, History and Philosophy of Logic 24 (2003) 111-129 — though she was perhaps preceded as far as the main idea is concerned by J.D.G. Evans, ‘The Classifi cation of False Refutations in Aristotle’s De Sophisticis Elenchis’, Proceedings of the Cambridge Philological Society NS 21 (1975) 42-52, at 50.




are not identical to operators and cannot even be made identical to each other, so it seems that on Schiaparelli’s account Aristotle is committed to there being three kinds of division and combination fallacies, with-out a uniform nature.

What is more, her two proposed analogues are problematic in them-selves. To take the fi rst analogue fi rst, in ‘fi ve is two and three’ Aristo-tle does not consider ‘fi ve’ as the one- or two-place predicate which is predicated either of ‘two’ and ‘three’ separately or of ‘two’ and ‘three’ together, but as the subject which either has ‘two’ and ‘three’ as two separate predicates or ‘two and three’ as one single predicate. For oth-erwise he cannot deduce, as we saw he does, the further point that fi ve is odd and even from the divided reading of ‘fi ve is two and three’ without committing a further fallacy.

The analogue of an elliptical expression with empty slots is even more defi cient, as it lacks a crucial feature of the analysis in terms of operators with wide and narrow scope. For while that analysis allows us to say that there is a combined reading if some string of words as a whole is governed by an operator, and a divided reading if only part of that same string is governed by the same operator, this feature is lost with the analogue. Thus in the example of ‘I made you free while being a slave’, it does not matter whether we divide the string of words ‘free while being a slave’ over one or two slots in the elliptical expression ‘I made you (...) (...)’: there is nothing in the so-called divided reading which necessitates us to take ‘while being a slave’ with ‘you’ rather than with ‘free’, because a specifi cation to that effect is not part of the elliptical expression.

This is not to say, however, that Schiaparelli is not on to something with her proposal to analyse these fallacies as involving an operator with wide and narrow scope. For with the clear criterion for what counts as a combined reading and what as a divided reading there is defi nitely something in her proposal worth preserving.9 This element is that whereas on a divided reading two strings of words make in-dependent contributions to the sentence as a whole, on a combined reading the same two strings of words contribute something together. That is, what needs to be brought out if we want to come up with an informative as well as uniform account of the fallacies of division and combination is that there is more than one way the same sentence (in

9 And because of which I was woken from my, perhaps not dogmatic, but certainly ignorant, slumber.




terms of a string of words in a certain order, not in terms of a statement with a certain grammatical structure and a certain meaning) may be hierarchically composed out of these words. However, while looking for different hierarchies of composition, we should abstract from the logical terminology of operators with scope and analyse the examples as hav-ing different hierarchical structures of grammatical composition.

These different hierarchical structures are most easily represented with the device of grammatical trees exhibiting their composition. The main idea of the analysis in terms of grammatical trees is that within one sentence there can be several levels of grouping words together, groupings which are then embedded the one in the other. If we regard the level of the sentence as a whole as the highest, then the lower the connection between (groups of) words is, the more closely these (groups of) words belong to each other within the context of the sentence as a whole. So if there are several possible grammatical trees for the same sentence, then there are several interpretations of the compositional structure of the sentence.

Now if we look at the examples Aristotle uses to introduce the falla-cies of combination and division, an analysis in terms of grammatical trees suggests itself immediately. For the difference between the two readings of (i) can be represented as follows:

This is exactly the distinction Schiaparelli wants to capture by em-ploying the terminology of operators with a scope. But unlike with her proposal, the analysis in terms of grammatical trees works equally well in order to bring out the difference between the two readings of (iii) . For that example can be represented by the following trees:




and:

where in the second analysis the function of is to combine the two trees into one sentence.

2.2 The remaining examples

Thus the benefi ts of the analysis in terms of grammatical trees rather than in terms of logical operators with scope are immediately clear. What I want to show next is that this approach is also heuristically very valuable: all of Aristotle’s examples can be made sense of by presup-posing that such an analysis in terms of trees of composition can be ap-plied — and some of the examples have hitherto proved to be resistant to any convincing analysis.10 However, primarily for reasons of space I shall hardly discuss previous attempts at reconstruction; I shall set forth my analyses in a rather dogmatic way, and confi ne myself to some comparative remarks in the footnotes. In giving the analyses, I shall not characterize the obtained readings as combined or divided, as that is-sue will be addressed in the next section.

The third example of a fallacy of combination (v) Aristotle formu-lates as follows:

10 Notably the examples which I have numbered (v), (xii) and (xiv) — see below. For the limited heuristic value of the approach of analysing these examples in terms of logical operators with scope, see Schiaparelli’s rather strained attempts (in her ‘Combination and Division’, 117-19) at fi nding anything like a logical operator in examples (v) and (xii).




And [v] learning now letters, since he was learning what he knows (). 11 (SE 4, 166a30-1)

This is a summary of an argument,12 in which it is fi rst admitted that someone ‘was learning the things he knows’ and then this concession is interpreted as being on a par with assigning to someone the apparently absurd predicate ‘learning now letters’ (which is absurd in the sense that it is false of this person because he already knows letters). For the statement can be analysed either as:

imperfectum

or as:

imperfectum

In the former case it is about someone who was learning things he now knows, while in the latter case it says that this person was in the process of learning things he already knows. If someone makes the concession that someone ‘was learning things he knows’ as interpreted in the lat-ter way, he could just as well concede that one may ascribe instances of the predicate ‘learning now things one knows’ to someone, for example

11 In maintaining the imperfect I follow the consensus of all manuscripts; the emendation into proposed by Ross is unnecessary. In writing the infi nitive I follow manuscripts A1, B and u as well as Boethius’ transla-tion and Michael of Ephesus’ commentary. It is the reading attested by the two best manuscripts A and B and by our oldest source, Boethius’ translation. It is also clearly the lectio diffi cilior.

12 For a justifi edly critical discussion of alternative interpretations, see Schiaparelli, ‘Combination and Division’, 115-17; there is some similarity between my interpre-tation and hers (119) in that she as well sees it as a summary of an argument.




the predicate ‘learning now letters’ — on the assumption that at least this person already knows letters and does not have to learn them any more.

Aristotle’s next example of a fallacy of combination (vi) is:

[vi] While being able to carry only one thing being able to carry many things (). (SE 4, 166a31-2)

Again this is the summary of an argument,13 namely one in which it is fi rst conceded that someone can only carry one thing and then that this person can carry many things. For the predicate is either to be analysed as:

or as:

This is Aristotle’s analysis of what we would call a quantifi er-shift. In-terpreted in the fi rst way, there is no inconsistency with the earlier con-cession that this person can only carry one thing (unless we would wish to propose a similar distinction between two readings for that statement as well), but if interpreted in the second way, it is in straight contradic-tion with it. Thus someone could be refuted in a sophistical way.

That this is the correct analysis is confi rmed by another example of the same quantifi er-shift, but which has not been identifi ed yet as a case of combination and division: example (vii). It appears in De Genera-tione et Corruptione I 2 and concerns the property ‘everywhere divisible’ ():

13 But not the argument envisaged by Schiaparelli, ‘Combination and Division’, 122-3.




This, then, is the argument which seems to necessitate that there are atomic magnitudes. Let us state, however, that it commits a hidden fallacy and [say] in what way it is hidden ( ). For since a point is not contiguous to a point, being divisible everywhere belongs in one sense to magnitudes, but in another sense not ().

It seems that, when that [scil. being divisible everywhere] has been posited, there is a point both anywhere and everywhere (), in the sense that it is necessary () that a magnitude is divided into nothing. For [it seems then that] there is a point everywhere, in the sense that it either consists of contacts or of points ().

However, there is a sense in which [being divisible] belongs every-where, because there is one point anywhere (), and all are like each (). ...

This is division or combination (). (316b34-17a12, omitting 317a9-12)

One of Aristotle’s goals in this passage is to explain that the argument for the existence of atoms as ascribed by him to Democritus is based on the confusion of two senses of the phrase ‘everywhere divisible’.14 For the absurdity of composing a magnitude from what would result if there were a division everywhere may be enough to infer that a mag-nitude does not have the property of possibly divided everywhere, but not enough to follow Democritus and claim that it is not everywhere, but only at some places, possibly divided. That is, Aristotle somehow wants to distinguish between the following two readings of ‘every-where divisible’:

(a) at every position on m, m is possibly divided

(b) m is possibly [divided at every position on m]

14 For a full discussion of the issues involved with this passage and of the mysterious phrases in it, see my ‘Aristotle’s Diagnosis of Atomism’, Apeiron 39 (2006) 121-156.




He does so by introducing, with the notion of ‘points’, possible divi-sions and by correlating them to the positions (which we would call points) on a magnitude. The basic correlation is that between a possible division and a position, which Aristotle describes in terms of there be-ing a point anywhere, which is common to both senses — we could represent this correlation with the property of there being a possible divi-sion at x, that is, being divisible at x. Now in order to describe sense (a) of ‘everywhere divisible’ Aristotle quantifi es over these possible divisions or over these correlations between possible divisions and positions: ‘all [points or possible divisions] are like each’ in that they belong to a posi-tion. So we get:

all possibility of division position

On the other hand, in order to describe sense (b) of ‘everywhere divis-ible’ Aristotle does not quantify over these possible divisions or over these correlations, but only over the positions: not only is there a point or possible division anywhere, but there is also a point everywhere. So we get:

possibility of division all position

Applying this distinction to itself we get either:

-

or:

-




This distinction between two interpretations of ‘everywhere divisible’ Aristotle has thus every right to describe in terms of ‘a hidden fallacy’ and of ‘division or combination’15 — it follows exactly the same pattern as I have ascribed to the similar example from Sophistical Refutations 4. With the fi rst analysis in mind, we conceive of the possibility that a magnitude is divided everywhere and thus of the possibility that it merely consists of points. Such a conception does not result from the second analysis.

After these examples of fallacies depending on combination, Aristot-le introduces the fallacy depending on division by way of the examples mentioned in the introduction and analysed above. Then he continues his discussion with what seems a general remark about there being di-vided and combined readings of the same sentence:

For the same sentence divided and combined would not always seem to signify the same, such as: [viii] ‘I made you free while being a slave’ () and [ix] ‘Fifty to a hundred men the divine Achilles left behind’16 (). (SE 4, 166a35-8)

As this seems a general remark, it is not clear under which fallacy each of these two examples (viii and ix) should be classifi ed — probably they are not even meant as examples of fallacies, but merely of sentences which can be read in two ways.17 But again they may be analysed with the help of trees. The fi rst example (viii) can be interpreted either as:

15 In ‘Aristotle’s Diagnosis’, 141, I offered a different interpretation of the sentence: , but the one given here seems much more plau-sible. It should be noted, though, that the reinterpretation of this one sentence does not affect anything else I have said there.

16 This translation is not literally correct, but is meant to capture the ambiguous structure of the Greek example.

17 Cf. Schiaparelli, ‘Combination and Division’, 125-8.




or18 as:

On the fi rst analysis this statement turns out to be the absurd claim that I have made you free while at the same time being a slave, while on the second analysis it merely says that I have made you, while being a slave, free. (That there are here in fact two trees is meant to signify that the state indicated by has nothing to do with, or is at least relatively independent from, the act referred to with , but is merely tagged on to .)

The second example of this passage (ix) allows both for the follow-ing tree:

and for:

<>

18 Alternatively, we could group together with , so that we get a fi rst tree with [ [ ]] and a second composition with [] tagged on to and only functioning as predicative with . For present purposes the two alternative pairs of analyses are equivalent. The rea-son why I have adopted this pair is that it is closer to the allusion to this sentence, presumably taken from a comedy-play, in Terentius, Andria, 37: ‘feci ex servo ut esses libertus mihi’.




where the fi rst disappears with the combination of <> with , just as <> might also be said to disappear on the second reading of (iii) if it is to be constructed as: < > . (Again, the fact that there are two trees here is meant to signify that has nothing to do with or is at least relatively independent from the act referred to with , but is merely tagged on to in order to indicate the group out of which these fi fty are taken.) On the latter analysis the divine Achilles left behind fi fty <men> of the hun-dred men, while on the former analysis the divine Achilles left behind fi fty and a hundred men.19

Aristotle resumes the discussion of fallacies depending on division and combination in Chapter 20 of the Sophistical Refutations. There his fi rst two examples are the ones already mentioned in the introduction: (x) ‘Was he being hit with that with which you saw him being hit?’ () and: (xi) ‘Did you see him being hit with that with which he was being hit?’ (;). It is the part with or which lends itself to being analysed in two different ways, either as:

/

or as:

/

19 As Schiaparelli, ‘Combination and Division’, 126, note 32, remarks correct-ly, because of its hexametric form one need not expect the example to ad-here to the normal rule that in composed numerals the smaller unit (here: ) may only precede the larger (here: ) if linked by way of It is also possible to have a tree of the second type with and <> switching rôles: {} [ <>] : ‘Of fi fty men the divine Achilles left a hundred behind’ (see e.g. Schiaparelli, ‘Combination and Division’, 126), but as this tree does not differ in structure from the one given, and yields a completely absurd and therefore unin-teresting reading, it does not seem likely that Aristotle had this one in mind.




On the fi rst analysis, this part of the sentence refers to that with which he was being hit, as you saw it, while on the second analysis it is about that with which you saw it happening. Thus on the fi rst analysis one would be asking the trivial question whether that with which he was being hit, as you saw it, was indeed the same thing as that with which he was being hit. On the second analysis, on the other hand, the ques-tion would be whether that with which you saw that happening was the same thing as that with which he was being hit — a question which can only be answered with an emphatic ‘no’.

The next example (xii) Aristotle gives of this kind of fallacy is notori-ously short:

And there is Euthydemus’ argument: [xii] ‘Do you know now be-ing in Sicily the triremes being in Peiraeus?’ ( .) (SE 20, 177b12-13)

In principle there are three elements one may move around in a possible tree which for the rest consists of and its object : and , for all three could in principle both belong and not belong to what is known ( may take both a noun-phrase or a participle-phrase for its object and could latch on to either kind of phrase). However, that alone would be the element to have different places in a tree seems unlikely, as Aristotle gives such an example only a little later, at 177b20-22. That could belong to different branches in a tree seems again unlikely, as it would involve positing a grammatically strained participle-phrase (with or without it seems equally strange) in at least one tree. Therefore it is preferable to interpret the example in such a way that may appear in two different roles. Aristotle’s example seems most effective if it is analysed20 either as:

or as:

20 In the following trees I have, for the sake of brevity and simplicity, left out the phrase , which should be understood as tagged on to .




(in which latter case we have again two trees, one for the main state-ment and another for a statement tagged on). Thus according to the fi rst analysis you, rather problematically, know that some triremes are now in Peiraeus, even though you are in Sicily, while on the second analysis you know, while you are in Sicily, of some triremes, which, as a matter of fact, without you knowing so, are now in Peiraeus.

That this is the right interpretation of the point of the example is con-fi rmed by Aristotle’s other reference to the argument of Euthydemus, which we fi nd in the Rhetoric:

Another [way of giving an apparent enthymeme] is talking about something divided while combining it or about something combined while dividing it. For since often it seems to be the same without be-ing the same, one should do that, whichever of the two ways is more useful. This is the argument of Euthydemus, such as knowing that there is a trireme in Peiraeus — for one knows each ( <> ). (II 24, 1401a24-8)

Just as in my proposed analysis, the focus is completely on knowing a trireme (or triremes) to be in Peiraeus.

One may object, however, that it is diffi cult to use the reference to the argument of Euthydemus in the Rhetoric as evidence regarding the interpretation of the reference in the Sophistical Refutations.21 Tradition-ally the example in the Rhetoric has been interpreted very differently, because of Aristotle’s explanatory remark: . In the context this remark suggests that one knows that a trireme is in Pei-raeus because one knows each element. Thus one would know the tri-reme in Peiraeus because, say, one knows the trireme and one knows

21 Cf. Dorion, Les réfutations, 344, who despairs of getting anything even relatively secure from the passage in the Rhetoric.




Peiraeus.22 However, that is not the only possible way of reading this remark; it could also be a theoretical remark about grammar, to the ef-fect that verbs of knowing may also be complemented with a noun-phrase: ‘For one knows of x’.23 And one may know of something under different descriptions: one may know a trireme merely as that trireme (because one has seen it once, for example, or even because one has heard about it), but also as it is now, namely as a trireme which is in Peiraeus. It is this construction which is abused by Euthydemus in his argument, by phrasing the question in such a way that it is ambiguous under what description you know some triremes, whether just like that or as triremes which are now in Peiraeus.

The next example (xiii) is very simple:

And again: [xiii] ‘Is it possible to be a miserable cobbler who is good?’ ( ;) But [then] there could be some miserable cobbler who is good ( ). Hence there will be a good miserable cobbler. (SE 20, 177b13-15)

The initial question (and also the fi rst affi rmative statement) could be read either as:

<>

or as:

<>

22 See e.g. C. Rapp, Aristoteles: Rhetorik II (Darmstadt 2002), 782; cf. Schreiber, False Reasoning, 71-2, Fait, Le confutazione, 186, and the translation in CWA, 2233.

23 This use of for, as we would call it, a free variable without any generalis-ing import can be seen as an extension of the use of with widest possible scope.




The second reading then licences the fi nal conclusion through a fallacy dependent on accident.

The next example (xiv), however, is far more obscure, and even in-volves textual issues. The text as read by all the authoritative manu-scripts is as follows:

[xiv] 24 25 . (SE 20, 177b16-20)

Commentators, not being able to fi nd anything remotely similar to com-bination or division in the rest, have only paid attention to the inference from ‘what is bad is both bad and a thing learned’ to ‘what is bad is a thing learned which is bad’,26 even though they are quite aware that it is in fact a fallacy dependent on accident. There may be a problem here, but even if there is, it seems quite unlikely that that inference consti-tutes the core of the example. For if it were, Aristotle’s presentation of examples in this chapter would be inconsistent, for they are all adduced in the form of questions27 in reply to which the answerer must draw a distinction ( at 177b10).28 Moreover,

24 With the exception of c1 and u, which merely have , all manuscripts (A, B, D, V and also c2) as well as Boethius’ translation and Michael of Ephesus’ commen-tary have . Ross, however, following Poste, reads . The thought behind this emendation is that otherwise the initial ques-tion does not seem to play any real part in the argument, but that is only correct if one assumes that the question is syntactically unambiguous — which is not the case, as we shall see below.

25 Ross reads, with Michael of Ephesus, after , but none of the manu-scripts have it, and it is not necessary at all, since Aristotle could just as well be talking about a science of bad things. I suspect that Ross’ insertion of derives from his adoption of Poste’s emendation at 177b17 (see the previous note).

26 Dorion, Les réfutations, 345-6; Schreiber, False Reasoning, 66-7; Fait, Le confutazio-ni, 187.

27 The fi rst question concerned is referred to in 177b10-12 (and is stated in 177b36-8), the others are mentioned at 177b12-13, b13-15, b20-2, b22-6.

28 This phrase should not be translated as: ‘The answerer must bring about a divi-sion’ in the sense of giving a divided reading, as it seems to be almost universally rendered (e.g. Dorion, Les réfutations 172, CWA, 302, and Forster, Sophistical Refu-




why would Aristotle, this most succinct of philosophers, go through a whole stretch of dialectical argumentation if only a fragment would il-lustrate the fallacy he is concerned with?

If one looks carefully, however, one can fi nd an ambiguity of a syn-tactical nature in the question. It concerns the hidden antecedent of : that may be either or . In the fi rst case we get the analy-sis:

<>

whereas in the second case29 we get:

<>

Conceding this syntactically ambiguous question thus allows the so-phistical interlocutor to use both constructions, the one in which goes with an genitive of object, and the other in which a

tations, 105; see, however, Fait, Le confutazione, 63). In addition to the fact that then Aristotle is advising something else than what he himself does in the subse-quent examples, it is then not possible either to make sense of Aristotle’s reason for this advice: (177b10-12). By adding quotation marks, Ross tries to get two versions out of the identical phrases , in or-der that one may translate: ‘for ... is not the same as ...’ (cf. Dorion, Les réfutations, 172-3). However, this interpretation would leave one wondering what the function of were — indeed, Ross suggests that it should perhaps be omitted. This problem is avoided by understanding Aristotle as saying that , that is, saying is not [something which is one and] the same [thing].’ (Thus I take to be used in an only implicitly comparative way — one should supply ‘understood with combination or division’ to indicate the domain of comparison.) Thus interpreted, the reason can only be a reason for the advice that ‘the answerer must draw a distinction’ between two different readings — a pertinent meaning of the verb in the Sophistical Refutations (e.g., 18, 176b36 and 177a4-5).

29 For the construction, see W.W. Goodwin, A Greek Grammar (London 1879), § 919.




is identifi ed with something, and to switch between them. And that is precisely what we see in the remainder of the passage quoted. The switch occurs in the inference from the statement that ‘of what is bad something learned is benefi cial’ (), to the statement that ‘what is bad is a thing learned which is benefi cial’ ( ). I take it that Aristotle holds both this former statement and the fi rst analysis of the initial concession to be unproblematically true, but is aware of the smell of paradox in-volved in the second statement: how can what is bad be benefi cial, even if only as a thing learned?30

It is this danger the sophistical interlocutor, being allowed to talk about in the second way as well, is going to exploit by stat-ing that: ‘However, what is bad is also bad and a thing learned — hence what is bad is a thing learned which is bad.’ This follows the pattern of a fallacy depending on accident, as ‘what is bad’ does not signify what is bad in itself, but something which has being bad as an accident, to which the further accident of being a also belongs. However, that this is a fallacious inference should not blind us for the fact that in this context Aristotle is more concerned with the point that with the construction of as identifi ed with something there is room for the fallacy; the conclusion arrived at is not solely due to the fi nal falla-cious inference.31

30 One might be tempted, as I initially was, to posit a switch in meaning of the term , from ‘what is learned’ (or ‘study’) to ‘the object of what is learned’ (or ‘object of study’), but then it would be hard to understand what Aristotle thought possibly problematic about the second statement and about the second analysis of the initial concession. Moreover, in Greek is what is learned, and that comprises, just as in the case of ‘what is known’ and ‘what is said’, both the things or facts one acquires knowledge of and the content of the knowledge one acquires about these things or facts. I suppose that if Aristotle did feel a difference in mean-ing, he would locate it precisely where he seems to locate it here, in the difference between as identifi able with something, and with a genitive of object: where with genitive can only be interpreted as the content learned about things, as identifi ed with things can be ambiguous.

31 It is in order to play down the emphasis on the fallacious inference that I have translated the fi nal conclusion as: ‘Hence what is bad is a thing learned which is bad’, rather than more straightforwardly as: ‘Hence what is bad is a bad thing learned.’ One may even be tempted to deny that this inference is fallacious, by in-sisting that what is bad is a bad thing to learn as an art (‘the art of evil’ is obviously evil itself), but this interpretation would involve a shift in meaning in from




This is confi rmed by the fact that it is apparently necessary to have a second application of the concession formulated with the syntactically ambiguous sentence, this time only as analysed in the second way. For Aristotle’s remark: ‘But the science of things which are bad is benefi -cial’ is only relevant and suggesting a contradiction with the statement that what is bad is a thing learned which is bad, if from that remark one can infer that things which are bad, are things learned which are benefi cial. It is precisely this inference which is licensed by the conces-sion, which on the second reading says: ‘The things whose sciences are benefi cial, are things learned which are benefi cial.’ Thus in this passage the syntactically ambiguous sentence is both used to facilitate the some further inference the sophistical arguer wishes to make, by allowing for a switch from one type of vocabulary to another, and to point out that this inference is inconsistent with a generally accepted proposition, by applying one of its readings.

Aristotle continues his list of problematic questions with an easy ex-ample (xv):

[xv] ‘Is it correct to say now that you have been born?’ ( ) Therefore you have been born now (). Or does it signify something else when a distinc-tion has been brought about ()?32 For it is now correct to say that you have been born, but not that you have been born now (). (SE 20, 177b20-2)

As in so many constructions in Greek with indirect speech introduced with , part of what is said may appear before . Often it is the sub-ject of the reported statement, but here it concerns the temporal adverb . Thus we get the two analyses:

something learned in an intellectual way to something learned as an art to be prac-ticed.

32 My choice for this translation is based on the considerations that at 177b10 should be translated similarly (see note 28) and that what Aristotle does in the next sentence is only draw a distinction between two different readings of the same sentence (just as he does so in a completely parallel way at 177b25-6). Though I do prefer this translation, it is not mandatory; one could also render the question as: ‘Or does it signify something else when a division has been brought about?’




Finally Aristotle concludes his discussion with a generalised ver-sion (xvi) of the two fallacies depending on combination (i and ii) with which he introduced them in chapter 4 of the Sophistical Refutations:

[xvi] May you do the things which you can [do] in the way in which you can [do them]? () But while not playing the guitar you have the ability of playing the guitar. Therefore you may play the guitar while not play-ing the guitar. Or: he does not have the ability of that: of playing the guitar while not playing the guitar, but when he is not doing it [the ability] of playing the guitar.(SE 20, 177b22-6)

The crucial relative clause in the initial question one may either analyse as:

<> <>

or as:

<> <>33

33 For the crucial addition of , compare SE 20, 177b27-8: ... ..., and b29: ... ...




The syntactical ambiguity of this general rule is then used to licence the inference from the statement that while you are not playing the gui-tar you have the ability to play the guitar to the statement that you therefore may play the guitar while not playing it. If one compares Ar-istotle’s discussion here to the examples with which he introduced the fallacy of composition there is in fact nothing new here.

3 Aristotle’s theoretical account of the fallacies of division and combination

Now that all examples Aristotle gives have been discussed and shown to be susceptible to an analysis by way of trees of grammatical compo-sition, we are in a position to take up the theoretical issues concerning the fallacies of division and combination. First I shall formulate the cri-teria Aristotle apparently presupposes for calling a reading combined or divided and for classifying a fallacy as dependent on combination or division; thus the fi rst two counts of incompleteness will be taken care of. Then I shall address Aristotle’s inconsistency in saying that combination and division involve one or two separate statements, as well as the related charge of incompleteness, that he has not given us a reason to consider the divided and combined readings as two sepa-rate statements rather than as one ambiguous statement, as is the case with amphiboly. Finally I shall try to absolve Aristotle from the two re-maining accusations of inconsistency, by showing that despite the fact that combination and division, just as the fallacy of accent, involve the same kind of doubleness, there are nevertheless grounds for counting two fallacies of combination and division, without these considerations likewise leading to two fallacies of accent.

3.1 Combined and divided readings

As already stated at the introduction of the analysis in terms of gram-matical trees as the framework in which to understand these fallacies, the fi rst benefi t to be reaped from this way of analysing them is that it should yield a criterion as to what will count as a combined and what as a divided reading. For the idea suggested by Schiaparelli’s analysis in terms of operators and their scope which I strove to retain by apply-ing grammatical trees was that:




In case of there being a string of words consisting of parts X and Y, there is a combined reading of a sentence S featuring X and Y if X and Y together fulfi l a single grammatical function within S as a whole, and a divided reading of S if X and Y fulfi l different grammatical functions within S.

With this rule in hand it will in most cases be intuitively clear which reading is combined and which divided. For example, in (i) it is natural, as I suggested, to assume that the second tree [] represents the combined reading, with to-gether fulfi lling the grammatical function of the complement required by ; whereas the fi rst tree [} {]34 exhibits the divided reading, as stills functions as the comple-ment of , but now has a different rôle.

Nevertheless, however intuitively clear this may be, the rule as for-mulated above still does not fully capture the idea. For what are we go-ing to say about cases in which there is string of words X which in the one tree is grouped with Y and in the other tree with Z? There are three such cases among our examples: (x) and (xi) as well as (xv). In (x) and (xi) and are either grouped with or with , in both cases fulfi lling the rôle of indicating an instrument with which one sees or is beaten. In (xv) is either a temporal adverb belonging to or going with . What we need is a criterion in order to privilege one of these groupings over the other.

Once we recognize this problem, we also see that it can be gener-alised to all examples. For even in the supposedly obvious example (i), we could entertain the possibility that it is not [ ] which is the combined reading, but rather [ } {]. Certainly the fact that in this example X and Y are connected in the sense of being adjacent and forming one uninter-rupted stretch of words, is not suffi cient for calling the reading which groups X and Y more intimately together, rather than X and Z, the com-bined reading. For if connectedness in this sense were the criterion, ex-ample (i) should be treated differently from example (xvi) , whereas the latter is

34 In this representation of the compositional structure, the words between squared brackets [...] belong together as a group on a relatively low level in the grammati-cal tree; I use ‘}’ and ‘{’ to indicate that such a group is interrupted within the sentence.




clearly meant to be a generalisation of the former. Without the criterion of connectedness, however, it seems conceivable that and together make up the string of words which on one reading are to be combined and on another divided.

A more successful way of deciding the issue would be to introduce the concept of what I call a grammatical determinator — this is my, more fl exible, substitute for Schiaparelli’s logical operator. A gram-matical determinator is a word or string of words which requires cer-tain complements which it can be said to govern. In (i), for example, requires an infi nitive clause as a complement to specify the contents of the ability — the same applies to examples (ii), (vi), (vii) and (xvi). In examples (iii), (iv) and (xiii) it is the copulative , requiring a predicate as its complement, which functions as a grammatical deter-minator. In (x), (xi), (xii) and (xv) we have with , and verbs which require to be complemented with verbal phrases in the form of an accusative with infi nitive or participle, or of a subordinate sentence introduced with , in order to describe the content of what is seen, known or said. But also verbs requiring just an object, as in (ix), or verbs with an object and a predicate, such as in (viii), can be grammatical determinators, and even the morphology indicative of the imperfect tense, as in (v), or of capacity, as in (vii). The only example in which it may be diffi cult to fi nd such a grammatical determinator would be (xiv), as the difference between the two readings seems so great: in the fi rst tree is the subject of which is predicated, while in the second tree is the subject with as a predicate, to which belongs in a predicative position.35 However, in both readings there is a close predicative connection between and ; therefore I propose to take as the grammatical determinator, requiring a complement to be true of.

With the help of this concept of a grammatical determinator we can formulate our rule adequately:

In case of there being a string of words (not necessarily con-nected) consisting of parts X and Y, there is a combined reading of a sentence S featuring X and Y if X and Y together constitute a single group within S as a whole, as governed by a single

35 Again, see Goodwin, Greek Grammar, § 919.




grammatical determinator, and a divided reading of S if X and Y form within S different groups with regard to the single grammatical determinator.

Thus in (x) and (xi) the combined reading is [/} {] and / [ ] the divided reading. Similarly in (xv) belongs to on the combined reading and to on the divided reading. Finally, in (xiv) [} {] is the combined reading, as there is one phrase serving as a subject to the predicate , while with the divided reading [ ] it is only of which says something.36

3.2 Fallacies dependent on combination and fallacies dependent on division

Thus having a clear criterion why the one reading is called divided and the other combined, we seem to be in an excellent position to explain why Aristotle calls some fallacies dependent on combination and oth-ers dependent on division: as already hinted at in the introduction, a fallacious argument is dependent on combination or on division if the conclusion is based on the combined or on the divided reading of a cer-tain sentence, while it is the opposite, divided or combined, reading of that sentence which the answerer has in mind when accepting it. This is indeed the pattern for most of the examples. In (i) it is the divided reading [} {] which makes the sentence featuring that clause acceptable, but the questioner fallaciously uses the combined reading to derive the unacceptable conclusion that one may be walking while sitting. In (iii), on the other hand, it is the combined reading [] which is acceptable, but the absurd conclusion that fi ve is odd and even is derived through the divided reading [ ] [<> ].

There are, however, counter-examples to and a diffi cult case for this explanation. The counter-examples are (x) and (xi), which Aristotle calls

36 It is interesting to note that it is possible to construct examples with multiple gram-matical determinators, so that a certain reading may be both combined (relative to one grammatical determinator) and divided (relative to another): ‘On what ground do you think he assumes that the decision is taken?’




dependent on combination,37 even though the questions can only be an-swered affi rmatively because of their combined reading and can only be used to derive unacceptable conclusions if they are understood in a divided sense. The diffi cult case is (xiv), for there the sentence which lends itself to two readings may be accepted because of only one of its readings, but it is not the case that it is subsequently not used on only one of them to derive a further, unwished for conclusion; rather it serves as a kind of derivational principle which allows for jumping from the one grammatical construction ( with a genitive of ob-ject) to the other ( identifi ed with an object).

There are three remarks to be made about the two apparent coun-ter-examples. The fi rst is that if (x) is dependent on combination, also (xvi) should be dependent on combination, for it has exactly the same structure: both consist of a relative clause (starting with and re-spectively) which has a divided as well as a combined reading and a main clause which, by leaving out the grammatical determinator, un-ambiguously combines the two parts which can be either divided or combined in the relative clause. Now in the case of (xvi) we have the following argument:

(a) You may do the things which you can do in the way in which you can do them.

(b) While not playing the guitar you have the ability of playing the guitar.

(c) Therefore, while not playing the guitar you can play the guitar.

(d) By (a) and (c), you may, while not playing the guitar, play the guitar.

The easiest way to describe the use of (a) is to take (c) to be a reformu-lation of (b) to make (a), including its possibility of being read in two ways, applicable for use in modus ponens. In a quasi-formal way (with ‘gd’ standing for the grammatical determinator) the argument can be represented as follows:

(a*) XY (if gd [XY] / X[gdY], then XY)

37 See SE 20, 177b1, quoted above in section 1.




(c*) Gd[X1Y1] / X1[gdY1]

(d*) Therefore X1Y1

And the initial concession in (x) is put to the same kind of use as (a) in (xvi), in order to arrive at a conclusion featuring a problematic combina-tion (X1Y1). Aristotle hints at the use (x) is put only a few lines further:

, that is, saying is not [something which is one and] the same [thing]. (SE 20, 177b10-12)38

That you saw with eyes him being hit is only acceptable on a divided reading, but leads through (x) immediately to the conclusion that he was being hit with eyes.

The second remark is that, though Aristotle does not say when dis-cussing (xvi) whether it constitutes a fallacy dependent on division or combination, we know from (i) and (ii), which tacitly presuppose a gen-eral scheme as formulated in (xvi), that he considers this use a fallacy of combination. The reason is that (c) is crucially readible in two ways and, as Aristotle assumes when discussing (i) and (ii), is acceptable on the divided reading alone, but is subsequently abused in its com-bined reading. Therefore it is not surprising that he also states that (x) is dependent on combination, for it is used to argue from a proposition which is accepted because of its divided reading, to a conclusion which is based on its combined reading.

The third remark is, however, that we shall have to admit that exam-ple (xi) cannot be called dependent on combination, precisely because it is the converse of (x) and can only be put to use for converse purposes, like arguing from the proposition that he was being hit with a stone to the conclusion that you saw it with a stone. Such an argument depends on the divided reading of , and should therefore be called dependent on division. Having said that, though, it seems to me perfectly possible that Aristotle only had (x) in mind when saying that we have here an argument dependent on combination.

The diffi cult case (xiv) can also be made sense of by describing simi-larly in a quasi-formal way the use to which its initial concession, read-able in two ways, is put. As said in section 2.2, the concession

38 For the translation, see note 28.




is fi rst used to jump from propositions which exhibit a combined pattern ( with a geni-tive of object) to propositions with a divided pattern ( identifi ed with an object), and then solely on its divided reading (<> []) applied to a particular case of something the science of which is benefi cial. The initial conces-sion can be represented as follows:

X (gd [XY] / X[gdY]),

from which, on the basis of the fallacious idea that if one concedes this sentence, then if one accepts it on one reading, one should also accept it on the other, and vice versa, an inference-rule is derived:

X (gd [XY] if and only if X[gdY]),

that is:

For all things of which the branches of science are benefi cial, if of them are benefi cial, then they are which are benefi cial, and vice versa.

This then is applied to infer for an instance of X, namely ‘what is bad’, that, since of it something learned is benefi cial, it is a thing learned which is benefi cial:

Gd [X1Y] X1[gdY]

As stated above, the second application of the initial concession is confi ned to its divided reading:

X X[gdY].

For it is used to infer for an instance of X, again for ‘what is bad’, that it cannot be true that what is bad is a thing learned which is bad (and thus not benefi cial):

X1[gdY] not: X1[not-gdY]

Now do these two applications of the syntactically ambiguous initial concession fallacies of division or of combination? For the second ap-plication the answer is easy: as we have seen, Aristotle holds that the initial concession is only unproblematical on its combined reading, but




on the second application only its divided reading is used, in order to show, somewhat more problematically, that one cannot hold that what is bad is a thing learned which is bad. That should thus constitute a fal-lacy of division.

For the fi rst application we cannot answer that question in a way analogous to examples (x) and (xvi), for these concerned fallacies of combination because the concessions (c*) to which the syntactically ambiguous inference-rules were applied, allowed themselves for a divided and a combined reading, and were admitted in their divided reading, while being abused in their combined reading — there is not such a syntactically ambiguous sentence here. We cannot say either that the initial concession is admitted on one reading, namely the combined one, and then abused on the other reading, for what is abused is not the divided reading, but rather the fact that the two readings can be confused: if confusion is apparently allowed, then we may also jump from the one reading to the other. Still, as the initial concession is only unproblematic on the combined reading ( with genitive of ob-ject), and are suspicious on the divided reading, just as non-quantifi ed statements featuring as identifi ed with something (e.g. ‘what is bad is a thing learned which is benefi cial’), we may say that the initial concession is abused because it can crucially be read in a divided way too. Therefore the fi rst application of the initial concession concerns a fallacy of division as well.

3.3 One or two statements?

As said in the introduction, it is Aristotle’s offi cial doctrine that the fal-lacies of combination and division involve two different statements (constituted by two different readings of a single sentence as a string of words, neither of which is ambiguous), rather than a single statement with two different meanings. At the same time, however, Aristotle seems to be vacillating between holding that a sentence which allows for a di-vided and a combined reading does not express one , and talking about these readings as two uses of one and the same . Should we take this variation seriously? Some commentators have taken it very seriously indeed, suspecting it betrays uncertainty on Aristotle’s part as to what counts as a single .39 Assuming that the only reason why

39 C. Atherton, The Stoics on Ambiguity (Cambridge 1993), 205-6




with combination and division there are two statements rather than one ambiguous one, is that the difference between the two readings always shows up in pronunciation, others have seen this variation as an indica-tion that the syntactical fallacies of combination and division are in fact merely superfi cially different from the syntactical fallacy which does depend on there being one statement with two different meanings, am-phiboly.40 In reply I want to argue in this sub-section that there are other indications that at least for Aristotle the point that combination and di-vision involve two separate statements expressed with one sentence is one of importance, that the assumption that the difference between the combined and divided readings always shows up in pronunciation is mistaken, and that we may ascribe to Aristotle a more relevant account as to what counts as a single in the sense of a single statement. Aristotle may be loose in using both for the sentence allowing two readings and for the statement constituting one of these two readings, but that does not mean that the underlying account is inconsistent or unclear.

One sentence, two statements. A fi rst small indication that in the case of combination and division Aristotle distinguishes between the two statements and the one sentence expressing them appears, if my trans-lation is correct, in the following remark, quoted before:

, that is, saying , is not [something which is one and] the same [thing]. (SE 20, 177b10-12)41

This emphasis that it is the sentence as formulated which is not one and the same thing (in the combined and divided readings) only makes sense if we assume that Aristotle distinguishes between a sentence and the two statements expressed by it.

A slightly more signifi cant indication can be found in the following claims:

[The deception] of [fallacies] dependent on combination and division comes about because of thinking that a combined or divided does not differ at all, as in most cases. (SE 7, 169a25-7)

40 Dorion, Les réfutations, 82; cf. Schreiber, False Reasoning, 57-8.

41 Again see note 28 for a defence of this translation.




[T]he same divided and combined would not always seem to signify the same. (SE 4, 166a35-6)

The additions of ‘as in most cases’ and ‘not always’ imply that there are cases in which the combined reading and the divided reading do not differ at all in meaning. The same conclusion can be drawn from the conditional remark:

If a divided and combined signifi es something different, ... (SE 20, 177a34-5)

The one Aristotle is referring to in these passages, therefore, can-not be one statement with two different meanings, as with amphiboly, but must be the sentence which can be construed in two different ways so as to produce two different statements which may or may not have the same meaning.

A third and fi nal consideration can be found in an argument Aristo-tle gives us as to why some argument does not constitute a fallacy of amphiboly but one of combination:

It [i.e., example (x)] has, then, also something belonging to am-phibolous questions, though it is dependent on combination. For what is dependent on division is not double ( ). For not the same statement comes into being when it is divided (), as it is not the case that as well as , as pronounced with the accent, signify something else ().42 Rather, in the case of writing there is the

42 There are textual issues here. I omit the accents and breathings on , as Aris-totle himself did not read them. The rest of the text I have adopted it is as read by manuscript V, with the exception of and interchanged. It is also the text trans-lated, of course without articles and with other examples, by Boethius: ‘si quidem non et malum et malum secundum accentum prolata signifi cant aliud.’ With the exception of the plural it is also read by manuscripts D and c. On the oth-er hand, all the other manuscripts have the singular and, moreover, A and B as well as Michael of Ephesus leave out . If we were to follow those readings, we would get: , which would make the very same point as the text adopted: ‘since it is not the case that also , that is, pronounced with the accent, signifi es something else.’ It thus does not matter a great deal which text we adopt, though in defence of my




same word (),43 if it is written consisting of the same letters and in the same way () — though also there they al-ready avail themselves of additional signs ( ) — , while when pronounced they are not the same ( ). Hence what is dependent on division is not double. (SE 20, 177a38-b7)

This argument runs as follows: a particular fallacious argument is not dependent on amphiboly but on combination, because, on a universal level, what depends on division is not ambiguous, as what depends on accent is not ambiguous either. It consists of two steps, the fi rst imply-ing that it is because what depends on division is not ambiguous that some particular argument is not a case of amphiboly but rather one of combination, the second arguing that what depends on division is not ambiguous because what depends on accent is not ambiguous either. This second step we shall return to below — here I confi ne myself to the fi rst step. Now there are three points which are puzzling about the fi rst step. One is that Aristotle argues from what is the case with division to the classifi cation of an example as one of combination — why not say something about combination from which it follows that this is a case of it? A second puzzling point is that Aristotle argues immediately, with-out any apparent application of a criterion, from what is the case with division in general to the classifi cation of one particular example as one of combination — as if that would be relevant. And thirdly, the step as a whole has the same structure as the following argument: some particu-lar argument is not a case of amphiboly, but rather one depending on one sense of an amphibolous statement, because an amphibolous state-ment as understood in the other sense is not ambiguous — clearly that is nonsense, so what is it about Aristotle’s argument here that could make it meaningful?

reading I want to point out that Boethius’ translation is actually our oldest author-ity and represents a tradition which apparently survives in the old Byzanthine manuscript tradition (V is from the tenth century). I cannot exclude the possibility, however, of Boethius’ translation and V featuring convergent modifi cations of the alternative text. What is anyway clear is that we do not have reason to follow Ross in emending to <> “” [] “” .

43 I leave out the which Ross inserts before ; it is completely unnecessary.




In order to understand Aristotle’s argument we need to take into ac-count the context in which Aristotle presents it. This concerns the solu-tion of fallacious arguments depending on combination and division:

It is clear as well how one should solve [fallacies] depending on divi-sion and combination. For if a sentence divided and combined sig-nifi es something different, one should, once the conclusion is being drawn, state the contrary (). (SE 20, 177a33-5)

Aristotle makes the same point in a passage already quoted before:

In general in the case of arguments dependent on the formulation the solution will always be according to the opposite of that on which the argument is dependent.

For example, if the argument is dependent on combination, there is a solution for someone who has divided it, while if the argument is dependent on division, there is one for someone who has combined it. (SE 23, 179a11-14)

This explains why considerations about what depends on division is relevant for characterizing the fallacy as one of combination: apparently assuming that a divided reading is the solution for this particular argu-ment, Aristotle may thus conclude that the argument is one depend-ing on combination. However, in order for this conclusion to follow, he needs to secure on a general level that a divided reading is itself not ambiguous, at least not in so far it is divided, for if that were the case, it could not be a solution to an argument depending on combination — there would then not be an argument depending on combination, but rather one depending on amphiboly. For since an amphiboly concerns one ambiguous statement with two meanings, there is in case of an am-phibolous argument no such thing as giving the contrary statement as a solution; rather, we should give a specifi cation of at least one of the two meanings involved. This is also what Aristotle says elsewhere concern-ing amphiboly (as well as homonymy):

At the beginning [of the discussion, when one has to choose a thesis] one should answer to what is twofold, both in word and in statement, thus: that there is a sense in which it is so, and a sense in which it is not so, such as to ‘speaking of silence’ () that there is a sense




in which it is so and a sense in which it is not so. ... While if it goes unnoticed, one should make a correction at the end by providing an addition to the questioning: ‘Is speaking of silence possible?’ ( )44 ‘No, but for this man speaking of silence is.’ ( ) And with those [discussions] having what is manifold among the propositions [asked] similarly: ‘Do people there-fore not understand what they know?’ ‘Yes, but not those who know in this sense.’ (SE 19, 177a20-8, with one short omission)45

With this picture in mind even the third puzzling point ceases to be troublesome: it is precisely because it is possible to solve a fallacy de-pending on combination or division by giving its contrary, while it is not with amphiboly, that one cannot run the same argument for falla-cies dependent on amphiboly. Thus the difference between amphiboly

44 The translation is meant to be ambiguous between speaking by silence and speak-ing of silence as a subject. Unfortunately the element of amphiboly is thus lost (the example is Aristotle’s standard case of amphiboly, as may both be construed as the subject of and as its object).

45 I think Aristotle makes the same point in the following passage:

If, however, the argument is dependent on homonymy, it is possible to solve it after one has admitted to the opposite word ( ), for example if it follows that one states [that something is] en-souled (), by indicating, after one has denied that it is, in what sense it is () ensouled (); while if one has claimed that it is soulless, while the other has deduced [it to be] ensouled, by saying in what sense it is soulless. Similarly also in the case of amphiboly. (SE 23, 179a15-20)

This is the text as given by all the manuscripts for the fi rst occurrence of (though Ross, following Poste, emends to ) and by A, B, V and u as well as Michael of Ephesus for the second occurrence of (against , which is read by D and V2 as well as Boethius’ translation). (Ross also brackets , but I have no idea why.) Normally Aristotle is thought to discuss two separate argu-ments, that is, arguments with different conclusions (see e.g. Dorion, Les réfuta-tions 365-6); it is to ensure that the conclusions differ that Ross follows Poste in his emendation. However, we can do without such an emendation if we assume that Aristotle is not thinking of two separate arguments, but rather of two different responses to an argument in which one is forced to assent to an ambiguous state-ment (because of the syntax or of a term): one may deny it, but confi rm it in one sense of the term or statement, or one may confi rm it, but indicate that the oppo-site term or statement also holds in some sense. Thus this passage would rehearse to the two possible responses (‘No, but still ...’ and ‘Yes, but not ...’) of SE 19.




as involving one ambiguous statement and combination and division as involving two statements expressed with one sentence is crucially refl ected in Aristotle prescribing different strategies for solving them.

No necessary difference in pronunciation. In the quoted argument that a certain argument is one dependent on combination rather than on amphiboly the second step was that what depends on division is not ambiguous because what depends on accent is not ambiguous either. What are we to make of that connection?

Many scholars conclude from this passage that Aristotle assumes that any sentence which lends itself to a combined and a divided analy-sis, just as some words consisting of the same letters in the same order, is to be ‘disambiguated’ in pronunciation (whether or not it is indicated by further signs) and therefore in its written form represents in fact two sentences, neither of which is ambiguous.46 This view is a development of an idea already to be found in antiquity itself. For Quintilianus, go-ing back to others before him, states that in such cases a difference in pronunciation can keep the two readings apart:

In words which are combined there is more ambiguity. Now it comes about ... [o]n the grounds of arrangement [of words] (per collocatio-nem), where it is unsure what ought to be related to what (quid quo referri oporteat) — and very frequently [1] precisely while it is in be-tween because it may be drawn to either side, for example as Vergil [says] about Troilus: ‘holding the reins still’ (lora tenens tamen). Here it may be asked whether he still holds the reins or whether he, though holding them, is still dragged along.47 Hence there is the following point of contention (controversia): ‘By testament someone ordered a statue holding a spear made of gold be placed’ (Testamento quidam ius-sit poni statuam auream hastam tententem). The question is: should there be a statue made of gold holding a spear or a spear made of gold in a statue of some other material? The same comes about more often [2]

46 Dorion, Les réfutations, 82, 228; Schreiber, False Reasoning, 64; R.B. Edlow, Galen on Language and Ambiguity. An English Translation of Galen’s De Captionibus (On Fallacies) with Introduction, Text and Commentary (Leiden 1977), 26; C.L. Hamblin, Fallacies (London 1970), 83

47 The reference is to Aeneis I 476-7: ‘fertur equis curruque haeret resupinus inani / lora tenens tamen;’




on the grounds of a turn [in the sentence] (per fl exum)48: ‘Then Achilles killed fi fty there being a hundred’ (Quinquaginta ubi erant centum inde occidit Achilles). ...

However, ... [this] is remedied by a division or a transposition of words (divisione verborum aut translatione) ... Division consists in breathing and pause (respiratione et mora): ‘statue’, then ‘holding a spear made of gold’,49 or ‘a statue holding a spear’, then ‘made of gold’. (Institutio Oratoria 7.9.7-11, with omissions)

Quintilianus treats the examples as cases of real ambiguity, but for the rest they are identical in structure to Aristotle’s examples, one of which even reappears in an only slightly changed form. And indeed Quin-tilianus states that the ambiguity can be removed by a division, that is, a clear way of relating a word or a string of words to the one side rather than the other, through a break in the fl ow of the sentence as pronounced. However, it would go too far to use this as even an indica-tion that also Aristotle might be thinking along these lines. First of all, Quintilianus does not claim that division by way of an audible break in the sentence is the only solution, for he mentions the transposition of words as well. Apparently division might not work everywhere. Sec-ondly, as Quintilianus presents it, a division is brought about by a con-scious effort, with the clear goal to disambiguate, rather than that every confusion between two readings disappears in spoken language.

If we then turn to Aristotle himself, we do have evidence that he thought that it was possible to disambiguate sentences with ambigu-ous syntax by way of pronunciation. The clearest evidence comes from a passage in the Rhetoric:

In general what is written should be easy to read and easy to deliver ( ... ) — that is the same. Precisely that ... [sentences] which are not easy to punctuate () do not [have],

48 Here fl exus cannot refer to the ‘infl ection of the voice’, as Atherton, Stoics, 479 and H.E. Butler in: Quintilian: Institutio Oratoria Books VII-IX (Cambridge, MA 1921) have it, for that could not be the source of the ambiguity. For my translation, see the lemma in the Oxford Latin Dictionary.

49 The translation differs slightly from the example in Latin, in order to make it fi t the translation of the ambiguous sentence as a whole. In Latin the division is: ‘statuam, deinde auream hastam; vel statuam auream, deinde hastam.’




such as those of Heraclitus. For it is a real job to punctuate those of Heraclitus because of it being unclear to which [part] it is attached, to the later [part] or the earlier [part], for example at the very beginning of his book; for he says: ‘While this account holds forever men fail to understand it.’ ( ). For about ‘forever’ it is unclear with which part [it goes]. (Rhetorica III 5, 1407b11-18)50

Moreover, the verb itself, containing the word for point (), refers to signs inserted in the text in order to indicate the com-positional structure of the sentence. That there existed such a practice we may also infer from a remark in our passage: ‘though also there [i.e. in cases of accent] they already avail themselves of additional signs’ — also there, that is, just as somewhere else, which in the context refers probably to this practice of punctuating sentences.

However, this evidence does not establish that the difference be-tween a divided and a combined reading necessarily shows up in pro-nunciation, or even could always show up thus. Punctuating by adding pauses would not help, for instance, with example (v), and not even alternatives, such as intonation, could do the job with example (xiv). In addition, there are also positive indications that Aristotle does not think so. Firstly, while regarding a fallacy of accent he explicitly states that it ‘in discussions without writing it is not easy to produce an argument’ (SE 4, 166b1-3),51 and indeed there is only one example of an argument, rather than a mere sentence, he comes up with,52 the examples of argu-ments depending on combination or division are plentiful, coming, as we saw, not only from the Sophistical Refutations itself. Secondly, Aristo-tle adds, as a corollary to the argument quoted above that what depends on division is not double, that ‘it is also clear that not all refutations are dependent on something double, as some claim’ (SE 20, 177b7-9). In SE 20, 177b27-34 he discusses extensively an alternative solution to ex-ample (xvi) which does not depend on distinguishing a divided and a

50 I follow the text as edited by R. Kassel, Aristotelis Ars Rhetorica (Berlin 1976).

51 Cf. SE 21, 177b35-7: ‘Dependent on accent there are no arguments, not among those in written form nor among those in spoken form, save that some few might come about.’

52 At SE 21, 177b37-178a2, which depends on the fact that can be pronounced as and as .




combined reading, but rather on the distinction between granting that in the way () one can do things one may also do them, and granting that in every way () one can do things one may also do them. These alternatives would not be worthwhile referring to in the context if the difference between combination and division would necessarily appear in pronunciation.

An identity-criterion for a single statement. Even though it would thus go too far to assume that Aristotle thinks that the difference between the combined and divided readings is necessarily refl ected in pronunci-ation, we still need to account for the connection suggested by Aristot-le’s argument between the fact that with accent pronunciation is crucial and the point that combination and division do not involve any ambi-guity (reinforced by his ‘also’ when remarking on the use of additional signs). We would not be able to make sense of it if we were to assume that pronunciation is completely irrelevant to Aristotle’s point. As it is, however, in order for it to be relevant it is not necessary that in every case of combination and division the difference between the two read-ings shows up in pronunciation; it is enough for Aristotle’s argument to make sense if it may show up in some cases. For whereas with accent, where the identity of the sounds making up a word changes with the addition of accent, the word itself thus becomes different with the dif-ference in pronunciation, difference in pronunciation is only secondary with combination and division. For the words remains the same, so the difference between the two statements only arises at the level of the sentence as a whole. Thus the difference between the two readings does not essentially involve difference in pronunciation, but consists rather in being composed in different ways — ways which may lend themselves to expression in pronunciation, but are not reducible to dif-ferences in pronunciation. Underlying Aristotle’s account, then, is the following necessary and suffi cient condition of identity for statements:

Statement S is identical with statement S* if and only if they exhibit the same tree of composition with all the same words.

To understand the import of this identity condition a comparison with amphiboly will be useful. The only examples Aristotle gives of amphibolous statements are statements in which one or several accusa-tives may be assigned different functions. His introductory example, for instance, is: (SE 4, 166a6-7), which has a different meaning depending on whether is the subject




for , with being the object, or vice versa. How-ever, there is only one tree of composition:

In other words, the tree only shows how the grammatical functions are distributed over the words of the statement, not what these grammati-cal functions are.

According to Aristotle this is also true for those cases where we would feel the difference between the two interpretations depends on whether or not a word ought to be supplied, as with the following ex-ample:

And: For one can signify both the person knowing and the thing known as knowing with this statement. (SE 4, 166a7-9)

One of the reasons why this example is untranslatable is that in English one cannot suppress the subject of a verb as in Greek: we would have to choose whether or not to supply ‘one’ () or an anaphoric expression referring to . Depending on this choice we would get different trees. For Aristotle, on the other hand, this would not be so much a matter of different trees but rather of different sentences altogether, as the words making it up would be different.

That in case of amphiboly there is only one tree of composition also makes it in principle impossible that the ambiguity is to be resolved by way of pronunciation. Similarly we do not fi nd any recommendation to that effect in later ancient authors. Quintilianus, for example, says that such cases are to be solved by changing the grammatical cases,53 so that we would be able to differentiate from . In disambiguating the second exam-ple Aristotle in fact uses a similar device.

Finally, with this difference between combination/division and amphiboly in mind, we may understand why Aristotle thinks there

53 Institutio Oratorio 7.9.9-10




is something smacking of amphiboly in example (x). Overlooking the importance of the grammatical determinator, one could interpret the difference between the two readings merely as a matter of assigning different grammatical functions to (and in the appli-cation), namely as signifying the instrument of seeing or the instrument of hitting. However, for Aristotle a statement is not merely a series of words or even groups of words to which functions can be assigned, but a string of words structured in a tree-like way, as determined by a grammatical determinator; grammatical functions are only to be deter-mined after one has established this structure.

3.4 One kind of doubleness, two fallacies

Now that we have established how serious Aristotle is about his claim that combination and division involve two, rather than one, statements, and what this claim involves for him, we will be able to deal with the two remaining charges of inconsistency. They can be summarised in the form of one question: how does Aristotle come to count two fallacies if they are both based on the same kind of doubleness? Why not one fal-lacy, as in the case of the similar doubleness in the case of accent?

An answer to this crucial question can be formulated if we compare the possible arguments dependent on accent with those dependent on combination or division. Taking stock of the examples, there seem to be three contexts in which confusion between a combined and a divided sentence can play a part. The fi rst is simple confusion, without any-thing else, to be represented as follows:

(1) [C/D]

This occurs in examples (viii), (ix) and (xii), though the last example is probably the result of an argument having the divided sentence for its conclusion which is then understood in a combined sense. The second context is that from (1) an inferential principle is derived to the effect that we may go from a statement with the same structure as the divided reading to a statement with the same structure as the combined reading and vice versa:

(2) [C/D] [C*] [D*] and [D*] [C*]

As explained above, we encounter this use in example (xiv). And third-ly, there is the context in which a premiss which lends itself to both




readings is used to establish a conclusion which only follows on one reading, typically being the reading on which the premiss would not have been admitted:

(3) [C] and [D] , therefore

[D] and [C] , therefore

This structure we see in all the other examples, even if we are not given arguments by Aristotle, as with example (xi), and if the actual structure of examples (x), (xi) and (xvi) is slightly more complicated because of quantifi cation.

In the case of accent, on the other hand, we do not have so many examples to go on, but a little consideration is enough to conclude that there are likewise three contexts in which accent may play a part. First again is the simple confusion of two ways of having an accent:

(1) [A1/A2]

This we see in almost all examples provided by Aristotle.54 Secondly, there is the argument with one premiss admitted with one accent and the other admitted with another, from which a conclusion follows which still feature the confusing word:

(2) [A1] and [A2], therefore [A1/A2]

However, as far as the confusion caused by accent is concerned, this is just a more complicated case of (1), the only difference being that the conclusion [A1/A2] may be unacceptable on both readings, rather than just one, as [A1/A2] in (1). The only real type of argument based on accent has similar premisses, but now has a conclusion which does not feature the confusing word any more:

(3) [A1] and [A2], therefore

The only example of an argument based on accent Aristotle gives is of this type.55

54 See SE 4, 166b4-5, 7-8 and 20, 177b3-4.

55 See note 52.




Now bearing in mind that Aristotle is after a classifi cation of falla-cies, that is, deceptive arguments, rather than a classifi cation of types of confusion, we see that there is a striking difference between the two lists of contexts. In the case of combination and division we have with argumentation pattern (3) two separate types of argument, one called dependent on division as it illicitly uses the inferential possibilities of the divided reading, the other called dependent on combination as it illicitly uses the inferential possibilities of the combined reading. Also with (2) we have reason to call, as explained already before, to call the use of the one derived implication [C*] [D*] division and the use of the other derived implication [D*] [C*] combination. In the case of accent, on the other hand, we do not have any reason to call argumentation patterns (2) and (3) after the one accent rather than the other. They are perfectly symmetrical, so there is no reason to privilege one over the other as the ground of the fallaciously derived conclu-sion.

It may be objected that I have left out in the case of accent a fourth type of argument which does show asymmetry. For why could there be not an argument of the following pattern:

[A1] and [A2] , therefore

However, every such an argument can be reduced to a two-step argu-ment, the fi rst consisting of the substitution of a synonymous word or phrase for the confusing word (on one of its readings):

[A1] and A2 = B, therefore [B]

[B] and [B] , therefore

And this fi rst step is of type (3), and can thus not be called after one of the two readings of the confusing word.

On the other hand, such a reduction is not possible for (3) in case of combination and division, for, unlike with accent, there are no sub-stitutions with a synonym possible. We could of course paraphrase a sentence, in the way Aristotle paraphrases the divided reading of ‘be-ing able to write while not writing’ ( ) as: ‘[having] the ability, when one does not write, of writing’ ([] ) (SE 4, 166a29-30). But this goes much further than the mere substitution for one word in a larger con-text — we have a whole new sentence.




Thus in the case of combination and division there are two fallacies based on single kind of doubleness because there are logically two dis-tinct ways of making use of the confusion caused by this doubleness. We should therefore understand Aristotle’s claim that there are six lin-guistic fallacies because there are six ways in which ‘we may indicate with the same words and sentences what is not the same’ in a similar vein: from a logical perspective there are six ways — that is, two ways based on combination and division — in which we may delude our-selves into thinking that while using the same word or statement we are employing something with the same meaning in our arguments. These delusions may occur on three levels: on the level of meaning, on the level of words or statements and on the level of argumentative use. We may be using the same word or statement, but are not aware that it has several meanings (homonymy, amphiboly and form of expression); we may be confusing the one word or statement for another (accent and combination/division); and we may employ the confusion between combined and divided statements in opposite directions (combination and division).

4 Conclusion

The account I have offered thus of Aristotle’s fallacies of combination and division as they are discussed in the Sophistical Refutations features both logical and linguistic elements, in a somewhat complicated inter-play. On one linguistic level, that of words, a fallacy of combination or division concerns one string of words rather than two strings which differ at least by one word, as is the case with the fallacy of accent. On the linguistic level of groupings, combination and division are distin-guished from the fallacy of amphiboly, as amphiboly occurs if there is one string of words which is grouped in one way (by one tree), but there is at least one element having two possible grammatical func-tions, whereas combination and division concern one string of words with at least two groupings.

Also the distinction between combination and division itself is based on a linguistic point, namely the existence of what I have called a gram-matical determinator, a word or a string of words requiring a comple-ment, which it can be said to govern. A reading of a string of words is divided as opposed to combined if there is a word or words which are not governed by the grammatical determinator, while if they had been governed by it, the reading of the same string of words would have been combined.




In addition to these linguistic elements, also matters of logic play a part in Aristotle’s account of the fallacies of combination and division. On one, immediate, level an argument constitutes a fallacy of division as opposed to one of combination, if a sentence agreed to in a combined sense is used in its divided sense in order to draw further conclusions, while if it had been agreed to in a divided sense and used in a combined sense, it would have been part of a fallacy of combination. On a more theoretical level the fact that there are these two different possible uses of a sentence, while such a differentiation cannot be found in the case of fallacies of accent, accounts for Aristotle’s position that there is one fallacy of accent and two fallacies of grouping (combination and divi-sion).

Both these two matters of logic, however, depend on the logical use one can or cannot make of the underlying linguistic situation. Notably, the explanation for there being two fallacies in case of combination and division, while there is only one in the case of accent, refers ultimately to the difference between words and groupings. It is this interplay be-tween logic and linguistic which we need to understand if we are to make sense of Aristotle’s account of the fallacies of combination and division.

Faculty of PhilosophyUniversity of GroningenOude Boteringestraat 52

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Apeiron Volume 42 issue 2 2009 [doi 10.1515%2FAPEIRON.2009.42.2.105] Hasper, Pieter Sjoerd -- Logic and Linguistics- Aristotleâs Account of the Fallacies of Combination and Division