Understanding Aristotles Theory of Fallacy in the Sophistical Refutations

Pieter Sjoerd Hasper In his Sophistical Refutations Aristotle offers the first theoretical account of fallacies in the history of philosophy. Aristotles initial presentation of his theory in chapters 4 and 5 consists of a list of thirteen fallacies, and also later the solutions to these fallacies are discussed one by one (chapters 19 to 31). Thus in our attempts at understanding Aristotles theory it is only natural to focus on these thirteen fallacies separately or, if the inquiry concerns the interrelations between fallacies, to treat these fallacies as given. However, Aristotle has more pretensions than to give a list that is based on just going through lots of arguments or on taking over a nomenclature of fallacies from a pre-established tradition. He purports to present not a mere theory of fallacy, but a systematic theory of fallacy, and even a complete theory of fallacy. So he should have or at least presuppose an answer to the question why there are the fallacies he distinguishes, and not more or less. If we are to understand fully Aristotles theory of fallacy, we shall have to find out what such an answer looks like. The only way in which we can ever hope to achieve that is by reconstructing the conceptual framework in which Aristotle is working when making his claims for completeness and when discussing fallacies, both the separate types of fallacies and all the examples he provides. For it is this conceptual framework that is going to yield the classificatory criteria on the basis of which we may finally understand that for Aristotle there really could not have been more fallacies than the ones he distinguishes. My primary aim in this article is therefore to explicate this conceptual framework and to discuss Aristotles ideas, distinctions and arguments in the light of it. 1. The object of the theory of fallacy In the first lines of the Sophistical Refutations Aristotle introduces his account of fallacy by saying that he is going to discuss arguments which appear to be refutations, but in fact are fallacies, and not refutations (164a20-21). This characterization of the object of his theory Aristotle gives a more determinate content in the ensuing discussion of the primary things in this field of study (164a22). Implicit in this further determination is the larger domain to which the study of fallacies belongs: that of dialectical arguments. In a dialectical debate between two interlocutors the one person, called the answerer, has adopted some thesis in reply to some issue raised (the problem), while the other person, called the questioner, tries to obtain concessions from the answerer by asking yes/no-questions (propositions) so as to use the answers to them as premisses (also called propositions) with the purpose to derive a conclusion from them which is somehow troublesome for the answerer. Ideally the questioners conclusion should contradict the thesis of the answerer we would then have a refutation. Within this larger domain there is a distinction between genuine refutations and fallacies, which are merely apparent refutations. In order to distinguish them, we need a definition of a genuine refutation. Aristotle supplies this definition by first defining deduction:

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[a genuine deduction is an argument which] is based on some things which have been conceded, in such a way that it states by way of necessity something different from the things laid down.1 (SE 1, 165a1-2),

and then defining a genuine refutation as:

a deduction accompanied by a contradiction [of some thesis] with the conclusion [of the deduction] (SE 1, 165a2-3).

According to Aristotle, there are several grounds why arguments may seem to produce such a refutation, without in fact doing so (165a3-4). In the first chapter he mentions, by way of example, only the most common ground, that because of words (165a4-5), but he promises to give a full list (165a17-19). This list he provides in chapters 4 and 5 note the causal language of bringing about the appearance [of there being a refutation] at the beginning of chapter 4 (165b25) and consists of the thirteen fallacies he distinguishes, the six fallacies dependent on the formulation: homonymy, amphiboly, composition, division, intonation (traditionally known as accent) and form of expression, and the seven fallacies independent of the formulation: accident, secundum quid, ignoratio elenchi, consequent, begging the question, non causa, and many questions. Thus Aristotles theory of fallacy should give an account of the grounds because of which some dialectical arguments appear to meet the requirements of the definition of a genuine refutation, without being one. 2. A systematic theory of fallacy That Aristotle does not mean to provide a mere account of some ways in which there may seem to be a refutation without there being so, but pretends to offer us a complete theory of fallacy, appears from two statements he makes in the Sophistical Refutations. The first of these statements we find in the following passage:

[We know the grounds] dependent on which fallacies come to be. For they could not be dependent on more [grounds]; all [fallacies] will be dependent on the [grounds]

1 In Greek: .. . Against W.D. Ross (ed.), Aristotelis Topica et Sophistici Elenchi (Oxford, 1958), I follow all but two of the manuscripts whose readings are available to me, as well as Boethius, in not reading (after ) , a clause which only features among the manuscripts whose readings are available to me in manuscript B and in a manuscript hitherto unused for Aristotles organon: Laurentianus 72.4 (from the late 13th or early 14th century). Not only is the addition of rare in the manuscriptual tradition, but I also find it more plausible that some scribe added it than that it was in whatever way dropped. For the verbally close definition of deduction at Topica 1.1, 100a25-27 does contain this clause, also at the end of the definiens: , so that it may have seemed to some scribe that it is lacking from the definition here and thus should be added. A proponent of could of course by appeal to haplography try to account for the dropping of after the first , but that does not seem a viable explanation given that the clause is rare in the tradition and the manuscripts which do and do not feature it do not constitute clearly separated groups. It is also unlikely that scribes decided to drop the clause for philosophical reasons; the only possible reason I can think of is that a redundancy with .. was felt, but if it were felt, then it could easily be explained away by interpreting in terms of consisting of which is, indeed, the translation proposed by P. Fait (transl. & comm.), Aristotele: Le confutazioni sofistiche (Rome and Bari, 2007),100-101. Rather, it is precisely the possible force of as on the basis of (cf. SE 6, 168a21) which seems to have been ignored by those who wanted to bring the definition here verbally in line with the one at the beginning of the Topics by adding .

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mentioned ( , ). (SE 8, 170a10-11)

Aristotle makes here in fact, by way of a ... -construction, two claims, one weaker and one stronger even though Aristotle may not have been aware of the difference in strength. The weaker claim is that his classification of thirteen fallacies is extensionally complete in the sense that every particular argument which is such that it appears to be a refutation, but is in fact not one, is of some type on Aristotles list. The stronger claim is that his classification is also complete on the type-level: there are no other ways of characterizing ways of being fallacious than the thirteen ways on Aristotles list. Moreover, we may safely assume that implicit in these two completeness claims is yet a third claim, namely that we need all the different types of fallacies in order to have an extensionally complete account of fallacy. The second statement is not so dramatic, but equally important. Discussing some alternative solution to a particular fallacy, Aristotle remarks:

However, it is clear that they do not solve it correctly, for of arguments depending on the same point there is the same solution, and this one will not apply to all [arguments of the same type], not [when they are] asked in all ways either ( 2). (177b31-34)3

As an argument against alternative solutions this remark would be pointless if Aristotle were to allow for the possibility that some particular fallacy could really be classified in two different ways and would depend on two different points. And one can see the point of ruling out such a possibility, for a general theory of fallacy would be less systematic, if there could be extensional overlap between types. Moreover, this might threaten Aristotles claim to type-completeness, for if there is nothing against fallacies falling under several types, what would there be against introducing some further type of fallacy which does not add anything to the theory in extensional terms, but equally is not a mere sub-type of one of the fallacies on Aristotles list, but rather overlaps with several distinct types of fallacy? Thus there must be a system behind Aristotles theory of fallacy, a system which provides the classificatory criteria to distinguish the different fallacies by classifying the different points on which the fallacies depend. For only in such a way can Aristotle maintain his two main claims, that his list of fallacies is complete on the type-level and that there is only one point on which each token-fallacy depends. 3. Two problems Aristotle seems to refer to such classificatory considerations in his argument for the completeness claims in chapter 8:

An apparent [refutation] depends on the parts of a genuine one. For with each [of these parts] lacking, there could appear to be a refutation, for example:4 (1) the one depending

2 I follow here the reading of all the manuscripts, against Ross emendation into . I do not know what reason Ross might have had for emending the text here. 3 For a similar statement, see SE 24, 179b11-12. 4 Translating this list of examples is very difficult, because Aristotles formulations are extremely concise. I take all the items on the list to have the following structure: they merely list the ways in which an argument can appear to be a refutation because of some part of the definition lacking, and they do so by describing these fallacies by reference to the point on which they depend, mostly by using with accusative, except in the case of (5). Some of the items on the list also contain some further information: in (1) the context in which this

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on what does not result on the ground of the argument ( ) (the [argument reducing] to absurdity); and (2) the [argument] depending on the proposition by turning two questions into one ( ); and (3) the [argument] depending on the accident instead of the thing for itself ( ), as well what is part of that, (4) the argument depending on the consequence ( ); further (5) what results not in the case of the object, but in the case of the argument5 ( ); next, (6) instead of the contradiction [being] universal and in the same respect and in relation to the same and in the same way it depending on what is the case to a certain extent, or also depending on each of those [qualifications] ( 6 ); further (7) depending acquiring the point at issue even though the point at issue is not counted [among the premisses] ( 7 ). Hence we know [the grounds] dependent on which fallacies come to be. For they could not be dependent on more [grounds]; all [fallacies] will be dependent on the [grounds] mentioned. (SE 8, 169b40-170a11)

Aristotle here picks up on an idea which he formulates earlier in the Sophistical Refutations, when he, after having finished his introductory discussion of the thirteen fallacies on his list (SE 4 and 5), he starts the sixth chapter in the following way:

Now, either one should distinguish the apparent deductions and refutations in this way, or one should reduce all of them to ignoratio elenchi, having made that a principle. (SE 6, 168a17-19)

The basic idea is that all fallacies on Aristotles list can be reduced to the fallacy of ignoratio elenchi, in that every type of fallacy can be related to one element in the definition of a genuine refutation failing to notice the fallacy is a sign of ignorance of this definition. It should be noted, though, that even in this passage,8 and certainly in the completeness argument of chapter 8 Aristotle goes beyond this idea in that he not merely reduces every type of fallacy to that of ignoratio elenchi, but conversely also holds that from every part of the definition we may derive either one type of fallacy or one distinct class of fallacies (which are then to be distinguished on the basis of further criteria). However, it is not at all clear how to assess this argument for the completeness claim. The first problem is that Aristotle seems to be working with a list of requirements for a genuine refutation (corresponding to the parts of its definition) a list that is nowhere defended or explained, let alone that one may grasp that the list is complete. Moreover, the fallacy may occur is mentioned; in (2) the fallacy is further specified; in (3) and (6) the feature which is lacking from the definition of a genuine refutation is mentioned by way of a clause introduced by instead of ( with genitive); similarly in (5) and (7) the feature lacking from the definition is mentioned, in (5) by way of a negative description of the fallacy (not ..., but ...), and in (7) by spelling out the part of the definition which is lacking. 5 The conception of argument here is one of mere manipulation of words, without reference to the meaning of words (for such a conception see SE 1, 165a6-10). The alternative translation of here is sentence, which then presumably refers to any statement in the argument in so far as it consists of these words in this order. I prefer argument, because following in the case of the sentence seems strained. 6 There is no reason to strike here, as Ross does. I can think of two reasons he might have had. First, the combination .. .. .. seems odd. However, there are other cases of that combination in De Caelo 2.6, 289a3, De Generatione et Corruptione 2.2, 329b21 and Ethica Nicomachea 10.4, 1174b34. Second, perhaps Ross objected against immediately after a preposition. However, there are enough examples of such a construction elsewhere in the corpus Aristotelicum. 7 I do not deem it necessary to insert, with Ross and Pichard-Cambridge, an extra here. Assuming the uniform structure of the items on the list (see footnote 4), such an insertion would indeed be mistaken. 8 In this passage Aristotle seems to present the reduction to ignoratio elenchi as an alternative way to distinguish the fallacies he has listed in the previous two chapters.

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list features requirements which cannot easily be connected with the many definitions of a refutation or a deduction stated or referred to throughout Aristotles works, notably the requirement (4) that the refutation concern the thing for itself. It is remarkable that this first type of problem is not discussed at all in the literature, as it goes to heart of the issue as to what the system behind Aristotles classification of fallacies is.9 A second problem does not concern the argument as such, but the conceptual framework in which it is formulated. A definition of refutation is going to list conditions that are separately necessary and jointly sufficient for there being a genuine refutation. So clearly an argument that fails to meet a single part of that definition is not going to be a refutation. However, as we saw at the beginning, a fallacy is according to Aristotle not just an argument that fails to be a genuine refutation, but also one that appears to be a genuine refutation. What is more, in Aristotles framework the fallacies seem to correspond to the grounds for this appearance, not to the failures themselves. So how can Aristotle maintain here that one gets a systematic theory of fallacy on the basis of the definition of refutation alone? In fact the same point, though with a different twist, can be made with regard to the idea formulated in the other passage which I advanced as evidence that Aristotle purports to present a systematic theory of fallacy: the passage where he claims that for fallacies depending on the same point there is the same solution, in order to discount alternative solutions. For this idea is also implicitly present in the completeness argument, when, in addition to the reference of the part of the definition to which the several (groups of) fallacies are related, there is a positive description of the fallacy this positive description is especially clear in the case of (3), (5) and (6). From the context in which Aristotle presents the completeness argument it appears that these positive descriptions are the points on which these fallacies depend and thus the points to which Aristotle refers when discounting alternative solutions to particular fallacious arguments. For Aristotle introduces the completeness argument in the following way:

If, then, the fallacies for the contradiction ( ) depend on the apparent refutation, it is clear that deductions of falsehoods could depend on as many [points] as the apparent refutation [could]. (SE 8, 169b37-40)

So the completeness argument, by establishing in how many ways there could be a merely apparent refutation, establishes the number of fallacies for the contradiction10 and thus also in how many ways there could be deductions of falsehoods. With deductions of falsehoods Aristotle does not have just any deduction with a false conclusion in mind, but, as appears from the context, only those deductions which have a false conclusion because some false dialectical principle has been admitted.11 Now Aristotle says the following about these false dialectical principles: 9 S. Ebbesen, Commentators and Commentaries on Aristotles Sophistical Refutations. A Study of Post-Aristotelian Ancient and Medieval Writings on Fallacies I The Greek Tradition (Leiden, 1980), already remarks that the principles underlying the classification are never clearly stated, referring only to the article by J.D.G. Evans, The Codification of False Refutations in Aristotles De sophisticis elenchis, Proceedings of the Cambridge Philological Society NS 21 (1975), 42-52. 10 See also the conclusion of the completeness argument, which is phrased in terms of fallacies (170a10). 11 In SE 8 Aristotle is concerned with sophistical refutations of two kinds: (1) refutations which appear to be refutations without being so; (2) refutations which by themselves are correct, but which merely appear to be proper to the subject ( ) (169b20-23). Whatever Aristotle may mean exactly with this last phrase I address this question in another paper it is clear that (2) only comprise arguments in which all the non-dialectical premisses are true: Sophistical refutations, even if they do deduce a contradiction, do not make clear whether [someone] is ignorant [in a certain field of science], for [people] also ensnare someone who does have [scientific] knowledge with these arguments. (169b26-29) As someone with real scientific knowledge will answer all questions concerning his area of expertise correctly, he can only be caught in a contradiction on the

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The points depending on which it appears to the listeners that a deduction has been brought about, as if these points have been put forward in the form of questions ( .. )12 depending on them ( )13 it might also seem so to the answer ( ). Hence deductions will be false because of them, either all of them or some of them. For what one thinks to have granted without having been asked, one might also admit if asked ( ). (SE 8, 169b30-34)

So there is a one-to-one correspondence between the types of apparent deductions of a contradiction, that is, apparent refutations, and the types of genuine deductions of falsehoods on the basis of a false dialectical principle: if the point responsible for the appearance has not been admitted, there is a fallacy and an apparent refutation, while if it has been admitted, there is a genuine deduction of a falsehood.14 Thus Aristotle identifies the points responsible for the appearance of there being a genuine refutation, of which he gives positive descriptions in the completeness argument, with the points responsible for there being a genuine refutation of a false conclusion. The problem with that, however, is that while it may be true that if one admits to a false dialectical principle, one will be forced to accept an argument with a false conclusion, the converse does not hold: it is not always true that ones assenting to a fallacious argument is due to ones admitting to a false dialectical principle. It is not necessary to admit that, say, the conclusion only need follow in the case of the argument (in the sense of verbal manipulations), in order to suffer a refutation based on, for example, homonymy. One need not be wrong about the definition of a genuine refutation in order to be the victim of a fallacy in the case of homonymy, for example, one may simply fail to notice the ambiguity of the term, and still maintain that the conclusion should follow not merely in the case of the argument, but also in the case of the object. Likewise one need not admit to a false general dialectical principle in order to suffer a genuine refutation with a false conclusion it suffices to accept, for example, that some particular term, which happens to be ambiguous, has a single meaning.

basis of a genuine deduction if he admits to a principle that is false and does not belong to his area of expertise. Such principles are false dialectical principles. 12 The several possible ways of translating the clause have been nicely classified by Fait, Le confutazioni, 137: either (1) it is an absolute clause, referring to independent questions asked, or (2) it picks up ; either (a) has causal power or (b) it should be translated with as if. Most translators opt for (1a), as does Fait himself: quante sone le cose che fanno sembrare agli ascoltatori che qualcose sia stato sillogizzato in virt di domande poste (27) cf. Dorion, Les refutations, 139, E.S. Forster (transl.), Aristotle, On Sophistical Refutations, On Coming-to-be and Passing-away [together with: D.J. Furley (transl.), On the Cosmos] (Cambridge, Mass., 1955), 47, and possibly E. Poste (transl.), Aristotle on Fallacies or the Sophistici Elenchi (London, 1866), 27. Boethius translates, as I do, (2b): secundum quae videtur audientibus velut interrogata syllogizare. There are two reasons why (2b) is to be preferred. First, there is an important difference in meaning between (1) and (2), for with (1) there are three elements referred to in the sentence: the questions asked (the propositions), the conclusion deduced on the basis of these propositions, and the points responsible for the appearance, whereas with (2) there are only two elements mentioned, the conclusion and the points responsible for the appearance. In the context, however, questions asked, as distinguished from points responsible for the appearance, are of no relevance whatsoever. What is important is that there are some points which in fact are not asked, but which would have been granted if asked, as appears from the last sentence quoted. For in that sentence the point which is asked or not must be taken to be responsible for the appearance, as otherwise the justification is not relevant. And if we are to prefer (2), we should adopt (2b), as a causal reading of does not seem to make sense in that case. Second, both (1) the accusative absolute and (a) the use of in a causal sense are rare, much rarer than (2) and (b). Moreover, construing the sentence along the lines of (2) and (b) is grammatically far more natural especially the accusative absolute I find strained. 13 Following all the manuscripts, against Ross . 14 Aristotle calls both deductions incorrect or false () see SE 18, 176b31-33.

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Thus with these positive general descriptions of the points responsible for the appearance of there being a genuine refutation Aristotle seems to presuppose a meta-theoretical account of fallacies which is far too strict, in the same way in which his completeness argument on the basis of clauses in the definition of refutation does not sit well with the conception of fallacies as ways in which an argument may appear to adhere to the definition of a genuine refutation without doing so. 4. The logic of dialectical fallacies In order to get to grips with these problems, I propose to take a step back and look at the logical space in which dialectical fallacies are committed. The idea is to take seriously Aristotle conceptual framework of fallacies as ways in which or grounds on which dialectical arguments may appear to be genuine refutations without being so, and to give an almost a priori overview of all the possible ways in which something may appear to be a refutation without being so. For the logical space in which fallacies are being committed is that of dialectical discussions and dialectical discussions have, as I explained at the beginning, a fixed structure and therefore only allow for so many ways in which the argument might be deficient while still appearing to be correct. By subsequently comparing with this overview Aristotles completeness argument as well as his discussions of individual fallacies, especially with regard to the conceptual framework in which he does so, we may then come to a better understanding why Aristotle thinks to be entitled to his completeness claim, and why he argues for this claim on the basis of the somewhat surprising conception of fallacy as an actual breach of one of the requirements listed in the definition of refutation. Any dialectical discussion in which the internal purpose is to refute the thesis of the opponent consists of four phases:

(I) There is an initial question, the problem (), of the form or ? asked by the questioner to the answerer. The answerer chooses between the two alternatives, thus adopting a thesis () let us say .

(II) The questioner asks a string of questions () of the form ?. The answerer can only answer by yes or no, thus conceding either affirmations or negations of each of these questions. Let us say that these concessions together are the i.

(III) The questioner uses the i as premisses (again ) in a deductive (in terms of the form) argument () with a conclusion () .

(IV) If = , then there is a refutation of the thesis of the answerer. Given this procedural framework, it is clear that a genuine refutation has been brought about only if the following requirements are met:

(a) the deduction should be valid in the sense that follows necessarily from the i; (b) should not be one of the i (for otherwise the dialectical procedure would be

pointless); (c) should indeed be in contradiction with .

In fact, apart from the at first sight rather trivial requirement that the argument is based on some things which have been conceded, these are the only three requirements mentioned by Aristotle in his definition of a genuine refutation at the beginning of the Sophistical Refutations quoted in the introduction. These are the kind of requirements which follow

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immediately from the nature of a dialectical discussion aimed at refutation, providing constitutive rules for this game. However, that does not mean that these three conditions are sufficient for a genuine refutation. There are many things which may go wrong even if these three conditions have been met in one way or another. For our purposes it is therefore useful to draw up a more complete list of what might go wrong. Assuming as an identity-condition for propositions (in the sense of , questions asked or concessions used by the questioner) that they are made up of exactly the same words in the same order (but not that they have the same meaning), this yields for each of the four stages in the discussion the following failures: (I) (i) the choice between and is not innocent, in that asserting or both commit one to some further non-trivial proposition ; (ii) has more than one meaning because of some word or string of words x appearing in has more than one meaning; (II) (i) the choice between yes and no to a question n? is not innocent, in that saying yes or no both commit one to some further non-trivial proposition ; (ii) some n of the i has more than one meaning because of some word or string of words x appearing in n has more than one meaning; (III) (i) some n of the i has more than one meaning and is conceded on one interpretation, but then used as a premiss on another interpretation; (ii) some n of the i as used as premisses is not conceded; (iii) some n is the same as ; (iv) does not follow on the basis of the i; (v) does not follow necessarily; (IV) (i) is not in contradiction with ;15 (ii) has more than one meaning because of some word or string of words x appearing in has more than one meaning and on the interpretation of on which is the conclusion of the deduction it does not contradict on the interpretation on which is accepted as thesis. There are two kinds of points to be made about this list of possible failures. Most important to note is that this list is complete: given the identity-criterion for propositions, these are all the possible shortcomings at each stage of a dialectical discussion. Questions asked at stages (I) and (II) can be either not innocent in the sense indicated, or contain an ambiguity; all other questions are correct. The premisses used at stage (III) can either be obtained because of some ambiguity or not obtained at all at stage (II); there is nothing wrong with any other premiss. The conclusion can either not be based on these premisses or not follow necessarily from these premisses (for the distinction see below); all other inferences are correct. The conclusion may repeat merely one of the questions asked at stage (II), without being based on a deduction from more than one premiss; all other conclusions are dialectically purposeful. The conclusion may fail to contradict the thesis at all (see note 15) or fail to contradict the thesis on the interpretation on which it is accepted; all other conclusions do constitute genuine refutations.

15 In accordance with the identity-criterion for propositions, two propositions are in contradiction if they consist of the same words in the same order and one of them features an additional negation apparently governing the whole proposition.

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In addition some more specific remarks about this list of possible failures are in order. Obviously there are two duplicates on this list: (I)(i) and (II)(i) as well as (I)(ii) and (II)(ii). Moreover, (I)(ii) and (II)(ii) are not really themselves troublesome, even though the answerer might feel uneasy about answering the question it is rather the abuse of the ambiguity in (III)(i) and (IV)(ii) which constitutes the failure, which is merely made possible with (I)(ii) and (II)(ii). Thus (I)(ii) and (II)(ii) serve as pendants for (III)(i) and (IV)(ii). Further, (III)(i) and (IV)(ii) themselves are of the same nature, merely differing in context in which the ambiguity leads to error. Similarly (III)(ii) and (IV)(i) are of the same nature, for they both consist in failing to state a proposition which is related to a proposition accepted by the answerer: in (III)(ii) the questioner uses a proposition which is not identical to any proposition conceded by the answerer and in (IV)(i) the questioner states a proposition whose contradictory is not identical to the thesis adopted by the answerer (in the sense specified in note 15). Finally, there might not seem to be any real difference between (III)(iv) and (III)(v), for if a conclusion does not follow on the basis of certain premisses, it seems not to follow necessarily, and vice versa. One could try to justify the distinction in modern terms, for example by pointing out that some statements are logically necessary even without being based on premisses but that seems a bit too anachronistic. But it should be noted that Aristotle himself distinguishes clearly between the two deficiencies in several other works, more so than at the beginning of the Sophistical Refutations, by listing separate requirements to avoid them.16 In the Prior Analytics, it is true, he explains the requirement that the conclusion be based on the premisses in terms of the necessity of the conclusion:

By because these things are so I mean that things follow because of these things, and by things follow because of these things [I mean] that no external term is further required in order that the necessity [of the conclusion] comes to be. (Analytica Priora 1.1, 24b20-22)

However, even if the requirement that the conclusion be based on the premisses cannot be understood independently from the necessity-requirement, it still goes beyond the necessity-requirement in that one needs to single out those premisses which really contribute to the conclusion being the case, leaving out the dispensible ones something which does not come with the necessity-requirement by itself. One can see the point of such a requirement for dialectical discussions, because given the external goals of dialectic, such as finding out about the relative strength of propositions, it is important to know what follows exactly on the basis of what. However, justifying it as a separate requirement in this way, by reference to an external goal, had better be avoided.17 The only context, then, in which this further requirement has a place in dialectic is the context in which, as we shall see, Aristotle himself invokes it, in the context of reductio ad absurdum arguments, for we should avoid making a

16 See Topica 1.1, 100a25-27: follows by way of necessity through the things laid down, Analytica Priora 1.1, 24b18-20: follows by way of necessity because these things are so; cf. SE 5, 167a23-27: on the basis of the things granted by way of necessity, and SE 6, 168a21-23: the conclusion must follow on the basis of the things laid down in such a way that it states by way of necessity. 17 It may be thought that failing to meet requirement (b), that the conclusion be different from one of the premisses deficiency (III)(iii) is also justified by reference to an external goal, in that otherwise the dialectical procedure would be pointless. However, it is by its very nature that a dialectical discussion should yield a conclusion different from one of the premisses, whereas knowing precisely which premisses are sufficient for the conclusion to follow is not required because of the very nature of a dialectical discussion, but because of one of the possible uses it is put to.

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proposition responsible for the absurdity which is not necessary for it arising in the first place.18 So abstracting as much as possible from the contexts in which these failures occur, we may clean up the list of failures as follows:

(1) the question is not innocent, in that any answer to it commits one to some further non-trivial proposition ;

(2) the proposition has more than one meaning and is used by the questioner on an interpretation which is different from the interpretation on which the answerer accepted it;

(3) the proposition as used by the questioner is not identical to a (contradictory of the) proposition accepted by the answerer;

(4) some n is the same as ; (5) does not follow on the basis of the i; (6) does not follow necessarily.

Finally, in accordance with Aristotles conception of fallacies as arguments which not merely fail to be genuine refutations, but also still appear to be refutations, we need to consider how one might set up a dialectical argument with one of these six deficiencies while at the same time giving the impression of being correct on the relevant point. Taking such sources of delusion into account, we get the following list:

(1) the question is not innocent, in that any answer to it commits one to some further non-trivial proposition , but this is not noticed because is phrased in such a way that it suggests, together with its negation, an exhaustive dilemma;

(2) the proposition has more than one meaning and is used by the questioner on an interpretation which is different from the interpretation on which the answerer accepted it, but this is not noticed because the words and their order in the proposition are the same and one is not aware of the ambiguity of the relevant word or string of words;

(3) the proposition as used by the questioner is not identical to a (contradictory of the) proposition accepted by the answerer, but this is not noticed because the proposition as used by the questioner resembles very closely some proposition accepted by the answerer, with a real difference which might easily escape notice;

(4) some premiss n is the same as conclusion , but this is not noticed because the identity between this n and is not a matter of having the same words in the same order, but rather one of content (which need not require the very same words in the very same order);

(5) does not follow on the basis of the premisses i, but this is not noticed because some sub-set of the i provides the basis for ;

(6) does not follow necessarily, but this is not noticed because the premisses are so connected that the inference seems to be licenced, either by two premisses featuring some connecting phrase which refers to the same thing or fact, but not in such a way as to be sufficient to ensure the necessity of the inference, or

18 It must be said that Aristotle sometimes goes further with regard to reductio arguments, for in SE 24, 179b18-24 he implies that we should not only not make an irrelevant proposition responsible, but also point out exactly which of the necessary propositions is really responsible. (For a philological discussion of the passage, see my Aristotle, Sophistical Refutations 24, 179b17-26, Classical Quarterly 58 (2008) 82-88.)

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by the logical connective in a premiss lending itself to such a misinterpretation that there seems to be an inference-licencing connection with another premiss.

Again some comments are in order, primarily concerning (4) and (6): in (4) the identity-criterion assumed before is played out against another identity-criterion, namely one couched in terms of identity of meaning; (6) is deliberatively vague, but any logical theory has some exhaustive distinction between terms determining the logical form of a proposition and terms which are not so, even if implicitly. A more general comment is that here I have made the sources of delusion somehow objective, that is, not dependent on the stupidity of one particular person who fails to get something. The real circumstances should make it more difficult to unmask an incorrect refutation. 5. Aristotles classification in the light of the scheme If we then turn to Aristotles completeness argument and his further discussions of the several fallacies and study them in the light of this scheme, we see that the similarities are very close. I shall go through the six types distinguished in this scheme one by one. [1] The question is not innocent, in that any answer to it commits one to some further non-trivial proposition , but this is not noticed because is phrased in such a way that it suggests, together with its negation, an exhaustive dilemma. With the first possibility on the list of a dialectical argument which appears to be correct without being so, we immediately have the case in which Aristotles actual discussion of fallacies deviates most from the way the type of fallacy according to the scheme is formulated. For we will have to recognize that Aristotle does not have the general concept of a question which is not innocent because it has a non-trivial presupposition to which one is committed when answering the question. Rather, Aristotle seems to have a more narrow understanding of the possibility of error in this respect.

The type of fallacy on Aristotles list which is clearly of a nature similar to the description here is that of many questions. With some good will one might be tempted to understand Aristotles description of this fallacy in terms of the presupposition of there being a single question to be answered:

[Fallacies] dependent on turning two questions into one [occur] when it is not noticed that they are several, and one answer is given, as if there is one [question]. (SE 5, 167b38-168a1)

However, rather than characterizing such fallacies as involving yes/no questions with a material presupposition in the way the question: Did you quit smoking? presupposes that I at least did smoke Aristotle analyses them as yes/no questions with a formal presupposition, namely that the question meets the standard of correctness that the question be a single question. This account cannot properly be called one of a question with a non-trivial presupposition. By itself, however, this point does not exclude the possibility that Aristotle, in stating a standard of correctness for a dialectical question, would show some grasp of the concept of a loaded question. The approach dominant in his discussion of many question, though, is not promissing. According to this dominant approach, the standard of correctness is enshrined in the definition of a proposition as one thing affirmed or denied of one thing. That seems to be

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why in the completeness argument Aristotle refers this fallacy to the proposition (170a3-4). He states the concomitant requirement most explicitly in the following passage:

The [fallacies] dependent on turning many questions into one reside in us failing to articulate the account of proposition. For a proposition is one thing of one thing ( ). If then a proposition is one thing of one thing, clearly this [fallacy] also [resides] in ignorance of the refutation, for something which is not a proposition appears to be a proposition. If then one has given an answer as if to a single question, there will be a refutation, whereas if one has not given [such an answer], but it appears [one has], then [there will be] an apparent refutation. (SE 6, 169a6-8, 14-18)

If we apply this standard of correctness to the example of: Did you quit smoking?, then we will have to say that it does seem to meet it, even though it is obvious that answering such a question with yes or no may get one into trouble. However, there are two indications that Aristotle also conceives of this fallacy in different terms, namely as answering a question which does not present an exhaustive dilemma. For the very first example Aristotle gives of the fallacy cannot really be discounted on the basis of the criterion that a proposition (and thus a question) should be one thing affirmed or denied of one thing:

Is the earth sea or the sky? (SE 5, 168a2-3) Aristotle says of this question that it is easy to see that [there are] several [questions] and that one should not give a single answer (SE 5, 168a1-2), but does not specify this in terms of the one thing of one thing-criterion. That would not have been possible anyway, because what is wrong with this question is not that there are in fact two yes/no questions turned into one, but rather that it is a question which poses as an exhaustive dilemma without being one.19 The second indication of such a conception being in Aristotles mind is the fact that in a passage from the Posterior Analytics he mentions, in addition to the requirement of one thing of one thing another one:

A proposition is one half of a contradiction, one thing [said] of one thing. ( 20 , ) (Analytica Posteriora 1.2, 72a8-9)

As a contradiction is an opposition of which there is nothing in between with regard to itself (72a12-13), a correct proposition is thus a question or statement which together with its negation forms an exhaustive dilemma.21

19 Thus I think that Ackrill is somewhat uncharitable towards Aristotle when he complains, in his Aristotles Categories and De Interpretatione (Oxford, 1963) 146, that a question with a presupposition cannot generally be analysed into a conjunction of two questions. Of course that is correct, but the point I am trying to make here is that Aristotles notion of there being one question should not be understood in terms of there not being a conjunction of several yes/no questions, but rather in terms of there being an unproblematic yes/no question. 20 Ross reads , with all the manuscripts, but it seems more likely that the text should read , just as in DI 11, 20b23-24 (cf. Barnes, Mignucci 143 check Detel). That it is common error to write instead of appears, among other things, from the fact that at 72a19 manuscripts ABCd have the former, whereas n and c read, correctly, the latter (V reads the latter as well, but corrects to the former). 21 I am being cautious concerning the precise relation between the two criteria for a proposition: being one half of a contradiction and being one thing said of one thing. From the context (Analytica Posteriora 1.2, 72a8-14) it cannot really be ascertained whether Aristotle assumes them to be equivalent or whether he thinks that the second criterion supplements the first.

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On such a conception of a correct proposition loaded questions like: Did you quit smoking? will turn out to be incorrect, even though they do pass the one of one test. So we might say that Aristotle has some inkling of the concept of a loaded question, be it that his grasp is tenuous. However that may be, the dominant approach in Aristotle is clearly based on the conception of a proposition as predicating one thing of one thing:

A question is one to which there is one answer, so that one must affirm or deny neither many things of one thing nor one thing of many things, but one thing of one thing. (SE 30, 181a37-39)

Also most of the examples provided by Aristotle concern conjunctions of yes/no questions asked at once:

Are this person and this person a human being? [scil. or are they not?] (SE 5, 168a5) Are all these things good or not good? (SE 5, 168a8)

The reason that such insiduous questions escape notice in these cases22 presumably lies in the linguistic structure of the question, which is that of a grammatical subject of which something is predicated. Primarily quantifiers like both and all lend themselves to such misleading questions, for they can be read in a distributive way in which case many questions are asked together but also in a composite way, with the whole of the several parts is taken as the subject of the question, which then seems perfectly legitimate. Real trouble, of course, comes about if the legitimacy of the question on the latter interpretation is used to ask questions of the former type. All this may give the impression that it is primarily the ambiguity of some subject-terms in a sentence which gives rise to the fallacy, so that there is no separate type of fallacy. Aristotle is aware of this:

These arguments fall also under other solutions, for both as well as all signify several things. Thus it is not [one and] the same thing, except in word, which happens to be affirmed and denied and that was not a refutation. (SE 30, 181b19-22)

However, Aristotle has a reply:

However, it is clear that if a single question of several things does not occur, but someone affirms or denies one thing of one thing, the impossibility [i.e. the impalatable conclusion of a fallacious argument based on many questions] will not be there.23 (SE 30, 181b22-24)

Thus Aristotle turns the requirement that a proposition be one thing of one thing into a norm for questions which should be adhered to prior to any other requirement. The fact that some cases of many questions seem correct because of linguistic ambiguity, does not undermine the independent status of this fallacy. Finally, I want to make a remark about the connection between this fallacy and the definition of refutation. The definition of proposition is not a real part of the definition of refutation: one can have a perfectly good understanding of what is logically involved in a refutation, and still fail to understand that one should not commit the fallacy of many 22 See SE 5, 168a3-5. 23 For the same idea, see SE 17, 175b39-41.

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questions. That is, the fallacy does not concern the argument and its result. However, the premisses of the argument are obtained in a dialectically incorrect way, so that the argument becomes dialectically irrelevant. [2] The proposition has more than one meaning and is used by the questioner on an interpretation which is different from the interpretation on which the answerer accepted it, but this is not noticed because the words and their order in the proposition are the same and one is not aware of the ambiguity of the relevant word or string of words. It is immediately clear that Aristotle conceives of the language-dependent fallacies in exactly the way as described in (2): as arguments which seem correct in terms of words only, but in terms of what these words mean contain deficiencies. This is how he discusses them in chapter one:

Since it is not possible to have a dialectical discussion while moving the things themselves, and we rather use, instead of the things, words as symbols, we assume that what follows in the case of words also follows in the case of the things. .. But it is not similar, for the words are limited as well as the quantity of statements, whereas the things are unlimited in number. It is then necessary that a sentence and a word which are one and the same ( ) have several meanings. (SE 1, 165a6-13)

Aristotle clearly assumes in this passage the identity criterion for propositions I have adopted as well. But identity of words and their order is not sufficient for identity of the things signified, so that what follows in the case of the argument conceived as mere manipulations of words and sentences may not be what follows in the case of the things themselves. This is precisely the phrase by which Aristotle refers to the language-dependent fallacies in the completeness argument of chapter 8:

what results not in the case of the object, but in the case of the argument ( ) (SE 8, 170a5-6)

There are three further points to be made about Aristotles actual discussion of the language-dependent fallacies. First, there are six of them, which Aristotle distinguishes on the basis of further criteria. Also here he has a completeness argument:

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 the same ( ). 24 (SE 4, 165b27-30)

24 For alternative translations of this sentence, see e.g. L.-A.Dorion, Aristote: Les rfutations sophistiques (Paris and Laval, 1995), 124, J. Barnes (ed.), The Complete Works of Aristotle: The Revised Oxford Translation [CWA] (Princeton, 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] (London and Cambridge, Mass., 1955), 17, and P. Fait (transl. & comm.), Aristotele: Le confutazioni sofistiche. 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 1.8, 103b3-8. It might be objected against my translation that I cannot supply any masculine word with from the context. However, in a classification of fallacious arguments the word easily springs to mind (cf. a few lines further, at 165b31).

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In () Aristotle refers to an exhaustive classification of ways in which a word or a sentence may have more than one meaning. This classification is explained in an appendix to this article. There it will also become clear that Aristotle assumes here the same identity criterion for sentences and words as above. The idea behind this completeness argument is the following. Given a sentence (whose identity again consists in having these words in this order), may be ambiguous on three different levels: (i) the word-level, (ii) the sentence level, and (iii) the morphological level. In case of (i) and (ii) the ambiguity may be either (a) a matter of meaning (same word or sentence, different meaning) or (b) a matter of having two different words or sentences, or (in order to avoid confusion with the identity condition given) two different lexemes or statements. (ib) One written word may be pronounced in two different ways, with different meanings, thus constituting two different lexemes in Aristotles days accents were not commonly written. This is a case of intonation or accent (). (ia) If there is one written word and it is also pronounced in one way, but still has several meanings, we have a case of homonymy. Aristotle distinguishes (iia) sentence constituting one statement with several meanings and (iib) forming two statements by reference to the grammatical tree of composition of . (iia) If there is one tree of composition, but the words or groups of words may be assigned different syntactical functions (e.g. being subject or object of the sentence), then we have a case of amphiboly. (iib) If there are several possible trees of composition, and the statements have different meanings, then we have cases of composition and division. It is extremely difficult to give examples of (iia) in English, because of its very strict rules for word-order, but in Greek, with its cases, which, moreover, bring together several syntactical functions, there are plenty. Finally, in (iii) some part of the morphology, primarily the ending of a word indicative of gender, case or type of action, normally indicates one thing, but in some cases indicates something else. Most of the ideas behind this completeness argument I have discussed in Logic and Linguistics: Aristotles Account of the Fallacies of Combination and Division in the Sophistical Refutations, Apeiron 42 (2009) 105-152. Second, it seems that Aristotles classification of the language-dependent fallacies is not so much tailored to cover dialectical practice, but rather is based on a priori considerations about the possibilities for ambiguity. Aristotle himself admits that there are few examples of the language-dependent fallacy of intonation.25 Similarly, the fallacy of form of expression does not lend itself for regular use in dialectical discussions, certainly not in the way envisaged in the scheme above. For it is not so much matter of a word or sentence admitted in one sense and used in another sense, but rather a matter of misclassification on a meta-level on the basis of morphology. Third, the requirement for a correct refutation these fallacies fail to meet is that the conclusion should be established in the case of the things. This requirement is clearly mentioned in the completeness argument in SE 8, as well as in the passage quoted from SE 1. It is also referred to in passing in the paragraph discussing the reduction of the language-dependent fallacies to ignoratio elenchi:

Also that [scil. there being the same sentence or word] was required, just as the thing [being] the same, if there is to be a refutation or deduction .... (SE 6, 168a28-30)

This requirement is less strict than the requirement alluded to in the definition of a refutation cited in SE 5:

A refutation is a contradiction of one and the same, not [of one and the same] word, but of [one and the same] thing, as well as of a word which is not synonymous, but the same,

25 See SE 21, 177b35-37.

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by way of necessity on the basis of the things granted, without the point at issue being counted together [with the premisses], in accordance with the same thing, in relation to the same thing, in the same way and in the same time. (SE 5, 167a23-27)

Here the requirement which is meant to rule out language-dependent fallacies is strictly tied to the contradiction between the conclusion of the argument and the thesis of the answerer. A similar remark we find at the end of SE 6, as a kind of conclusion to the reduction of all fallacies to that of ignoratio elenchi:

Hence all types ( ) fall under ignoratio elenchi, the ones dependent on the formulation because the contradiction is apparent what was particular to a refutation and the others dependent on the definition of a deduction. (SE 6, 169a18-21)

The problem with the requirement thus formulated is that it is too strict, because language-dependent fallacies do not only bedevil arguments by way of the contradiction not being up to standard, but also in the argument itself as Aristotle himself is well aware.26 There are two possible responses to this problem. The first is to posit that Aristotle is working with two slightly different definitions of refutation, and that he saw himself forced to tie the language-dependent fallacies to the contradiction between the conclusion and the thesis of the answerer when working with the one definition. In support of there being two definitions at work, one could, for example, point out that it is striking that apart from these concluding remarks the broader and more accurate requirement of the contradiction following in the case of the thing seems to be presupposed in SE 6. The alternative would be to stretch the meaning of contradiction here so as to include not only contradictions which themselves feature some ambiguity, but also contradictions which follow on the basis of ambiguities. If possible I would prefer that solution, but I do not think it is possible, precisely because Aristotle shows himself so clearly aware of the distinction between deficiencies residing in the contradiction and those residing in the deduction. Therefore we must assume that in these two passages Aristotle is working with a slightly different definition of refutation. [3] The proposition as used by the questioner is not identical to a (contradictory of the) proposition accepted by the answerer, but this is not noticed because the proposition as used by the questioner resembles very closely some proposition accepted by the answerer, with a real difference which might easily escape notice. Also with regard to (3) Aristotle seems to conceive of this possible type of fallacy in the terms of the scheme, namely when he discusses the fallacy of secundum quid:

The [fallacies] dependent on this being said without qualification or in a certain way and not properly [occur], when what is said in a particular respect ( ) is taken as if it has been said without qualification. .... Being something and being without qualification are not the same .... Not being something and not being without qualification are not the same. But they appear [to be the same] because of being something is very close in formulation to, and differs little from, being, just as not being something to not being. (SE 5, 166b37-167a6)

However, if one looks at the examples Aristotle provides of this fallacy, they all concern the contradiction between thesis and conclusion deduced: one of the contradictory statements is given, the other is arrived at in a single step by disregarding a relevant qualification. This

26 See SE 10, 171a1-11 and SE 19, 177a9-32; cf. SE 6, 168a21-23.

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impression is confirmed by the description of this fallacy in the completeness argument of chapter 8:

instead of the contradiction [being] universal and in the same respect and in relation to the same and in the same way it depending on what is the case to a certain extent, or also depending on each of those [qualifications] ( )

Also in the reduction to ignoratio elenchi in chapter 6 we encounter the same point:

The [fallacies] dependent on in a certain respect and without qualification [come about] because the affirmation and denial are not of the same thing. For of in a certain respect white [the denial] is in a certain respect not white, whereas of without qualification white the denial is without qualification not white. If then, when it is granted [that something] is in a certain respect white, it is taken as if that is said without qualification, one does not produce a refutation. (SE 6, 168b11-15)

The last sentence of the passage might be taken as concerning a premiss of an argument as well, but the first sentence leaves no doubt that it concerns the relation of contradiction between conclusion and thesis. Remarkably enough, though, the conclusion of the same chapter (169a18-21), quoted above, again is not consistent with this reduction, for there Aristotle states that all the language-independent fallacies, among them secundum quid, do not concern the contradiction between conclusion and thesis, but should be referred to those parts of the definition which concern the deduction. Moreover, it is not at all clear whether the description of this type of fallacy only applies to secundum quid, or also to ignoratio elenchi narrowly conceived (that is, as one of the thirteen fallacies rather than as the mistake to which all fallacies can be reduced). There are passages where Aristotle has difficulty distinguishing between them, notably in the following one:

The delusion of the [fallacies] dependent on a lack of the definition and of those dependent on in some respect and without qualification resides in something imperceptible, for we agree universally as if in relation to something, in some respect, in some way and now do not signify anything in addition ( ). (SE 7, 169b9-12)

Similarly, the practical advises Aristotle gives for solving the fallacies of secundum quid and ignoratio elenchi are almost identical:

The arguments which depend on what is properly said this either in some respect or somewhere or in some way or in relation to something ( ), and not without qualification, should be solved by investigating the conclusion with regard to the contradiction, whether any of them can have occurred. (SE 25, 180a23-26)

To [arguments] which come to be depending on the definition of a refutation, one should, as has been described before, respond by investigating the conclusion with a view to the contradiction [with the thesis], taking care that it will be the same thing, in accordance with the same thing, in relation to the same thing, in the same way and in the same time ( ). (181a1-5)

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The only difference seems to be that with ignoratio elenchi both contradictory statements feature or should feature some qualification, whereas in the case of secundum quid the statement without qualification is not by itself without sense.27 It seems to me that the description in the completeness argument of chapter 8 would apply to both fallacies. [4] Some n is the same as , but this is not noticed because the identity between this n and is not a matter of having the same words in the same order, but rather one of content (which need not require the very same words in the very same order). This coincides almost exactly with the description of begging the question:

The [fallacies] dependent on taking the point at issue come to be in this fashion and in just as many ways as it is possible to ask for the point at issue, but they appear to refute because of our inability to distinguish what is the same and what is different. (SE 5, 167a36-39)

The reference is to Topics 8.13, where Aristotle distinguishes five ways in which one may beg the question. There he emphasizes at least with respect to the first way that the circumstances may also be conducive to making the mistake:

[Asking for the very thing one needs to show] is in the case of the thing itself not easily failed to notice, but in the case of synonyms and in those cases in which a word and a phrase signify the same, it is easier. (Topica 8.13, 162b36-163a1)

Presumably this point also applies to the other four ways, as they do not concern identical words either: asking for the universal when one needs to establish a particular case, asking for a series of particular cases when one needs to establish the universal, asking for parts of the issue separately (if the issue is divisible), and asking for a logically equivalent point. [5] does not follow on the basis of the i, but this is not noticed because some sub-set of the i provides the basis for . Aristotle follows this description in almost identical terms when describing the fallacy of non causa:

The [fallacy] depending on [taking] what is not a ground [for the conclusion] as a ground [comes to be] when what is a non-ground is taken in addition on the supposition that the refutation comes to be depending on that. Such a thing occurs in the case of deductions [which lead] to impossibility, for in those one must demolish one of the things laid down. When then something is counted among the questions necessary for the impossibility to follow, it will often seem that the refutation comes to be depending on that [point]. (SE 5, 167b21-26)

Aristotle specifies that it is only in the context of reductio ad absurdum arguments that such a mistake leads to problems. In the reduction of this fallacy to ignoratio elenchi Aristotle states that it infringes the requirement that the conclusion come about because these things [i.e. the premisses] are the case. In the completeness argument, however, the reference to this fallacy differs:

27 Cf. the discussion of the difficult cases involving secundum quid in SE 5, 167a14-20, which are: (i) if something is the case with qualification, it also seems to be the case without qualification; and (ii) it is difficult to determine which side should be without qualification: either they both are or they both are not.

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the one depending on what does not result on the ground of the argument ( ) (the [argument reducing] to impossibility)

The idea behind this description, though, is the same: there is only one argument and one set of premisses responsible for the impossibility, and if one makes a proposition responsible which does not belong to this set, and claims that it should be denied, then one commits the fallacy of non causa. Nowhere does Aristotle refer to a source of delusion concerning this fallacy. It might be, however, that it is the questioner who is responsible for some kind of delusion, by counting some proposition among the questions necessary for the impossibility to follow this is suggested by the last sentence of the passage quoted. [6] does not follow necessarily, but this is not noticed because the premisses are so connected that the inference seems to be licenced, either by two premisses featuring some connecting phrase which refers to the same thing or fact, but not in such a way as to be sufficient to ensure the necessity of the inference, or by the logical connective in a premiss lending itself to such a misinterpretation that there seems to be an inference-licencing connection with another premiss. In order to show that Aristotle conceives of a type of fallacy in the terms of the scheme as well, it should be clear that Aristotle distinguishes two sub-types, one concerned with logical connectives and another one concerned with referring phrases, and that he tightly links this type of fallacy to the requirement that the conclusion follow by way of necessity. I think both of these points are clear, though there are some complications. How exactly the source of delusion is conceived depends of course on the logical-semantical theory in the background. The logic underlying Aristotles dialectic is a simple propositional logic, including the logical connectives and, or (presumably exclusive) and if .... then ...., together with the principle of non-contradiction and the principle of excluded middle as a kind of axioms (even though they can be established in the discussion as well). Of these logical connectives Aristotle mentions if .... then .... as a possible source of delusion, when describing the fallacy of the consequent:

The refutation dependent on the consequent [occurs] because one thinks that the relation of following () converts, for if it is, while this is the case, necessary that that is the case, people think that also while that is the case, the other thing is necessary as well. (SE 5, 167b1-3)

And later on he even distinguishes two ways in which one might make a mistake here, either by inferring from if p then q, that if q then p, or by inferring from it that if not-p then not-q.28 He notes that people often make this mistake. Also referring phrases may be involved according to Aristotle in making an argument seem correct without being so. That is the upshot of his discussion of the fallacy of accident, which occurs when:

It is assumed that anything belongs in a similar way to the object and to the accident. For since many things are accident of the same thing, it is not necessary that all the same things belong to all the things predicated [of something] and to that of which they are predicated. (SE 5, 166b29-32)

28 See SE 28, 181a23-27.

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It is not necessary that all the same things belong Aristotle does allow for the possibility that in some cases one may infer that something belonging to an object or an accident of an object, also belong to the accident or to the object itself respectively. This he states explicitly in the following passage:

Since it is undetermined when one should say [something] in the case of an object, if it does belong in the case of an accident that is, in some cases it seems so and people say it does, but in other cases they deny that it is necessary one should, when it is inferred, respond to all [such arguments] equally that it is not necessary, though one must be able to bring forward an example. (SE 24, 179a27-31)

The inference is only necessary in all cases if the connection is tighter than that between object and accident:

Only to things which in substance are indistinguishable and one all the same things seem to belong. (SE 24, 179a37-39)

So Aristotle conceives of both the fallacies of accident and of consequent Aristotle as failures regarding the necessity of the inference, and he distinguishes two possible ways in which one may fail in this regard, one involving the misinterpretation of the logical connective if ... then ..., the other involving an identity of reference which is not tight enough for all contexts just as in (6) in the scheme. However, both in the completeness argument and in the reduction to ignoratio elenchi Aristotle wants to make the fallacy of consequent a sub-type of the fallacy of accident.29 Moreover, in both of them he also seems to cash out necessity in terms of non-accidence, namely in terms of a for itself-relation. In the completeness argument he characterizes this type of fallacy as:

the [argument] depending on the accident instead of the thing for itself ( ), as well what is part of that, the argument depending on the consequence ( )

The same idea behind is behind the following argument from chapter 6:

If then there is no deduction of something accidental, a refutation does not come to be. For it is not the case that if with these things being there, it is necessary that that is there, and [if] that is white, it is necessary because of the deduction that white is there. (SE 6, 168a37-40)

I take for itself and accidental to be complementary terms. Presumably being indistinguishable and one in substance is meant to be synonymous with being for itself. However, in these two chapters Aristotle is stricter than necessary, for he seems to exclude the possibility that there are cases in which a merely accidental relation allows one to make an inference. To be honest, I am at a loss why Aristotle is so strict here and in the completeness argument. Similarly, I do not really know why Aristotle wants to analyse the fallacy of consequent as a special case of the fallacy of accident, however philosophically interesting this analysis might be. Is it mere parsimony? It should be noted, though, that there is something half-hearted about this analysis, for there are two remarks which indicate that

29 It is beyond the scope of this paper to discuss this reduction of the fallacy of the consequent to the fallacy of accident. One can find the reduction in SE 6, 168b27-3.

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Aristotle does not see it as the only way of linking the fallacy of consequent to ignoratio elenchi:

Since then the refutation dependent on accident resides in ignoratio elenchi, it is clear that also the one dependent on the consequent is. However, this must also be investigated in another way. (SE 6, 169a3-5) [The source of delusion] of the [fallacies] dependent on accident is due to the inability to distinguish something which is one and something which is different, something which is one and something which is many, and to what kind of predicates all the same things belong as to the object. Of the [fallacies] dependent on the consequent [the source of delusion] is similar, for the consequent is some part of the accident. Further, in many cases it also seems, and it is assumed thus, that if this does not separate from that, that does not separate from this either. (SE 169b3-9)

Conclusion All in all it seems that Aristotle stays remarkably close to the scheme, with some peculiarities, such as the limitation of secundum quid to the contradiction between conclusion and thesis, the analysis of the fallacy of consequent as a sub-type of the fallacy of accident and the requirement that there is only a refutation in case of a for itself-connection. That does not mean that Aristotle has this scheme explicitly in mind when claiming that his classification of fallacies is complete. What it does show, however, is that the definition underlying the completeness claim of chapter 8 does not come falling from the sky, but stems, to say the least, from a good and complete insight into what may go wrong in dialectical arguments, what types of mistakes the circumstances of dialectical argumentation may be conducive to. Because Aristotle stays so close to the scheme, we may take the scheme to justify every single clause of the full definition of refutation as mentioned or hinted at in the completeness argument. 6. Fallacies as deficiencies or as grounds for the appearance of correctness? Now that we have thus given substance to Aristotles completeness claim that there are only so many types of fallacy, and neither more nor less, we need to tackle the problem concerning the conceptual framework in which Aristotle sets out his theory of fallacy. As we saw, Aristotle presents in chapter 1 of the Sophistical Refutations fallacies as the grounds for arguments appearing to be refutations without being so. However, in the completeness arguments as well as in the reduction to ignoratio elenchi fallacies do not seem to be treated as grounds of appearance, but rather as the deficiencies themselves: the parts of the definition of refutation are each necessary and jointly sufficient for there being a genuine refutation, and if some requirement is not met, the argument is deficient in this respect; the part of the definition does not correspond to further grounds why such a deficiency might be hidden.

In dealing with this problem regarding Aristotles conceptualisation of fallacy it will be useful to point out that in the scheme generating more or less Aristotles full classification of fallacies I also distinguished between deficiencies and sources of delusion, assuming, just as Aristotle, fallacies to be arguments which are incorrect, but which nevertheless do appear to be correct. However, I did not make the further step of identifying the fallacy with the source of delusion or with the dialectical mistake. And this turned out to be all for the good, for when comparing the different possible fallacies of the scheme with Aristotles actual discussion, we encountered with regard to the issue of appearance two kinds of fallacies. Some Aristotelian fallacies are called after the plain error: many questions, begging the

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question and non causa. It is therefore no coincidence that in the case of the first two of them Aristotle tells us that there are simple cases and cases which are more difficult because of further reasons (which in both cases have to do with language). He does not make this point concerning non causa, but he easily could have: sometimes the answerer will notice immediately that after a reductio ad absurdum a proposition is taken to be reduced which is not reduced, while on other occasions, for example when the reductio is long and complicated, he might not notice. Similarly I do not think it is a coincidence that Aristotle, when giving an overview over the sources of delusion of all the different types of fallacy in chapter 7, only in the case of these three fallacies is very unspecific:

Also in the case of [arguments] assuming what is at issue, of things which are not caused, and of [arguments] which bring about many questions as one [things are thus]. For in all of them the delusion [comes about] because of something negligible ( ). For we do not carefully check the definition of proposition or of deduction because of the ground stated ( ). (169b13-17)

It should also be noted that only these three fallacies relate immediately to clauses in the original definition of a refutation of Sophistical Refutations 1 or to the definition of a proposition (which states a kind of prerequisite for correct dialectical questions): begging the question relates to the requirement that the conclusion be different from any of the premisses, while non causa is a breach of the requirement that the conclusion be based on the premisses. The other types of fallacy are characterized in a very different way, for they have the source of delusion built into them, as it were. All the language-dependent fallacies consist in not noticing that the same words have several meanings the fact that the words are the same being the source of delusion. The fallacies of accident and consequent get the necessity-requirement wrong, but not just any breach of that requirement constitutes a fallacy, for example arguments with a huge gap in it these fallacies do refer to the phenomenon which is conducive to getting it wrong. Also the fallacies of secundum quid and ignoratio elenchi seem to refer to such sources of delusion, for they concern the kind of differences between propositions which are easily overlooked it is not just any deletion of a word in a sentence which constitutes a secundum quid. Thus Aristotle also has a specific story to tell about the source of delusion for each of these types of fallacy in chapter 7.30 Similarly it is therefore not a coincidence either that the references to the several parts of the definition of a genuine refutation in the completeness argument of chapter 8 for these fallacies do not feature in the official definition of refutation at the beginning of the Sophistical Refutations, but add or rephrase them: necessity is rephrased into for itself, the precise requirements to avoid secundum quid (and ignoratio elenchi in the narrow sense) and language-dependent fallacies are added. There is yet another feature which unites these remaining types of fallacy: they are all of a logical-semantical nature, involving the meaning of words and their concomitant contribution to the inferential capacities of propositions, whereas the first three types are more of a procedural nature, not affecting the correctness of the inference to some conclusion itself. This is obvious in the case of language-dependent fallacies, but also in the cases of accident and consequent and of secundum quid and ignoratio elenchi semantical issues play an important part. From the mere statement itself one cannot find out whether the relation between subject and predicate is accidental or for itself. Often the exact contribution of added qualifications is not clear. This is also related to the fact that all of these fallacious patterns of reasoning are sometimes quite successful or even perfectly legitimate. In most cases one can 30 See SE 7, 169a22-b12.

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rely on the principle one word-one meaning, but not in the case of language-dependent fallacies. Often there is nothing wrong with inferences based on accidental identity or the conversion of an implication (for example in sign-inferences), but not in those cases. It is often allowed to argue from what applies in a particular respect or in a particular context to something which applies without qualification, but not in those cases. From the distinction relating to the source of delusion between these two types of fallacy one may draw two conclusions. The first conclusion is that Aristotle to some extent overstates his theoretical characterization of fallacies as the grounds for the appearance of there being a correct dialectical argument and refutation. It is clear that in chapter 1, as well as in chapter 4, where this characterization returns, he has primarily the language-dependent fallacies in mind, and there this characterization is quite appropriate. But it should not be taken to apply to all types of fallacy indiscriminately. On the other hand, one may also conclude that the apparent characterization of fallacies as mere deficiencies in the completeness argument of chapter 8 and its underlying definitions of refutation and proposition, as well as in the reduction to ignoratio elenchi in chapter 6, is misleading. For as we saw, the clauses in the underlying definition of refutation pertaining to the fallacies with an in-built source of delusion are added on to the official definition of chapter 1. Instead of accusing Aristotle of the inconsistency of having turned mere sources of appearance into characterizations of the deficiencies themselves, we should acknowledge that the distinction between deficiency and source of appearance is one which fails to be helpful in our efforts at understanding Aristotles theory of fallacy. We should rather wonder why it is that Aristotle incorporates in chapters 6 and 8 the relevant references to the sources of appearances in the definition of refutation. The answer to this last question is, I think, twofold. The first purpose this extended definition of refutation (including as a kind of preamble the definition of proposition) has is to serve as a kind of check-list for participants in a dialectical discussion, which they can use in order to avoid falling victim to fallacious arguments or committing fallacies themselves. This appears from the passage just quoted from the end of chapter 7, where Aristotle states that some source of delusion may cause us to not carefully check the definition of proposition or of deduction. The clauses of the extended definition thus make us alert to the possibility of error and assist us in looking for errors. The most important function of the extended definition, however, is not to describe or prescribe what should and should not happen in dialectical discussion, but lies rather at the level of the meta-theory of fallacy. It is just there to make the completeness argument of chapter 8 possible; similarly its function is said in chapter 6 to be a principle for distinguishing all the fallacies on the list:

Now, either one should distinguish the apparent deductions and refutations in this way, or one should reduce all of them to ignoratio elenchi, having made that a principle. (SE 6, 168a17-19)

For the ignoratio elenchi Aristotle refers to here is ignorance of the definition of refutation, and from the discussion in chapter 6 it is clear he has the extended definition in mind. Given these two functions of the extended definition, the objection stated in 3 that someone who commits a fallacy unintentionally or is victim of a fallacy may perfectly know this definition, but still (incorrectly) think there is nothing wrong with the argument, does not cut any ice. For fully knowing this extended definition in all its clauses (including the definition of proposition), one may still fail to apply it and in that sense be ignorant of the definition of refutation, because one is deluded by some feature of the argument there is nothing in this that is incompatible with the function of providing a checklist, and certainly

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not with the meta-theoretical function of providing the foundation for the completeness argument. Similarly the function of the point on which the fallacy depends, which Aristotle refers to in order to rule out alternative solutions of the fallacy of arguments depending on the same point there is the same solution (177b31-32) and of which he gives the content for some types of fallacy in the completeness argument, is primarily meta-theoretical. Of course the participants in a dialectical discussion may not have any of these points in mind, even when committing fallacies. What they do think is that a certain word only has one meaning in the context of the argument, that in this case an accidental relation suffices for the inference, or that the relation of consequence does convert in this case.31 But these thoughts, which would, if conceded, make the argument valid (though, of course, not sound), are of certain general types and it is these general types Aristotle is interested in for his theoretical discussions of fallacy.32 Therefore there is not really any element in Aristotles theory of fallacy which is incompatible with the concept of fallacy as an incorrect dialectical argument which appears to be correct.

31 Or their behaviour may be described in terms of them thinking so. I do not think Aristotle draws any distinction in this respect. 32 Likewise I think that the points referred to in the passage SE 8, 169b30-37 (quoted above in 3) are particular, but Aristotle is interested in them because they belong to several types.