The Ingredients of Aristotle’s Theory of Fallacy
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In chapter 8 of the Sophistical Refutations, Aristotle claims that his theory of fallacy is complete in the sense that there cannot be more fallacies than the ones he lists. In this article I try to explain how Aristotle could have justified this completeness claim by analysing how he conceptualizes fallacies (dialectical mistakes which do not appear so) and what conceptual ingredients play a role in his discussion of fallacies. If we take the format of dialectical discussions into account, we will see that there are only so many mistakes one can make which still do not appear to be mistakes. Aristotle’s actual list is almost identical to these apparent mistakes.
KeywordsAristotleFallaciesCompleteness claimDialectical discussion
Form of expression
But for the rest there is in these chapters hardly any indication as to on the basis of what considerations and criteria Aristotle arrived at this list. Thus in our attempts at understanding Aristotle’s 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.
Aristotle, however, 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 (as happened with few exceptions in the tradition after Aristotle, as documented by Hamblin in his ground-breaking book Fallacies from 1970). 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 Aristotle’s theory of fallacy, we shall have to find out what such an answer looks like.
My aim in this article is therefore to distinguish carefully the conceptual ingredients employed in Aristotle’s account of fallacies and in this way to reconstruct the framework in which he is working when making his claims for completeness and when discussing the separate types of fallacies. It will appear that if we take seriously the way Aristotle introduces the concept of fallacy as well as the dialectical context of his theory of fallacy, we already get a list of possible fallacies that resembles Aristotle’s one. Still closer to Aristotle’s list we get when we take a few of Aristotle’s assumptions about logic, predication, grammar and meaning into account. In the end I shall argue that there is reason to be optimistic about Aristotle really having been aware of how to develop a convincing argument for the completeness of his theory of fallacy. Moreover, we shall also see that Aristotle’s theory of fallacy can only be a systematic theory because it is a theory, not of mere mistakes, but of explainable mistakes in dialectical discussions.
2 The Object of a 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). Implicit in this determination of fallacies as apparent refutations 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 questioner’s conclusion should contradict the thesis of the answerer—we would then have a refutation.
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, ‘the one based on words’ (165a4-5), but he promises to give a full list (165a17-19). This list he provides in chapters 4 and 5 (see above); one should note the causal language of ‘bringing about the appearance of refutation’ at the beginning of chapter 4 (165b25). Moreover, the ‘appearance of refutation’ seems to be based on there being some similarity with real refutations, since Aristotle declares that ‘just as in other cases [something seeming to be something, without in fact being so] comes about because of a certain similarity, so too with arguments’ (164a24-25).
[A] deduction is an argument based on certain granted points, such that it states, by way of necessity, something different from the points laid down, while a refutation is a deduction together with the contradictory of its conclusion. (SE 1, 165a1-3)1
do not meet the requirements of the definition of a genuine refutation,
but still seem to meet these requirements,
because they, on several possible grounds, resemble genuine refutations.
In characterizing an argument as fallacious Aristotle thus seems committed, not only to explaining why it does not meet the requirements for a genuine refutation, but also to explaining why it resembles a genuine refutation and thus can be mistaken for the real thing—a fallacy is never a mere mistake, but involves a reference to what one may call a source of delusion.
3 A Systematic and Complete Theory of Fallacy
Aristotle makes here in fact two claims, one weaker and one stronger—even though Aristotle may not have been aware of the difference in strength. The weaker claim (‘they will all depend on those mentioned’) is that his classification of thirteen fallacies is extensionally complete in the sense that every particular argument that meets the four conditions listed above, is of some type on Aristotle’s list. The stronger claim (‘they could not depend on more’) is that his classification is also complete on the type-level. Moreover, we may safely assume that implicit in these two completeness claims there 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.
[W]e should know on how many grounds fallacies come about, for they could not depend on more; they will all depend on those mentioned. (SE 8, 170a10-11)
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 Aristotle’s 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 subtype of one of the fallacies on Aristotle’s list, but rather overlaps with several distinct types of fallacy?
However, it is clear that they do not solve it correctly, for arguments depending on the same point have the same solution. This solution, however, will not apply to all arguments asked in every way. (SE 20, 177b31-34)
Thus there must be a system behind Aristotle’s theory of fallacy, a system that provides the classificatory criteria for distinguishing 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.
4 Two Problems
Here Aristotle refers seven types of fallacy to seven points these fallacies are due to or depend on. These points are clearly negations of, infringements of or incorrect alternatives to requirements for a genuine refutation, as described by clauses in its definition.2 In one way or another Aristotle refers for each of the types of fallacy to these positive requirements as well. In doing so Aristotle picks up on an idea he formulates earlier in the Sophistical Refutations, when he, after having introduced his list of thirteen fallacies in chapter 4 and 5, starts chapter 6 as follows:
Now, apparent refutations depend on the parts of a genuine refutation, since for each part that is omitted there would appear to be a refutation, for example, (1) one is due to what does not follow on the basis of the argument (the one inferring an impossibility); (2) the one which makes two questions one is due to the proposition; also (3) one is due to what is accidental (instead of the thing in itself), and a part of this, (4) the one due to the consequence; further, (5) for the conclusion not following at the level of the object, but at the level of the sentence; next, (6) (instead of the contradiction holding universally, in the same respect, in relation to the same thing and in the same way) due to it holding to a certain extent, or also due to each of those qualifications; further, (7) due to securing the point at issue, despite the clause ‘the point at issue not being included’. Thus we should know on how many grounds fallacies come about, for they could not depend on more; they will all depend on those mentioned. (169b40-170a11)
The basic idea is that all fallacies on Aristotle’s 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 constitutes ignorance of this definition. It should be noted, though, that even in chapter 6,3 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).
Thus apparent deductions and refutations are either to be classified in this way or to be traced back to ignorance of refutation, making this the principle. (168a17-19)
However, it is not at all clear how to assess this argument for the completeness claim. The first problem is that the list of requirements for a genuine refutation (corresponding to the parts of its definition), already not being very explicit, is nowhere defended or explained, let alone that one may grasp that the list is complete. It is remarkable that this first problem is not discussed at all in the literature, since it goes to the heart of the issue as to what the system behind Aristotle’s classification of fallacies is.4 It thus seems hard to understand Aristotle’s clear confidence when stating his completeness claim.
A second problem does not concern the completeness argument as such, but the conceptual framework in which it is formulated. A definition of refutation is going to list requirements 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. Somehow the source of delusion must be involved in the concept of the fallacy at issue as well. So how can Aristotle maintain here that one gets a systematic theory of fallacy on the basis of the definition of refutation alone?
In this article I propose solutions to these two problems. In doing so I shall ignore the fallacy of ignoratio elenchi and not try to account for its appearance on Aristotle’s initial list of thirteen fallacies. For in his theoretical discussion of chapters six through eight, Aristotle treats it as a super-fallacy, which one commits if one commits any fallacy, rather than as fallacy separate from the other ones. Moreover, Aristotle does not give any good independent characterization of it, not even by way of examples.
5 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’s conceptual framework of fallacies as ways in 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 in Sect. 2, 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 both Aristotle’s completeness argument and 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 conception of fallacy as an actual breach of one of the requirements listed in the definition of refutation.
There is an initial question, the problem (problêma), of the form ‘ψ or ¬ψ?’ asked by the questioner to the answerer. The answerer chooses between the two alternatives, thus adopting a thesis—let us say ψ.
The questioner asks a string of questions (protaseis) of the form ‘φ?’. 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 φi.
The questioner uses the φi as premisses (again protaseis) in a deductive (in terms of the form) argument (sullogismos) with a conclusion (sumperasma) γ.
If γ = ¬ψ, then there is a refutation of the thesis of the answerer.
Sentences are used (whether as questions, concessions, theses, premisses or conclusions).
Sentences used earlier are cited (concessions as premisses, conclusion as one half of the possible refutation, thesis as the other half);
Questions are asked (for the thesis or for concessions);
Conclusions are drawn on the basis of premisses;
Sentences are conceded (agreed on) or adopted (as theses).
There are no other dialectical acts to be distinguished in dialectical discussions.
Sentences should be grammatically and semantically well-formed;
As sentences citations should be identical to what is cited;
Questions should be innocent, that is, only ask for one thing at the time;
a. Conclusions should follow necessarily from the premisses;
b. Conclusions should be different from each of the premisses;
c. Conclusions should require each of the premisses;
Only unproblematic sentences should be conceded or adopted.
That sentences should be grammatically well-formed is not of immediate relevance for understanding Aristotle’s completeness argument. But he does mention and discuss (in SE 3, 14 and 32) as a secondary aim for the questioner to achieve in a dialectical discussion if a proper refutation is unattainable, that he may bring the answerer to making an ungrammatical statement (a soloikismos). Even in such cases, though, the sentences used in the discussion leading up to the conclusion should be grammatically well-formed. Thus Aristotle would presumably not recognize a discussion in which grammatically unwell-formed sentences are used as a proper discussion at all.
That sentences should be semantically well-formed is meant to rule out ambiguity, for ambiguity may affect the correctness of the acts in which these sentences are used. Since ambiguity concerns a single sentence with several meanings, this correctness condition presupposes an identity criterion for sentences. It will prove useful to assume for Aristotle the following identity criterion: there is one and the same sentence if and only if there is the same string of words in the same order (regardless of grammatical structure); there is, again, one and the same word if and only if a lexical unit consists of the same letters in the same order (regardless of intonation). The identity criterion for words may seem too weak, but Aristotle clearly assumes it for the relevant fallacy, even though he himself acknowledges that the relevant fallacy does not occur in normal dialectical discussions (SE 5, 166b1-3).
Also in condition 2. there is a reference to sentences being identical, and the relevant identity criterion may be taken to be the same, provided we assume condition 1. to be fulfilled.
Conditions 4.b. and 4.c. are peculiar to Aristotle’s conception of a dialectical discussion. A dialectical discussion would be superfluous if it were possible to obtain a single concession which by itself suffices to refute the answerer: that is not a dialectical discussion, but just a self-contradiction on the part of the answerer at the outset. This justifies 4.b. It is also part of Aristotle’s ideal of a dialectical discussion that it be completely clear which premisses are needed to establish the conclusion and which are not, for one of the external purposes of dialectical discussions is to find out about the relative strength of propositions and about there logical relations. Having said that, however, it is not as such that condition 4.c. is relevant for Aristotle’s theory of fallacy. As we shall see, its relevance concerns the fact that if one is not clear about what propositions are necessary for reaching a certain conclusion, one may take a certain proposition to be thus necessary, and thus think one has to give up or retract it if the conclusion is unattractive for one reason or another.
Here I have listed condition 5. as a separate condition, because the act of acceptance is a separate dialectical act. But in fact in terms of its correctness condition is concerned, it reduces to 3. and, again, 1. Therefore I will subsequently ignore 5., also because infringements of 3. comprise cases which are not cases of infringement of 5.
Sentences are grammatically or semantically not well-formed by being ungrammatical or ambiguous;
Citations are not identical to what is being cited, but are different by some words having been omitted or added;
Questions are not innocent, in that one question is not isolated from another;
a. Conclusions do not necessarily follow from the premisses;
b. One of the premisses is not different from the conclusion;
c. There are premisses superfluous for the conclusion.
Sentences are ambiguous, but because of being composed of the same words in the same order the sentences seem to have a single meaning (here I presume grammatical well-formedness);
Citations differ in some words, but this difference seems unimportant;
Several questions are asked in the form of a single question;
a. In so far as their logical properties are concerned, the premisses lend themselves, due to some similarity, to being understood incorrectly in such a way that they, thus understood, would license the conclusion;
b. Premisses which are not different from the conclusion appear to be different by being phrased differently;
c. By being mentioned as if they were premisses, some statements merely appear to be premisses.
Since the list of dialectical acts is complete, this list of possible types of fallacy must be complete as well: there could not have been more types; all fallacies to be distinguished by Aristotle should either correspond to a type on this list or to a sub-type of a type on this list.
6 Aristotle’s List
If we then proceed to check the list of all possible types of fallacy in a dialectical discussion against Aristotle’s actual list of fallacies, we see that there is an almost exact correspondence. In this section I will go through the list of possible fallacies one by one and discuss the corresponding actual fallacies as distinguished by Aristotle. For reasons of space I will not be able to do justice to all the complications some of Aristotle’s discussions give rise to, but in order to become aware of some of the conceptual ingredients of Aristotle’s account of fallacies, it will be necessary to indicate some of them and to explicate some of the limitations of Aristotle’s conceptualisation of fallacies.
corresponds to Aristotle’s language-dependent fallacies, which are all subtypes of it. At the beginning of chapter 4 Aristotle refers to a separate completeness argument for them (for discussion of the translation, see my (2006) 107–108):
In order to make sense of this completeness claim, we must assume that Aristotle distinguishes between three levels of elements bearing meaning: morphemes, words and sentences. If we then list the kinds of ambiguity which might arise at each level, we get the following:
The ways of bringing about the appearance of refutation dependent on the expression are six in number; they are: homonymy, amphiboly, combination, division, intonation and form of expression. There is a proof of this through induction (whenever one considers another argument) as well as through deduction, namely that this is the number of ways in which one can indicate with the same words and statements what is not the same. (SE 4, 165b24-30)
morphemes (suffixes with Aristotle, but he could have included pre- and infixes as well) in ancient Greek standardly provide certain semantical information about the word, e.g., of what gender the word or notably the thing signified is, what type of things are signified (events, states, doings or undergoings, individual things, quantities, qualities, etc.),6 but they do not reliably so, creating room for misclassification on the basis of morphology: a word or the thing signified by a word is classified as being of the wrong gender or of the wrong type of thing, for example a state as an action, a general thing (e.g., man) as an individual thing, a quantity as a quality, and so forth—this is Aristotle’s fallacy of form of expression.
words (in the sense of the same letters in the same order) may constitute two different words (as lexical units), depending on pitch or intonation—this is Aristotle’s fallacy of intonation, which crucially depends on the loose identity criterion for word outlined above.
words (lexical units) may have several primary meanings—this is Aristotle’s fallacy of homonymy.
sentences (in the sense of the same words in the same order, in accordance with the identity criterion for sentences given above) may constitute two different statements, depending on the grammatical hierarchy of composition (‘grammatical tree’); in the case of Aristotle’s fallacy of combination the reading which groups words together lower in the tree is misused in the argument, while in the case of Aristotle’s fallacy of division there is a misuse of the reading which distributes words which on the intended reading belong together over several groups or levels (this is a summary of the results obtained in my 2006).
statements (a sentence having one grammatical hierarchy of composition) may distribute grammatical functions (e.g., subject and object in accusativus cum infinitivo constructions, as they often occur in ancient Greek and other case languages) in different ways over the words (of course in so far as the case-morphology allows)—this is Aristotle’s fallacy of amphiboly (for the distinction between combination and division, on the one hand, and amphiboly, on the other, see my 2006, 146–147).
In the completeness argument of chapter 8 Aristotle lumps all these language-dependent fallacies together under ‘(5) for the conclusion not following at the level of the object, but at the level of the sentence’, which is an apt description provided we ascribe to Aristotle the right identity criterion of sentences; it thus fits perfectly to possible fallacy 1 on our list. As far as the different sub-types are concerned, however, they can only be distinguished in the way Aristotle does if we bring in Aristotle’s somewhat peculiar considerations about grammar (in the case of combination, division and amphiboly) and take into account the system of morphemes and cases particular to the Greek language (in the case of form of expression and amphiboly). Moreover, one may think that identity conditions for words underlying the fallacy of intonation is too loose. Only the fallacy of homonymy is independent of such particular considerations.
The source of delusion in the case of language-dependent fallacies consists in sentences being composed from the same words in the same order. Commonly such sentences have a single meaning, having a single grammatical structure with a single possible distribution of grammatical functions, and with words which can only be pronounced in one way and have a single meaning. Thus normally a sentence being composed similarly, that is, from the same words in the same order, is a good sign of it having a single meaning; however, not always, so that this similarity can function as a source of delusion.
corresponds to Aristotle’s fallacy of qualification. With this fallacy some apparently unimportant qualification or clause is deleted or added between uses of allegedly the same sentence within one dialectical discussion. Aristotle’s actual examples seem to be confined to contradictory pairs in which either on one side or on both sides a clause has been dropped, and also the relevant clause ‘(6) (instead of the contradiction holding universally, in the same respect, in relation to the same thing and in the same way) due to it holding to a certain extent, or also due to each of those qualifications’ is limited to the contradiction between the conclusion of the questioner and the thesis of the answerer. Elsewhere, however, he states that this fallacy is related to the deductive part of a refutation (SE 6, 169a18-21, though the whole passage is problematic). Moreover, the limitation is irrelevant to his conception of the fallacy. The source of delusion is, as Aristotle states (SE 7, 169b10-11), the small difference between the two sentences used—we may assume, so small as to seem negligible for the discussion of the issue at hand. It seems to be Aristotle’s idea that often such a small difference really is negligible, for example in the case that if someone is pale with regard to his skin: he will also be pale ‘without qualification’, as Aristotle formulates it. Thus the cases in which it is not allowed to drop or add a clause resemble those in which it is.
corresponds to a large extent to Aristotle’s fallacy of many questions. In this fallacy several questions are combined into one question. The criterion for a question or proposition being a single question or proposition Aristotle employs is that ‘one thing is said of one thing’ (SE 6, 169a6-14, compare the clause in the completeness argument: ‘(2) the one which makes two questions one is due to the proposition’), but it is not exactly clear how strictly we should understand this criterion. For example, I would guess that Aristotle would consider the question ‘Are we giving him this book?’ as a single or atomic question, provided it is interpreted as asking whether we are giving or not giving this book together (rather than each of us separately). Similarly he should not have any qualms about the question ‘Are zebras black and white?’, provided a negative answer only commits one to zebras not being black as well as white. But these examples are already more complicated than the ones mentioned by Aristotle himself, which features structures like: ‘p or q?’ (SE 5, 168a2-3) and ‘p and q?’ (168a5-7) (where p and q are each atomic propositions saying one thing of one thing), but also propositions with distributive quantifiers (every …, both …—see SE 30), so that it asks several atomic questions together; he also implies that ambiguous questions are cases of many questions (SE 17, 175b39-176a11) (which makes sense if one supposes, with Aristotle, that the single things which in a single proposition are predicated the one of the other are indeed single things, rather than words, so that an ambiguous question has in fact the form ‘p and q?’ because the ambiguous sentence refers to two states of affairs).
Thus Aristotle does not provide examples which problematize what counts as ‘one thing’, whether as the subject of a single question or as the predicate. Likewise he conspicuously does not give examples like: ‘Have you stopped smoking?’, which involve predicates that problematically can be analysed into several simpler predicates in a relation of presupposition. One may speculate about possible reasons for Aristotle’s failure to deal with such more complicated cases. In the case of questions with a presupposition this may be due to them not having been ‘discovered’, but since Plato discusses propositions with a collective subject (Hippias Major 300–303), this explanation cannot be applied generally.
We therefore have to conclude that there are limitations to Aristotle’s discussion of the fallacy of many questions, at least if one compares it to the fallacy as it could be conceived, and that they are due to Aristotle’s failure to consider problematic subject and predicate terms.
Aristotle does not say much about the source of delusion in the case of the fallacy of many questions, except that it concerns a ‘small difference’ (SE 7, 169b12-17). In the context, however, it is clear that this small difference is not at the material level, as in the case of the fallacy of qualification, but at the theoretical level: the criterion that there should be a single question is easily overlooked or failed to be applied. Aristotle does, however, distinguish between cases that are easy to detect and cases that are more difficult, where the difference seems to be that a question of the structure ‘p or q?’ is easy, while questions of the structure ‘p and q?’ where, moreover, p and q have the same subject or predicate, are more difficult to unmask (SE 5, 168a3-11). The reason, presumably, is that or-questions quite often lead to dilemmas, including false ones, whereas and-questions are far more often unproblematic. Thus the source of delusion is more effective if there are more unproblematic cases for the problematic cases to be similar to.
is by far the most difficult one; it corresponds to some extent to Aristotle’s fallacy of accident, the most difficult one on his list anyway, and partly to Aristotle’s fallacy of consequence, which he officially treats as a subtype of the fallacy of accident (e.g., in the completeness argument and at SE 7, 169b6-7), but regularly also as an independent fallacy (e.g., SE 5, 167b1-12 and 28; compare SE 7, 169b7-9).
Aristotle clearly assumes that there is only one way in which premisses that do not necessitate a conclusion may nevertheless seem to do so (see SE 6, 168a34-b5). The framework in which he makes this assumption this is that of predication as a kind of identity statement: a proposition saying one thing of one thing ‘S is P’ is interpreted by him as ‘S is identical to a P-thing’, ‘Some S-thing is identical to a P-thing’ or ‘Any S-thing is identical to a P-thing’. Since the identity relation is transitive, it seems that whatever P-thing is said to be identical with the P-thing said of S or of some or any S-thing, may be said directly of it, and vice versa (see, e.g., SE 6, 168b27-33; 7, 169b3-9); thus what applies to an accident of a thing is also assumed to apply to the thing itself or vice versa (SE 5, 166b29). As it is, however, Aristotle claims, the identity relation is only always transitive in the case of strict identity, that is, identity in being (SE 24, 179a35-b1).
The source of delusion for the fallacy of accident, however, is not so clear. As Aristotle seems to present it at SE 7, 169b3-9, it is the transitivity of identity in being, and thus also of the non-accidental type of predication, which constitute the correct case giving rise to the mistaken belief that every type of identity and of predication is transitive; in the completeness argument the phrase ‘(3) one is due to what is accidental (instead of the thing in itself)’ gives the same impression. The similarity between these two types of identity and predication would thus explain the source of delusion. Elsewhere, however, Aristotle is less clear, and does seem to hint at some ‘accidental’ predications and identity relations being transitive as well (e.g., SE 24, 179a28-30). However that may be, it seems anyway difficult to distinguish between accidental and non-accidental identity or predication. Aristotle does not really give a criterion in the Sophistical Refutations, and it would go too far in the present context to delve into arguments and theories from other Aristotelian works.
Whether Aristotle is right in his assumption that the fallacy of accident is the only way of an argument appearing necessary without being so (in so far as this appearance cannot be traced back to other types of misleading dialectical acts, of course), seems equally difficult to assess. If one, like Aristotle, assumes that every proposition has an ‘S is P’-structure, he seems to be right, for the only logical relation is then that of predication. It is, however, a questionable assumption; thus we see again that Aristotle’s logical assumptions determine how he classifies and characterizes fallacies.
Moreover, Aristotle does not seem to be quite consistent, for as said, he does on occasion analyse the fallacy of consequence independently of the fallacy of accident. On those occasions it is not the transitivity of identity which provides the logical framework, but rather the convertibility of the relation of ‘consequence’ (SE 28): if x follows upon y, it also seems that y follows upon x, where x and y can be properties, but also facts without a common subject (see, e.g., SE 5, 167b6-11). It is impossible in the latter case to consider the fallacy of consequence as a subtype of the fallacy of accident.
Once one accepts, as Aristotle does in this latter case, that there are several ways in which a conclusion seems to be necessitated by the premisses without in fact being so, one seems saddled with the burden that one should show that there cannot be any fallacies of type 4a beyond accident and consequence. For example, often it is true that if for every F there is a G, there is a G for every F—or at least, it is often taken to be true. Sometimes Aristotle can analyse such quantifier shifts as cases of the linguistic fallacies of division and combination (see, e.g., SE 4, 166a30-31, and De generatione et corruptione 1.2, 317a1-10), but even if they cannot because the shift is explicit, they may still appear correct and thus ought to be assigned to some fallacy.
Thus one might appeal to the limitations of Aristotle’s logical theory in order to explain the fact that the fallacies of accident and consequence do not exhaust the possibilities of type 4.a.
corresponds to Aristotle’s fallacy of petitio principii, also known as ‘begging the question’, that is, asking immediately for the thing at issue, namely the conclusion to be reached by the questioner. The clause in the completeness argument is: ‘(7) due to securing the point at issue, despite the clause “the point at issue not being included”.’ Normally Aristotle does not mention a source of delusion (except that one may easily fail to apply the clause in the definition of a genuine refutation—see again SE 7, 169b12-17). However, he does show awareness that there may be a material source of delusion, for example, in the case there are synonymous statements with different words, or cases which either stand in a relation to the conclusion to be reached of being a more specific or more general version of it (see SE 5, 167a36-37, referring to Topics 8.13, 162b34-163a13). For generally the fact that a different word is used is a reliable sign that the conclusion really differs from the premiss.
finally, corresponds to Aristotle’s fallacy of non causa: what is taken to be a ground for the conclusion is actually not a ground for the conclusion. In order to arrive at a fallacious argument, this is only relevant in the course of reductio ad absurdum arguments, as Aristotle also makes clear in the relevant clause of the completeness argument: ‘(1) one is due to what does not follow on the basis of the argument (the one inferring an impossibility)’, for only in such arguments is it necessary for the further argument to identify correctly the premiss leading to the unacceptable conclusion.
Again Aristotle does not mention a source of delusion, except that it concerns a small difference in that we easily forget to apply the relevant clause in the definition of a genuine refutation (SE 7, 169b12-17). But it is easy to supply one: that the statement is mentioned as a premiss or even only together with the premisses, for normally that is a reliable indication that it does concern a premiss.
If we compare the results of Sect. 5, listing all the possible ways in which in an Aristotelian dialectical discussion an argument may seem to constitute a refutation without being one, with the descriptions and examples of Aristotle’s actual fallacies, we see that there is a more than remarkable overlap. Only in the cases of many questions and type 3.-fallacies and of accident/consequence and type 4.a.-fallacies does Aristotle not fully exhaust the potential of the relevant types. As we saw, this is due to particular Aristotelian assumptions, in the case of many questions that predicates and subject terms whose unity is problematic are not to be considered, and in the case of accident that all propositions have a ‘S is P’-structure, which, moreover, is to be taken to involve a kind of identity relation. But most importantly for our purposes, Aristotle does link the fallacy of accident uniquely to the requirement that the premisses should necessitate the conclusion (SE 6, 168a37-40), and thus to the correctness condition for the dialectical act of drawing conclusions; also in the case of many questions he links the fallacy to the requirements of a certain type of dialectical act, namely asking questions. Though it cannot be proven conclusively, the best explanation, therefore, for Aristotle’s confidence when he states at the end of the completeness argument of chapter 8 that ‘Thus we should know on how many grounds fallacies come about, for they could not depend on more; they will all depend on those mentioned’, seems to be that he was aware of the different types of dialectical acts involved in a dialectical discussion and of the relevant correctness conditions. His own views about the nature of predication and logic may have hindered him in fully exploiting the possibilities provided by that awareness, but just as in the case of the language-dependent fallacies, where features of the ancient Greek language and Aristotle's views on grammar determine the characterizations of the actual fallacies, these limitations are of a rather accidental nature to that awareness.
Moreover, even if one does not share my optimism in having found an explanation for Aristotle’s self-assured completeness claim, it remains the case that the approach adopted in this article shows us how Aristotle goes about in constructing his systematic theory of fallacy: since we know the full extent of the possibilities inherent in the material of dialectical discussion, we are in a much better position to appreciate what conceptual ingredients determine the outcome of Aristotle’s endeavours. In that case only the psychological description of Aristotle’s account is different, in that Aristotle rather coincidentally stumbled upon all the correctness conditions for dialectical acts, perhaps by having gone through many dialectical arguments, but was partly blinded by his own preconceptions.
Thus the first problem formulated in Sect. 4 has been solved. In the course of solving it, however, we have also acquired the means to deal with the second problem formulated there, namely how to understand the role of the source of delusion, the real fact of there being a similarity between a fallacious refutation and some real refutation, in Aristotle’s theory of fallacy, and more particularly, how to make sense of Aristotle’s claim in chapters 6 and 8 that a definition of a genuine refutation suffices for a complete theory of fallacy, apparently without sources of delusion playing any role whatsoever.
Source of delusion
Same words in same order
Part of sentence/qualification added or dropped when cited
Difference being small
More than one question asked
Question seeming normal
What is said of accident being ascribed to thing itself or vice versa
Identity seeming always transitive
[Implication seeming always convertible]
Conclusion identical to premiss
This identity being obscured by use of synonyms etc.
Irrelevant proposition held responsible for unacceptable conclusion
This proposition being mentioned as premiss
What we see is that also for Aristotle fallacies are consistently characterized in terms of the mistake being made and that the source of delusion does not enter into the characterization. That does not mean, however, that the source of delusion does not play a constitutive role in Aristotle’s way of conceptualizing fallacies. For the source of delusion is that objective feature of arguments which makes it possible that we fail to see that some dialectical discussion does not conform to the standards required. A source of delusion can only work in this way if it resembles a feature of such discussions which normally is a sign of the discussion meeting all requirements—but in some cases it is not. Thus it is only the very possibility of us being deluded by some feature of a dialectical discussion that provides a real explanation of us making the mistake which is the fallacy; if there had not been an objective source of delusion, we could perhaps have made the mistake as well, but it would not have been explainable—it would have been the kind of mistake we make due to some accident, and thus not amenable to be accounted for in a systematic theory of fallacy. For that reason a simple failure to meet the requirement that the conclusion follow necessarily from the premisses, for example in argument with a glaring hole in it, does not count as a fallacy.
Thus fallacies are nothing more than the mistakes being made and can be characterized by reference to a list of requirements for a genuine refutation, as Aristotle does in chapter 8, but what fallacies there are, is also determined by what kind of sources of delusions there are. It follows from this that what clauses feature in the definition of a genuine refutation, at least in so far as such a definition is going to provide the basis for a completeness argument for a list of fallacies, is also determined by what kind of sources of delusions there are. Thus the definition of a genuine refutation underlying Aristotle’s argument in chapters 6 and 8 of the Sophistical Refutations cannot be a mere definition of refutation describing what it is, regardless of possible sources of delusion, nor can it be meant thus, as presumably the definition of refutation in chapter 1 is meant.7 It is rather an extended definition, meant to function as a normative rule and presumably also as a checklist (one should compare SE 7, 169b15-17). If we fail to apply it, we may still know what a refutation in fact is, but as knowledge of the rules consists in their application, we fail to know the extended definition of refutation, and thus fail to know really the refutation: every fallacious argument we accept shows that we suffer from ignoratio elenchi.
Translations are taken from my (2012), a new translation of the Sophistical Refutations into English. Occasionally I do not translate the text as established by Ross (1958), but stay closer to the majority of the manuscripts; for a list, see my translation.
In the case of (2) Aristotle alludes to an infringement of the requirements mentioned in the definition of a proposition.
In chapter 6 Aristotle seems to present the reduction to ignoratio elenchi as an alternative way of distinguishing the fallacies he has listed in the previous two chapters.
Ebbesen (1980) already remarks that ‘the principles underlying the classification are never clearly stated’, for the rest only being able to refer us to the article by Evans (1975), which is not of much help either.
The vocabulary of dialectical acts with correctness conditions is similar to the way fallacies are conceptualized in the pragma-dialectical school of argumentation theory: fallacies are infringements of correctness rules for speech acts pertinent in discussion—see: Van Eemeren and Grootendorst (2004). The difference is that they have a far less strict conception of the structure of a dialectical discussion, and at the same time bring in considerations of reasonableness, instead of or in addition to Aristotle’s logic-based requirements.
One may also compare the morphology indicating tenses of verbs, though Aristotle does not mention the phenomenon in the context of his discussion of this fallacy, presumably because in ancient Greek there are very few ambiguities to be constructed that depend on them.
Though the point that the conclusion be different from any of the premisses is a normative element which is also mentioned in the definition of chapter 1 of the Sophistical Refutations.