The Importance of The Sophistical Refutations

The work of Aristotle which we call the Sophistical Refutations has received relatively little attention from modern scholars. This neglect persists still today despite the importance of the work for various topics of special current interest. The professed aim of the Sophistical Refutations is to consider the nature of the sophistical elenchus, i.e. of the elenchus, or refutation, which is only apparent, and thus false and not true, the elenchus of which the sophists are the masters (SE 1.164a20f). Aristotle’s purpose is to enable us to understand all of the types of false but apparent refutation so that we will be able to identify and expose them, and not be deceived by them, when we encounter them (see, e.g., SE 1.165a34–7, 16.175a3–12). But Aristotle investigates the nature of sophistical and false refutation in large part by considering how it differs from true refutation (see e.g., SE 5.167a21ff, 8.169b40ff, 11.171b34ff.). So this work gives us some of our best information as to what is required for and what is accomplished by a true refutation, in Aristotle’s view. This is a matter of some importance since Aristotle devotes a good deal of attention, throughout his works, to the refutation of the views of his opponents. It is necessary for us to know just what it is that Aristotle thinks is accomplished by these refutations in order to understand their role in his inquiry overall.

This matter is of special relevance for our understanding of Aristotelian dialectic. One mode of elenchus which Aristotle discusses prominently in the Sophistical Refutations, and often employs in his works, is dialectical elenchus (see, e.g., SE 9, 11). On one account of dialectic, the aim of dialectical refutation is only, at most, to bring out that an opponent has inconsistent views and thereby to show not that any one of these views is false (or true) but only to show that, because the opponent has inconsistent views on some subject, he lacks knowledge of any of his views.¹ If this is so, then no specific conclusion, whether positive or negative, can be taken to be established by a dialectical elenchus. If, however, a dialectical refutation can establish that some particular view of an opponent is false, then specific claims, and things inferable from them, can be established through dialectical elenchus and taken as established in Aristotle’s further discussion. A study of the Sophistical Refutations should enable us to decide which of these views is correct and in so doing enable us to see, in some detail, the nature of an Aristotelian elenchus. This question is also of further interest for our understanding of the earlier history and development of dialectic. The issue of what it is that is accomplished by a dialectical elenchus has figured prominently also in discussions of the Socratic elenchus, the mode of elenchus employed by Socrates in the early dialogues of Plato. Aristotle himself relates his own account of elenchus in the SE to Socratic practice, most explicitly in SE 34. A proper view of the aims of the Aristotelian elenchus will, thus, have a significant bearing on how we should understand the history and development of views on that subject.²

Aristotle’s Introduction: SE 1

Aristotle begins his study of sophistical elenchus with ‘what comes first by nature’ (1.164a20–2). This turns out to be the task of showing that the object of his inquiry exists, i.e. that there are sophistical refutations and people who produce them, namely the sophists (1.165a32–7). This follows the natural order of inquiry because, as Aristotle makes clear in the Analytics, successful inquiry must establish that the object of inquiry exists as a prerequisite to learning what it is (see, e.g., An.Post. 2.1–2, 8). So Aristotle goes on to make it clear that sophistical or only apparent refutations exist by pointing to and explaining the mechanics of the ‘most prolific and common’ type of familiar apparent, but false, refutation – namely the type which involves the fallacy of equivocation (1.165a3–19). He begins his task of identifying this familiar type of apparent elenchus or refutation with a preliminary specification of what a genuine elenchus or refutation requires.

So far this tells us what form an elenctic argument has, namely syllogistic, and what form its conclusion has, as the contradictory of an opponent’s view; but nothing more (cf. 6.168a36–7, An.Pr. 2.20.66b11). Still, even this already raises significant questions for exploration. Why must a refutation be syllogistic, and thus deductive, in form? Why can one not refute someone by a sound inductive argument? Also, why must a refutation have for its conclusion the precise contradictory (ἀντίφασις) of some thesis of an opponent (cf. 5.167a23–7; An.Post. 1.2.72a12–13)? If it is sufficient, in order to refute an opponent’s claim to knowledge of any thesis in some area, to show that he is committed to inconsistent or incompatible views in that area, why does Aristotle insist on the stronger requirement for a refutation that the opponent be shown to be committed to explicitly contradictory views? These are among the questions which we must try to answer.

Types of two-party argument in SE 2

It is clear from the first chapter of the SE that Aristotle is treating an elenchus or refutation, whether real or apparent, as a type of two-party argument typically produced in a question and answer discussion or dialogue. Therefore, to make further progress in his study of what a refutation is, both true and false, he lists and describes in chapter 2 all of the types of two-party arguments used in question and answer discussion or dialogue (ἐν τῷ διαλέγεσθαι, 2.165a38). These types are didactic, dialectical, peirastic and eristic arguments. It is clear enough already which of these four types of arguments is the one used in merely apparent or sophistical elenchus, namely eristic arguments. Aristotle defines eristic arguments as follows:

This is to say that eristic arguments are those which employ either valid, or invalid but apparently valid, syllogistic inference from premises which appear to be accredited or noted opinions (ἔνδοξα) but are not (cf. Top. 1.1.100b23ff. There Aristotle also counts invalid but apparently valid syllogistic inferences from actual ἔνδοξα as eristic arguments). This description of eristic argument introduces a point which Aristotle will later want to emphasize, namely the similarity between eristic or sophistical argument and dialectical argument, given that proper dialectical argument is based on genuine ἔνδοξα (2.165b3–4). But Aristotle does not yet tell us clearly which of the three types of argument that he lists along with eristic argument is the one to be used for genuine and not merely sophistical refutation. The definition which he offers of dialectical argument in SE 2 might appear to make all dialectical arguments conform to the requirement for genuine refutation already given above.

However, we cannot in fact use this account of dialectical argument to immediately conclude that successful dialectical arguments as such always provide us with a type of true refutation of an opponent. To begin with, dialectical arguments are arguments from ἔνδοξα, and, as Aristotle makes clear in the Topics, these are restricted to certain types of standing opinion – namely the opinions of everyone, of most people, or of the wise – either all of the wise, or most or the most celebrated (Top. 1.1.100b21–3, 101a10–14). Aristotle makes it evident in his discussion of the requirements for a respondent in dialectic in Topics 8.5–6 that a respondent is required to concede appropriate ἔνδοξα, as premises for dialectical argument, whether they are his own opinions or not. In fact, though Aristotle there describes a form of dialectic in which the respondent is required to concede premises in accord with his own views, he also says that a respondent in dialectic will standardly be expected and required to concede premises by reference to what is ἔνδοξον or accredited without qualification (ἁπλῶς), by contrast with what is accepted and accredited by him (8.5.159b23–7). In that case, obviously, the respondent’s concessions need not at all be his own convictions, and in such a case a genuine dialectical argument which does genuinely deduce the contradictory of a respondent’s thesis from conceded ἔνδοξα will not even show that the respondent himself, or anyone else, has inconsistent beliefs. So such an argument cannot count as a refutation of the respondent himself in this sense. Moreover, Aristotle also points out in the Topics that the ἔνδοξα from which the reasoning proceeds in a genuine dialectical argument are sometimes false, since the things accepted by the many or the wise are often false (8.11.161a24ff). In this case, of course, dialectical argument can hardly establish its conclusion, namely the contradictory of the respondent’s thesis. Therefore, it can hardly show that the respondent’s thesis is false and refute him in that sense. Thus it is clearly possible for a successful dialectical argument neither to show that an opponent has inconsistent beliefs nor to show that any thesis which he is maintaining is false. So, despite the closeness of the initial descriptions of refutation and dialectical argument in SE 1–2, there are good reasons to doubt that Aristotle means us to conclude right away that a successful dialectical argument always counts as such as a true refutation of some opponent or of some opponent’s view. We shall shortly see quite clearly that Aristotle does not mean us to conclude this.³

The other two types of argument which Aristotle lists in SE 2 appear to be somewhat more promising on this score. Didactic arguments are defined as follows:

Since didactic arguments have the actual principles of some actual branch of learning for their premises, they obviously have true premises. Since, as Aristotle later makes clear, all didactic arguments are demonstrations (ἀποδείξεις) by which respondents come to know certain results, it is also clear that they are capable of establishing their conclusions (2.165b8–11). But there is no reason to think that Aristotle wishes to count all didactic arguments, as such, as refutations since there is no reason to think that, either in Aristotle’s view or in fact, to teach someone something requires a refutation of any previous false belief or false claim to knowledge by that person. We easily can and do learn new things from teachers without having any previous false beliefs or pretensions corrected. So though, as later becomes especially clear in SE 9 (170a23ff), didactic arguments will in some cases serve as refutations, didactic arguments are not, as such, elenctic arguments.

This leaves us with peirastic arguments. The name peirastic is already an indication that peirastic arguments are used to put someone to the test (πεῖρα). This suggests that these arguments will conform to the requirement for a refutation (at 1.165a2–3), that when successful they have as conclusion the contradictory of an opponent’s actual claim. This is later confirmed when Aristotle makes it clear that successful peirastic arguments are all genuine dialectical refutations which, thus, conform to this feature of the account already given of dialectical arguments (see SE 8.169b23–5, 9.170b8–11, 11.171b4–5; cf. 34.183a37–b1). Moreover, the official definition of peirastic arguments in SE 2 goes as follows:

This makes it clear that, since the premises of a peirastic argument must be the actual beliefs of the respondent, if successful peirastic arguments do deduce the contradictory of some further claim of the respondent, as they must do as dialectical arguments, then peirastic arguments will show that some respondent has inconsistent beliefs. But it is also clear that peirastic arguments aim to do more than this. If this was their only objective then the first requirement for the premises of a peirastic dialectical argument, that they be the actual beliefs of the respondent, would be sufficient and there would be no need for the second requirement – that the premises be things which are bound to be known by anyone who pretends to have expert knowledge. That second requirement is entirely unnecessary if peirastic arguments aim only to show that an opponent has inconsistent beliefs and to expose an opponent’s ignorance simply by this means.

The importance of this is as follows. If peirastic arguments are just the arguments which are required for a genuine dialectical elenchus or refutation that exposes the ignorance of a respondent then it is clear that it is not sufficient, in Aristotle’s view, for such a genuine dialectical refutation of someone, to show that he has inconsistent beliefs. Since, in fact, Aristotle does later explicitly say in SE 8, that it is indeed peirastic to which the task of dialectical refutation and exposure of ignorance belongs (169b23–5, cf. 11.171b4–7, 172a17ff), we can already determine from the opening definition of peirastic arguments that such a dialectical elenchus or refutation does not aim simply to show that some pretender to knowledge has inconsistent beliefs. What more such a refutation aims to accomplish will depend on what Aristotle means by his second requirement for the premises of peirastic arguments. Since this does not become fully clear for some time in the SE, it will be best to postpone our consideration of it and to follow the track of Aristotle’s own presentation.

Types of apparent refutation: SE 3FF

Once he has set out the types of question and answer argumentation in SE 2, with at least some indication of the types to which true and false elenctic arguments or refutations belong, Aristotle turns his attention (in SE 3ff) to a detailed consideration of eristic and sophistical arguments, those whose primary aim is apparent refutation (3.165b18). This discussion, as we have seen, is relevant for our purposes since, as Aristotle sees it, ‘the apparent refutation depends on the ingredients of a genuine refutation, since if any one of these is lacking, there can only [at best] appear to be a refutation’ (8.169b40f). So Aristotle’s detailed discussion of eristic or apparent but false refutation can help us further to see what is required for a genuine refutation. The first point of special interest in this discussion, for our purposes, comes right at the outset where Aristotle lists the aims of competitive and eristic argument. As we have noted, he says that the primary aim is refutation, or, in eristic, the appearance of refutation (3.165b18). A second distinct aim, however, is to show (or appear to show) that an opponent is saying something false (3.165b19). So it seems that refuting an opponent involves something different from simply showing that the opponent says something false. Also, a third distinct aim is to lead an opponent into paradox (3.165b19–20). It is clear from Aristotle’s later discussion of this procedure that one way, at least, to do this is to lead the opponent to agree to inconsistent views (SE 12.172b36–173a18). So it also seems from the outset that refuting an opponent will involve something more than, or something different from, showing that the opponent is committed to inconsistent views. It is important for our purposes to try to determine what this is as we consider Aristotle’s discussion of the modes of false refutation.

The first general type of apparent but false refutation which Aristotle discusses, in SE 4, is the type based on the various sorts of ambiguity or equivocation which can occur in the use of language, i.e., on ‘the number of ways in which we can fail to indicate the same thing by the same words or expressions’ (4.165b29–30). A proper elenchus or refutation avoids all such failures, as Aristotle is at some pains to point out in his new expanded account of an elenchus in SE 5.

This emphasizes for us, once again, how important it is for Aristotle that the conclusion of a refutation be the precise contradictory, both in word and in fact, of the opponent’s thesis. It is not enough for refutation that inconsistencies be exposed (cf. SE 6.168a28–33). We begin to see why this is so when Aristotle turns his attention in SE 5 away from the fallacies or apparent refutations based on ambiguities of language to the study of those apparent refutations which are ‘independent of language’ (SE 4.166b21).

Under this second rubric, of course, are included the familiar traditional fallacies such as affirming the consequent and begging the question. However, for our purposes here perhaps the most interesting of these fallacies that are ‘independent of language’ is the so-called fallacy of non causa pro causa (τὸ μὴ αἴτιον ὡς αἴτιον), or the fallacy of false cause(4.166b26). This occurs, says Aristotle, when a premise which is not responsible for the conclusion of some purported refutation appears to be responsible. It occurs paradigmatically in elenchus by reductio ad impossibile where the opponent’s thesis is taken as one of the premises of the purported refutation and from it, together with other premises, a conclusion which is impossible is deduced with the result that the opponent’s thesis is destroyed (see SE 5.167b21ff.). Aristotle comments on this as follows:

The most interesting fact about this passage for our purposes is that it makes it clear again that the aim of an elenchus is not accomplished simply by showing that an opponent has inconsistent beliefs. The aim of an elenchus, at least of the type of elenchus which employs reductio ad impossibile, is to destroy one specific belief of the opponent. It does this by showing through use of a syllogism that this belief on its own is the thing responsible for (is the αἴτιον of) something which is impossible and that, therefore, it cannot be true or known by any opponent who professes to know it. It is apparent from the discussion in the SE that Aristotle believes that refutation by reductio can legitimately be used in dialectic since he believes that all the various modes of sophistical reasoning and refutation – including that which commits the fallacy of false cause – employ apparent versions of genuine dialectical reasoning and refutation (see e.g. SE 8.169b40ff, 11.171b34ff.). This is also clear from Topics 8.2. There Aristotle does counsel against the use of reductio in dialectical argument, except in cases where it cannot be avoided, ‘unless the falsity [of the conclusion] is completely obvious (λίαν περιφανές)’. Where this is not so, he says, an opponent may just assert that the conclusion is not impossible so that the questioner will not achieve his objective (8.2.157b34ff). This makes it clear that, for Aristotle, while in some cases the use of reductio in dialectic is risky, in some cases it is necessary, whether risky or not, and in some cases it is unproblematic (cf. also Top. 8.10.).

If, however, genuine elenchus by reductio in the sense just identified is legitimate, and sometimes necessary, in dialectic, then the following things must be possible. First, it must be within the resources of dialectic which are available to questioner and respondent to identify conclusions which are false and impossible, including those whose falsity and impossibility is ‘completely obvious’. Second, since more than one premise must be involved in a syllogism which does deduce an impossibility, it must be within the resources of dialectic to identify which one of the premises is truly responsible for generating that impossibility so that this premise itself, and not any other, can be seen, by questioner and respondent, to be the thing destroyed by the refutation. In this type of case, then, dialectical elenchus or refutation is clearly refutation of a specific proposition which is understood to be refuted and shown to be false by the persons involved; and dialectical refutation does not simply rely on the ability of dialectic to show that an opponent has inconsistent beliefs and to show, thereby, that none of these beliefs amounts to knowledge. It is clear now from this, moreover, why Aristotle wants to insist that refutation comes about, in this type of case at least, through use of a syllogistic and, thus, a deductive argument. This is needed in order for the impossibility, or the obvious impossibility, of the conclusion of the argument to guarantee the falsity of one of the premises.

How to Refute Individual Propositions in Dialectic

Just how it is that dialectic comes to have the resources necessary to refute and to show to be false individual propositions does not begin to become clear until SE 8 when Aristotle turns his attention away from the two types of apparent refutations which involve fallacious or invalid forms of argument – both those which depend on ambiguities of language and those which are independent of language – to the consideration of a distinct third type of sophistical or apparent refutation. As he says:

This is a difficult but crucial passage for our purposes since it both identifies peirastic as the branch of dialectic which is able to genuinely refute and ‘establish’ the ignorance of a respondent and also explains for us how it is able to do this, by contrast with sophistical refutations which always fail to do this however much they may appear to do it. To draw this contrast most sharply Aristotle focuses particularly not on those two types of sophistical refutations previously discussed that are only apparently syllogistically valid and that fail to refute and to establish ignorance on that score.⁵ Rather he focuses his main attention on those sophistical refutations which are syllogistically valid just as genuine peirastic dialectical refutations are but which are nevertheless defective, by comparison with peirastic refutations, on another count. The difference is that these sophistical refutations are ‘only apparently appropriate (οἰκεῖον) to the subject’ and only apparently ‘in accord with the subject’ (κατὰ τὸ πρᾶγμα), while peirastic refutations, Aristotle insists, are not only syllogistically valid but genuinely appropriate to and in accord with the subject at hand. It is this which permits them to truly refute and establish ignorance in the subject. Sophistical refutations of the corresponding type, Aristotle adds, even when they do entrap knowledgeable opponents on the basis of what they grant, by actually deducing the contradictory of what they (rightly) claim to know from what they grant, do not show that they are ignorant of what they claim to know.

The first point of interest in this contrast, for our purposes, is that it shows once again that it is not enough, in order to establish that someone does not know something, to show that he has beliefs inconsistent with what he claims to know. Aristotle clearly indicates here that even someone with genuine knowledge can have the contradictory of one of his own theses validly deduced from what he accepts and grants without showing that he is ignorant of that thesis or of other things in the subject. Earlier, in Topics 5.4, Aristotle makes a similar point which reinforces and illuminates this one.

Here again it is clear that, as Aristotle sees it, even someone with scientific knowledgein some area can come to accept and truly believe things which are inconsistent with those principles of that science which he knows well, when for instance, he misdraws or misreads the import of his geometrical constructions and argues on this basis (cf. Top. 1.1.101a5–17). The kind of error and deception produced by these arguments based on false constructions Aristotle regards as different from the kind produced by eristic or sophistical arguments and refutations (Top. 1.1.100b.23ff), as we shall shortly see in more detail. Nevertheless, these arguments are like certain sophistical refutations in that, even though they may reveal that someone has inconsistent beliefs about a subject, they do not necessarily reveal any fundamental ignorance of the subject. Even genuine geometers with ἐπιστήμη in the subject can, on occasion, misapply the principles of geometry and misdraw or misread their diagrams and thus accept and believe things inconsistent with the principles of geometry without this showing that they lack knowledge of those principles which are inconsistent with the accepted misdrawn or misread results. The situation here is comparable to that of the acratic or incontinent person who, according to Aristotle, has genuine knowledge that, on occasion, he fails to properly use (EN 7.3).

Peirastic arguments, on the other hand, do ‘establish’ that the respondent is ignorant in the subject. The main clue as to how they do this, in the present passage, is that they ‘are able to syllogistically deduce a falsehood because of the ignorance [in the subject]’ of the respondent (8.169b25–7). One might suppose that this remark is meant to draw attention to some deficiency or limitation in peirastic argument on the ground that like all dialectical arguments peirastic arguments can deduce false conclusions, since the ἔνδοξα granted by the opponent as premises can turn out to be false (cf. Top. 8.11.161a24ff). But this interpretation would miss entirely the contrast which Aristotle clearly means to draw in the passage. Aristotle means here to contrast defective sophistical refutations, which cannot expose ignorance, with non-defective peirastic refutations which can and do expose ignorance precisely because they are able to deduce falsehoods which follow due to the ignorance of the respondent, and thereby expose the respondent’s ignorance. That is, peirastic arguments are able to validly deduce a conclusion which can be identified as clearly false where the responsibility for this particular error can be traced to the opponent’s ignorance and false belief on some specific point in the subject. By this means the opponent’s false belief and ignorance on this very point become manifest and he is, thus, refuted.

A paradigm case of what Aristotle seems clearly to have in mind here is the type of refutation by reductio which we have already considered where, indeed, the responsibility for some manifestly false conclusion is traceable to some particular false pretension of the opponent.⁶ Here the ignorance of the opponent on some significant point in some subject is made evident. But, as we have already noted, for this to be workable it must be within the resources of dialectic to distinguish, among the premises of the elenctic syllogism, those which are not responsible for the resulting falsehood by contrast with the premise which is. We find further indication of Aristotle’s confidence in the ability of dialectic to do this in Top. 8.10 where he discusses how one can avoid the situation where one’s concessions are responsible for a falsehood by identifying the premise proposed by a questioner which is, or would be, responsible for some derived falsehood should it be granted and exposing this premise as false (he compares this at Top. 8.10.160b23–9 with the situation where one can expose a false geometrical proof by identifying as such a falsely described figure on which the false proof is based).

The only information offered here in SE 8 as to how this is to be done in peirastic comes with Aristotle’s indication that the premises in the peirastic refutation (other than the premise destroyed in a reductio, of course) are ‘appropriate’ (οἰκεῖαι) to the subject at hand, or ‘in accord with the subject’ (κατὰ τὸ πρᾶγμα). If they are, then the remaining premise, in a reductio, which the opponent professes to know, can be identified as the one which is responsible for the resulting falsehood and is thereby refuted, and shown to be false, so that the opponent’s ignorance and false belief is exposed to himself and others. The comparable premises of deductively valid sophistical refutations, by contrast, are (either all or some) only apparently appropriate to the subject, so they do not permit the genuine refutation of the opponent’s thesis, and exposure of his ignorance and false belief on a particular point in the subject, when a falsehood is deduced. What, then, does this appropriateness, or lack thereof, involve? As we have seen, Aristotle has already pointed out that arguments can still be eristic or sophistical, even when they are syllogistically valid, when the premises are only apparent ἔνδοξα (SE 2.165b7–8). Things that appear to be appropriate to a subject, e.g. geometry, will no doubt be things that appear to be items held by experts, i.e. by the wise, in that subject. As such they will indeed be apparent ἔνδοξα. This might seem to suggest that it is enough, for Aristotle, in order for the premises of a peirastic dialectical argument to be actually appropriate to, or in accord with, the subject at hand, that they be genuine ἔνδοξα concerning that subject. However, it hardly seems to be enough to guarantee that a premise of a peirastic argument is not responsible for any falsehood validly deduced from it (together with other premises) that this premise is a genuine ἔνδοξον concerning the subject in question. For, as we have just noted, ἔνδοξα may be false and where they are, clearly, they may be responsible for the deduction of falsehoods from them. Aristotle is himself quite fond of showing that the false beliefs of famous philosophers (which are prime examples of ἔνδοξα) lead in combination to manifest absurdities. Nor will it help to draw on Aristotle’s requirement (in Top. 8.5–6) that dialectical premises should be more ἔνδοξα than the conclusion inferred from them in direct argument, and to suggest that in reductio the premise to be rejected when a false conclusion is deduced is the one which is less ἔνδοξον than the others. For even if, in a reductio, the premises other than the opponent’s thesis are more ἔνδοξα than that thesis, they may still be false and, thus, responsible for a false conclusion deduced from them. This procedure simply cannot show through reductio that an opponent’s thesis is false and, thus, that he lacks knowledge of his specific thesis.

This is, presumably, why Aristotle does not emphasize or even mention the fact that proper peirastic premises should be ἔνδοξα in his initial description of the requirements for these premises in SE 2 (he does emphasize it later in SE 34.183a37; see also 9.170a34–b11, with 11.172a17–b4). Rather, what he emphasizes, as we have seen, is that these premises, in addition to being the actual beliefs of the respondent, are ‘things which are bound to be known by anyone who pretends to have expert knowledge (ἐπιστήμη) of the subject in question’ (2.165b4–6). We can now see clearly what the point of this requirement is, namely to guarantee what Aristotle wants to guarantee in SE 8 (169b20ff), that peirastic premises are ‘appropriate’ to or ‘in accord with the subject at hand’, and as such true, in a way in which the premises of even syllogistically valid sophistical arguments are not. It is this which will permit a genuine peirastic refutation, whether direct or through reductio, to truly expose ignorance, when the contradictory of the opponent’s false profession to knowledge on some point is deduced from such things or when, in reductio, this false profession taken together with such things entails a manifest falsehood. How then does this help us to understand what Aristotle means by the requirement that premises be appropriate to or in accord with a subject, given that he does not simply mean that the premises must be genuine ἔνδοξα concerning the subject from which the appropriate conclusion can be deduced, or that they must also be more ἔνδοξα than the opponent’s thesis?

How Are Peirastic Premises ‘in Accord with’ a Subject?

The requirement that premises be appropriate (οἰκεῖαι) to or in accord with a subject is one which figures prominently in Aristotle’s account of demonstrative scientific reasoning. He uses this requirement as a main basis for arguing that the premises of demonstration must be ‘true, primitive and immediate; and better known than, prior to and explanatory of the conclusion’ (An.Post. 1.2.71b19–23, cf. 1.6.74b21–6). This kind of appropriateness is required, as Aristotle goes on to make clear in SE 9, for the premises of one type of refutation, namely the type which employs demonstration and ‘depends on the first principles of geometry [or some other science] or on things which are concluded from these principles’ (9.170a23–34). But Aristotle goes on there to contrast this type of refutation with peirastic dialectical refutation which does not operate from premises which are ‘in accord with the discipline’ (κατὰ τὴν τέχνην) in the sense of being ‘in accord with the first principles’ (κατὰ τὰς ἀρχάς) in the way just described. In fact, Aristotle initially describes the bases for peirastic dialectical refutation as things which are ‘common’ (κοινά) by contrast with the ‘special’ (ἴδια) principles of a given science that are the basis for demonstrative refutation (9.170a36, 39; b9 with 11.172a4–9). The first clue which he gives us in SE 9 as to what he means by this comes in his indication that these common things are not things from which proper scientific reasoning proceeds, in the sense that they are not based on lines of argument (τόποι) which only those with scientific knowledge in a given subject can employ. Rather they are based on τόποι which can be employed by skilled or trained dialecticians to reach syllogisms based on the ἔνδοξα on a given subject (ἔνδοξοι συλλογισμοί) (9.170a34–40).

However, we already know from Aristotle’s characterization of the two special requirements for the premises of peirastic arguments in SE 2 (165b4–6) that it is not enough that these premises be ἔνδοξα. This becomes further apparent in SE 11 where Aristotle discusses further the requirement that peirastic operates from ‘the common things’ (11.171b6). Here Aristotle returns to the language which he uses to describe peirastic in SE 8 and insists that the common things used as premises in peirastic must be things which are ‘in accord with the subject’ (κατὰ τὸ πρᾶγμα, 11.171b6). Just as he has already done in SE 8, he particularly contrasts peirastic argument, which is based on these common things, with that type of sophistical reasoning which, though valid, only ‘appears to be in accord with the subject’ (11.171b19–21). To illuminate this contrast further, Aristotle relates it to another contrast, that between genuine demonstrative geometrical arguments which are genuinely based on the principles of geometry and false geometrical arguments (παραλογισμοί) such as are used by pseudographers who employ falsely described figures (τὰ ψευδογραφήματα) which are, nonetheless, ‘in accord with the things which fall under the discipline’ (11.171b12–14). Aristotle explains this as follows:

In this important passage Aristotle aims to clarify further the nature of even deductively valid eristic or sophistical argument and refutation by distinguishing it from another type of deductively valid false argument, namely the pseudographic (cf. 11.171b7–22). He distinguishes these two types of false argument and refutation by showing that each bears a special relationship of similarity to a distinct superior type. As the pseudographic argument and refutation is to the demonstrative, on a certain point, so is the valid eristic argument and refutation to the dialectical or peirastic. The point of similarity is that the members of each pair reason on the basis of ‘the same things’. However, this clearly cannot be true in the most literal sense. Pseudographers use false premises based, for instance, on false constructions (Top. 1.1.101a9–17). Genuine geometers, in their proper demonstrations, do not. Nevertheless, both reason from ‘the same things’ because both base their arguments ‘on the special first principles’ of geometry (11.172a5). Thus, they employ arguments of a type which can only be used (for good or ill) with those ‘who know what is permitted and not permitted’ in geometry (11.172a2–7). For example, even the pseudographers who misconstruct their figures are (mis)applying the proper principles, i.e. the proper construction rules, of geometry, which they and other geometers know well. But what these rules permit and do not permit will only be known by these geometers not by people in general. So people in general will, as it were, find these arguments too technical to understand, so they will simply not respond to these arguments, whether they be truly demonstrative or only pseudographic. Thus, people in general, unlike geometers, will not have any tendency to be deceived by pseudographic arguments. So these arguments are not eristic or sophistical arguments or refutations which, especially the valid ones, do have the tendency to deceive people in general (11.171b21; cf. Top. 1.1.100b23–9).

Eristic refutations, by contrast, acquire their capacity to deceive not from their similarity to pseudographic arguments but from their similarity to peirastic dialectical arguments. As in the previous comparison of geometrical to pseudographic arguments, eristic arguments are said to be based on ‘the same things’ as these dialectical arguments. Just as in the previous case, however, this is, again, in the most literal sense, clearly false. All dialectical and peirastic arguments are based on ἔνδοξα, eristic or sophistical arguments, at least the valid ones, are based on merely apparent ἔνδοξα (SE 2.165b7–8). These classes are mutually exclusive. So, contrary to what commentators often suppose, when Aristotle says that eristic and peirastic arguments reason on the basis of the ‘same things’, namely the ‘common things’, he cannot mean that both draw their premises at will from a single body of information such as, for instance, information which is sufficiently general to apply to all or many different subjects and not just one subject alone.⁷ Rather, just as Aristotle says, eristic and peirastic operate from common things because they use premises which work ‘with people in general who do not know what is permissible and what is not permissible [as a genuine demonstrative premise] in a given subject’ (11.172a6–7). The common things, as understood here, are, thus, things which tend to work in argument with common people, not simply, or necessarily, things which work in argument on many subjects.⁸

Why then, for Aristotle, does eristic argument work, or have a tendency to work, with common people? It is because the premises of eristic arguments, as we have seen, ‘appear to be in accord with the subject’ (κατὰ τὸ πρᾶγμα, 11.171b21, cf. b6–7). That is these premises seem, to people in general, to be truths genuinely proper to the subject in question, even though they are not. So people will be deceived into thinking that they have been refuted when the contradictory of even some correct belief which they hold about the subject is deduced from these apparent truths and apparent ἔνδοξα (11.171b21ff). Even scientists with knowledge, as we have noted, can be deceived into thinking that they have been refuted about things which they actually know, by such eristic arguments, because of their susceptibility to ordinary ways of thinking, in a way in which they would not be deceived by pseudographic arguments (8.169b26–9, 9.170a36–9, b8–11). But for the contradictory of something which they know, and which is thus true, to validly be deduced from some item that only appears to be in accord with the subject, that latter item must, of course, be false. Let us explore then how such a sophistical refutation from such a false premise takes place.

Two Eristic Refutations

Aristotle mentions in SE 11 several examples of sophistical or eristic arguments or refutations which are such not because they are only apparently syllogistically valid but because, even though valid, they have premises which only appear to accord with the subject (11.171b8–22, b34–172a13). As one example of such an eristic refutation, with a crucial premise which only appears to be in accord with the subject, Aristotle mentions a certain use of Zeno’s argument which concludes that motion is impossible. This is employed against an opponent who rightly claims that it is better to take a walk (than a nap?) after dinner. The eristic refutation of this correct claim, as Aristotle describes it, goes roughly as follows:

1. (1) Motion is impossible.

2. (2) If motion is impossible then it is not better to take a walk (than a nap) after dinner.

3. (3) Therefore, it is not better to take a walk (than a nap) after dinner.

This Aristotle puts forward as an example of an argument which is eristic, not peirastic, because it has a first premise which only appears to be in accord with the subject, namely medicine or, more generally, physics. Of course, one may well wonder how Aristotle can suppose that the premise that motion is impossible could even appear to be in accord with physics. But a passage in Topics 1.11 gives us the likely answer to this question. There Aristotle argues that even such a paradoxical or strongly counter intuitive claim as this can come to be accepted and held to be correct by an interlocutor ‘because it is supported by [dialectical] argument’ (104b27–8). So for instance, Zeno’s doctrine that motion is impossible could well be accepted because it appears to follow from such commonly credible (ἔνδοξον) premises as: To go a given distance one must first go half way (see Physics 8.8.263a4ff). Such premises clearly appear to be (and, of course, are) in accord with physics, so that what appears to follow from them, e.g. Zeno’s conclusion, could also appear to be in accord with physics even though it is false (and in fact does not follow from them). Thus the purported refutation, in this case, is eristic not peirastic.

As we have seen, Aristotle also mentions Bryson as another paradigm example of someone who was deceived, and presumably deceived others including some geometers, by such an eristic argument and refutation which, though valid, only appears to be in accord with geometry (11.171b7–22). Bryson wrongly thought that he had shown that the circle can be squared by the construction techniques of plane geometry. In Cat. 7.7b27–33 and EE 2.10.1226a28–30, Aristotle makes it clear that he himself knows well that this had not been done and that there is no knowledge, or even possibility he supposes, that the circle can be so squared. Our ancient sources are in much disagreement about exactly what Bryson’s procedure was. However, it is reasonably clear from these sources that Bryson aimed to square the circle by approaching the circumference of the circle from both inside and outside, with two series of constructible regular polygons with an increasing number of sides such that the areas of the members of each series come closer and closer, from both inside and outside, to the area of the circle. Bryson then seems to have argued in the following way:

1. (1) Wherever there exists with respect to a given thing something greater than it and something less than it, of any given sort, there exists something equal to it of that sort.

2. (2) There exist polygons constructible by a proper geometrical procedure which are in area greater than and also in area less than any given circle.

3. (3) Therefore, there exists a polygon constructible by a proper geometrical procedure which is equal in area to any given circle.⁹

The first premise of this very clever and seductive argument has, arguably, the chief characteristic which Aristotle attributes to the premises of (valid) eristic arguments and refutations. Namely it is the sort of thing which would seem, to people in general, to be truly in accord with the subject, and to be held and known by experts in the subject, namely here geometry. So, though the premise is false, because it does not in fact hold of the sort of thing in question (i.e. polygon constructible by proper geometrical procedure), even an expert geometer could be taken in by it because of his susceptibility to ordinary ways of thinking, just as Aristotle says (8.169b28–9). Given this, when this geometer agrees to the true second premise of the argument, which is in fact established in proper geometrical fashion by Bryson’s construction, he will have no choice but to agree to the (false) validly deduced conclusion. Should he have (correctly) denied this conclusion to begin with he will be the victim of a sophistical refutation, a refutation whose falsity it is the function of the dialectician to expose not the geometer (9.170a36–9). This refutation would be sophistical because it would not truly expose the geometer’s ignorance of the principles of geometry even if he should accept and believe and find no reason to doubt the premises. It would rather expose his lack of dialectical skill.

Genuine peirastic dialectical refutation, Aristotle indicates, is like this sort of syllogistically valid sophistical refutation, illustrated by our two arguments, because it also draws its premises from things that might seem to people in general to be appropriate to or in accord with the subject. It differs from valid sophistical refutation because it also draws on what is in accord with the subject (8.169b23–5; 11.171b6–7). Its premises are not in accord with the subject in just the way in which both demonstrative and pseudographic premises are since in both of these cases the premises have that status because they are reached by genuine demonstrative procedure, by being based on the application (or misapplication) by experts of the genuine first principles of geometry, and are in accord with the subject in that way. Peirastic proceeds in quite a different manner, as Aristotle explains in the following passage in SE 11.

This passage shows, first of all, that peirastic premises are not ‘in accord with the subject’ by virtue of being based on the use or application (correct or incorrect) by experts of its principles – as is the case in both geometrical and pseudographic arguments. Peirastic premises are reached by questioner and respondent without any dependence on expert knowledge and use (or misuse) of such special principles. These premises are nevertheless genuinely in accord with the subject in another way because they belong among those consequences of the special principles which are such that though knowledge of them does not prevent the respondent from still being ignorant (e.g., of the principles) in the subject, they must be known to properly know the subject. So these premises are in accord with the subject because they in fact are appropriately in accord with the first principles. This explains why they must be known to know the subject since what one must know, other than the principles, to know a subject, is just such proper consequences of the principles and nothing more (cf. 2.165b4–6, 9.170a28). As such they must be true, since no one can know what is false. Also, as such, they are things which truly accord with the subject, unlike eristic premises which merely appear to do so. Aristotle describes them as commonly known things employed by some genuine particular discipline or other (11.172a29–33, a36–b1).¹⁰ Thus, these common things make up an area of overlap between common knowledge and expert knowledge. There are, Aristotle says, some such things in every area of expertise. Moreover, these things can serve as premises for a genuine, and not merely sophistical, refutation because knowledge of them does not rule out further ignorance in the subject such as, most importantly, ignorance of the principles. Someone may know these premises, Aristotle indicates, and still hold to some false belief about principles, so that he fails to know the subject. This ignorance can be exposed when the contradictory of such a false belief about principles is deduced from things known by the respondent which are in accord with the subject in the way indicated.

We can see here, once again, that Aristotle clearly does not hold that whenever one has inconsistent beliefs on some subject none of those beliefs can amount to knowledge. He explicitly says that a respondent can know certain consequential facts in a subject which can serve as peirastic premises sufficient to expose some false belief and pretension to knowledge on his own part in the subject. This will be done, of course, in direct argument in peirastic, by deducing the contradictory of his false belief from the known premises. In this case the respondent clearly will have inconsistent beliefs some of which are also items of knowledge. So it cannot be by merely showing that one has other beliefs inconsistent with a given belief that this belief is shown not to be an item of knowledge. Rather, what does show this is that the contradictory of this belief follows from genuine truths employed in the subject which one may know, and which even ordinary people do know Aristotle says, without knowing the principles. This is how it comes about that peirastic genuinely exposes ignorance in a subject, by drawing on those commonly known things which are actually used in, and as such are actually in accord with, the subject in question (11.172a29–30, a36–b1). However, Aristotle seems sometimes not to use the term common only for such commonly known things which are genuinely in accord with the subject. He also seems sometimes to use it for the false premises of eristic arguments which might commonly appear to accord with the subject, such as Zeno’s doctrine or the false premise of Bryson’s argument (11.172a1–9). When he is being careful, however, Aristotle says only that such arguments appear to argue from what is common (11.171b6–7). It is obviously important for the skilled practitioner of peirastic, in order to avoid sliding into eristic argument and refutation, to be able to distinguish these two types of common or apparently common things, and Aristotle explicitly says himself that the skilled practitioner of peirastic as such has the resources to do this (SE 9.170b8–11).

Ignorance and inconsistency in Aristotle

The upshot of our discussion so far is, then, that Aristotle does not believe that it is sufficient, for the dialectical refutation and exposure of someone’s ignorance and lack of knowledge, to show that that person has inconsistent beliefs, or inconsistent beliefs some of which are more ἔνδοξον than others, concerning the matter or matters in question. Rather, dialectical refutation and exposure of ignorance is accomplished when someone’s particular conviction is shown (either directly, or indirectly in reductio) to conflict with commonly identifiable truths of the subject in question which are available as such to practitioners of dialectic as well as to experts. If we can see, then, that Aristotle rejects the view that inconsistency establishes ignorance we may now ask, finally, why he rejects this.

At the most simple level, the answer to this question is clear. Aristotle rejects the view that inconsistency establishes ignorance because he has convincing counterexamples to this. He supposes, quite plausibly, that, like an incontinent person, even a master geometer can fail to use his genuine knowledge and can misdraw or misread diagrams in particular cases, and thereby deduce and accept conclusions inconsistent with the principles of geometry without failing to know those principles. He also supposes, again quite plausibly, that even a master geometer can accept things which commonly appear to be true and in accord with his subject, though they are false, such as the false first premise of Bryson’s argument, and be led to conclusions inconsistent with certain scientific principles without failing to know those principles.

But we may also give an answer to this question at a deeper and more theoretical level. To see why Aristotle rejects the view that inconsistency among beliefs establishes lack of knowledge or ignorance of the beliefs in question, we may ask why someone might want to hold the view that such inconsistency does rule out knowledge. Let us approach this, starting from the assumption that, roughly at least, for a belief to count as knowledge the belief must be (1) true, (2) accepted by and (3) properly warranted for the believer. We may then ask which of these conditions for knowledge is necessarily violated by a belief which is inconsistent with other beliefs. It cannot be the truth condition or the acceptance condition since the fact that a belief is inconsistent with other beliefs obviously does not imply either that it is false or that it is not accepted. So it can only be the warrant condition for knowledge that one could plausibly suppose to be violated by a belief that is inconsistent with other beliefs. If this is so then the consistency of a belief with one’s other beliefs is required for that belief to be properly warranted. If Aristotle accepts this then he is committed to some form of a coherence test for justification or warrant for belief. Conversely, however, if Aristotle rejects coherence tests for the justification of or warrant for belief then he may reject this consistency requirement. We can already see from the counterexamples mentioned that Aristotle would reject coherence theories of warrant which involve a strong consistency requirement. But this rejection also follows from his general views about the nature of dialectical justification. It is often claimed that dialectic for Aristotle involves a form of a coherence theory of justification.¹¹ But this, I believe, cannot be correct. Any support supplied by dialectical argument for any belief must conform to the requirements for all dialectical argument, that the premises must be more ἔνδοξα than the conclusion inferred from them, and that the more ἔνδοξα the premises are the better the argument is (see Top. 8.5–6, 11). That is, beliefs and ἔνδοξα acquire weight and authority in dialectic not simply from their consistency or coherence with other beliefs or ἔνδοξα but also from their own independent degree of endoxicality or that of beliefs or premises which are more ἔνδοξα than they are from which they can be inferred. Given this, there will be certain convictions which are maximally ἔνδοξα which can provide maximum dialectical support for other convictions inferable from them but which cannot be given dialectical support from any other convictions since there are no other convictions which are more ἔνδοξα than they are. So if these convictions are inconsistent with any others that are less ἔνδοξα than they are that can only create trouble for the others and not for them in dialectic. This is why, speaking from the dialectical point of view, the inconsistency of a belief with others is not by itself a basis for questioning that belief.¹²