Abstract
From Aristotle’s Sophistical Refutations the following classifications are put forward and defended through extensive excerpts from the text. (AR-PFC) All sophistical refutations are exclusively either ‘apparent refutations’ or ‘proofs of false conclusions’. (AR-F) ‘Apparent refutations’ and ‘fallacies’ name the same thing. (ID-ED) All fallacies are exclusively either fallacies in dictione or fallacies extra dictionem. (ID-nAMB) Not all fallacies in dictione are due to ambiguity. (AMB-nID) Not all fallacies due to ambiguity are fallacies in dictione. (AMB&ID-ME) The set of fallacies due to ambiguity and fallacies in dictione together comprise the set of arguments said to be “dependent on mere expression”. Being “dependent on mere expression” and “dependent on language” are not the same (instances of the latter form a proper subset of instances of the former). (nME-FACT) All arguments that are not against the expression are “against the fact.” (FACT-ED) All fallacious arguments against the fact are fallacies extra dictionem (it is unclear whether the converse is true). (MAN-ARG) The solutions of fallacious arguments are exclusively either “against the man” or “against the argument.” (10) (F-ARG) Each (type of) fallacy has a unique solution (namely, the opposite of whatever causes the fallacy), but each fallacious argument does not. However, each fallacious argument does have a unique solution against the argument, called the ‘true solution’ (in other words, what fallacy a fallacious argument commits is determined by how it is solved. However, if the solution is ‘against the man’ then this is not, properly speaking, the fallacy committed in the argument. It is only the ‘true solution’—the solution against the argument, of which there is always only one—that determines the fallacy actually committed).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
I owe this suggestion to an anonymous reviewer who also suggests that fallacies are the genus of both sophistical refutations and apparent refutations. This seems to be a rather unnatural reading. Aristotle is defining ‘sophistical refutation’; if he had simply wished to say that a sophistical refutation is a type of fallacy (a predication rather than a definition) I don’t think he would have written it like this. Also I think he would have called his book “On fallacies” rather than “On sophistical refutations.” Fallacies are the genus, however, of things that fail to be refutations because they fail to be proofs at all (‘apparent syllogisms’) or because they are not proofs against the point in question, that is to say, what has been proved only appears to be a contradiction, which might also be called by the name ‘apparent refutation’. Perhaps this is what the reviewer means and our disagreement stems from this terminological muddle. By ‘apparent refutation’ I mean something that falsely appears to be a refutation irrespective whether the falsity of this appearance is located in the contradiction or the proof. This is the same broad sense Aristotle uses when he reduces all fallacies to cases of ignorance of ‘refutation’.
At the end of (SR, §2) Aristotle claims his interest to be in contentious arguments, but this constraint seems to be loosened in the course of (SR, §8).
To elaborate: nature is arranged in a taxonomic structure of genera and species and whatever one is studying has an ultimate genus, from the definition of which every truth falling under the genus (or in other words, belonging to that particular ‘science’) can be demonstrated by a syllogism in which some element of the definiens is used as a middle term. Defining the ultimate genus amounts to giving its essential properties; thus, the middle terms belong to their ultimate subjects per se rather than per accidens.
Perhaps Aristotle could here be interpreted as placing an epistemic condition over detachment: in modern logic you can never really detach a conclusion in practice because it is always possible that there will come a time when a premise from which the conclusion was derived is rejected by an application of modus tollens, but this is not the case in a demonstration because the premises and conclusion here are necessary truths.
It is an interesting question that I will not consider whether the scientist knows that these are necessary truths, whether he knows that what he uses as a definition really is the definition and does not contain a mistake, and if he does not know these things whether this prevents him from having knowledge of the meaning and of the fact. In the Posterior Analytics Aristotle (1976) concedes that we can never prove the definition to be correct (and hence we cannot know that what we use as a middle term really is a cause) and that the first principles are known not by deduction but by a slightly mysterious process of induction. My view is that we may be mistaken about first principles, but first-order knowledge does not require us to be able to rule out any possibility of being mistaken. I would say that we do know in this situation (that is to say, when the middle term is a cause but we do not know this absolutely but only relative to the definition), but perhaps do not know that we know. However, I admit that this would imply a rejection of the KK-Thesis, which otherwise Aristotle seems to endorse.
It must also be remembered that in Aristotelian logic a proposition can literally change its truth-value; unlike modern logic where propositions have their truth-values timelessly, for Aristotle a proposition is true or false at a time. Prior to the existence of a man who is not risible, “All men are risible” is true. The problem with an accidental generalization seems to be that although it is true now, it is possible for it to become false.
Actually I think there is an asymmetry here in that something necessarily cannot be false at any time (and hence showing that it is false at some time amounts to showing that it is not necessarily true) but it is not so obvious that something necessarily true cannot be false in a particular respect. Certainly, there are good reasons to think that something can be true without qualification yet false in a certain respect.
This may introduce some uncertainty into how I have presented (AR-PFC). I am inclined to think of sophistical refutations as a genus of which apparent refutations and proofs of false conclusions are species, but I admit that this is not usually what we mean when we say that something has a double meaning: there is no genus corresponding to the word “bank” that includes river-banks and financial institutions as species. Ultimately, I don’t think this matters too much. What does seem to be true is that both apparent refutations and proofs of false conclusions are arguments occurring in dialogue.
I admit that there may be another way of interpreting this quotation. I have argued that a ‘proof of false conclusion’ is a genuine refutation in every respect except that its premises are inappropriate, which is to say that it does conclude with a genuine contradiction, which in turn is to say that it is not a fallacy but is a sophistical refutation, sophistical refutations therefore being wider than fallacies. This quotation talks about proving false conclusions. By this it could mean the same the same as the narrow sense of ‘apparent refutation’ and then contrasting this against ‘apparent proof’. But inappropriateness of premises does seem to be a different kind of error than that described as ‘apparent refutation’, and in §8 Aristotle says “the considerations on which both proofs of false conclusions and an apparent refutation depend must be the same in number. Now an apparent refutation depends upon the elements involved in a genuine one,” implying that proofs of false conclusions are distinct from apparent refutations and that the former are, in some sense at least, ‘genuine.’ Also, why is it not included among the fallacies if, as before, ‘false conclusion’ means only that which appears to be a contradiction but is not? But another, equally compatible interpretation can be given if ‘false reasoning’ is taken as ‘fallacy’ and a ‘false conclusion has been proved’ is taken to refer to the narrow sense of ‘apparent refutation.’
In (SR, §9) Aristotle writes:
[T]o exhaust all possible refutations we shall have to have scientific knowledge of everything: for some refutations depend upon the principles that rule in the geometry and the conclusions that follow from these, others upon those that rule in medicine, and others upon those of the other sciences… Clearly, then, it is not all refutations, but only of those that depend upon dialectic that we need to grasp the common-place: for these stand in a common relation to every art and faculty. And as regards the refutation that is according to one or the other of the particular sciences it is the task of that particular scientist to examine whether it is merely apparent without being real… whereas it is the business of dialecticians so to examine the refutation that proceeds from the common first principles that fall under no particular special study.
“Common first principles” also likely includes the topoi.
I am tempted to express the Law of Non-Contradiction as “It is not possible that S is P-and-not-P”, i.e., as a conjunction of predicates rather than propositions. However, on the principles of On Interpretation it is questionable whether Aristotle would allow this (where one of the predicates in question contain something that excludes the other) as a conjunction of predicates and would not after all consider “S is P-and-not-P” as two propositions.
Aristotle does not explicitly say so, it is strongly suggested that it is a fallacy of many questions. This is reinforced when he says later (SR, §17):
If people never made two questions into one question, the fallacy that turns upon ambiguity and amphiboly would not have existed either, but either genuine refutation or none. For what is the difference between asking ‘Are Callias and Themistocles musical?’ and what one might have asked if they, being different, had had one name? For if the term applied means more than one thing, he has asked more than one question. If then it be not right to demand simply to be given a single answer to two questions, it is evident that it is not proper to give a simple answer to any ambiguous question, not even if the predicate be true of all the subjects, as some claim that one should. For this is exactly as though he had asked ‘Are Coriscus and Callias at home or not at home?’ supposing them to be both in or both out: for in both cases there is a number of propositions: for though the simple answer be true, that does not make the question one. For it is possible for it to be true to answer even countless different questions when put to one, all together with either a ‘Yes’ or a ‘No’: but still one should not answer them with a single answer: for that is the death of discussion. Rather, the case is like as though different things have actually had the same name applied to them. If then, one should not give a simple answer to two questions, it is evident that we should not say simply ‘Yes’ or ‘No’ in the case of ambiguous terms either: for the remark is simply a remark, not an answer at all, although among disputants such remarks are loosely deemed to be answers, because they do not see what the consequence is.
In (SR, §19) Aristotle talks about cases where the apparent refutation is valid but what has been refuted is the name, not the fact. What Aristotle seems to be talking about here is cases of ignoratio elenchi brought about because of equivocation in the conclusion. Resolving this fallacy consists of making a linguistic distinction, i.e., showing that the name that has been refuted is not that of the thesis (and consequently the appearance of contradiction is false). Thus, this is an argument ‘against the expression’ according to what I have said. Schreiber (2003) makes a similar point with regard to fallacies in dictione (see footnote 1). If all fallacies in dictione are arguments ‘against the expression’ then this may work out to the same thing, but if ‘against the expression’ is taken as the same as ‘depending on mere expression’ then this goes against (AMB&ID-ME).
It is not altogether clear what the mistaken belief is in this case, but my guess is that it involves a mistaken belief about the kinds of entities that can be truth-bearers. Now, in a truth-functional logic there is no obstacle to a conjunction being considered as a truth-bearer; indeed, its truth or otherwise is a function of the truth-values of the propositions involved. But Aristotelian logic does not recognize truth-functions or any of what we would call the logical connectives apart from negation. Therefore, p ∧ q is neither true nor false, and not the kind of thing to which the Law of Non-Contradiction and the other laws of logic apply. This would explain why one should not answer “Yes” to many questions even if the answer to each individually would be “Yes.” This is another reason why ¬(p∧¬p) does not express the Law of Non-Contradiction as it applies in Aristotelian logic.
To say that it has not been conceded is not to say that it is false. It is often held that the problem with equivocation is that the ambiguous term makes the argument valid but the premise false under one of its possible interpretations, and makes the premise true and the argument invalid under the other of its possible interpretations. Although it undoubtedly often happens this way, this does not seem to me quite right. The answerer concedes one interpretation, and presumably has grounds that support its truth. Those grounds do not support the other interpretation, and she should not concede that interpretation, since if she were to concede that interpretation on those grounds, or on no grounds at all, then she would be unjustified. Similarly, if she does not concede that interpretation she is justified, even if the premise is true with that interpretation—in fact, the premise may be true with both interpretations, in which case the argument would be sound (in the more usual sense but not in the sense where it is relative to the concessions of an arguer), yet a fallacy of equivocation would still have been committed.
It should be remembered here that the Law of Non-Contradiction is not simply a rule about the use of a representational system such as language as the modern formalistic view of logic has it, but a metaphysical principle that describes what is possible in the world.
Consider the following sentences: (1) He could not strike a blow with a white hand, (2) He could not strike a blow with a hand quickly, and (3) He could not strike a blow with only one hand. Syntactically, (3) is more similar to (1) than to (2) and gives the mistaken impression that “only one” plays the same role in (3) as “white” does in (1), namely as describing a quality of the hand. Semantically, (3) is similar to (2) and describes a manner in which the striking takes place.
The fallacy of secundum quid has in my view been misrepresented and should be considered as depending on ambiguity in any way. Rather, it is a misapplication of the Law of Non-Contradiction and is therefore correctly classified as a fallacy extra dictionem. I cannot argue for this here.
I prefer the formulation that fallacies are things that look like valid arguments but are not. This seems closer to Aristotle, and importantly implies that something can be a fallacy if it is not an argument but looks like one, whereas the traditional formulation has the consequence that in order to be a fallacy something has to be an argument. I follow the claim in Botting (2011) that cases of petitio principii are fallacies partly because they are not arguments.
This theme Hansen takes up again in Woods and Hansen (1997). In his reply, Hintikka (1997) argues that for Aristotle, or at least for Aristotle at the time of the Sophistical Refutations, there is no distinction between what we would now call a logical inference and moves in a question-and-answer game. Aristotle’s insight was to notice that once particular moves had been made, some other moves become impermissible; for instance, if, in previous moves, the answerer has made moves that concede “All men are mortal” and “Socrates is a man” (the premises of a valid argument) then she cannot concede “It is not the case that Socrates is mortal” and to the question “Is Socrates mortal?” the answerer is compelled by the rules of the game to answer “Yes”.
To make a different argument, it is not an actually existing dialogue partner that is required for speech act performance, but only the speaker’s belief that there is one. Since one cannot have a relation to what does not exist this is not really a relational concept. Dialogue itself is a relational concept because it necessarily involves two actual speakers, but it would be a kind of fallacy of division to infer that any of the individual speech acts composing it are relational. Of course, it would be anachronistic to ascribe such a view to Aristotle.
This seems to me consistent with Aristotle’s text, but I leave to the Aristotelian scholars whether this is in fact how Aristotle viewed the fallacies.
Petitio principii violates the rule that the conclusion cannot (for epistemic rather than strictly logical reasons) occur in the premises. Many questions violates the rule that propositions always involve one thing attributed to another thing; the answer to a complex question would not be a proposition. It is a matter of debate that need not concern us what the rationale behind these rules is (see Woods and Hansen 1997 for further explication). It is unlikely that they are mere stipulations added in an ad hoc manner to disallow forms of argumentation felt in some way to be incorrect, although they do seem to give this impression in the Sophistical Refutations.
An alternative treatment of these fallacies seems to me both possible and preferable. See Botting (2011) for an alternative treatment of petitio principii where only certain trivial examples of petitio principii such as p ⊢ p where p is atomic and has only one referring term commit that fallacy. As for asking many questions as one I do not consider it a fallacy, although if done deliberately the questioner is no longer being a co-operative dialogue partner.
It is tempting to read the fallacy of accident in this way, i.e., as producing an argument whose current token is sound, but which is not guaranteed to be sound for all tokens, which is the same as saying that it is not demonstrative. Thus, this would seem to be both an apparent refutation and a proof of false conclusion, which otherwise Aristotle would seem to be keen to keep apart.
References
Aristotle. 1941. Metaphysics. In The basic works of Aristotle, ed. Richard McKeon (trans: Ross, W.D.). NewYork: Random House.
Aristotle. 1976. Posterior analytics (trans. Hugh Tredennick). Cambridge: Harvard University Press.
Aristotle. 1984. Sophistical refutations. In The complete works of Aristotle, ed. J. Barnes (trans: Pickard-Cambridge, W.A.). Princeton: Princeton University Press.
Botting, David. 2011. Can “big” questions be begged? Argumentation 25(1): 23–36.
Hansen, Hans V. 1996. Aristotle, Whateley, and the taxonomy of fallacies. Practical Reasoning 1085: 318–330.
Hintikka, Jaako. 1987. The fallacy of fallacies. Argumentation 1.3:211–238.
Hintikka, Jaako. 1997. What was Aristotle doing in his early logic anyway? A reply to Woods and Hansen. Synthese 113: 241–249.
Hitchcock, David. 2007. Why there is no argumentum ad hominem fallacy. In Hansen and Pinto, ed. Reason Reclaimed, 187–209. Newport News: Vale Press.
Kirwan, Christopher. 1979. Aristotle and the so-called fallacy of equivocation. The Philosophical Quarterly 29(114): 35–46
Poste, Edward. 1866. Aristotle on fallacies, the sophistici elenchi: With translation and notes. London: MacMillan.
Schreiber, Scott G. 2003. Aristotle on false reasoning. Albany: SUNY Press.
Woods, John, and Hans V. Hansen. 1997. Hintikka on Aristotle’s fallacies. Synthese 113: 217–239.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Botting, D. What is a Sophistical Refutation?. Argumentation 26, 213–232 (2012). https://doi.org/10.1007/s10503-011-9231-x
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10503-011-9231-x