5. LOGIC, DIALECTIC, RHETORIC

1. 5. LOGIC, DIALECTIC, RHETORIC Demonstrative (or apodictic) reasoning is characterized by a sort of “closed” rationality, in which nothing can be questioned: not the premises of the reasoning, nor the inferential rules, neither the conclusion – that, given those premises and inferences, is necessary. By contrast, the main feature of argumentative (or anapodictic) reasoning is its “open” rationality: each and every step not only can, but must be questioned. As to premises, they might have or have not the status of universal principles: they are disputable. Therefore, given that both premises and inferences are debatable, the conclusion of an argumentative reasoning is not and cannotbe necessary.

2. In demonstrative reasoning whoever accepts the premises, is forced to accept the conclusion as well. 1. if we all agree thaty = f(x) is real with x real is defined and continue in [x1, x2] is derivable in [x1, x2] and f(x1) = f(x2)then, necessarily, there is at least one pointx є [x1, x2] for which df/dx = 0. 2. if the angular momentum of a physical body is constant, that that body moves on a plane. All these conclusions are apodictic: there is no room for discussion. The system is closed: either we accept it as a whole, or we reject it as a whole.

3. In demonstrative reasoning we have only one problem, that of defining the logical status of the premises: if they are true, then the conclusion is true if they are hypothetical, the conclusion is hypothetical if they are conventions, the conclusion is a convention etc. In a demonstrative reasoning – or proof – the epistemological status of the conclusion reflects that of the premises. The rationality of argumentative reasoning, by contrast, turns from apodictic into anapodictic: - the conclusion is no longer necessary, nor the only possible one - its epistemological status has little – if anything – to do with the epistemological status of the premises

4. Whereas in demonstrative reasoning the inferential process guarantees the necessity of the conclusion, in argumentative reasoning the conclusion is neither necessary nor the only possible one. Such a key difference, however, does not prevent the possibility of exchange and “communication” between these demonstrative and argumentative of reasoning. For, the argumentative level is often a fundamental basis for the demonstrative one. Aristotle, for example, appeals to argumentation in order to justify the principles of non-contradiction and excluded middle. In fact, if they could be proved, they would be inferred from a proposition that would depend on them (circulus in probando). Or they would be theorems themselves, thus depending from other principles (infinite regress).

5. Having abandoned the option of proving them, Aristotle appeals to argumentation (Metaphysics, IV): - first, he analyzes all possible refutations of the principle of the excluded middle; - all of them turn out to be contradictory; - therefore, Aristotle concludes, the principle of the excluded middle is valid. This is a typical reductio ad absurdum: having denied the thesis, we come to a contradiction and therefore conclude that the thesis was valid. But if we conclude that the thesis is valid because its negation entails a contradiction, then we assume the validity of the principle of non-contradiction. In other words, we proved the validity of the principle of the excluded middle by appealing to the principle of non-contradiction: it is a deductive justification, made within logic (the realm of necessity).

6. But how can we justify the principle of non-contradiction, then? To repeat: we cannot appeal to deduction, otherwise we would either incur into a circulus in probando, or we would have to admit that the principle of non-contradiction is not, in fact, a principle (infinite regress). The way out it finding an argumentative reasoning that would reasonably convince us that the principle of non-contradiction is a good one. Aristotle’s own choice falls on a strictly cogent argument – so persuasive, in fact, that it seems more a deduction than an argument. But we know it cannot be a deduction, because it is anapodictic. It is an argument based upon the elenctic principle.

7. The elenctic principle is the peculiar feature of some propositions that, when denied, are at the same time affirmed. The principle of non-contradiction is indeed one of these propositions: denying it equals affirming it, because it can be denied only at the cost of contradiction. “Now negative proof [elenchos] I distinguish from demonstration proper, because in a demonstration one might be thought to be begging the question, but if another person is responsible for begging the question we shall have negative proof, not demonstration. The starting point for all such arguments is not the demand that our opponent shall say that something either is or is not (for this one might perhaps take to be a begging of the question), but that he shall say something which is significant for himself or for others; for this is necessary, if he really is to say anything. For, if he means nothing, such a man will not be capable of reasoning, either with himself or with others. But if anyone grants this, [negative] demonstration will be possible; for we shall already have something definite. The person responsible for begging the question, however, is not he who demonstrates but he who listens; for while disowning reason [that is, the principle of non-contradiction] he listens to reason” (Metaphysics, IV, 1006a 16-28).

8. The elenctic refutation of the negation of the principle of non-contradiction is not a deductive proof, as Aristotle also stresses, but it is nonetheless cogent. The “elenctic way” (and therefore the elenctic principle that underlies it) is merely a step of a possible argumentative reasoning. As such, it does not lead to any final conclusion. To repeat: we are working within an open framework, in which any element can be questioned and criticized. Generally speaking, then, there is no argumentative reasoning that may finally found the principles of classical logic. As a consequence, deductive reasoning, with its logical necessity, requires – for its very justification – principles that are not necessary themselves.

9. In other words, what is more rigorous – deductive reasoning – can be justified only by appealing to what is less rigorous: argumentative reasoning. It is dialectic. To quote Aristotle once again: “Our treatise proposes to find a line of inquiry whereby we shall be able to reason from opinions that are generally accepted [endoxa] about every problem propounded to us, and also shall ourselves, when standing up to an argument, avoid saying anything that will obstruct us. […]Now reasoning is an argument in which, certain things being laid down, something other than these necessarily comes about through them. (a) It is a 'demonstration', when the premises from which the reasoning starts are true and primary, or are such that our knowledge of them has originally come through premises which are primary and true: (b) reasoning, on the other hand, is 'dialectical', if it reasons from opinions that are generally accepted. Things are 'true' and 'primary' which are believed on the strength not of anything else but of themselves […]. On the other hand, those opinions are 'generally accepted' which are accepted by every one or by the majority or by the philosophers -i.e. by all, or by the majority, or by the most notable and illustrious of them” (Topics, I, 100a-b)

10. Dialectical argumentation grows from the need to cope with contexts in which the truth of the premises is not taken for granted, by appealing to rational discussion. It is not any sort of discussion, though. It is the comparison of different positions in which: - logical principles (first and foremost, the principle of non-contradiction) are respected, and - no appeal is made to dishonesty or argumentative incorrectness. Because of this very logical structure is it possible to refute an opposing position. And that is why dialectic is not a mere discussion, but “the art of dialogue governed by rules”.

11. The exercise of dialectic – putting dialectic into action, that is – also requires sharing a number of assumptions. Aristotle uses the word endoxa = “elements founded upon opinion”. If we do not share the same endoxa and do not abide by the rules of logical inference, there can be no dialogue – but sheer juxtaposition of monologues. The aim of dialectic, in Aristotle’s eyes, is that of - testing a position; - getting to know and assessing others’ opinions; - assessing the epistemic value of the principles from which any science starts from. In so doing, Aristotle follows Plato, who understood dialectic as the art of finding principles (Republic, VII, 531c-534a).

12. A second form of anapodictic rationality described by Aristotle, besides dialectic, is rhetoric. Whereas dialectic takes the form of a dialogue between (at least) two speakers, rhetoric is a form of reasoning that is best displayed in monologues. Since such monologues often require many words, Aristotle’s teacher, Plato, regarded rhetoric as negative. Indeed Plato, in Gorgias (449c), portrays Socrates (the philosopher) inviting Gorgias (the rhetor) to give up his “macrology”, that is, his long and tedious talk without much substance. Generally speaking, according to Plato, the rhetor is the expert of an art that aims more at the result rather than at the truth – the aim is to widen his consensus, that is. Aristotle, by contrast, frees rhetoric of its negative import, and re-evaluates it by comparing it to dialectic.

13. According to Aristotle, rhetoric is the “the faculty of discovering the possible means of persuasion with reference to any subject whatever” (Rhetoric, I, 1355b). Rhetoric deals with consensus, not with truth. For sure, its aim is persuasion – but persuasion only by means of valid arguments, not by appealing to word-games or by moving expressions. Furthermore, it does not aim at success for the sake of success, but rather – if it is “good” rhetoric – it becomes a powerful and effective tool in order to show the actual state of affairs.

14. Whereas dialectic appeals only to rational arguments, rhetoric appeals to persuasive arguments as well, that are alien to dialectic. Both dialectic and rhetoric can justify a thesis and its negation, but never at the same time and from the same point of view – therefore never violating the principle of non-contradiction. Such a violation would amount to debasing both dialectic and rhetoric into empty eristic (that is, an argument where the participants do not have any reasonable goal: the aim is to win the argument, not to potentially discover a true or probable answer to any specific question or problem; it is arguing for the sake of conflict, fighting, and seeing who can yell the loudest).

15. Furthermore, both dialectic and rhetoric are universal in their dealing with any subject (they are not specific to any discipline). Finally, both dialectic and rhetoric can distinguish what is true from what is apparent: dialectic distinguishes true syllogisms from mere sophisms, and rhetoric distinguishes persuading arguments from merely deceptive ones. To sum up: both dialectic and rhetoric are important, though in different ways and contexts. Argumentative (= dialectical or rhetorical) rationality fundamentally differs from strict proof because of the non-necessary character of the conclusion – but this does not imply that such a conclusion has not been reached rationally.

16. It is only in 1958 that someone called attention back to the need for a theory of argumentation. For, in 1958 two important works were published: Stephen Toulmin, The Uses of Argument, Cambridge: Cambridge University Press, 1958 Chaim Perelman, Lucie Olbrechts-Tyteca, Traité de l’argumentation: la nouvelle rhétorique, Paris: Presses Universitaires de France, 1958 Both these books present Aristotle’s distinction between demonstrative and argumentative reasoning, also developing a modern theory of argumentation.

17. From the very first pages of his book, Toulmin raises the logical, philosophical and epistemological problem of rational criticism for what concerns argumentation: “[…] if we stand back for once from the engrossing problems of technical logic, it may still be important to raise general, philosophical questions about the practical assessment of arguments […]; and it may be surprising to find how little progress has been made in our understanding of the answers in all the centuries since the birth, with Aristotle, of the science of logic” (p. 2)

18. Toulmin reconstructs the steps of an argumentative process, describing its “physiological” complexity, all too often constrained into the schemes of the theory of syllogisms and, in more recent times, of formal logic. His model highlights a high number of possible kinds of statements, playing the role of data, guarantees, requirements, demands, modal conditions, conditions of rejection, and so on. Only a considerable simplification allows their reduction to the distinctions of classical logic into major premise, minor premise and conclusion. Such an oversimplification, though, occurs even more conspicuously in the argumentative process as portrayed by formal logic:

19. “One central distinction we studied at some length: that between the field of analytic arguments, which in practice are somewhat rare, and those other fields of argument which can be grouped together under the title of substantial arguments. As logicians discovered early on, the field of analytic arguments is particularly simple; certain complexities which inevitably afflict substantial arguments need never trouble one in the case of analytic ones; and when the warrant of an analytic argument is expressed in the form ‘All As are Bs’, the whole argument can be laid out in the traditional pattern without harm resulting – for once in a while, the distinction between our data and the backing of our warrant ceases to be of serious importance.

20. This simplicity is very attractive, and the theory of analytic arguments with universal major premises was therefore seized on and developed with enthusiasm by logicians of many generations. Simplicity, however, has its perils. It is one thing to choose as one’s first object of theoretical study the type of argument open to analysis in the simplest terms. But it would be quite another to treat this type of argument as a paradigm and to demand that arguments in other fields should conform to its standards regardless, or to build up from a study of the simplest forms of argument alone a set of categories intended for application to arguments of all sorts:one must at any rate begin by inquiring carefully how far the artificial simplicity of one’s chosen model results in these logical categories also being artificially simple.

21. The sorts of risks one runs otherwise are obvious enough. Distinctions which all happen to cut along the same line for the simplest arguments may need to be handled quite separately in the general case; if we forget this, and our new-found logical categories yield paradoxical results when applied to more complex arguments, we may be tempted to put these results down to defects in the arguments instead of in our categories; and we may end up by thinking that, for some regrettable reason hidden deep in the nature of things, only our original, peculiarly simple arguments are capable of attaining to the ideal of validity” (pp. 143-144).

22. Very much along the same lines, Perelman and Olbrechts-Tyteca encourage a new interest towards rhetoric. Their starting-point is two-fold: - on the one hand, ‘truth-like’ and ‘probable’ play a key role in our choices, much more than what is true or certain does; - on the other, the arguments that determine such choices are, in most cases, developed in front of an audience. The first consideration leads to an analysis of the forms and ways in which arguments are employed within rational discussions. The second intertwines with a new attention towards pragmatics.

23. From the very opening of their treatise, they insist on the rationality of argumentation: “The publication of a treatise of argumentation and its reference to an ancient tradition, that of Greek rhetoric and dialectic, constitute a sharp break with respect to an idea of reason and reasoning, born with Descartes, that has shaped Western philosophy in the past three centuries. In fact, despite no one could deny that the ability to make decisions and advance arguments characterizes reasonable beings, the study of the means employed in order to gain consensus has been totally neglected, in the past three centuries, both by logicians and epistemologists. This is due to the non-cogency features of the arguments advanced in support of a thesis. The very nature of argumentation and deliberation opposes necessity and evidence, since we do not deliberate when the conclusion is necessary, nor do we argue against evidence. The field of application for argumentation is that of truth-like and probable, as far as it escapes the certainty of calculus”.

24. The second feature of Perelman and Olbrechts-Tytecha’s treatise is the appreciation that any arguments take place in front of an audience, thus producing effects of belief or persuasion in a public or interlocutor: “Whereas a deductive system presents itself as isolated from any context, an argumentation is necessarily inserted within a context. In order to be effective, in requires an exchange among different subjects. It is required that the orator (he who advances an argument, either orally or in writing) aims at exercising, by means of his speech, an action over an audience, that is, over those whom he aims at influencing”. The pragmatic aspect thus becomes crucial in determining the choices of argumentative strategies and in assessing their effectiveness.