VIII.1, Winter 1986 Informal Logic A Question of Begging DILIP K. BASU There are two accounts of the petitio in Aristotle. One is in the Prior Analy- tics which is justly celebrated for con- taining Aristotle's syllogistic; the other is in the Topics whose business it is to discuss dialectical and sophistic refuta- tions. The former, according to Aristo- tle, is the true account, an account valid for scientific arguments, while the lat- ter is an account of the matter on the le- vel of general opinion(Topics 162 b 31-3) i.e. opinion accepted by all, or by the majority, or by the most notable of them, the philosophers (Topics 100 b21- 3). Richard Robinson suggests that the two accounts are incompatible and that the Analytics account, far from being the true account, is a failure, having no application in most of science.[1] The Topics account, he argues, is relevant only to the Academic game of elenchus, a game no longer played. Robinson therefore thinks that begging the ques- tion, as the petitio is usually called in English, is something of a muddle. In this paper we shall try to find out if this is really the case. I. Setting the scene Any scientific activity, in Aristotle's opinion, requires at least two partici- pants, a questioner and an answerer in a relationship, we might say, of aiding and abetting. There are four situations to consider. First, we have the master and the pupil, the master offering his fare to his pupil in the form of argu- ments developed from the basic princi- ples of his science. This is a dialogue by courtesy, for the pupi I is no more than a sleeping partner in the enterprise with the argument developing in complete University of Burdwan disregard of his beliefs and reactions which are not so much as sought. Sec- ondly, there is the typically Greek situa- tion in which two men are locked in a dialectical argument on the level of ge- neral opinion. A third pair consists of a questioner and an answerer who up- holds a thesis and claims to back it with facts bearing on the subject. Such an argument is the very serious business of the testing of a thesis. The sophist and his interlocutor make up the fourth pair, the argument here proceeding va- lidly or invalidly from premisses that- appear to be generally accepted but are not so. The result is an exhibition of professional sophistry. We have thus four classes of arguments in dialogue form: didactic, dialectical, examination- arguments, and contentious arguments (Topics 165a 38-9). Didactic arguments are the concern of the Analytics, the remainder that of the Topics. What the scientific tutor does by em- ploying his didactic arguments is to de- monstrate to his pupil the conclusions he has already reached by means inductive as proceeding syllogistically from the basic principles of his science. The first or basic principles of the science are not themselves demonstrated. As Aristotle tells us, we know the first principles na- turally through themselves. They are, in other words, self-evident. The fact that the first principles are regarded as self-evident does not, however, mean that we do not have to search for them or that they strike us in the face with their self-evidence. Of course we have to look for them and find out by employ- ing such resources as induction. But when teaching the scientific tutor ought to present his findings in the form of a 20 Dilip K. Basu demonstration proceeding from a set of truths not themselves demonstrated, but discovered, in the first place, in the same arduous way as the conclusions demonstrated. So the first principles are first among equals. Jonathan Bar- nes has correctly argued that Aristo- tle's theory of demonstration was never meant to guide scientific research, but to offer' a formal model of how teachers should present and impart knowledge.' [2] The very first line of the Posterior Analytics leaves no one in doubt about its didactic orientation: 'All instruction given or received by way of argument proceeds from pre-existent knowledge.' The scientific tutor thus has a job that is quite different from the practising scientist's; the latter searches for the truths of his science by inductive me- thods and keeps the tutor well supplied who then goes on to exhibit the causal interconnexions among them, and he proceeds to do this by taking truths of the form 'A belongs to B' and 'A be- longs to no B' as basic for which he has been unable to find middles that me- diate between A and B. These truths he regards as immediate, uncaused or self-evident, but only relative to the de- monstration or the development of the science in question. Should later inves- tigations reveal a middle C intervening between A and B, the truths would ha- ve to lose their pride of place and get accustomed to taking a back seat. This relativistic interpretation of first princi- ples is not something I am forcing on Aristotle who himself suggests it. In the immediate premiss there is no interval between the subject and the predicate which become indivisible or one, and there we reach our unit in demonstra- tion (Post. An. 84 b34-S). But this unit is not something which is final.Aristotle goes on to explai n: And as in other spheres the basic ele- ment is simple but not identical in all- in a system of weight it is the mina, in a music quartertone, and so on-so in syllogism the unit is an immediate premiss, and in the knowledge that demonstration gives it is an intuition (naGs) (Post. An. 84b37-85a l, my em- phasis). Just as there can be different systems of weight or music with different units, there can be different demonstrations with different first principles as units. There is nothing final about such units, which are purely relative to the systems they are units of. What is an immediate premiss or an intuition is so only in rela- tion to a demonstration which in turn is relative to the state of the development of the science in question. When the first principles are regarded as neces- sary they are being viewed as proposi- tions relating to the essences of things but under the proviso that our empirical methods made no mistake about the es- sences. So we hold on to them until fur- ther notice. Kripke's idea that necessa- ry propositions might be contingently known is not therefore stunningly new. Whether a proposition is regarded as necessary or not depends on the state of the investigation. Thus the proposition 'All men are animals' might be neces- sary for some, accidental for others (Post. An. 89 a 33-39). We need not the- refore look askance, as Robinson does, at Aristotle's notion of self-evidence or intuition. They are relativistic notions correlative to the relativistic notion of the immediate premiss. The field scientist thus keeps the scientific tutor supplied with his propo- sitions from amongst which he separa- tes _ome as basic premisses from which he works his way to the rest by means of syllogistic arguments. The tutor be- gins a particular piece of demonstration by saying of a particular proposition that that is the proposition he wants to prove. Thus he begins with the conclu- sion, a practice that Euclid so consis- tently follows. As Johnson says, this is also usually the case with the actual course of our thought; we first entertain the conclusion and then go on to search for the premisses that yield the conclu- sion. This practice of beginning with the conclusion is also in the best of In- dian logical tradition. Aristotle's word 'to en archie aiteisthai' means 'asking or begging for the beginning proposi- tion'. This sense is rightly caught in the Latin 'petitio principii' but not very illu- minatingly in the English 'begging the question' which is to be understood as meaning 'begging for the conclusion', the conclusion being the question-at- issue, the proposition to begin with. The most common understanding of the petitio is that it consists in assu- ming the very conclusion to be proved, and it comes down to us from Aristotle. He refers to the petitio as the fallacy 'which depends upon assuming the ori- ginal conclusion' (De Sophisticis Elen- chis, 166b 26). If we have an argument such as P Therefore P the argument is obviously valid, for the premiss entails the conclusion. Any number of steps might intervene bet- ween the premiss P and the conclusion P, each step entailing the next, and the argument would be valid all right. So what is the trouble, if any, with such ar- guments? There are two ways to view the mat- ter. One is to regard the argument as proceeding from the premiss P, already established, to the conclusion P and therefore committing what the Indian logicians call 'the fallacy of establishing the established' (siddhasadhana). We start from an established premiss only to be driven back to it in an exercise of futility. We go full circle, and the geo- metrical notion suggests itself as a way of representing the situation: o We shall say that in such a case the ar- gument is guilty of circularity (but not of vicious circularity) as an alternative way of saying that it is guilty of siddha- sadhana. But there is no petitio here, which needs to be distinguished from circularity. The other approach to the matter is to view the argument 'P, therefore P' from the side of the conclusion, the pro- position we begin with as requiring to be established. To have P as a premiss when P cries out to be established is simply to assume the conclusion. The argument in such a case 'depends upon Question of Begging 21 assuming the original conclusion' and is thus guilty of the petitio. As Aristotle puts it, in the case of the petitio 'the mistake lies in regard to the conclusion for it is by a glance at the conclusion that we tell that the original question has been begged' (Topics 163a 2S-6). In the same vein we might says that the mistake in the case of circularity lies in the premiss, for it is by a glance at the premiss that we say that circularity has been committed. To have a circular proof is not neces- sarily to be guilty of circularity. If we have an argument such as P Therefore Q Q Therefore P we have a circular proof on hand, for a circular proof, as Aristotle tells us, is proof by means of the conclusion (Pr. An. S7 b 18-9). Whether this argument is guilty of circularity in the sense of siddhasadhana depends on whether we start off from P (or Q) as established to get back to P (or Q). This is generally not the case with the circular proof. For if we had drawn Q (or P) from P (or Q) already established, the matter would end there without further ado. A circular proof is generally under way when the premiss which we use to establish the conclusion itself needs establishing, when, in other words, we have two assumptions each seeking to be establ ished by the other. The trouble here is the petitio, for what is to be proved is assumed as a premiss, whether it is the proposition P or the proposition Q in the above schema, both of which remain assumptions all the way. When we have a circular proof guilty of the petitio we have the familiar vicious circle, the notion of the circle being invoked again to represent the situation: () Q We are said to be moving in a circle and the fact that P and Q are both as- sumptions fails to stop the movement 22 Dilip K. Basu at any stage. Hence the accusation of viciousness. Since when we are arguing in a vicious circle we are guilty of the petitio, there is a tendency to identify the two. For Aristotle arguing in a vicious circle is just one of the ways to beget the petitio. Since the metaphor of the circle has been used to represent our attempt to establish an already established pro- position as well as the one to prove by means of the conclusion to be estab- lished, it is necessary to note the dif- ferences. In the former case the meta- phor suggests no more than one's coming back to one's starting point, that one's starting point is again one's terminal. In the latter case it is sug- gested that one is caught in a vicious movement with no terminal to get off. It is good to travel hopefully but it is also necessary to arrive and in a vicious circle you don't. 2. The account of the petitio in the Prior Analytics In the Prior Analytics Aristotle brands the petitio a defect of syllogism, 'a failure to demonstrate the problem proposed.' And a syllogism is 'dis- course in which certain thing being stated, something other than what is stated follows of necessity from their being so' (Pr. An.24b19-20). Aristotle of course goes on to put more flesh into this spare statement so that we know what it is to have a syllogism. The sti- pulation that the conclusion has to be something other than what is stated, Kapp says,[3] is a prohibition on the petitio, and proceeds from dialectical rather than epistemological or psycho- logical considerations. For the syllo- gism in its application to science is not, in Kapp's opinion, a principle of intellectual advance but of intellectual retreat. There is a lot sensible in what Kapp says, but it seems to me that if the syllogism is employed as a prin- ciple of intellectual advance, the stipu- lation might be viewed as a prohibition on circularity, i.e. siddhasadhana. Now the structure of the syllogism is such that the conclusion we want to prove cannot itself figure as a premiss. How, then, is it possible for us to beg for or assume the conclusion in the premisses of a syllogism? The subject of analytics is demons- tration and demonstration in any sci- ence proceeds from its first principles, which, as we have already noted, Aristotle regards as self-evident and indemonstrable relative to a demons- tration. The propositions that need demonstrating are not to be self- evident, and 'whenever a man tries to prove what is not self-evident by means of itself, then he begs the original question' (Pr. An. 64 b37-8). From what has been said above in Section I it should be clear that this account of the petitio is not in any way besmirched by Aristotle's appeal to the notion of self-evidence which is not allowed to function in any inscrutable or objectionable manner. The petitio is danger to beware of in a situation that m,ight be stated less picturesquely thus: the scientific tutor wants to prove certain propositions to his pupil as pro- ceeding from certain propositions not to be proved. All the propositions in- volved here, the ones to be proved and the ones not to be, are the fruits of painstaking scientific investigations al- ready undertaken. The petitio, then, consists in proving a proposition, that needs proving, by means of itself. And the propositions that need proving are the ones that can be shown to be subordinate to others, while the first principles cannot be subordinated. How do we prove a proposition by means of itself? According to Aristotle, one way to do it is to assume 'what is in question at once', as we do in 'P, therefore, P' to prove P; the premiss might be phrased differently to conceal the deceit. Another way is to argue in a circle. This is all very well, but how do we commit the petitio in a syllogistic argument? We turn to Aristotle for help: If then it is uncertain whether A belongs to C, and also whether A belongs to B, and if one should assume that A does belong to B, it is not yet clear he begs the original question, but it is evident that he is not demonstrating: for what is as uncertain as the question to be answered cannot be a principle of de- monstration. If however B is so related to C that they are identical, or if they are plainly convertible, or the one belongs to the other, the original ques- tion is begged (Pr. An. 65 a10-15). Hamblin finds this text puzzling, as do Woods and Walton.[4, 5] For the latter the 'worrisome question' is why the argument A belongs to C B is identical with C therefore, A belongs to B should be a petitio. Hamblin thinks that Aristotle's account does fine as long as the relation between Band C is one of identity, not one of mutual convertibility, i.e. coextensiveness without identity of meaning. Hamblin's argument is that because of the trivial satisfaction of one of the premisses, the other premiss and the conclusion are each as good or as bad as the other, so that the arg ument from the one to the other is nugatory; and that th is is so is shown, among other things, by the fact that the pre- miss will, in this case, be as uncertain as the conclusion .[6] Hamblin's argument seems to be that if the second premiss is a trivial enough identity then the first premiss and the conclusion are close enough to be logic- ally equivalent, if not identical, and an accusation of petitio would seem to be in order. But Hamblin himself has a different interpretation up his sleeve: If it is uncertain whether all Bs are As, and equally uncertain whether all Cs are As, we cannot use one to prove the other, since premisses must always be more certain-more immediately known-than their conclusions. If Bs and Cs are the same things whether be- cause the concepts are identical or merely because the terms are convert- ible, 'all Cs are As' seems to be infer- able from 'All Bs are As', but also vice versa; but there cannot be genuine inferences both ways, or there could be argument in a circle. Hence the apparent inference is really falla- cious.[?] Question of Begging 23 Hamblin here is arguing that if Band C are identical or mutually convertible then we have a right to use' All Bs are Cs' as well as 'All Cs are Bs', and we have the makings of a circular proof to run as follows: All Bs are As All Cs are Bs therefore All Cs are As All Cs are As All Bs are Cs therefore All Bs are As Hamblin thus holds the argument cited by Aristotle fallacious because someone might make a circular proof, involving the petitio, out of it. Woods and Walton (op. cit.) rightly reject this view failing as it does to show that the argument as it stands involves the petitio. Their view of the matter is that the relation between Band C of identity, or convert- ibility, or mutual implication, tra~s­ parently establishes 'the first premiss as a near-equivalent of the conclusion to make the argument a petitio.' I am afraid we must reject this interpreta- tion too. Hamblin's view that the argument cited by Aristotle commits the petitio in the case where the terms Band C are identical would not work for cases where the terms are convertible or are such that one belongs to the other, and thus fails to take full measure of the problem. Hamblin therefore goes on to offer a more general explanation, but it would work only if a circular argu- ment were in question, which however is not the case. He is of the opinion that 'there cannot be genuine inferences both ways', but the question here is whether there can be a genuine argu- ment even one way. In his explanations Hamblin is implicitly guided by the insight that if one of the premisses is an assumption, it has got something to do with a petitio being there, but he did not figure out what it was. Woods and Walton thus wonder why the argu- ment A belongs to C B is identical to C therefore A belongs to B should be held by Hamblin to be a 24 Dilip K. Basu petitio, when 'A belongs to C' is un- certain. (Fidelity to Aristotle's text Pro An. 65 a 10-15 demands that the major premiss and the conclusion in the above statement change places.) It is a pity Hamblin does not let his in- sight come into its own. The inter- pretation by Woods and Walton is re- cognized by themselves to be inad- equate. It relies on a notion of near- equivalence which is vague, and fails to establish the argument as an overt petitio. Let us have a fresh look at the argu- ment Aristotle cites. We want to prove 'A belongs to C'. We know for certain that Band C are so related that they are identical or mutually convertible or belong to one another. That is to say, we are entitled to the use of 'B belongs to C' as premiss (and also of 'C belongs to B' if need be). If we are a little permissive in our selection of premisses so as to use 'A belongs to B' although we are uncertain about it, we have the following argument going: A belongs to B B belongs to C therefore, A belongs to C The trouble with this argument is this. Since we are uncertain about 'A be- longs to B', we are begging for it when we use it as a premiss, and in begging for it we are also begging for everything that it, along with other things that we accept, entails. So we are begging for' A belongs to C' in order to prove 'A belongs to C' and are thus guilty of the petitio. There are as many ways to commit the petitio as there are ways to beg for the conclusion to be proved; within the confines of the syllogistic it may be committed in the way just indicated or in the way of a circular proof. 3. The account of the petitio in the Topics The demands on dialectical argu- ments, arguments in which 'we are able to reason from opinions generally accepted', are less exacting than on scientific demonstrations, making for a little bit of variety in the way of argu- ments. Here we are permitted re- sources other than the syllogism. There is on the one hand Induction, permit- ting a passage from individuals to uni- versals, on the other Reasoning (Topics 105a12). And reasoning is 'an argu- ment in which, certain things being laid down, something other than these necessarily comes about through them' (Topics 100a25-6). In a dialectical situa- tion forms of reasoning other than syllo- gising, such as what nowadays we call adjunction, are admissible. Since the arguments here are more various, the petitio also has greater possibilities. There are, in fact, five different ways to commit the petitio, says Aristotle (Topics 162 b35-163a 12). I) The first way is to directly beg for the actual point to shown, as when we assume P to prove P. The assump- tion may be couched in different terms but meaning the same thing as the point to be proved. II) 'A second way occurs whenever anyone begs universally something which he has to demonstrate in a parti- cular case.' How is the petitio involved here? As we have already said, in assu- ming a proposition one is assuming everything that the proposition, in con- j unction with other accepted proposi- tions, is used to support. The universal assumption combined with other ac- cepted propositions yields the particu- lar proposition which remains an assumption all the way. In this case one is assuming the very point to be proved and is thus guilty of the petitio. As Aris- totle himself explains, a person in such a case 'is generally thought to be beg- ging, along with a number of other things, that which he ought to have shown by itself.' III) A third way to commit the petitio is to beg in particular cases what is to be shown universally. Woods and Walton (op. cit.) wonder why there should be a fallacy in trying 'to prove that everything in some domain has property F by successively showing that for individuals a, b, c, ... in the do- main, a has F, and b has F, and c has F, and so forth' (my emphasis). I am afraid they missed Aristotle's point altogether. There would be a fallacy, not if one showed, but assumed, that a has F, and b has F, and so on, and Aristotle is considering the latter contingency. To get back to Woods and Walton: Arguing for a universal statement on the basis of its instances has well- known inductive shortcomings, but it is hard to see exactly why the petitio must be one of them ... it is possible that the wrong that it comments on is that the evidence for each of the particular propositions that is put forward as a premiss is somehow dependent on the universal conclusion to be demonstra- ted (op. cit.). There is not much evidence in Aristotle to suggest that this is the way to look at the matter. Since inductive reasoning is one form of dialectical argument, one might justifiably use it to establish a universal conclusion. There is a petitio when one assumes or begs for the parti- cular cases which one should have taken the trouble of establishing on their own. In assuming the particular cases we are also assuming the uni- versal proposition arrived at on the strength of the particular cases. We are thus landed in a situation in which we establ ish a universal proposition by assuming it. IV) Another way to beg the question is to beg for the conclusion' piecemeal,' as when we establish a conjunction by assuming each conjunct. Since the conjuncts P, 0, are assumptions, P&O being derived from them fares no better, and we end up establishing P&O by assuming it. V) Finally, we commit the petitio when we 'beg the one or the other of a pair of statements that necessari Iy involve one another.' For example, we are to show that the diagonal is incommensurable with the side, and we do so by begging that the side is in- commensurable with the diagonal. But where is the petitio that it is accused of? Woods and Walton (op. cit.) find Question of Begging 25 the specification obscure and wonder whether case (I) at all differs from case (V). It does, as we hope to show. Two propositions, P and 0, mutually imply one another; we want to prove 0 (or P), and we do so by begging for P (or 0). Since P (or 0) is an assumption, 0 (or P) also remains one having been derived from the former. Hence our attempt to prove 0 (or P) is an attempt to prove 0 (or P) on the assumption o (or P), and is therefore guilty of the petitio. In (I) we try to prove a proposi- tion by assuming it at once so that there is no transition necessary from what is assumed to the conclusion, whereas in (V) such transition is essen- tial. 4. Concluding remarks From the foregoing discussion Aris- totle comes out as having only one no- tion of the petitio, namely, as the pro- cedure of assuming the very conclusion to be proved, but displaying a variety of ways to beget it. The particular way in which the petitio is committed depends on the type of argument em- ployed, but whatever the context, the nature of the defect is the same. And we have Aristotle's word for it: 'Those (fallacies) that depend on the assump- tion of the original point to be proved, occur in the same way, and in as many ways, as it is possible to beg the original point' (Topics 167a 37-9). There remains one misunderstanding to set aside, the one that the petitio in Aristotle survives in an epistemo- logical interpretation rather than a dialectical one. This is the view of Hamblin, who is supported by Woods and Walton, when he holds that the clue to an understanding of Aristotle's notion of the petitio is 'his concern with how we come to know things' (op. cit. p. 76, emphasis Hamblin's). Hamblin is led into this view by Aris- totle's reference to the notion of self- evidence in his account of the petitio in the Prior Analytics. From what we have said in the preceding Sections it should be apparent that the notion of self-evidence, or for that matter any 26 Dilip K. Basu other notion that reeks of epistemology, forms no essential part of the notion of the petitio and that Ari stotle' s appeal to the idea of self-evidence was neces- sitated by the requirement to set the petitio in the context of scientific de- monstrations. The petitio is a defect to guard against in scientific demons- trations as well as in dialectical con- texts; in fact, it is a defect to guard against as long as we have something to establish and are looking for support. So I should not be saying that my view about Aristotle is right, because it is. References [1] R. Robinson, 'Begging the Ques- tion, 1971', Analysis, 31.4, March 1971. [2] J. Barnes, 'Aristotle's Theory of Demonstration' in Articles on Aris- totle, (eds.J J. Barnes, et aI, Vol. I, Duckworth, 1975, p. 77. [3] E. Kapp, 'Syllogistic' in 2, p. 39. [4] C. L. Hamblin, Fallacies, Methuen, 1972. [5] J. Woods and D. Walton, 'The Peti- tio: Aristotle's Five Ways', Cana- dian Journal of Philosophy, 12.1, March 1982. [6] Hamblin, op. cit., p. 75. [7] Ibid, p. 77. All references to Aristotle's wri- tings are from the Oxford transla- tion of The Works Of Aristotle un- der the editorship of J. A. Smith and W. D. Ross. Dilip K. Basu, P-I, Tarabag, Burdwan- 4, West Bengal, India. D