Ignacio Angelelli, "The Techniques of Disputation in the History of Logic," The Journal of Philosophy 67 (October 22, 1970): 800-815.

THE TECHNIQUES OF DISPUTATION IN THE HISTORY OF LOGIC

Ignacio Angelelli
The University of Texas at Austin

The aim of this paper is to outline tentatively some aspects of the techniques of disputation in their history, on the basis of some texts. Modern logic ("mathematical" logic) was conceived more geometrico by Frege, who intended to improve upon Euclid essentially by adding an explicit list of rules of inference (Grundgesetze I, p. vi). Thus, the notion of dialectica in the sense of "speech between two," so important in the past, could hardly be found relevant by modern historians of logic, who were guided by the new model. These, in fact, have so far neglected to investigate this portion of the logical heritage.¹ Only recently there has been an increasing interest in the Topica, not extended, however, to the medieval and post-medieval developments. Good old Prantl seems to be still the best source in this respect. Historical works of a more general nature are of very little help even when they abundantly refer to disputation, because the formal aspects are usually overlooked. For example, a direct examination of the sources mentioned by Thurot would be very rewarding, but what Thurot himself says on disputation is simply useless from a technical point of view.²

The dialogical logic developed in the last ten years by Paul Lorenzen and his school provides the needed "modern" motivation to go back to the ars disputandi.³ Sources for antiquity and for medieval obligationes (a form of disputation) are known. Before 1800 disputation was considered by a very large number of books on logic; after 1800 at least by most neoscholastic treatises. Fortunately, in recent years bibliographical research in the history of logic has increased so much⁴ that now we also know of a small, yet interesting list of postmedieval (second-scholastic) works especially devoted to the theory of disputation.

I. THE TWO METHODS

Heine (1710)⁵ distinguishes two forms of disputation: his contemporary method of attacking someone else's thesis by constructing an argument whose conclusion is the negation of that thesis, and the ancient (Greek) form of asking questions that may lead the defendant of the thesis into some contradiction. Let us call these the argument and the question method.⁶ (A third form of disputatio, the so-called methodus megarica, does not seem to play an equally significant role, as far as the history of logical theory is concerned.⁷)

Heine apparently ignores the medieval period; his sources are entirely post-medieval. But if we apply his distinction to the Middle Ages, the typically medieval ars obligatoria appears as a theory of the question method, whereas the argument method (apparently not favored by medieval logicians) may be recognized in the literary style of medieval philosophers and theologians. Grabmann⁸ emphasizes that such a style is a literarischer Niederschlag of "real" exercises in disputation (II, p. 218). He also stresses that such disputations were well-defined ("by art and not just by chance" -- as he likes to quote from John of Salisbury) as a consequence of the appearance of the Topica. This is another example of how a major historical work overlooks logical technicalities, for the Topica contain a theory of the question method rather than of the argument method.

A study of exactly when a theory of the argument method originated should be the object of further empirical research. We may content ourselves with the knowledge that, roughly, the study of the argument method definitely prevails only in the second scholastics (catholic and protestant). The pseudo-Albert the Great's treatise on disputation represents to some extent the argument method, but it seems to be as late as the fifteenth century.⁹ Perhaps the seventeenth and part of the eighteenth century was the golden age of this method. Afterwards, it became an esoteric business.

II. THE "OLD" METHOD

By the "ancient" method of disputation Heine means the Topica discussion games; these have been described recently by Moraux.¹⁰ Let us consider the medieval ars obligatoria, as formulated in the Logica Magna¹¹ and Logica Parva¹² of Paulus Venetus. It is important to observe that the treatise on obligations occupies the final part of Paul's encyclopedic work. This is not by way of exotic appendix; on the contrary, obligations are a sort of culmination of logic. Obligations are nothing less than the theory of consequences stilo subliori procedens (178b).

Paul's treatise on obligations in the Logica Magna covers the equivalent of 180 typewritten pages. Much of this discusses other authors and the soundness of the rules given by Paul himself. In what follows, I shall try to capture the logically essential.

Obligation is the respondens' commitment to avoid falling into a contradiction once he has accepted or denied an initial sentence proposed by the opponens. This commitment is not made "forever" but only for a period of time called tempus obligationis. The limits of this tempus are imposed by the opponens, who says "cedat tempus!' But the respondens' acceptance is needed, and there is also a hint that the respondens may choose a certain limit for the obligation ("I admit until instant b," 178a). During the tempus obligationis, propositions are to be understood with respect to the same temporal instant -- apparently to avoid any change of truth value for contingent propositions during the lapsus of the time of the obligation (178c; this may appear superfluous from my explanation of the rules below). There is perhaps a hint at obligations "inside" other obligations (179a: prima and secunda obligation).

We may conjecture that the winning rule is as follows: the respondens wins if the opponens gives up (cedat tempus) without bringing the respondens to a contradiction. The respondens loses if he has to assert a contradiction ("has to" relative to the rules).

The game is started by the opponens and goes on by alternating moves. The opponens has two possible moves: "I propose that you assert A₁" (pono tibi A₁, positio) and "I propose that you deny A₁" (depono tibi A₁, depositio). The respondens has three possible answers: "I accept" (consedo, admitto), "I deny" (nego), and "I doubt" (dubito). It seems that positio alone would be enough, since the result of depositio appears to be the same as the denial of a positio. In the Logica Magna, however, Paul introduces still a third species of obligation: suppositio (178c), which does not differ from positio except that the opponens does not intend to "try" or to "deceive" the respondens: everything the opponens proposes in a suppositio is "true." This is the formally irrelevant question of the various ends for which disputations may be used. In the Logica Magna there is no special treatment of suppositio, and in theLogica Parva it does not occur at all.

In his first answer, the respondens is restricted by the following rule: if he knows that A₁ is possible, he has to accept a positio of A₁ and deny a depositio of A₁; otherwise, he has to doubt or deny a positio of A₁ and accept a depositio of A₁. In the greatest logic of ordinary language ever written, the principle that from the impossible everything follows, occurs frequently. The assertion of an "impossible" propositio would end the game prematurely, by compelling the respondens to grant anything that the opponens asks him to accept.

Next, the opponens moves again, by making either a positio or a depositio of any arbitrary sentence A₂ and the respondens has the same three possible replies as before; and so on. The opponens is not restricted at all in his choice of A₂, A₃ ^{. . .} , but the respondens has to satisfy all the rules previously formulated in the Logica Magna and he must pay attention to his own preceding assertions. Let us call the respondens' assertions B₁, B₂ ^{. . .} . If the opponens moves a positio of A_n, the respondens has to determine if A_n is pertinens: if it either follows (sequitur) from B₁ & ^{. . .} & B_n-1 or or implies the negation of this conjunction (repugnat). Only if A_n is not pertinens (impertinens), the respondens should accept or deny A_n according to its "real" (outside the obligation) truth value. If A_n follows from B₁ & ^{. . .} & B_n-1, A_n should be asserted; if A_n implies the negation of B₁ & ^{. . .} & B_n-1, then A_n should be denied. For example, let B₁=Every man is running, B₂=I am a man. Then "I am running" is pertinens sequens, and "I am not running" is pertinens repugnans (Logica Parva, p. 53).

This is essentially what the respondens should know. The troubles for him will probably arise when he has to decide, in a concrete case, whether a given ordinary Latin proposition follows from B₁ & ^{. . .} & B_n-1 or not. This "follows" is in fact relative to hundreds of rules, and the respondens may have to consider very tricky proposals. For example, he may be invited to accept "You have to accept all possible propositions" (Logica Parva p. 54). In view of these complications it is only natural that many rules should be added to the dry scheme of accepting what follows and denying the repugnans. Let us consider some of them.

The respondens should grant any time (within the same obligation) what he has granted once (Logica Parva, p. 52). Every A_n falsum non sequens should be denied and every verum non repugnans should be accepted (Logica Parva p. 53). If A_n is not just false but impossible, then A_n implies everything, in particular the negation of B₁ & ^{. . .} & B_n-1 (repugnat cuilibet, ibid.); and by contraposition this conjunction implies the negation of A_n. If A_n is not iust true but necessary, it is implied by everything (sequens cuilibet, ibid.), in particular by the conjunction B₁ & ^{. . .} & B_n-1 From this we gather that if A_n is impossible or necessary, the respondens does not have to check whether A_n is sequens or repugnans; every impossible A_n has to be denied and every necessary A_n must be accepted, independently of the previous assertions B₁, B₂, ^{. . .}, B_n-1.¹³ Paul claims that "impossible" and "necessary" in this context are understood in a strong sense (per se), not in a weak sense (per accidens). For example, "Adam existed" is now necessary, but only per accidens. In a disputation, "Adam did not exist" (Adam non fuit) is to be regarded as possible. In fact, from "Adam did not exist" nothing more follows now than what followed when it was true that Adam did not exist (179b), whereas from a really impossible proposition everything follows. "Man is an ass" (homo est asinus) and "God exists" (deus est) are examples of impossible and necessary per se.

Other rules concern disjunction and conjunction. Briefly, if the opponens makes a positio of the conjunction B_i & B_j (i, j ≤ n-1), this proposition has to be accepted; if the opponens makes a positio of the disjunction B_i V C (i ≤ n-1, C arbitrary), this has to be granted too. For the conditionalis (si, if) there is no such "introduction" rule, the reason probably being that for Paul all true conditionals are necessary and all false conditionals are impossible (Logica Parva, p. 8).

It may be convenient to consider some examples given by Paul for his several rules of "elimination" of the conditional, combined with negation (Logica Parva).

Opponens positio: Every man is in Rome, A1 positio: You are a man, A2 positio: You are in Rome, A3

| | | | |

Respondens concedo: Every man is in Rome, B1 concedo: I am a man, B2 concedo: I am in Rome, B3

B₁ is asserted because it is possible. B₂ has to be asserted because it is impertinens (with respect to B₁) and true (regardless of the disputation). B₃ has to be accepted because it follows from B₁ and B₂.

positio: Every man is running, A1 positio: You are running, A2 positio: You are not a man. A3

| | |

concedo: Every man is running, B1 nego: I am not running, B2 concedo: I am not a man, B3

Notice that B₂ is not regarded as sequens from the assumptions; "I am a man" is not assumed. B₂ is asserted independently of the game, being impertinens. B₃ then has to be accepted by one of the rules given in the text. B₃ is the correct answer; the respondens has not been led into any contradiction. In fact, even with

positio: You are a man, A₃     | nego: I am not a man, B₃

B₃ would be the correct answer, according to another example.

If the opponens makes a depositio of A_n, the respondens should reply as for a positio of not-A_n. But many special rules are given anyway. Being offered a depositio of A_n, the respondens should not accept the proposal to deny A_n if B₁ & . . . & B_n-l implies (antecedit ad) A_n, and he should assert not-A_n if A_n, implies the negation of B₁ & . . . & B_n-1.

depositio: some man is not running, A1 positio: you are not running, A2 positio: you are a man, A3

| | |

concedo: All men are running, B1 concedo: I am not running, B2 nego: I am not a man, B3

B₂ is asserted because it is impertinens and true. A₃ must be denied because the conjunction of A₃ and A₂ implies the depositum A₁.

In the Logica Magna the rules for positio and depositio contain a special condition that does not occur in theLogica Parva. For example, the rule that what follows from the premises B₁, B₂ ^{. . .} must be accepted, includes the additional clause: scitum esse tale, i.e. "known to be such (by the respondens during the time of the obligation)". Example:

positio: Marcus is running, A1 positio: Tullius is running, A2

| |

concedo: Marcus is running, B1 dubito

The respondens happens to ignore that 'Tullius' and 'Marcus' are nomina synonima. By answering "dubito" he is not violating any rule of substitutivity: indeed, he has to doubt "until he knows" (debes dubitare illam quousque sciveris tales terminos synonimos esse, p. 179 b). Incidentally, we see that the "dubito" is not merely intended to remove ambiguities of language, as is the later "distinguo".

III. THE "MODERN" METHOD

The largest work on the argument method is Quadros 1722.¹⁴ Initially, however, it is more convenient to follow a concise treaties such as Heine's. Quadros' work may be important in a second stage, but his examples are too long, and one even wonders whether the essential rules are given or just presupposed.

In the new method the respondens starts the game by asserting a thesis A. Next, the opponens must produce an argument whose conclusion is not-A. As Heine points out, the modern opponens does not "ask," but argues (cap. 1). The respondens may then reject the argument; in particular, he may deny its premises. Then "the opponens assumes new propositions and by means of them he proves the denied proposition" (ibid.). This is the essential scheme of the disputation, which goes on until propositions are reached that belong to a set accepted by both partners. The opponens is under no obligation to prove anything that is a manifestum and maxime verum principium (cap. III, 27-28). The rule says that in such a case the opponens should point out to his partner that such principles are not to be doubted.

As in earlier formulations of the ars disputatoria, emphasis is laid on the variety of ends that disputation may serve: teaching, discovery, etc. (cap. I) . This sort of consideration, however, does not seem to have any effect on the formal structure. In science and teaching, "only true sentences are assumed" (cap. I, 10). This seems to coincide with the suppositio as a kind of obligatio.

Besides the two partners, the "president" (praeses) of the disputation is also in attendance. There are apparently many specific ways in which this "referee" fulfills his supervising task (cf. Quadros). A more precise example of this aspect of the disputation will not be attempted here. (Nor shall I consider the notion of a disputatio where the number of participants is reduced to one: "self" or "mono" disputation.¹⁵)

In chapter II Heine examines the conditions that must be satisfied by those who intend to engage in disputations. The first two are certainly relevant: good knowledge of language and of the logical rules. The other conditions are rather paychological in nature. The number of rules that must be known seems to be smaller than in the medieval period. Horneius¹⁶ points out that multa inutilia were given by earlier logicians (p. 53).

In chapters III-IV, Heine provides rules for the opponens, the respondens, the praeses, as well as some stratgemata that may help each of the two partners.

The opponens is urged both to understand precisely the meaning of the thesis against which he is going to argue, and to know the statum controversiae. Then he has to produce an argument directly or indirectly denying the thesis A. The indirect attack is made by taking a conjunction A & C, where C is unanimously accepted, and showing that this conjunction implies a false proposition. In the direct attack the opponens is advised to prove the contradictory rather than the contrary of A, because the auditores (a fourth kind of participant in the disputation) may gather, in the case of the contrary, that both opponens and respondens are wrong. If the thesis A is itself negative, say not-B, there are no signs that our logicians would distinguish between not-not-B and B. As a matter of fact, in Clauberg's section on disputation there is an explicit rule that B is the contradictoria (the negation) of A, both for elementary and compound A.¹⁷

Once the opponens has formulated his argument, the respondens should repeat ("two or three times", Hunnaeus¹⁸) the argument, word by word. We must appreciate the formalistic motivation of this rule: the well-formed formulas of our disputatores were not clear strings from symbolic logic; they were long and tricky sentences from ordinary language. There had to be some way of making sure that the same sentence was preserved in going from one partner to the other.

After the repetitio, the respondens may move in one of three possible ways: (1) distinguo, (2) concedo, (3) nego. Some authors mention a fourth possibility: to show that the opponens' argument actually proves the thesis claimed by the respondens. This is retorsio or inversio.¹⁹ The respondens should distinguish what is ambiguous, grant what is true, and deny what is false. Unless the respondens grants, his counterattack is called a solutio of the argument. In fact, unless he grants, he has to "solve" (solvere) the argument. If the argument does not really threaten the thesis, the respondens may also say "concedo", as he may do with respect to any proposition that appears to be irrelevant. One of the few flaws in Hunnaeus's excellent treatise is that in the list of tasks for the respondens, the move "concedo" is defined as what the respondens should do when the opponens' assertions are irrelevant (nihil obsint proposito, p. 97), whereas, in the rest of the work, "concedo" is understood as the obligation of granting what is true. Other authors more conveniently use a special term for the admission of the irrelevant, for example transeat (Toledo,²⁰ p. 30, Quadros, etc.). The distinguo move is rather external to the formal structure; its significance is to be understood against the background of ordinary-language logic. The result of the distinction is that the argument splits into two or more arguments, according to the different senses introduced by the respondens.

From Horneius (followed by Heine, cap. III, 33) we gather that the respondens should neither argumentare in contrarium nor prove his own thesis (p. 126). The notion of argumentare in contrarium is not defined by Horneius; it may be conjectured that it is an argument whose conclusion is the negation of premises asserted by the opponens. But the really important point here is that the respondens neither has to prove any of his assertions, nor is allowed to prove any of them. Two passages in Heine's treatise may suggest that there are exceptions to this rule. Among the stratagemata of the respondens, Heine mentions that he may.produce an argument to prove his own thesis (cap. VII, 7); this, however, may be understood in the psychological sense of making the opponens dubius or confused; as a rhetorical intermezzo and not as a formal step. In fact, Heine says that such a move does not "solve" the argument brought forward by the opponens, which means that formally this move is not recognized (cf. Horneius, p. 126). Also, Heine says that a trick for the opponens is to use "negative syllogisms" (apparently, "with negative premises"), so that in denying them the respondens becomes an affirmans and therefore "feels" that he has to prove his assertion. This polnt (included in the chapter on the stratagemata for the opponens, VI, 13) may be understood, again, not to suggest that the respondens should prove his proposition. I believe Heine means a psychological weapon, aimed at undermining the morale of the respondens ("in real life, not in disputatione, I really ought to prove my assertion"; cf. Horneius, p. 126).

Whereas the respondens is not allowed to prove his thesis, the opponens should have "in promptu" proofs for all his statements (Heine, cap. III, 29). Quadros quotes Caramuel as saying that caeteris paribus to argue well (to be a good opponens) is more difficult than to be a respondens (p. 53). The respondens privilege²¹ in this respect is vaguely described by Horneius as having to claim mere possibilities, whereas the opponens has to claim truth (p. 127-128). We might say that the respondens claims nonrefutability of a certain thesis; more precisely, that a certain thesis has not been refuted by this particular opponens.

Things however are not so simple. The respondens is not a machine arbitrarily uttering "nego" or "distinguo", until being stopped by unanimously accepted sentences. We know already that the task of the respondens is to produce a solutio of the argument. Obviously, there will not be such a "solution" unless the respondens is prepared to distinguish or to deny in a "reasonable" way -- he should be prepared to justify (reddere rationem) his distinctions and denials (Horneius, p. 126). If the respondens claims that the form of the argument is not correct, he should be prepared to mention the logical rule that is violated (Reneccius³²). The opponens has the right to demand that the distinctiones made by the respondens have a sound fundamentum and be really relevant. Not just any "cheap" distinction (distinctiuncula, Heine, cap. III, 35) should be accepted by the opponens. A mere negation will not do (nude enim negare aut falsum aliquid dicere non sufficit, Horneius, p. 130). The best move for the respondens will be to produce an instantia against the opponens' argument. An instantia is a single sentence that is obviously true without needing any proof (so that the respondens does not have to prove it, which would infringe the rule of not argumentare in contrarium). Usually, instantiae are particular propositions set forth against universal propositions.

One complication introduced by the requirements just mentioned is that the respondens loses the game if he is not able to "justify" or to show the rationale of his distinotions and denials. (Heine, cap. III, 34, causa vicisse censetur; the opponens will be said to have won. This is mentioned by Heine only with respect to unjustified denials.) The respondens does not have to produce an instantia. Heine simply says that he can (potest, cap. IV, 10); Horneius affirms that instantiae are the most powerful (potissimum, p. 130) way of denying, that is, of justifying one's denials. But what are the other ways? Some auctoritas? In any case, now we have to say that to win means for the respondens (1) that the opponens has not refuted the thesis and (2) that the respondens has shown in some way (ranging from "reasonable'' negations and distinctions to full instantiae) that the opponens' argument fails. On the other hand, to lose means for the respondens either that his thesis has been refuted or that he was not able to show the failure of the opposite argument.

Another complication depends on whether the opponens has the right to attack instantiae as he did with the initial thesis. Instantiae are supposed to be true, or to belong to the set of unanimously accepted propositions, But then, is the sentence asserted by the respondens really true? In fact, in some authors the opponens' attack on an instantia is officially recognized as a special move called reply (Toledo, replicare²³).

We shall now consider an example given by Hunnaeus where such replies and instantiae occur (Hunnaeus does not seem to recognize them in the theory). We shall skip many parts that are not logically relevant ("repetitions," moves that occur only because the opponens presents his argument as an enthymeme, etc.) . For convenience, let us abbreviate most of the propositions used in the example. Let

A1= Λ_x. x ∈ wise → x ∈ free (sapiens, liber)
A2 = V_x. x ∈ slave & x ∈ wise (sersus)
A3 = Λ_x. x ∈ slave → ∼x ∈ free
A4 = Λ_x. x ∈ free → x ∈ can live as he wants (vivit ut vult)
A5 = Λ_x. x ∈ slave → ∼x ∈ can live as he wants
A6 = Λ_x. x ∈ wise → x ∈ wants to live according to reason (nihil vult nisi quod recta ratio dictat)
A7 = Λ_x. x ∈ wants to live according to reason →› x x ∈ can live as he wants
A8 = V_x. x ∈ slave & x ∈ can live as he wants
A9 = V_x. x ∈ wise & x ∈ controls his passions (refrenat libidines)
A10= Λ_x. ∼x ∈ controls his passions → ∼x ∈ wise.

The disputation may be now represented as follows;

oppugnans (= opponens)		defendens (= respondens)
		A, (thema)
A3, A2 are true and they imply not-A1 (A2 is supported by one example: Aesopus)
		distinguo "free" in A3: for freedom of the body, concedo; for freedom of the mind, nego.
A4 and A5 are true and they imply A3 (Oppugnans apparently claims A4 to be true in spite of the distinction)
		nego A3, I assert A8 (by A6, A7, and A2. These seem to be the premises used by the respondens to prove A8. Note A2 already asserted by opponens)
A9 is true and it implies not-A6.
		nego A9, I assert A10
I prove A9 from history. Example: Aristotle.
		Proofs from history are not sufficient.

Disregarding the unexciting finale, we see that in his justification of nego A₅ and nego A₉, the defendens asserts instantiae; his justification of nego A₅, however, goes far beyond being an instantia, as it is a full argumentum in contrarium. A₁₀ is an instantia: it is presented without proof, as a generally accepted rule on the meaning of the predicate "wise". By means of A₉, the opponens attacks instantia A₈, or more precisely, premise A₆ of the pseudo-instantia A₈.

This shows that in order to reach a deeper understanding of traditional disputation, not only must we study the theory, but perhaps even more, we should carefully analyze the practice, as revealed by so many examples available in the literature.

We saw above that the respondens neither has to prove nor is allowed to prove. This suggests that the respondens would eventually like to prove. In fact, although the obligation of proving may appear burdensome in general, the respondens would be glad occasionally to have the right to produce some nice proof he already happens to know (which may confuse the opponens) rather than having to discover the weaknesses of an intricate argument he has just heard. This is surely why Horneius has to emphasize so much that the respondens should not attempt to prove his thesis. From this point of view, we also understand that the defendens in Hunnaeus's example denies A₅ by a full argumentum in contrarium rather than by an instantia. A strange example of how proving may be an escape rather than a burden is given in Joffre's brief account of disputation (in this case the escape is officially recognized in the theory).²⁴ The respondens is allowed to prove his thesis when the opponens has made a so-called insolubile argument; the intended result being that the opponens will have to conceive a new argument, not against the thesis, but against the proof of the thesis.

Lazy or mediocre respondentes would like to answer with a proof if, and only if, they have such a proof: however, they would not like to have to prove their thesis or their instantiae each time. A disputation system where this would be required would add an unpleasant onus probandi to the respondens. Somebody in the early eighteenth century conceived such a system and claimed that the respondens does have an obligatio probandi. Our author, Jacobus Antonius Jacobi,²⁵ affirms that both partners must present proof (uterque disputantium tenetur probare). He points out that the experts (eruditi) have in general considered the respondens to be free of obligatio probandi. Cornelius Martini and some others (quidam) are said to have recommended this obligation only in exceptional cases. It is not possible here to discuss Jacobi's arguments against the vulgaris opinio. We shall only observe that in his discussion the ambiguity of the crucial term 'defendere' comes to light. For Horneius, 'to defend' means only to show that the opponens' argument is not efficient (p. 126: cf. Geulincx²⁶): for Jacobi, it means proof as well (§XXIII).

CONCLUDING REMARKS

In comparing old techniques of disputation and our contemporary dialogical logic, there appear several differences that are philosophically or technically relevant.

(a) In Lorenzen's approach, the dialogue serves to define the meaning of the connectives; the logical constants are introduced by attack and defense rules. At least with respect to the few texts that we have examined, it seems safe to assert that there are no signs of using disputation as source of meaning for the logical particles. The ars disputatoria (Logica Magna 184a) is very important for Paul of Venise, but as an application or extension rather than as a foundation of logic. Logic is obviously for Paul the study and formulation of truth-preserving rules that allow people to move "safely" from well-formed Latin sentences to other well-formed Latin sentences. The number of such rules (which may be called adrnissible²⁷ with respect to the class of true sentences, or just regulae bonae) is infinite: only a few are selected because of their generalitv or usefulness. Thus, the Logica presupposes not only a clear definition of well-formedness (congruitas) but also of truth and meaning for propositiones, both elementary and compound. In his study of the medieval semantics of propositiones, Kretzmann²⁸ hints at the logical significance of the grammatical notion of congruitas (fn 12), as well as at "the distinctive contribution" of syncategorematic words (our logical constants) to the meaning of the propositio (cf. fn 3). On the basis of a sophisticated grammatica and semantics (in particular, of 'and', 'if', 'or', 'not', 'all', and 'some'), our logicians piled up as many admissible rules (regulae bonae) as they thought convenient. Perhaps all this was done with diputation in mind. The disparity, however, between application and foundation seems to remain.

(b) In the traditional ars disputandi we do not find the notion of "all opponents" that occurs in the recent dialogical logic as a basis for the definition of truth. In a sense, we might say that a persistent effort throughout the history of disputation theory has been directed toward the exclusion of such a notion, as the general advice has been that definitely true propositions (propositions defensible against all opponents) are not an appropriate subject for disputation (Contra principia negantes non est disputundum, Calov²⁹).

(c) From a technical point of view, one difference between traditional and modern dialogues is that the former are not subformula preserving. Referring to our example from Hunnaeus, the first attack by the opponent would not be in modern dialogues a full argument (bringing in many new propositions that are not subformulas of the thema), but the request to defend the thema for a specific object chosen by the opponent:

Opponent	Proponent
1. 2. Aesopus? 3. Aesopus ∈ wise	Ax. x ∈ wise → x ∈ free Aesopus ∈ wise → Aesopus ∈ free

where the proponent wins if and only if he shows that "Aesopus ∈ free" is true or the opponent does not show that "Aesopus ∈ wise" is true.³⁰

(d) The proponent of modern dialogues has a full obligatio probandi in the following cases: conjunction, disjunction, quantifiers "some" and "all". To defend each of these compound sentences, means to be prepared to prove some of their subformulas. In the case of the conditional A → B, and especially in the case of negation (∼A or A → falsum), the proponent of modern dialogues resembles the respondens of the argument method, in that whoever opposes these compound propositions must be prepared to assume a good deal of onus probandi. For the conditional, compare our example above for negation, obviously the proponent wins "A → falsum" if and only if the opponent does not show that A is true.³¹ In other words, negation does not involve any proof responsibility. (At this point it becomes essential that truth is defensibility against all opponents.)

Finally, it should be observed that the uncertainties we have found in some points of traditional disputation theory (mainly, in the justification of the respondens' moves), do not result from a "bad" logic or from the fact that the excellent logic of our authors was mathematically "unfinished." Rather, the trouble is that nonlogical elements arise in the development of the disputatio. How should one decide whether a given sentence is really an instantia? How does one know that a "nego" and a "distinguo" are really "reasonable"?^†

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Notes

* To be presented in an APA symposium on Medieval Logic, December 29, 1970; see this JOURNAL, this issue, pp. 767-787, 788-800.

1 There are hardly any references in the most distinguished works on the history of logic. In E. Moody's The Logic of William of Ockham (London: Sheed & Ward, 1935), the topic of obligations is considered "not very relevant to logic" 294).

2 Charles Thurot, De l'Organisation de l'enseignement dans l'Universite de Paris au Moyen Age (Paris: E. Magdeleine, 1850); pp. 87-90 for the disputes.

3 Paul Lorenzen, Normative Logic and Ethics (Mannheim: Bibliographisches Institut, 1967); Kuno Lorenz. "Dialogspiele als Semantische Grundlage von Logik-kalkulen," Archiv fur mathematische Logik und Grundlagenforschung (1966).

4 Above all W. Risse, Bibliographia logica (Hildesheim: 0lms, 1965). Additions in W. Redmond, Bibliography of Philosophy in the Spanish-Portuguese Colonies (The Hague: Nijhoff, forthcoming); L. Hickman, Late Scholastic Logic: Another Look; to appear in Journal of the History of Philosophy.

5 Io. Fridericus Heine, Methodus disputandi hodierna ex variis autoribus collecta (Helmstedt. 1710. approx. 40 p.). (Copy Universitatsbibliothek. Tubingen.)

6 Alia enim est ratio disputantium veterum et alia ratio hodiernorum disputantium (preface). Cf. Jungius: qui defendit thesin hodie respondens, qui oppugnat opponens (Logica Hamburgensia, 6,1). In Wolff's Logica (§1117) there is a distinction between methodus erotematica and methodus syllogistica (=argument method). In Heineccius (Elementa philosophiae rattonalis, 1740, §213) the methodus hodierna is opposed as in Heine to the methodus socratica. Both Wolff and Heineccius (as well as Baumeister, cf. fn 7) reveal that some of their contemporaries still commended the question method (magis alii commendant .... Heineccius). The question method, however, is regarded as demode (iam pridem obsolevit, Heineccius). Our Wolffian authors definitely prefer the argument method. In a twentieth-century scholastic textbook such as Gredt (Elementa philosophiae aristotelico-thomisticae), we still find the distinction between the two methods: methodus scholastica and methodus socratica.

7 J. F. Baumeister, Institutiones philosophiae rationalis..., (Vienna 1775), §527. Each player has to show that his partner's assertions imply a contradiction. According to Risse (fn 4), there is a special work on this methodus: Ioh. Gaspar Gunther: Dissertatio de modo disputandi megarico (Jena 1707). Risse mentions only one copy as available in Niedersachsische Landesbibliothek, Hannover, but unfortunately I was informed by this library that the book is not even recorded in the catalogues (1970).

8 M. Grabmann, Geschichle der scholastischen Methode, I (1909) and II (1911).

9 Pulcherrimus tractatus de modo opponendi el respondendi, necessarius valde omnibus volentibus acutissime arguere ad trahendum respondentem in oppositum suae positionis... Incipit tractatus de modo opponendi et respondendi venerabilis domini AIberti Magni... 1498 (copy Universitatsbibliothek, Erlangen). According to Fr. Meersseman, the author of this treatise is not Albert the Great; the work is nur albertistisch und wahrscheinlich ins 15 Jahrhundert zu plazieren ist. I am grateful for this information both to Fr. Meersseman and to Dr. Hans Burkhardt.

10 Paul Moraux, "La Joute dialectique d'apres le huitieme livre des Topiques," in G. E. L. Owen, ed.. Aristotle on Dialectic: The Topics (New York: Oxford, 1968).

11 Venice 1499 (copy at Biblioteca Apostolica Vaticana).

12 Summa totius dialecticae (= Logica Parva) (Venice, 1552) (private copy).

13 Concludo ergo quod infra tempus obligationis quotienscunque et quandocunque proponitur aliqua istarum, Deus est, homo est asinus, prima est concedenda, secunda neganda (Logica Parva, p. 53 v). This is stronger than propter possibile positum non est impossibile concedendum, nec necessarium negandum (p. 53). The Aristotelian doctrine (Analytica priora I, 15) explicitly includes the weaker formulation, not the stronger one. Notice that Paul proves the stronger rule by the principle ex impossibile quodlibet. For the Aristotelian origin of the weaker rule, cf. Boehner, Mediaeval Logic (Manchester: University Press, 1952), p. 18.

14 Didacus Quadros, Palaestra Scholastica (Madrid 1722, approx. 400 p.) (copy Biblioteca National, Buenos Aires).

15 Faber Stapulensis, In terminorum recognitionem introductio (Paris 1504), rule 13th. Si quis apud seipsum disputet: ipse unus est reipsa sed duo ratione; cf. also N. Dorbellus: Summulae Philosophiae Rationalis, Basel 1503.

16 Conradus Horneius De processu disputandi (Frankfurt 1633, approx. 130 p.) (copy Stadt-Staat-Bibliothek, Augsburg),

17 Joh Clauberg, Logica vetus el nova, iv, 16.

18 August Hunnaeus, Erotemata de disputatione, p. 87-116 of Prodidagmata de dialecticis (Antwerp 1583). Bound with Dialectica (Antwerp 1585) (copy University of Texas library); cf. p. 95.

19 Fridericus Dedekind, Artificium disputandi contractum, (Greifswald 1675) (copy Universitatsbibliotek, Greifswald): Retorsio...ut mediumter minum ab opponente allatum suae applicet causae....Majorem...invertere el in ipsos Calvinianos retorquere (p. 30-31). The term 'inversio' is used by Heineccius, cf. fn 6.

20 Franciscus Toledo, Introductio in dialecticam Aristotelis, (Venice 1602) (copy University of Texas library).

21 Abraham Calovius, Tractatus novus de Methodo Docendi et Disputandi (Roskok 1637) (Methodus disputandi = p. 375-518); cf. p. 508: Abutuntur hoc respondentium privilegio Sociniani.. .contendunt insuper, se non teneri nisi ostendere tantum, possibile esse ita vel ita rem se habere, ad ulteriorem probationem adigi non posse.

22 Jacobus Reneccius, Artificium disputandi, (Gera 1619, 189 p.) (copy Universitatsbibliotek, Tubingen); cf. p. 187: requires canonem logicum!

23 Toledo, op. cit., fn 20, liber I, cap. 9, second rule for argumentans ( = opponens): Si autem aliquid ei responderit (= respondens to opponens) vel aliquam solutionem adhibuerit, quae videatur vel falsa vel dubia vel non cum praecedentibus dictis aut assertionibus respondentis cohaerere, vel tandem ei libuerit impugnare (!), iliud alio argumento conetur repellere, quod dicitur replicare, et circa id poterit multoties eodem argumentandi methodo uti.

24 Petrus Joffre, Ars syllogistica demonstrata (Tarbes 1712) (private copy): Si argumentum sit ipsi insolubile, statim opponat argumentum argumento, idest probationem suae Theseos, quam si Adversarius evertere non possit, tunc neutir alteri cedere tenetur (p. 208).

25 Jacobus Antonius Jacobi, De obligatione probandi (Lipsiae 1716) (copy Universitatsbibliotek, Tubingen). It will be most interesting to know Leibniz's views on disputation, specifically, we hope, on this particular point of the onus probandi. There are some unpublished manuscripts on this subject (I owe this information to E. de Olaso).

26 A. Geulincx, Tractatus de officio disputantium, in Opera Philosophica, II, 112-122.

27 In the technical sense of Lorenzen's operative philosophy of logic, as formulated, for example, in Einfuhrung in die operative Logik und Mathematik (New York, etc.: Springer, 1955; 2nd ed., 1969). Only from this point of view, I believe, can we make sense of the ex impossibile quodlibet (cf. that book, p. 27).

28 This Journal, this issue, 767-787.

29 Calovius, op. cit. fn 21, p. 392.

30 Cf. Lorenz, op. cit. fn 3, p. 34/35, and P. Lorenzen and W. Kamlah, Logische Propadeutik (Mannheim: Bibliographisches Institut, 1967), p. 158. The earliest text perhaps is P. Lorenzen, "Uber Beweis und Definition," in A. Heyting, ed. Constructivity in Mathematics, (Amsterdam: North-Holland, 1959), p. 173/4.

31 Cf. Lorenzen-Kamlah, op. cit. fn 30, p. 159.

† In view of the many authors and topics that remain to be investigated (and copies of books that are to be located), this paper should be considered only as a provisional excursus into an area that deserves a full book. For future researchers, it may be helpful to note that there are many "misleading" titles, such as Facilis disputandi modus (by Elias Schneegass, Witteberg, 1663, copy Staatsbibliothek der Stiftung Preussischer Kulturbesitz) or Explicatio terminorum quibus frequentius in disputando scholastics utuntur (by Juan de San Anastasio, Mexico 1772, copy University of Texas Library), which are not intended to give a theory of disputation but only some useful equipment for those who wish to participate in these games.