Synthese (2010) 175:327–349 DOI 10.1007/s11229-009-9512-1
Petitio principii and circular argumentation as seen from a theory of dialectical structures Gregor Betz
Received: 9 August 2008 / Accepted: 22 March 2009 / Published online: 5 April 2009 © Springer Science+Business Media B.V. 2009
investigates stigates in how far a theory of dialectical dialectical structures sheds Abstract This paper inve new light on the old problem of giving a satisfying account of the fallacy of petitio principii, or begging the question. It defends that (i) circular argumentation on the one hand and petitio principii on the other hand are two distinct features of complex argumentation, and that (ii) it is impossible to make general statements about the defect def ectiv ivene eness ss of an ar argum gument entati ation on tha thatt ex exhib hibits its the these se fea featur tures. es. Suc Such h an ar argum gument entat ation ion,, in contrast, has to be evaluated on a case-by-case basis. “Petitio principii”, this paper thence suggests, is one name for, in fact, a multitude of different and quite complex dialectical situations which require specific analysis and evaluation. Keywords Petitio principii · Begging the question · Fallacy · Dialectical structure · Dialectics · Argumentation 1 Introduction
Petitio principii, or the fallacy of begging the question, is an important concept of our everyday argumentative practice. Despite the fact that it has been studied extensively in argumentation theory, 1 no consensus view on how to analyze that fallacy has yet emerged. In particular, it is still controversial as to whether begging the question is best analyzed in epistemic or in dialectical terms. This paper, by embedding the problem within the normative framework of a theory of dialectical structures ,2 attempts to develop a new proposal which is not committed to one of these views.
1 Walton ( Walton (2006 2006)) gives a review of current research. 2 “The “Theory ory of dial dialecti ectical cal struc structure tures” s” refe refers rs to an appro approach ach to arg argument ument reconstructio reconstruction n and ev evalua aluation tion
(Betz Betz cf. cf. 2005 2005,, 2008, 2008, forthcoming). Key concepts of that approach will be introduced later. G. Betz (B) Universität Stuttgart, Stuttgart, Germany e-mail: gregor
[email protected]@philo.uni-stuttgart.de stuttgart.de
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Petitio Petiti o pri princi ncipii pii,, or be beggi gging ng the que questi stion, on, is usu usuall ally y ass associ ociat ated ed wit with h cir circul cular ar argumentation..3 Moreover, such kind of argumentation is, at least traditionally, supargumentation posed to be fallacious. This paper challenges both views, defending: (i) Not every every circular circular argumen argumentati tation on begs the question question,, and not every every petitio petitio principii is based on a circular argument. (ii) (i i) It is im impo poss ssib ible le to ma make ke ge gene nera rall st stat atem emen ents ts ab abou outt th thee de defe fect ctiive vene ness ss of a co comp mple lex x argumentation solely on the basis that it realizes a circular dialectical pattern. Such an argumentation has to be evaluated on a case-by-case basis. It should be noted, though, that the first conjunct of claim (i) has already been defended in the literature; accordingly, Walton Walton ( (2005 2005,, p. 89) gives a persuasive example of a non-fallacious circular reasoning. As regards claim (ii), Wilson Wilson ( (1993 1993)) seems to reach a similar conclusion. 4 Moreover, it goes without saying that those claims are defended relative to the specific approach to argument reconstruction and evaluation this paper pursues. Ourr re Ou reas ason onin ing g ta take kess of offf fr from om th thee an anal alys ysis is of a si simp mple le an and d we well ll-k -kno nown wn ex exam ampl ple— e—th thee God and the Bible case (Sect. 2). Based on this analysis, we will subsequently distinguish three dialectical patterns which may characterize petitio principii (Sect. 3). An argum ar gument entat ation ion,, gen genera erally lly,, can be ev evalu aluate ated d aga agains instt the dis discur cursi sive ve aim aims, s, as ide identi ntified fied by the theory of dialectical structures, which rational proponents are supposed to pursue (Sect. 4). A case-by-case consideration in Sect. 5 then yields that for every aim and every dialectical pattern there exist both a fallacious and a perfectly correct argumentation. A second, more complex example illustrates how a case-by-case evaluation can be implemented (Sect. 6). Finally, the conclusion attempts to locate the notion of “petitio principii” in the normative framework this paper sets up. As a preliminary step, however, the remainder of this introduction reviews the key concepts of a theory of dialectical structures which will be used later. The theory of dialectical structures is an approach for reconstructing and evaluating complex argumentation and debate. 5 These are analyzed as so-called bipolar argumentation frameworks6 consisting in deductively valid arguments (premiss-conclusion structures) and theses. The set of reconstructed arguments and theses shall be labeled T . An argument a1 ∈ T supports (attacks) an argument a2 ∈ T if and only if the conclusion of a1 is equivalent to (contradicts) a premiss of a2 . The support- and attack-relation, U and A respectively, that are thus defined on T make up the dialectical structure of the debate τ = T , A , U . A two-colored, directed graph is an appropriate mathematical model of this structure, and a helpful visualization, too. Accordingly, arguments are the graph’s nodes; a green (red) arrow between two arguments signifies that one supports (attacks) the other. I will use line-style b and U (a , b) ⇐⇒ to ex expre press ss the these se rel relati ations ons con conve venie nientl ntly y, i.e i.e.. A(a , b) ⇐⇒ a
3 E.g. Walton E.g. Walton ( (2006 2006,, p. 278 278). ). 4 “I believe that the problem of analyzing question-begging argument, generally, cannot be satisfactorily
characterized syntactically; the fallacy is not a formal fallacy. Better prospects for a plausible account lie in investigating the pragmatics of argument” Wilson argument” Wilson ( (1993 1993,, p. 328 328). ). 5 For a detailed exposition of this approach see references in footnote 2. Sample argument maps which
illustrate this method can be found at http://www.argunet.org. http://www.argunet.org. 6 See See Cayrol Cayrol and Lagasquie-Schiex ( Lagasquie-Schiex (2005a 2005a,, b b)) who extend the framework of Dung ( Dung (1995 1995). ).
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a → b. An argument is said to be τ -valid, in contrast to deductively valid, if and only if it is not attacked by other τ -valid arguments.7 Premisses which are neither equivalent nor contrary to conclusions of τ -valid arguments are “ τ -free”, or simply “free” as we shall say for the sake of simplicity in this paper. If a sentence p can be deduced from other sentences Q by using but the inferential relations explicit in the dialectical structure τ , p is “τ -deducible” from Q . Eventually, different proponents might adhere to different arguments in a complex debate. The “stance-attribution” maps each proponent onto a subset of the debate’s arguments and theses, thereby specifying for each proponent which arguments she approves. In order to be a fully specified, rationally adoptable position, such a subdebate is required to be in equilibrium (i.e., roughly, must not contain contrary claims), closed (i.e. must comprise all arguments in the debate whose premisses have already been accepted in the subdebate), and complete (i.e. must contain the thesis p or the thesis ¬ p if both sentences occur in the debate) .8 2 A first example: the god and the bible case
The God and the Bible case is probably one of the most common illustrations of petitio principii and circular argumentation.9 Already Descartes, in his letter of dedication in the Meditations, noted that [...] although it is quite true that the existence of God is to be believed since it is taught in the sacred Scriptures, and that, on the other hand, the sacred Scriptures are to be believed because they come from God (for since faith is a gift of God, the same Being who bestows grace to enable us to believe other things, can likewise impart of it to enable us to believe his own existence), nevertheless, this cannot be submitted to infidels, who would consider that the reasoning proceeded in a circle.10 The argumentation is supposed to prove the existence of God by referring to the Bible which says that god exists; the trustworthiness of the Bible, in turn, is thence derived from its being the word of God. This informal argumentation can be reconstructed in different ways: we shall consider two versions in the following. The first version consists of two arguments: Argument A: Bible as testimony (A1) The Bible represents testimony of a source presumed to know about the existence of God. (A2) The Bible says that God exists.
7 Thus, a recursive status assignment is defined on the argumentation framework. Compare the review by
Prakken and Vreeswijk (2001) for alternative approaches. 8 Whereas only the requirement of being in equilibrium will figure prominently in this paper’s argumenta-
tion. 9 See also Walton (2005, pp.97–99). 10 Descartes (1996, p.3).
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(A3) If x represents testimony of a source who is presumed to be in a position to know and x says that p, then p is the case. (A4) Thus: God exists. Argument B: God omniscient (B1) God is omniscient. (B2) If God is omniscient and does exist, then the Bible represents testimony of a source presumed to know about the existence of God. (B3) God exists. (B4) Thus: The Bible represents testimony of a source presumed to know about the existence of God.
As premiss (A1) is equivalent to conclusion (B4), argument B supports argument A, in short B → A. Yet, as (A4) is also equivalent to (B3), A supports B, too, and we have a directed green circle B → A → B . Frankly, argument B is not really a very sophisticated reconstruction and its plain circularity does not really seem to do justice to the informal argumentation. Thus the following second version: Argument C: God omniscient (C1) The Bible is the word of God. (The Bible represents testimony of God.) (C2) God is omniscient. (God is presumed to know about everything.) (C3) Thus: The Bible represents testimony of a source presumed to know about the existence of God.
In contrast to B, C requires but two premisses to warrant (A1). Also, the argumentation’s circularity in C → A is not as apparent as in B → A. C → A does in particular not give rise to a directed green circle. Walton, whose reconstruction I tried to capture with arguments A and C, refers to the notions of equivalency and dependency circularity in order to distinguish between such cases .11 Accordingly, B → A is an instance of equivalency circularity, whereas in C → A the conclusion (A4) and the crucial premiss (C1) are not equivalent, “but one depends on the other, in a certain sense.” 12 The following analysis will give us a clearer idea about what kinds of dependencies are involved in circular argumentation. In C → A, the crucial premiss (C1) is not equivalent to the central conclusion (A4), yet it somehow presupposes its truth, or, more specifically, (A4) is a necessary condition for (C1). This means: “(C1) →(A4)” is analytic.13 So the conclusion which 11 See Walton (2005) and Woods and Walton (1975). 12 Cited from Walton (2005, p. 87). Yet, the notions of equivalency and dependency circularity are not
coherently defined in the literature. In Walton (2006), for instance, dependency circularity is said to hold iff “the line of reasoning used to support the premise requires the conclusion as a part of the reasoning” (p. 281). In that case, however, dependency circularity would simply reduce to equivalency circularity if the supporting argumentation were explicitly reconstructed. Ritola (2001), though, defines: “The dependency conception means, roughly, that an argument begs the question because at least one of the premises of the argument is dependent on the conclusion, i.e. cannot be true, reasonably believed or accepted unless the conclusion is also true.” (p. 295) We shall see that this later interpretation hints at the distinction between maximal redundant and circular argumentation I introduce below. 13 (C1) is only true if its names do refer, and if the name “God” refers then God exists.
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is supposed to be warranted by the argumentation follows from one premiss, namely (C1), plus an analytic truth alone, as the following argument makes explicit: Argument D: Short-circuit (D1) The Bible is the word of God. (The Bible represents testimony of God.) (D2) If the Bible is the word of God, God exists. (analytic) (D3) Thus: God exists.
The original arguments A and C, argument D which pinpoints the dependency, plus two theses that state (A4) and (C1) make up the following dialectical structure τ 1 :
This diagram shows that arguing for (A4) via C and A is redundant in the sense that there is a shorter inferential path that leads to (A4), namely via D. Is this a general characteristic of an argumentation we use to brand as petitio? Is not circularity in the sense of a directed green circle but the fact that an argumentation can be short-circuited by adding but analytic premisses what defines petitio? As a first step to sort this out, the next section systematizes the dialectical patterns at issue. 3 Three types of redundant dialectical patterns
First, a word on the notion of a dialectical pattern. Dialectical patterns are realized by dialectical structures. A green directed circle or a vicious circle 14 are examples of dialectical patterns. Types of argumentation can be distinguished by the dialectical patterns their corresponding dialectical structures realize. Thus, a directed green circle is, according to its first reconstruction, a feature of the God and the Bible argumentation. In the previous section we have rather unspecifically diagnosed a certain redundancy in the second reconstruction of the God and the Bible case. Let us now define a redundant argumentation as follows: A green tree (i.e. a dialectical structure with green edges, no circles and one sink) is called a redundant argumentation if and only if its central conclusion follows from a proper subset of the structures free, that is unsupported, premisses plus, possibly, additional analytic sentences. An apparently interesting special case of a redundant argumentation occurs when the central conclusion follows from a single free premiss alone plus, possibly, additional analytic sentences. We shall call such an argumentation maximal redundant . If, moreover, the single free premiss that warrants the central conclusion is equivalent to 14 Compare Betz (2005).
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that conclusion, the argumentation is called circular . The following diagrams depict the three dialectical patterns. Redundant argumentation (“ ( p ∧ r ) → q ” analytic), τ 2 :
Maximal redundant argumentation (“ p → q ” analytic), τ 3 :
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Circular argumentation, in an analogous diagram, τ 4 :
Note that this last diagram illustrates that a circular argumentation is a special case of redundant argumentation, on the one hand, and involves a directed green circle, on the other hand. The second reconstruction of the God and the Bible case as depicted in τ 1 is an example of maximal redundancy ( τ 3 ) whereas the first reconstruction (arguments A and B) exemplifies a circular argumentation ( τ 4 ). In the remainder of this section I would like to comment on some peculiarities of these dialectical patterns. First of all, it might have occurred to the reader that we have so far been dealing with green graphs only. Does circularity, however, not arise in debates where proponents do support as well as attack other arguments, too? This is certainly the case and that is the reason why it is interesting to note that the pattern depicted in τ 3 is equivalent to—i.e. the debate can equally be reconstructed as—the following structure τ 3 :
or τ 3 :
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which include red edges besides green ones. The further analysis of maximal redundant argumentation in the next section applies thus to dialectical structures that realize patterns τ 3 and τ 3 as well. Our discussion is hence not limited to green graphs only. As a next point, consider circular argumentation. Green circles are exempted from a theorem on dialectical structures 15 —which stated roughly that in a given dialectical structure a sentence can be τ -deduced from the free premisses if and only if it is the conclusion of a τ -valid argument—for reasons that relate to the proof-method applied. Reconsidering green directed circles we see that the theorem is actually false for these structures: Although all arguments in a (isolated) green circle, for not being attacked, are τ -valid, the truth of the free premisses doesn’t warrant the truth of any conclusion. In a circular argumentation, the premisses’ truth guarantees only that the arguments’ conclusions are equivalent. In fact, it is a common proof-strategy for equivalence claims in mathematics to construct such a circular argumentation. As this is well-known, scholars have wondered how to distinguish equivalence proofs whose validity is beyond any doubt on one side, and circular argumentation which seem to be, to put it mildly, at least questionable, on the other side. I will briefly indicate how these cases can be dealt with within a theory of dialectical structures. Assume that the central theses in a debate are ck and cl (k = l and 1 ≤ k , l ≤ n ) and that we want to distinguish a proponent who argues in a circular way for c k and a proponent who, on the same grounds, just holds that ck and cl are equivalent. What helps is that the reasoning can be reconstructed in two different ways, namely as arguments a 1 . . . an or as argument a n +1 :
15 Which is proven in Betz (forthcoming).
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where a n +1 has the following form: Argument E: Circular equivalence proof 1) ck 2) pk +1 . . .
i) pl i+1) Thus (from 1 …i): c l i+2) Thus (from 1, i+1): c k → cl i+3) cl i+4) pl +1 . . .
j) pk j+1) Thus (from i+3 …j): c k j+2) Thus (from i+3, j+1): c l → ck j+3) Thus (from i+2, j+2): c k ↔ cl
In the first case, circularity is a feature of the dialectical structure whereas in the second case, the circular reasoning occurs in the inference pattern of the argument (sharp brackets indicate assumptions for the sake of the argument). A proponent who merely claims that ck and cl are equivalent asserts but the argument an +1 whereas a proponent who additionally maintains that ck and cl are true would also stick to arguments a1 . . . an . Thus, the different reconstructions of circular reasonings as an inference pattern or as a dialectical pattern plus the stance attribution over a debate distinguish the two cases at hand.
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The importance of being able to distinguish between these cases stems from our intuition that one circular reasoning (the mathematician’s) is unproblematic whereas the other one isn’t. But what exactly is the problem with circularity or, more generally, redundancy? This is the question to be dealt with in the next two sections. 4 Evaluating redundant argumentation
Assume that once we have reconstructed the arguments put forward in a debate we see that the dialectical structure realizes a circular argumentation. What does this tell us about the debate? Did any of the proponents make a mistake? Not necessarily. In fact, the bare dialectical structure doesn’t allow for any such inference: Dialectical structures are evaluatively underdetermined. The thesis of evaluative underdetermination can be substantiated by a simple example. Reconsider structure τ 4 and assume that Anna argues with Bianca and Chris. Anna holds both q and p2 whereas Bianca believes but q while Chris thinks that p2 is true and q isn’t. Now, in order to convince Bianca (that p2 ) Anna introduces argument a1 and in order to convince Chris (that q ) she establishes argument a2 . Anna’s argumentation is perfectly fine, yet it gives rise to a green circle. Dialectical structures alone don’t tell us whether something goes wrong in a debate. In addition to (i) the dialectical structure, (ii) the stance attribution, that is who asserts which arguments, as well as (iii) the purpose of the respective arguments, or, as I would prefer to put it, the discursive aims the proponents are pursuing, have to be taken into account when evaluating redundant argumentation. This is not new. Walton recently reaffirmed this insight of argumentation theory: “It is assumed that putting forward an argument in a dialogue has a purpose, and that the success or failure of the argument can be judged in relation to the fulfillment of that purpose.” 16 What seems to be, in contrast, controversial is the nature of the purpose arguments are supposed to fulfill: Are, in particular, epistemic purposes necessarily involved in an evaluation or do they even have priority over other purposes, e.g. conversational ones? 17 I will not contribute to that particular dispute. Rather, I want to discuss the “success or failure” of redundant argumentation in the light of the discursive aims proponents can rationally pursue according to the theory of dialectical structures. All these aims can be equally interpreted as epistemic in a broad sense, or as dialectical. What is interesting and new is that, according to the theory of dialectical structures, there is not merely one epistemic (or dialectical) purpose of argumentation, namely “to get the other party to accept a proposition that s/he doubts”,18 but a plentitude of purposes. Table 1 is a systematic and slightly simplified exposition of these discursive aims. These different discursive aims are not on an equal footing. Categories I and II appear to be rather technical compared to III and IV. Moreover, I and II are hardly ideas proponents have consciously in mind when debating. This might suggest the following grading: Whereas aims I and II guide our interpretation of a debate and serve to 16 Walton (2005, p.87) 17 See Wilson (1988), Ritola (2001). 18 Walton (2005, p.91)
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Table 1 The system of discursive aims (cf. Betz, forthcoming)
I Completeness
II Closedness
III Equilibrium
IV Burden of proof
(a) Defensive
(b) Offensive
I assert exactly one of a pair of contradictory sentences occurring in the debate. There is no argument in the debate I do not assert but which I had to assert given the sentences I have already accepted. The sentencesa which occur in the subdebate I assert are consistent.
–
The central theses I want to maintain are τ -deducible from the free premisses in my subdebate. (1st order burden of proof)
The central theses I want to maintain are τ -deducible from the free premisses in my opponents’ subdebates. (2nd order burden of proof)
–
The sentencesa which occur in the subdebates of my opponents are inconsistent.
a More precisely: the free premisses and the conclusions of τ -valid arguments
determine the different proponents’ stances in the first place, i.e. represent standards of adequate reconstruction which are thence fulfilled qua rational reconstruction of the debate, this does not hold for aims III and IV: Even in an as rational reconstructed debate, they are not necessarily attained. The situation is similar to the evaluation of single arguments. As we reconstruct arguments as deductively valid, formal fallacies are excluded qua reconstruction and deductive validity is not an aim proponents can fail to meet in an as rational reconstructed debate. 19 With categories III and IV left, there are altogether still four different epistemic aims proponents pursue when introducing new arguments into a debate. The next section will investigate in how far the pursuit of these aims might bring about maximal redundant or even circular argumentation on one hand and whether the fact that the debate realizes one of these dialectical patterns might undermine the achievement of these discursive aims on the other hand. 5 A case distinction of redundant argumentation
According to the previous section, proponents can pursue different aims in a debate. Since an argumentation must be evaluated in the light of the purpose it shall serve, there are two questions we have to address for each dialectical pattern we are interested in: (i) Can the effective pursuit of the respective discursive aim bring about the dialectical pattern? (ii) Can the achievement of the respective aim be undermined because the argumentation realizes the dialectical pattern? This section discusses these two questions for 8 aim-pattern pairs, mainly by constructing examples of dialectical structures that warrant a positive answer. The results of this discussion are presented in Table 2, where “+” and “–” are indicating the affirmation of questions (i) and (ii) respectively. 19 I thank Christian Voigt for reminding me of this analogy.
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338 Table 2 The evaluation of discursive patterns in the light of the discursive aims according to the theory of dialectical structures, see text for explanation
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Circularity
Maximal redundancy
(IIIa)
+/−
+/−
(IIIb)
+/−
+/−
(IVa)
+/−
+/−
(IVb)
+/−
+/−
Accordingly, “+/–” symbolizes that the dialectical pattern can both result from the pursuit of as well as prevent the achievement of the discursive aim. The fact that for every aim-pattern pair both questions are answered positively is an indication of the dialectical patterns’ ambivalence: Redundancy and circularity have to be judged on a case-by-case basis because there are both situations where they facilitate or hinder the achievement of the discursive aims—where the argumentation which brings them about is thus rational or not. The systematic investigation spares redundant argumentation in order not to inflate the distinction of cases, leaving its discussion to a separate paragraph at the end of the section. ( IIIa)-C: Equilibrium, defensive, circularity To see whether a circular argumentation can arise because proponents pursue aim (IIIa), consider the following consecutive states of a dialectical structure that is asserted by a single proponent.
The green circle emerges because of the introduction of arguments a6 and a7 whose premisses are assumed to be well confirmed in the debate. As a consequence, the previously isolated argument a5 is now firmly embedded in the inter-connected main graph. Moreover, assume that a6 ’s conclusion is p1 and that a4 and a7 have equivalent conclusions. This implies that on the background of the free premisses in state (2), q is equivalent to a1 ’s conclusion. And so is p1 . Thus, while p1 and q could
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have contradicted argument a1 in state (1) of the debate, this is impossible in state (2). There is another way to put this idea. Both in (1) and (2) the following conditional equilibrium-claim holds: If the set of free premisses is logically consistent, then the set of free premisses plus the conclusions does not contain contrary sentences (i.e. the dialectical structure is in equilibrium). Because the green circle, however, reduces the set of free premisses significantly and thereby weakens the antecedent conditions, that equilibrium-claim is stronger in (2) than in (1). In sum, the introduction of the green circle supports the proponent’s goal of asserting a dialectical structure which is in equilibrium. Is it equally possible that a circular argumentation obstructs the achievement of consistency? Consider the following two states:
where a2 and a6 have equivalent conclusions. The introduction of a5 and a6 doesn’t increase the ‘inferential density’ of the dialectical structure since the equivalence of the arguments’ conclusions is already established in state (1). While (2) is therefore not less prone to inconsistency than (1), it introduces in turn arguments with new premisses which might conflict with other assertions and thence increases the chances that the entire debate the proponent asserts is not in equilibrium anymore. Here, the (circular) argumentation has a tendency to obstruct equilibrium. ( IIIa)-Mr: Equilibrium, defensive, maximal redundancy A maximal redundant argumentation can promote equilibrium of a proponent’s subdebate for reasons similar to those given above, as the following state illustrates (we assume throughout this section that “ p → q ” is analytic):
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If a2 and a3 —both resting on supported premisses—are simply introduced in order to integrate a1 into the main debate, this reduces the set of free premisses and therefore warrants a stronger conditional equilibrium-claim. Assume, however, that a 1 , being isolated, is introduced into a debate, yielding the following dialectical structure:
Here a 1 doesn’t increase the inferential density and causes a premiss-proliferation which might in turn trigger new inconsistencies. ( IIIb)-C: Equilibrium, offensive, circularity This is an example where a circular argumentation emerges because a proponent attempts to disturb the equilibrium of her opponent’s subdebate:
Consider state (1), first. There are two proponents, Anna and Bianca. Anna believes p and q , as well as a1 and a2 . Bianca believes q , but, strongly rejecting the conclusion of a1 , denies p which she attacks with argument a3 . With a view to demonstrating
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that Bianca’s subdebate is not in equilibrium, Anna introduces argument a 4 that rests on premisses Bianca has acknowledged elsewhere, including q . That is how the circle arises in state (2). The failure, however, to disturb the equilibrium of an opponent’s subdebate can also be linked to circular argumentation.
Here, Chris attacks p with a 1 . Dave, in an attempt to expose Chris’ inconsistency, introduces in state (2) arguments a2 . . . a4 whose premisses which are not supported in the circle are conclusions of other arguments Chris approves. Yet Dave failed to show that Chris’ subdebate is not in equilibrium: Rejecting the newly introduced arguments’ conclusions, and thereby a premiss of each, he can resist accepting them as τ -valid. ( IIIb)-Mr: Equilibrium, offensive, maximal redundancy To see how a maximal redundant argumentation can arise when proponents try to disturb their opponents’ subdebates’ equilibria, consider the following dialectical structure.
Assume that both Anna and Chris approve p and q . Morover, Anna holds that r and a1 , the latter being her reason to assert q . Here, Chris disagrees, backing up his
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belief with a2 . Anna exposes Chris’ inconsistency with argument a3 that rests on p, which Chris approves, plus other premisses he has already accepted. In a slightly modified dialectical context, Anna would have failed to do so. Consider
In contrast to the previous debate, Chris attacks q . Then, Anna’s introducing a3 is bound to fail: Chris won’t accept p . And if he did, his subdebate would not have been in equilibrium anyway because of the short-circuit argument. So introducing a 3 fails to achieve the desired goal because the dialectical structure realizes the pattern of maximal redundant argumentation. ( IVa)-C: 1st order burden of proof, circularity A circular argumentation can arise when several proponents successfully fulfill their 1st order burdens of proof. Consider
where Anna, Bianca and Chris are uncertain about p, q , and r respectively, while believing the remaining theses firmly. They meet their first order burdens of proof by introducing a1 , . . . , a3 , respectively, which, putting the arguments together, results in the green circle.
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Circular argumentation, however, can severely obstruct the achievement of this aim, too. Assume Dave were sceptical about p and started to convince himself by putting forward arguments a1 , a2 , . . . finally ending up at an argument with premiss p. In that case, p is not τ -deducible from the free premisses and Dave failed to meet his 1st order burden of proof because of circularity. ( IVa)-Mr: 1st order burden of proof, maximal redundancy Maximal redundancy can stem from the pursuit of 1st order burdens of proof in a multi-proponent debate.
Assume that Anna is not sure whether q , approving r while denying p. Chris, in contrast, approves both p and q , and wants to be certain that r . Anna and Chris fulfill their first order burdens of proof by introducing a 1 and a 2 , respectively. To see that an argumentation can be irrational with a view to 1st order burdens of proof because it is maximal redundant, reconsider the above structure but suppose that there were but one proponent, Bianca, who tries to convince herself that q by introducing a 1 and a 2 . Now Bianca either believes that p or she doesn’t. If she does, then the arguments a1 , a2 do not contribute to satisfying her 1st order burden of proof as q follows directly from p . If, however, she doesn’t believe that p, the argument chain a1 , a2 , presupposing p, is of no use, either. Thus, the maximal redundant argumentation is not effective. ( IVb)-C: 2nd order burden of proof, circularity In a many-proponent debate, circles may arise when proponents try to meet their 2nd order burdens of proof. Reconsider the dialectical structure given in (IVa)-C. Assume that Anna, Bianca and Chris each approve of exactly one of the theses, namely p, q , and r , respectively. Dave, however, holds that all of these theses are true. With a view to his 2nd order burden of proof, he effectively puts forward a 1 , a2 , a3 . Suppose, in contrast, that Bianca, in another context, argues with Chris alone and that she tries to convince him that p . If she puts forward a green argument circle, this will hardly compell Chris to approve p as he can refute the arguments’ conclusions altogether. This can be put differently: The last argument Bianca introduces which
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contains premiss p and closes the green circle is not effective in the light of her 2nd order burden of proof. ( IVb)-Mr: 2nd order burden of proof, maximal redundancy It is not too difficult to transfer our previous reasonings to this aim-pattern pair. Reconsider the dialectical structure depicted in (IVa)-Mr and assume that Anna accepts p and q but denies r and Dave approves r , yet neither p nor q . Chris holds that p , q and r , and thence puts forward a 1 to fulfill his 2nd order burden of proof with respect to q and Dave, and a2 to fulfill his 2nd order burden of proof with respect to r and Anna. This is effective and rational. Still, assume Dave didn’t approve r . Chris’ introducing a1 , a2 would hardly change Dave’s mind with regard to q . He doesn’t believe p. Even if he did, Chris’ argumentchain would be useless as q follows from p alone. Chris’ argumentation would in any case be irrational because it is maximal redundant. Eventually, a note on redundant argumentation in general. Can a redundant argumentation emerge from the effective pursuit of discursive aims? Can it, on the contrary, hinder their achievement? First of all, recall that every circular and every maximal redundant argumentation is a redundant argumentation. The answer to both questions is therefore positive. Now what about redundant argumentation that is not maximal redundant (and thence not circular)? The above investigation implies by an argumentum a minore that such an argumentation might arise in purposeful discussions. Yet, might it also be irrational, in the light of some discursive aims, to argue redundantly? This is at least indicated by the fact that the dialectical pattern of redundant argumentation (τ 2 ) can be transformed to the pattern of maximal redundant argumentation ( τ 3 ) and vice versa: If one reconstructs the two arguments on the right hand side in τ 2 as one argument with conclusion q that contains a premiss p ∧ r , the argumentation is indeed maximal redundant because the conclusion follows from one of the premisses, i.e. p ∧ r , alone. Likewise, splitting up p into two sentences whose conjunction is equivalent to p, a maximal redundant argumentation might be reconstructed as a redundant one. If redundant and maximal redundant argumentation can be transformed into each other and the latter is in some cases irrational, so is (probably) the former. Thus far our theoretical investigation into whether circular and maximal redundant argumentation are irrational or not. The next section shall apply our results to an example of a complex multi-proponent debate.
6 A second example: the scientific relativist
Redundant argumentation is not merely a theoretical possibility—it represents a dialectical pattern which does occur in real debates. Whether such an argumentation is purposeful and thence rational has to be judged, according to the results of the previous section, on a case-by-case basis. We will in the following have a closer look at a specific circular argumentation and see how such a case-specific judgment can be carried out.
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The example is taken from Larry Laudan’s ingenious book Science and Relativism: Some Key Controversies in the Philosophy of Science 20 which is a fictitious dialogue between four philosophers of science, namely Quincy Rortabender (the relativist), Percy Lauwey (the pragmatist), Rudy Reichfeigl (the positivist) and Karl Selnam (the realist).21 One of the pivotal claims these philosophers discuss is the thesis of underdetermination, which, in its general version, states Relativist : […] Strong relativism, in contrast, would hold that evidence is always powerless to choose between any pair of [rival theories] .22
After briefly touching the question whether this is an unreasonably strong version of underdetermination, the discussion proceeds as follows: Pragmatist : I don’t think anyone will accuse you of taking up an easy brief. Perhaps we could now get to the solid arguments you promised us on behalf of full-blown relativism? Relativist : The arguments are not only solid but they have the virtue of being straightforward. I begin by reminding you of Hume’s claim to the effect that no genuinely universal statement (and I mean such statements when I talk about “theories” or “hypotheses”) can be deduced from a finite set of its positive instances. Because that is so, no theory can ever be proved to be true. Positivist : Big deal. Relativist : Moreover, and this point was made by Duhem almost a century ago, we can no more derive the falsity of a theory or hypothesis from the evidence than we can derive its truth. Realist : You’re referring, I suppose, to the holistic character of the testing situation and the fact that we bring many assumptions to bear in the design of any test of a single theory or hypothesis. Relativist : Exactly. It is never single hypotheses or theories we test but entire networks of such assumptions. When the test fails, that is, when the predicted result differs significantly from the observed result, all we know, at best, is that we have made a mistake somewhere; it cannot be further localized. Pragmatist : I have serious doubts about this holism of yours, which I hope I will have the chance to voice later; but suppose we grant you, for now, both the Hume and the Duhem theses about the nonderivability, and the nonrefutability, of theories from their positive, or negative, instances. How does this establish your thesis that it is as reasonable to accept any theory as any other? 20 Laudan (1990). 21 My example is the slightly modified reconstruction from a project that drew up the dialectical structure
of Laudan’s entire book. I’d therefore like to thank Friederike Greb, Bianca Drefahl, Eugen Pissarskoi, Martin Ebert and Gema Ortiz del Castillo! 22 Laudan (1990, pp.55–56).
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Relativist : I would have thought the connection was more or less self-evident. If we can never show that any theory is true, and we can never show that any theory is false, then surely it is clear that whatever grounds we may have for choosing between rival theories must be practical rather than epistemic, or simply matters of convention and simplicity. Since there is nothing in the evidence which forces us to believe one thing rather than another, we can choose our beliefs in the light of our private and personal interests .23
The relativist’s reasoning can be reconstructed as two consecutive arguments. The first one starts from the Hume and the Duhem thesis and warrants that neither the truth nor the falsity of a theory can be deductively derived from empirical evidence. The second one, building on this conclusion, claims that, as a consequence, empirical evidence cannot decide between rivals. Argument F: Hume-Duhem (F1) No theory can be deduced from a finite set of empirical observations. (F2) Our empirical evidence is, necessarily, finite. (F3) Thus: No theory can be deduced from empirical evidence. (Hume thesis) (F4) Every test of a theory assumes other theories to be true. (Holistic character of testing situation) (F5) A theory’s falsity could only be derived from empirical evidence, if testing theories would rely on empirical evidence alone and not require other, non-observational statements to hold. (F6) Thus: A theory’s falsity cannot be derived from empirical evidence. (Duhem thesis.) (F7) Thus: Neither the truth nor the falsity of a theory can be deductively derived from empirical evidence. (F8) If neither the truth nor the falsity of a theory can be deductively derived from empirical evidence, then nothing in the evidence forces us to belief one rather than another theory. (F9) Thus: There is nothing in the evidence that forces us to belief one rather than another theory. Argument G: Underdetermination (G1) There is nothing in the evidence that forces us to belief one rather than another theory. (G2) If there is nothing in the evidence that forces us to belief one rather than another theory, empirical evidence is powerless to choose between rival theories. (G3) Thus: Empirical evidence is powerless to choose between rival theories.
Moreover, the relativist highlights some further implications of this last conclusion. As, in the first chapter of the book, he holds that theory change is irrational and that there is no scientific progress, it is not far fetched to assign the following argument to the relativist, too: 23 Laudan (1990, pp.56–57).
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Argument H: No progress (H1) Empirical evidence is powerless to choose between rival theories. (H2) If empirical evidence cannot choose between rivals, theory choice involves arbitrary criteria. (H3) If theory choice involves arbitrary criteria, there is no objective scientific progress. (H4) Thus: There is no objective scientific progress.
The proponents continue discussing several objections. Among others, certain methodological rules were proposed by the pragmatist and the realist whereupon the relativist asserts: Relativist : […] Indeed, as far as I’m concerned all the rules that Karl and Percy allude to are just conventions for doing science. They have no objective grounding in the facts of the matter and simply serve as convenient instruments for promoting a certain kind of epistemic interest. 24
Why does the relativist insist on this claim? Because its negation threatens his thesis that there is no scientific progress, provided he assumes that if there were objectively grounded scientific rules, then there would also be scientific progress. Now there is a further argument emerging around this very sentence, building on the conclusion of argument H: Argument I: No objective methodological rules (I1) There is no objective scientific progress. (I2) If there were objectively grounded scientific rules, then there would also be scientific progress. (I3) Thus: There are no objectively grounded scientific rules.
However, (G1) seems to be just a special case of the statement that there are no objective scientific rules; such rules, were they objective, would apparently force certain beliefs upon us. Thus Argument J: Evidence doesn’t force belief upon us (J1) There are no objectively grounded scientific rules. (J2) Only the existence of objectively grounded scientific rules could compell us to adopt certain beliefs rather than others in the light of empirical evidence. (J3) Thus: There is nothing in the evidence that forces us to belief one rather than another theory.
Taken together, arguments F-J make up the following dialectical structure:
24 Laudan (1990, p.66).
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As the relativist, explicitly or implicitly, subscribes to arguments F-J, the question arises as to whether he makes a mistake, whether he argues in a rational way at all. First of all, in the specific context of the debate cited above, the relativist puts forward only F and G in order to fulfill his 1st and 2nd order burdens of proof. H, I and J have been reconstructed in the light of other sections of the book. Thence, the argumentation is not fallacious as far as burdens of proof are concerned. Yet, is it in some sense purposeful, and with regard to which discursive aim? The relativist does not explicitly comment on this. Still, the green circle serves definitely some purpose: It demonstrates that the relativist’s claims and argumentation cohere; technically, the circular argumentation increases the chances that the relativist’s subdebate is in equilibrium. Putting forward F-J is thence, for the relativist, in the wider context of the entire debate, perfectly rational.
7 Conclusion
Analyzing a simple argumentation, we have seen that the fallacy of petitio principii can be characterized in different ways which led us to distinguish the dialectical patterns of redundant, maximal redundant and circular argumentation. The mere fact, however, that an argumentation realizes one of these dialectical patterns doesn’t tell whether something went wrong in the debate or not. Dialectical structures, we put it, are evaluatively underdetermined. This has further implications. First of all, argumentation has to be evaluated with regard to the purpose it is supposed to fulfill; where the theory of dialectical structures identifies what (kinds of) discursive aims proponents can pursue in a debate. Still, for every discursive aim there are debates where the respective dialectical patterns emerge because the proponents successfully pursue the discursive aim as well as debates where the respective dialectical patterns are the reason why proponents fail to achieve that aim. As a consequence, secondly, the dialectical context, that is the rest of the dialectical structure that realizes the dialectical pattern, as well as the stance attribution have to be taken into account when evaluating redundant argumentation. In other words, such evaluations have to be accomplished on a case-by-case basis and general statements about the defectiveness of redundant argumentation, including maximal redundant and circular argumentation, cannot be made. So let us return to our starting point. What is a petitio principii? Can we locate this informal everyday concept in our analysis? Our investigation suggests the following two alternative explications. One commits a petitio in a narrow sense if one fails to satisfy a 2nd order burden of proof because one’s argumentation is maximal redundant, possibly circular. These are the ‘negative’ examples given in Sect. 5 under case (IVb). A petitio, in a broad sense, however, refers to every argumentation which fails to achieve its aim, no matter what this aim, because it is maximally redundant, possibly circular. Accordingly, every ‘negative’ example in Sect. 5 is a petitio in this broad sense. Acknowledgements I would like to thank the τ -Klub’s participants at the Institute of Philosophy, Freie Universitaet Berlin, for a constructive discussion of ideas this paper unfolds.
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