ISSA Proceedings 2006 – Metadialogues And Meta-Arguments: Krabbe On Formal-Fallacy Criticism

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logo  2006“A metadialogue is a dialogue about a dialogue or about some dialogues. A dialogue that is not a metadialogue will be called a ground level dialogue” (Krabbe 2003, p. 641). With these definitions, Krabbe explicitly introduced the topic of metadialogues into argumentation theory. Similarly, I define a meta-argument as an argument about one or more arguments, and a ground-level argument as one which is not a meta-argument.
Here it is useful to stress the overlap between dialogues and arguments. Krabbe himself has stated that his main interest lies with persuasion dialogues, or critical discussions, and these entities involve arguments in an essential way. Moreover, Barth and Krabbe (1982) have famously proved the equivalence between the axiomatic and dialogical methods; and this proof may be taken to suggest (cf. Finocchiaro 2005, pp. 231-45) not only that the monolectical way of talking about arguments can be translated into a dialogical way of talking, but also that the reverse is the case. Here this reverse case will be exploited by discussing arguments and meta-arguments in a relatively monolectical manner, in the belief that this discussion could be translated into one about dialogues and metadialogues. Accordingly, in a few moments I will attempt to reconstruct some of Krabbe’s insights about metadialogues in terms of meta-arguments.
Finally, although the explicitly meta-argumentative, or metadialogical, approach is a valuable step forward, both meta-arguments and metadialogues have been implicitly discussed for a long time in argumentation theory. This has happened primarily in the context of the evaluation or criticism of arguments, which everyone will admit to be a crucial part of argumentation theory. In fact, argument evaluation can be done seriously only if one gives reasons supporting the evaluative claim; such a reasoned evaluation is obviously an argument, and since the subject matter is the original argument, the evaluation is clearly a meta-argument. Thus, it should come as no surprise if much of my analysis will consist of attempts to reconstruct in explicit terms of meta-argument relevant insights that deal with argument assessment.
An important type of meta-argument occurs when a ground-level argument is criticized for having committed a fallacy. As Krabbe (2002, p. 162) has stated, “in fallacy criticism it is upon the critic to show why an alleged move in critical discussion is so completely wrong that it cannot even prima facie be accepted as a serious contribution to the discussion. Thus fallacy criticism leads to a critical discussion on a second level, a discussion about the permissibility of a move in the ground level discussion.”

Krabbe’s thesis about fallacy criticism is in part presented by him as a solution to the problem of the asymmetry between favorable and unfavorable evaluations of arguments. In several challenging papers, Massey (1975a, 1975b, 1981) had asked and answered negatively the question, “Are there any good arguments that bad arguments are bad?” By contrast, Krabbe (1995) asks and answers affirmatively the question, “Can we ever pin one down to a formal fallacy?” Despite the terminological variance, and the opposition of their respective conclusions, the meta-argumentative dimension of the discussion is obvious. What is being discussed is the nature and cogency of meta-arguments to the effect that some ground-level argument is bad, fallacious, or invalid. Let us reconstruct Krabbe’s own argument (a third-level meta-argument!) that it is possible to construct cogent (second-level) meta-arguments to the effect that some ground-level argument is a formal fallacy.
First, what is a formal fallacy? For Krabbe (1995, p. 336), “a formal fallacy, in dialogue, is committed as soon a party presents a formally invalid (i.e., not formally valid) argument that violates the code of conduct of the dialogue.” Here it is important to note that, besides formal invalidity, there is a second element in this definition – code violation; that is, a violation of some rule either agreed upon by the two interlocutors, or arguably relevant in the context of that discussion. Although it is unrealistic to expect prior or explicit agreement about the rules of a particular discussion, learning the contextual relevance of various types of arguments and criticism is a normal part of the education designed to achieve mastery of a given field. For example, historians often argue for chronological theses by means of arguments which, however strong, are formally invalid; and the same happens in the more experimental branches of empirical science when one gives evidence to support some empirical generalization. But everybody knows, or ought to know, that in these contexts such formally invalid argument do not violate the rules of the game. My point here is simply to underscore the fact that, following Krabbe, there are two things and not just one that must done to prove a formally fallacy; and since these two things embody different claims, two distinct meta-arguments must be advanced in effective formal-fallacy criticism.

Next, what is formal invalidity? Or equivalently, what is formal validity? And more fundamentally and generally, what are validity and invalidity? Again, I follow mostly the spirit and occasionally the letter of Krabbe’s discussion. An argument is valid iff there is no “situation, actual or fictitious (a possible world, if one wishes) such that in that situation all the premises are true and the conclusion is false” (Krabbe 1995, pp. 335-36); i.e., iff it is impossible for the premises to be true while the conclusion is false; i.e., iff “there is no counterexample to it” (Krabbe 1995, p. 336). Such a counterexample to an argument should not be confused with a counterexample to an argument-form, which is an argument instantiating the form and having true premises and false conclusion; thus to be clearer, we may speak of counterexample-situations (to arguments) and of counterexample-arguments (to forms). Finally, an argument is invalid iff it is not valid.
Formal validity is a special case of validity. An argument is formally valid iff “it can be correctly paraphrased… such that its schema (or form) is valid” (Krabbe 1995, p. 336); i.e., iff it instantiates a valid argument form; i.e., iff it instantiates a form that has no counterexample arguments. And an argument is formally invalid iff it is not formally valid; i.e., iff it does not instantiate any valid argument form. Note that this is not equivalent to instantiating an invalid form. Thus, validity is more general than formal validity: all formally valid arguments are valid, but not all valid arguments are formally valid; and all invalid arguments are formally invalid, but not all formally invalid arguments are invalid.
Based on these definitions, Krabbe discusses several methods of proving formal invalidity, i.e., several types of meta-argument concluding that some ground-level argument is formally invalid.

One method is what Krabbe, following Massey calls “the trivial logic-indifferent method” (Krabbe 1995, p. 341; Massey 1975a, p. 64; Massey 1981, p. 494). This amounts to proving that the argument’s premises are true and the conclusion is false. I agree with Krabbe and Massey that here we have triviality and little if any logic. However, I would stress two things: we do have, inevitably, argumentation, indeed a meta-argument; and the proof is indirect in the sense that the meta-argument shows formal invalidity without appealing to anything “formal,” but rather by showing (simple) invalidity, and using the principle that all formally valid arguments are valid.
The same indirect proof is used in another method, which Krabbe discusses at greater length. He calls it “the method of counterexample. This is the royal road of showing invalidity” (Krabbe 1995, p. 340). Krabbe clarifies that “counterexample” is commonly used with several different meanings, but that here he is using it in the sense defined above, namely a situation in which the premises are true and the conclusion is false. The correctness of this method is grounded on the definition of validity (to intermediately conclude invalidity), and on the relationship between validity and formal validity (to finally conclude formal invalidity).
For example, suppose someone, perhaps in a context of learning geography, thought that: (1) Reno is the capital of Nevada, because (1.1) Las Vegas is not, and (1.2) if Reno is the capital of Nevada then Las Vegas is not. Without doing any empirical research or knowing whether Las Vegas or Reno is the capital, we can simply imagine a situation in which neither Reno nor Las Vegas is the capital. It would then follow that Las Vegas is not, and so the first premise is true; the second premise would still be true, by the rules of states’ administration; but it would also follow that Reno is not, and so the conclusion is false. Here is then a situation in which the premises are true and the conclusion false. Therefore, by the definition of validity, the argument is not valid. Therefore, formal validity being a special case of validity, the argument is formally invalid.
From the general description of the method of counterexample-situation, and from this example, the meta-argumentative nature of the process is obvious.

Krabbe (1995, pp. 341, 343-44) admits that because of the indirectness of such proofs of formal invalidity, it might be preferable to reserve the label “formal fallacy” to cases where one proves formal invalidity more directly by exploiting logical forms. This he calls the method of formal paraphrase (Krabbe 1995, p. 340). This method appeals explicitly and directly to the definition of formal validity. The ground-level argument is paraphrased in some more or less formal logical system, and “the reason that the argument is [formally] invalid is expressed as follows: ‘this paraphrase captures the gist of your argument (meaning: the ground of its presumed validity), and this paraphrase constitutes an invalid logical form” (Krabbe 1995, 340). It is crucial to understand that there are three things which the meta-argument must try to prove:
1. that the ground-level argument instantiates a particular argument form;
2. that this argument form is invalid; and
3. that that this argument form captures “the gist of the argument,” or “the ground of its presumed validity,” or all logically important features of the argument. The third clause is especially important; if it is ignored, one would conclude that a ground-level argument is formally invalid simply because it instantiates an invalid argument form, even though it also instantiates another form that is valid, thus committing “the fallacy behind fallacies” exposed by Massey (1981).

For example, consider again the argument about the capital of Nevada. One could claim that it is of the form:(2) R because (2.1) not-L and (2.2) if R then non-L. Indeed this is the well known form “affirming the consequent.” This form is commonly known to be invalid. If need be, this invalidity could be exhibited by assigning the truth value falsity to both R and L. It could also be exhibited by constructing this counterexample-argument:(3) New York is the capital of the USA, because (3.1) Boston is not the capital of the USA, and (3.2) if New York is the capital, then Boston is not. Thirdly, one would have to argue that affirming the consequent is all that is happening in the original argument; that is, that the form affirming the consequent does indeed capture the gist of the argument. To better grasp that this third point is correct in this case, let us contrast it to another case in which the claim would not hold.
Consider this argument, devised for this purpose by Massey (1981, p. 492): (4.1) if something has been created by God then everything has been created by God; (4.2) everything has been created by God; therefore, (4) something has been created by God. This argument instantiates affirming the consequent: if S then E; E; so, S. However, this form ignores another crucial feature of the argument, namely the relationship between the second premise and the conclusion; the conclusion is a special case of the second premise; indeed the conclusion follows from the second premise alone, by the rule of universal specification. Hence affirming the consequent per se is an improper paraphrase of the argument, and the third clause of the method of formal paraphrase rules out this paraphrase.

There is a fourth method briefly mentioned by Krabbe (1995, p. 340), the method of logical analogy. He does not elaborate. But he does refer to a paper by Woods and Hudak (1989), entitled “By Parity of reasoning.” This terminology and this reference led me to examine two other types of meta-argument, which I would want initially to keep distinct, even though a later deeper analysis might reveal that they share significant commonalities.
One type is what has been labeled “refutation by logical analogy.” Oliver (1967) used this label, although he wrongly criticized it as incorrect. Later, Govier (1985) published an insightful discussion in the journal Informal Logic, defending its essential correctness and claiming its applicability to inductive as well as deductive arguments. And at about the same time, it became incorporated into some textbooks, specifically in Copi’s (1986a, 1986b) seventh edition of his Introduction to Logic and the first edition of his Informal Logic. While agreeing that it is correct and applicable to inductive arguments, Copi also claimed that it is itself an inductive argument by analogy. I would define a refutation by logical analogy as a meta-argument of the following type: argument A is flawed in the sense F because A is logically analogous to argument B, and B is flawed is the sense F.
Finally, my reconstruction of Woods and Hudak’s (1989) discussion is as follows. They have defined an important class of arguments, called arguments by parity of reasoning. These are meta-arguments that argue that some original argument should receive the same logical assessment as some comparison argument because these two ground-level arguments share the same logical form. Judith Thomson’s argument about abortion and the violinist is a significant example of such a meta-argument by parity of reasoning. Such meta-arguments by parity of reasoning are deductively valid. Finally, by way of criticism, I would point out that arguments by analogy (as ordinarily understood) are not arguments by parity of reasoning, as Woods and Hudak claim.

Such meta-argumentative reflections have implications regarding metadialogues. At the beginning, I asserted such a connection based primarily on the conceptual overlap between dialogue and argument (via the notion of persuasion dialogue or critical discussion) and on the demonstrated formal equivalence between the axiomatic and dialogical methods. To these general reasons, we can now add (as a case study) the translation carried out above of Krabbe’s dialogical account of formal-fallacy criticism into a monolectical framework. Analogously, a metadialogical theorist could now undertake to translate into a dialectical framework the meta-argumentation of logical analogy and of parity of reasoning sketched above.

Barth, E.M. & E.C.W. Krabbe (1982). From Axiom to Dialogue. Berlin: Walter de Gruyter.
Copi, I.M. (1986a). Informal Logic. New York: Macmillan.
Copi, I.M. (1986b). Introduction to Logic, 7th edn. New York: Macmillan.
Finocchiaro, M.A. (2005). Arguments about Arguments: Systematic, Critical, and Historical Essays in Logical Theory. Cambridge: Cambridge University Press.
Govier, T. (1985). Logical analogies. Informal Logic 7, 27-33.
Krabbe, E.C.W. (1995). Can we ever pin one down to a formal fallacy? In: F.H. van Eemeren, R. Grootendorst, J.A. Blair, C.A. Willard & A.F. Snoeck Henkemans (Eds.), Proceedings of the Third ISSA Conference on Argumentation (vol. 2, pp. 333-44), Amsterdam: Sic Sat.
Krabbe, E.C.W. (2002). Profiles of dialogue as a dialectical tool. In: F.H. van Eemeren (Ed.), Studies in Pragma-Dialectics (pp. 153-67), Amsterdam: Sic Sat.
Krabbe, E.C.W. (2003). Metadialogues. In: F.H. van Eemeren, J.A. Blair, C.A. Willard & A.F. Snoeck Henkemans (Eds.), Proceedings of the Fifth Conference of the International Society for the Study of Argumentation (pp. 641-44), Amsterdam: Sic Sat.
Massey, G.J. (1975a). Are there good arguments that bad arguments are bad? Philosophy in Context 4, 61-77.
Massey, G.J. (1975b). In defense of the asymmetry. Philosophy in Context 4(Suppl.), 44-56.
Massey, G.J. (1981). The fallacy behind fallacies. Midwest Studies in Philosophy 6, 489-500.
Oliver, J.W. (1967). Formal fallacies and other invalid arguments. Mind 76, 463-78.
Woods, J. & B. Hudak (1989). By parity of reasoning. Informal Logic 11, 125-39.

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