Abstract
In this chapter, a selection is made from the postclassical backgrounds of contemporary argumentation theory, starting with discussions of relevant developments in logic and fallacy theory. In Sect. 3.2, it is shown that there are great differences between the way logicians approach reasoning and argument and the interests of argumentation theorists. Because some developments in logic form nevertheless part of the background of argumentation theory, the discussion of logic in Chap. 2 is in Sect. 3.3 continued with a focus on the crucial concept of “validity.” A number of formal and nonformal concepts of validity are presented.
As regards the developments in fallacy theory since Aristotle, special attention is given in to in Section 3.4 the addition of the so-called “ad fallacies” – a category of arguments introduced by John Locke. Ultimately, the developments that have taken place have resulted in what Hamblin (Fallacies. London: Methuen, 1970) called “the standard treatment.” Sections 3.5 and 3.6 are devoted to a discussion of this standard treatment, Hamblin’s severe criticism of it, and the reactions which this controversy provoked.
The chapter continues with discussions of the contributions of three philosophers who gave new impulses to the study of argumentation: Crawshay-Williams, Næss, and Barth. Their contributions to argumentation theory are less familiar than those of Toulmin and Perelman (discussed in Chaps. 4 and 5, respectively), but they are by no means less fundamental. The ideas of the three philosophers reveal a considerable degree of kinship. As is discussed in Sect. 3.7, Crawshay-Williams emphasizes the need for establishing the exact purpose of each statement that is being discussed. Section 3.8 explains that Næss, in the same vein, considers it a precondition for a rational exchange of ideas that the participants in a discussion make clear what exactly is being discussed. Section 3.9 makes clear how Barth, inspired by the ideas of Crawshay-Williams and Næss, put forward two concepts of validity (“objective validity” and “intersubjective validity”). Ultimately, any useful concept of validity must not only be acceptable to its users (intersubjectively valid) but also have proved its mettle as a sensible solution to problems of logic or the use of language (objectively valid).
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Notes
- 1.
Concepts of logical validity will be discussed in Sect. 3.3. There, it will be seen that there is a variety of such concepts, not all of them “formal.” In this section, however, we shall focus on the logician’s concern with formal validity.
- 2.
This exposition of abstraction steps in formal logic is to a large extent based on Nuchelmans (1976, pp. 173–180).
- 3.
This abstraction step is illustrated in definitions of “argument” in logic textbooks. Berger (1977, p. 3) notices that logicians usually define arguments as lists of sentences, one of which is regarded as the conclusion and the rest as the basis for that conclusion. This raises the question who is regarding the premises as the basis for the conclusion. Some authors (e.g., Mates 1972, p.5) avoid that problem by omitting from the definition of “argument” any claim or supposition that the premises support the conclusion, so that the question can no longer be asked.
- 4.
That the nonlogical constants we use are sentential (propositional) constants is because the examples we have chosen are suitable to be studied in sentential (propositional) logic. For other kinds of logic, different types of nonlogical constants are used.
- 5.
There are several kinds of propositional logic, and in different systems of propositional logic, the meaning of the constants may be different. For the roots of propositional logic in Stoic logic, see Sect. 2.7 of this volume.
- 6.
Other (systems of) symbols for these logical constants are also current. See Bonevac (1987, p. 43).
- 7.
There are also nonclassical semantic means, as well as syntactic (derivational) and pragmatic (dialogical) ways, to determine the meaning of logical constants (see Sect. 3.3).
- 8.
One may prefer to use distinct letters (such as p and q) as variables to keep them apart from constants, but that is not necessary as long as it is, at each occasion, clear how the letters are used. In our example, it suffices to retract the key list given earlier.
- 9.
For different kinds of counterexample in connection with logical validity, see Sect. 3.3.
- 10.
Thus, if an argument is valid in propositional logic, it is impossible that its conclusion be false whereas its premises are true. It is important to realize that this does not mean that the premises are required to be true. A valid argument may very well have false premises. Valid arguments that do have true premises are sometimes called “sound,” but generally the soundness of arguments is no concern of logicians. On the other hand, logicians study many other types of validity besides those relating to propositional logic. If an argument is not valid in propositional logic, it may still be valid in some other logic, such as predicate logic; see below.
- 11.
An optimal argument form of a given argument is found by a careful and thoroughgoing logical analysis. In propositional logic, each sentential variable used should correspond to exactly one atomic sentence and each atomic sentence to exactly one sentential variable (no logical constant should be missed).
- 12.
The term logic in this section will be confined to deductive logic. Deductive logic is concerned with the analysis and evaluation of deductive arguments: arguments which are claimed, or supposed, to be deductively valid (in fact, this can be any argument). The possible meanings of this validity claim, as developed in the history of modern logic, are the subject of this section.
- 13.
Sometimes the term semantic is used in a much broader sense, covering also the syntactic and pragmatic concepts of validity (because such systems, in a sense, give a meaning to logical constants).
- 14.
The term argument will in this section be used in this restricted sense.
- 15.
“Admitting no counterexample” can be taken to mean either that there is no counterexample or that there cannot be a counterexample. However, for the kinds of argument forms pertaining to logics that are commonly used, the two phrases amount to the same (if there can be a counterexample, there is one), in particular if mathematical structures are allowed to provide counterexamples.
- 16.
On the pages that follow, Copi refines his description of the method of refutation by logical analogy.
- 17.
The associated conditional of an argument is the conditional proposition whose antecedent is a conjunction composed of all the argument’s premises and whose consequent is equal to the argument’s conclusion.
- 18.
- 19.
This is not to say that he had been to any major extent influenced by them. According to Kneale and Kneale (1962), “he seems to have known little of the achievements of medieval logicians” (p. 359).
- 20.
Instead of writing Vorstellung an sich (idea in itself), Bolzano usually simply writes Vorstellung (idea). Bolzano’s concept idea (in itself) is very different from Frege’s concept idea, which refers to mental entities.
- 21.
The choice of the term Ableitbarkeit (deducibility) for this relation is somewhat infelicitous, since the relation is a semantic one and does not involve the syntactic notion of deduction.
- 22.
On the linguistic level, these ideas may correspond to the usual nonlogical terms, such as the terms of a syllogism, but they may also correspond to other constituents.
- 23.
About the ins and outs of choosing a logical theory, see Sect. 3.9.
- 24.
The notion of an optimal argument form depends on the selected theory. In Sect. 3.2, this notion was explained with respect to propositional logic.
- 25.
In the truth table method, the schematic letters are propositional variables, and the only relevant part of the meaning of a sentence is its truth-value (true or false). An interpretation or model is then an assignment of truth-values to the propositional variables.
- 26.
- 27.
Here, “{1,2}” stands for the set with precisely the numbers 1 and 2 as elements (members) {1, 2, 3} for the set with precisely the numbers 1, 2, and 3 as elements, and so on.
- 28.
The rules of derivation here presented are introduced for illustrative purposes. To our knowledge, they do not constitute any extant system of natural deduction, though each of them occurs in some such systems. For further instruction on extant systems of natural deduction, we refer the reader to textbooks of logic.
- 29.
Note that, since this rule (and the next one) is complex and refers to hypothetical parts, we are not dealing here with (part of) a “logical axiom system,” but with a natural deduction system.
- 30.
See Sect. 2.4.1, (1) Inconclusiveness.
- 31.
The argumentum ad judicium is certainly not fallacious but sets a standard for using proofs drawn from the foundations of knowledge or probability.
- 32.
Definitions of the argumentum ad hominem as an in principle acceptable kind of ex concessis arguing can be found in the works of Whately (1836, III.15, pp. 195-197), Schopenhauer (1970, p. 677), Johnstone Jr (1959, pp. 73, 81), and Perelman and Olbrechts-Tyteca (1969, pp. 110–114). See van Eemeren and Grootendorst (1993). See also Hamblin (1970, p. 41, pp. 158–163) and Finocchiaro (1974).
- 33.
For the Aristotelian roots of the pejorative and the non-pejorative meanings of the term argumentum ad hominem, see Nuchelmans (1993). See also Sect. 2.4.3, of this volume.
- 34.
A great many authors also use the term circumstantial ad hominem to refer indiscriminately to all indirect ad hominem attacks (e.g., Copi 1961) or to refer to one of its variants: either the bias variant (e.g., Rescher 1964) or the tu quoque variant (e.g., Walton 1985, 1998). Cf. Krabbe and Walton (1994). Whately (1836, III.15, pp. 195-197) does not yet differentiate between different types of ad hominem explicitly, but indicates that the argumentum ad hominem is often described as “addressed to the peculiar circumstances, character, avowed opinions, or past conduct of the individual.” He also gives a famous example of a tu quoque argument (known as “the sportsman’s rejoinder”) by means of which a sportsman accused of killing innocent animals defends himself by asking “why do you feed on the flesh of the harmless sheep and ox?” (1836, III.15, p. 196n).
- 35.
See Sect. 2.4.2.
- 36.
Because it is precisely the way in which the question is framed that offers the possibility of checkmating one’s adversary, it is not so obvious why exactly Aristotle classifies this wrong move in the category of language-independent fallacies.
- 37.
In the standard treatment, secundum quid is generally interpreted as an illicit inference from particulars to a general statement (hasty generalization) and the fallacy of accident as the converse inference (ignoring exceptional circumstances). See Hamblin (1970, pp. 26–31).
- 38.
Some authors make distinctions between those concepts.
- 39.
For differences within the standard treatment in the accounts of the argumentum ad hominem, see van Eemeren and Grootendorst (1993, pp. 54–57).
- 40.
Mackenzie (2011) argues that Hamblin’s book Fallacies was part of a much broader program. According to him, Hamblin used the subject of fallacies “as an illustration of how otherwise intractable questions about logic could be transformed by being considered in the context of dialogue” (p. 262).
- 41.
It is, however, doubtful to what extent this definition was indeed commonly accepted. See Hansen (2002b).
- 42.
Even for formal fallacies, the definition is not completely unproblematic: it is then still left unexplained why these fallacies seem to be valid.
- 43.
- 44.
For a critical overview of these reactions, see Grootendorst (1987).
- 45.
In his “Preface” to the fourth edition of Introduction to Logic, Copi (1972) states that in the chapter on fallacies he made grateful use of Hamblin’s critical remarks; however, a closer comparison reveals that, aside from a few minor alterations, Copi strictly adheres to the standard treatment.
- 46.
- 47.
- 48.
Crawshay-Williams (1970) records their relationship affectionately in Russell Remembered.
- 49.
Some of Crawshay-Williams’s most significant ideas can already be found in earlier publications (1946, 1947, 1948, 1951). See also Crawshay-Williams (1968). After his death, in 1977, he left behind the virtually completed manuscript for a book, The Directive Function of Language, which is still unpublished.
- 50.
- 51.
This type of fundamental misunderstanding bears some resemblance to the type of intractable disagreement about “framework propositions” which Fogelin (1985) called “deep disagreement.” Fogelin, however, focuses on the deep disagreements that arise because of conflicts between belief structures (rather than between methodological approaches) (p. 8).
- 52.
In using the words “method” and “methodology,” Crawshay-Williams refers to their “lay” meaning of “the way in which” (p. 30).
- 53.
Often the form of an empirical statement is more complicated than would appear from “S is P.” Some statements, such as “London is bigger than Amsterdam,” express more complicated relations. Crawshay-Williams’s analysis can be so adapted that such statements can also be formulated “methodologically.”
- 54.
In using the word “context” in this specific way, Crawshay-Williams gives it a more pronounced meaning than it generally has.
- 55.
Cf. the elucidation of the context of the statement “A language is a set of sentences” provided by the grammarians de Haan, Koefoed, and des Tombe (1974): “This postulate may appear banal, but one might equally well have chosen another. For example, language is the medium through which people can communicate […]. The difference is that the postulate chosen focuses all attention on the form of a language […], not on what it is used for” (p. 3 our translation). It is apparent that these authors do not regard their context as the universal context.
- 56.
Although logical rules and laws resemble in this respect statements like (6) and (9c), the difference remains, of course, that they relate to nondescriptive terms, whereas statements like (6) and (9c) are descriptive.
- 57.
Unlike the conventionalist view that logical validity is only a matter of agreements about usage, the concept of validity defended here requires these agreements to be methodologically motivated and thus not arbitrarily selected. Cf. Kneale and Kneale (1962, Chapter X.5).
- 58.
- 59.
Næss was chair of the philosophy department at the University of Oslo until an early retirement in 1970, about midway his career. In his obituary of Næss, Krabbe (2010) discusses Næss’s contribution to the development of argumentation theory.
- 60.
Næss wrote on many philosophical issues besides empirical semantics and argumentation theory. In Gullvåg and Wetlesen (Eds., 1982), various aspects of Næss’s philosophy are discussed. In 2005, The Selected Works of Arne Næss (ten volumes) were published.
- 61.
Næss’s skepticism can be characterized as Pyrrhonian, a kind of skepticism developed by Pyrrho and his followers in the fourth century. In Scepticism, Næss attempts to defend Pyrrhonism against “undeserved objections” (1968, p. 156). Although Pyrrhonism is the type of skepticism that insists on suspending any kind of belief in or adherence to any doctrine, according to Inga Bostad, in Næss’s interpretation, the Pyrrhonist may have convictions – “not in the sense of defending assertions or dogma, but by demonstrating a form of ‘trust’ or ‘confidence’” (2011, p. 44).
- 62.
Carnap’s first name is misspelt: it is Rudolf. Originally, this paper was written in 1937–1939; in 1956 important comments were added when a German version was made accessible as a mimeographed reprint.
- 63.
In English, there are no direct translations available for the German noun Präzisierung (Norwegian: presisering) and the verb präzisieren, which are crucial in Næss’s work. Taking up a suggestion by Barth in her translations of Næss (1992a, b), we shall make use of two neologisms, which were also used by the Næss translator A Hannay in Næss (1966): (1) to precizate an utterance or a formulation means, to make it more precise by replacing it by an utterance of another formulation which eliminates some reasonable interpretations without adding new ones; (2) a precization (of an utterance or a formulation) means the outcome of a precizating operation, as well as the operation itself. Alternative terms that could be used are precify or precisify and precification or precisification.
- 64.
Næss was particularly interested in eliminating nonempirical formulations by way of discussion (1992b, p.111).
- 65.
Interpretation and Preciseness served as the philosophical background of the “Oslo School,” a group of researchers investigating semantic relations, such as synonymy, by means of questionnaires.
- 66.
Communication and Argument is the English translation, published in 1966, of Næss’s (1947) Norwegian textbook En del Elementaere Logiske Emner [Some Elementary Logical Topics]. This book first appeared as a mimeographed edition in 1941. Since 1947, several new editions of En del Elementaere Logiske Emner have appeared.
- 67.
Though written for practical purposes, Communication and Argument also introduces some theoretical insights. After its publication, Næss participated but rarely in the discussions of argumentation theorists. An exception is Naess (1993).
- 68.
See Sect. 2.7.1 of this volume. The Stoics, however, had a square rather than a triangle.
- 69.
By a formulation (formulering), Næss means a linguistic expression (usually a sentence) that is used to express a statement.
- 70.
Næss here takes U and T to be different statements. We have omitted this stipulation in the definition given above because Næss omits it in later editions and because on the next page Næss claims that T is always an interpretation of T.
- 71.
Depending on the context, a specification for some may be a precization for others. “She is walking away from us,” for example, may be a specification of “She is leaving us” that adds information about the way she is leaving (namely, on foot). To those, however, who are tempted to interpret “She is leaving us” as saying that she is dying, “She is walking away from us” may be primarily a precization of “She is leaving us.” Although all reasonable interpretations of “She is walking away from us” may be reasonable interpretations of “She is leaving us,” “She is leaving us” has at least one reasonable interpretation, namely, “She is dying,” that “She is walking away” has not. “She is walking away” can therefore be seen as a limitation on the number of interpretations which may be assigned to the formulation “She is leaving us” and hence as a precization.
- 72.
The type of difference of opinion that Næss’s resolution procedure is intended for is a mixed difference of opinion, in which the parties involved take opposite positions with respect to a proposition, not the basic difference of opinion where one party has put forward a standpoint and the other party is in doubt whether to accept it (see Sect. 1.1 of this volume).
- 73.
In this connection, Næss (1966, p. 101) refers to the Greek philosopher Carneades (ca. 214–ca. 129 B.C.), who believed that there is always something to be said for and against an opinion. According to Næss, absolute certainty is not possible, and for assessing an argumentation, it is not necessary either.
- 74.
- 75.
Especially with public discussions, the compilation of a pro-et-contra survey containing all the arguments put forward by the parties, including the arguments that are untenable or irrelevant, provides a broad basis from which an evaluator may select for his pro-aut-contra survey the arguments he regards worth considering.
- 76.
The same kind of weighing of evidence for and against will often be required with regard to evidence for evidence and so on. Thus, an intricate web of separate “tugs-of-war” may arise.
- 77.
For the sake of clarity, it is often worthwhile to formulate the alternative (of the thesis (F 0 )) that is actually being considered: the antithesis.
- 78.
- 79.
Unfortunately, this publication is not available in English; however, a translation of its most crucial section can be found in Barth and Krabbe (1982, I.4, pp. 19–22).
- 80.
Barth (1972, p. 12, Note 15) quotes Russell’s 1905 paper “On Denoting,” in which the latter writes: “A logical theory may be tested by its capacity for dealing with puzzles, and it is a wholesome plan, in thinking about logic, to stock the mind with as many puzzles as possible, since these serve much the same purpose as is served by experiments in physical science. I shall therefore state three puzzles which a theory as to denoting ought to be able to solve; and I shall show later that my theory solves them” (Russell 1956, p. 47).
- 81.
Cf. Barth (1972, p. 14).
- 82.
Cf. Barth (1972, p. 13).
- 83.
The solution given above, which presupposes the notions of truth and falsity, may be adequate in relation to the problem of defining the logical constant not for ordinary reasoning (though some would contest this), it is not so in relation to the similar problem for mathematical reasoning about the infinite, at least not according to intuitionist philosophers of mathematics. The latter problem needs to be solved by providing adequate deduction rules.
- 84.
Cf. Barth and Krabbe (1982, p. 22).
- 85.
Cf. Barth (1972, p. 17).
- 86.
In van Eemeren and Grootendorst (1984), it is argued why Barth’s conception of rationality is better suited to the study of argumentation than that of Toulmin or Perelman.
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van Eemeren, F.H., Garssen, B., Krabbe, E.C.W., Henkemans, A.F.S., Verheij, B., Wagemans, J.H.M. (2014). Postclassical Backgrounds. In: Handbook of Argumentation Theory. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9473-5_3
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