Abstract
An appeal to features of some case in support of attribution of some status to that case is non-conclusively valid if and only if it is not conclusively valid but any case with those features either has the status or has some overriding negatively relevant feature not implied by lacking the status.
Bibliographical note: This chapter was previously published in New essays in informal logic, ed. Ralph H. Johnson and J. Anthony Blair (Windsor, ON: Informal Logic, 1994), 58–66. © 1994 by Informal Logic. Republished with permission from Informal Logic. An earlier version of the chapter was presented at the Third International Symposium on Informal Logic at the University of Windsor in Windsor, Ontario, Canada in June 1989. I am grateful for helpful comments by John Martin , Robert Pinto and Mark Weinstein , among others, as well as for comments by Erik Krabbe on a revised version of the conference paper. They are not responsible for any deficiencies which remain.
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Notes
- 1.
The simplification was for ease of presentation, and does not affect the point that only certain parallels are relevant objections. The actual argument read: “Cattle are monstrously inefficient. Even in a good area like England they convert only 5% of the potential food in the grain into meat, whereas in the tropics they destroy all the land they’re allowed to roam over.” (James Lovelock, Harrowsmith November/December 1988, quoted in SHAIR International Forum (April 1989), p. 1.1).
- 2.
- 3.
The restriction to the same category (i.e. ultimate genus) is meant to rule out such spurious counterexamples as the one provided in Plato ’s Euthydemus. The following argument is evidently valid: That pen is mine: that pen is a Bic; therefore, that pen is my Bic. The following argument is an apparent counterexample: That dog is mine: that dog is a father; therefore, that dog is my father. But the counterexample is only apparent, because “Bic” is a substantive term designating an object, whereas “father” is a relational term designating a relatum.
In some arguments it seems reasonable to restrict the range of substitution to a subcategory. Consider the argument: Marijuana should be legalized, because it is no more dangerous than alcohol, which is already legal. A possible counterexample is the argument: Driving without a seat-belt should he legalized, because it is no more dangerous than hang-gliding, which is already legal. But this objection seems unfair, since the argument focuses on two mood-altering drugs, and need not generalize its principle beyond that clam. Tomis Kapitan (1982), however, has pointed out (p. 209) that, if restriction can be to any class, any argument with a false premiss or a true conclusion will be valid; he suggests that subcategories must be essential to the items designated by the variable components.
Since we do not have a fully worked out theory of categories for natural languages, this conception of conclusive validity is to that extent schematic. In practice, however, uncertainties about the category of a variable component rarely cause problems.
- 4.
These components must be what 1 earlier (1985) called content expressions , expressions which in the context of their utterance can be regarded as referring to or otherwise signifying an actual or possible feature of the universe. Such content expansions can be molecular (“John’s cat”) as well as atomic (“cat”).
- 5.
The requirement that the set be non-empty is meant to exclude purely material “consequence” in which it just happens that it is not the case that the premisses are true and the conclusion false. “3 is larger than 2, so China is the world’s most populous country” is not a valid argument: there is no transmission of truth from premiss to conclusion.
- 6.
- 7.
As John Martin pointed out to me, the truth of this universally generalized conditional reflects the fact that metalinguistic principles stated as schemata are shorthand for universal quantifications over expressions. Strictly speaking, then, this universally generalized conditional is a generalization over expressions and belongs to the metalanguage. But the corresponding statements in the object language, in which the expressions are used rather than mentioned, will also be true.
- 8.
This generalized conditional is in turn logically equivalent to the proposition: “No herbivores are predators”, which “traditional logic” would identify as the “missing premiss” of this “enthymeme”.
- 9.
P(x1, …, xn) is the result of replacing all occurrences of ai in P (except those which are proper parts of another component aj) with xi, for 1 ≤ i ≤ n. Similarly for c(x1, … , xn). As indicated in note 8, strictly speaking the formal conception of conclusive validity should be formulated metalinguistically, as follows: There are no expressions e1, … , en such that, for 1 ≤ i ≤ n, ei is of the same category as ai, P(e1/a1, … , en/an) is true, and c(e1/a1, … , en/an) is false.
- 10.
The word “factual” needs a broad interpretation here, since it must include evaluative claims. Consider, for example, the argument, “Strategic bombing of cities is intentional killing of innocent persons, so it is morally wrong”. If valid, this argument is valid in virtue of the generalization, “Any intentional killing of innocent persons is morally wrong”. This generalization would be a factual claim, according to the distinction made above.
- 11.
For the terminology, see Grünbaum and Salmon (1988, p. 2).
- 12.
- 13.
Henry Kyburg Jr., however, has argued persuasively for a policy in reconstructing scientific reasoning of tolerating inconsistencies and not requiring deductive closure. See Grünbaum and Salmon (1988, pp. 61–94).
- 14.
These conditions are epistemic. One could also, as Hamblin (1970) pointed out, adopt dialectical criteria for a good argument, e.g. that the premisses are among the commitments incurred by the interlocutor in the conversation. I mean the account of validity in this paper to be usable in a variety of accounts of good argument. The conception of validity is in Hamblin ’s terms “alethic”, resting as it does on the truth of a covering generalization. But investigating the truth of such a generalization will usually involve implicit appeal to epistemic criteria. In a dialectical context investigation will have to proceed by agreement among the interlocutors.
- 15.
As I have argued elsewhere (1980, 1981), arguers generally neither tell us nor are aware of whether they are drawing their conclusions conclusively or non-conclusively. 1 would therefore prefer to characterize a conductive argument as one in which the conclusion does not follow conclusively rather than as one in which it is drawn non-conclusively.
- 16.
These arguments include what I referred to in my textbook (1983) as “balance-of-considerations arguments”, where negatively as well as positively relevant premisses occur. Wellman ’s examples are all arguments where the conclusion expresses a verdict or decision about how to act on, evaluate or classify the case. But the definition fits an argument like “Bessy is a cow, so she is brown”, where the conclusion is independently testable. If we wish to exclude such arguments, we would have to add a further condition that the conclusion is not even in principle testable in itself.
- 17.
According to the result mentioned in Sect. 11.1, if the argument is valid, at least one of its variable components will occur in both the premiss and the conclusion. (By hypothesis, the argument is not conclusively valid, so it will not be trivially conclusively valid.) The repeated components are “him”, “tell him he has terminal cancer” (repeated in the pronoun “it”), and the components of “tell him he has terminal cancer”. The use of the pronoun “it”, however, indicates that “tell him he has terminal cancer” is to be taken as a single component in looking at the form of the argument. Substituting only for “him” gives the argument an unduly narrow scope; as I have argued elsewhere (1985, 1987), any repeated content expression is to be taken as variable unless it would be implausible to do so. Substituting only for “tell him he has terminal cancer” would make it difficult to find parallel arguments with true premisses.
Added in the present republication: Reflection on this example indicates that the “him” in “tell him he has terminal cancer” needs to be treated as a separately variable component, in order to link with the “him” in “cause him severe distress”. Thus the most plausible interpretation of the argument involves treating as variable components “him” and “tell he has terminal cancer”.
- 18.
Added in the present republication: The formulation is elliptical. What is meant is that the proposition that the case under discussion has overriding negatively relevant features must not follow deductively from the proposition that the case lacks the property inferred in the conclusion.
- 19.
I owe this insight to Robert Pinto , who pointed out in a commentary on an earlier unpublished paper of mine (1986) that my formulation of the condition that there be no overriding negatively relevant features by itself entailed the conclusion, since it allowed the absence of the inferred property to be one such overriding feature.
- 20.
In a paper entitled “Relevance as a theoretical constraint in accounts of argumentation,” delivered at the Third International Symposium on Informal Logic, John Woods gave as the first condition of adequacy for an account of relevance that it be neither null nor universal. That is, some cases should be relevant and others irrelevant. Woods’ condition is a reasonable demand which I am trying to meet.
- 21.
Will even this restriction save this account of relevance from apocalyptically counting all considerations as relevant? Take an obviously irrelevant consideration: the colour of a car is irrelevant to how well it performs. Now consider the argument: “This car is yellow, so it will run well.” An objector will point to a yellow car which runs badly. But the arguer can always in any such case point to some feature of that car which makes it run badly (the electrical system tends to fail in wet weather, the engine is noisy, etc.), and can regard that feature as one which overrides the car’s yellow colour. We seem to need a parallel case in which the purportedly relevant feature is not just present but obviously irrelevant.
- 22.
Such a procedure would be necessary in order to argue for conductive validity in cases where the relevance of the premiss(es) was not obvious. Failure to find a counterexample might reflect a deficient imagination, rather than the invalidity of the argument.
- 23.
a is the case which the conductive argument is about.
- 24.
If one attempts to formulate this latter condition in the style of a recognized formal system, one seems to come up with an infinite sentence: For any situation x. if P(x) then either e(x) or there is a feature F such that x has F, not c(x) is consistent with x’s not having F, and for any situation x1, if P(x1) and x1 has F then either not c(x1) or there is a feature F1 such that xl has F, c(x1) is consistent with x1’s not having F1, and for any situation x2, ….
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Hitchcock, D. (2017). Validity in Conductive Arguments. In: On Reasoning and Argument. Argumentation Library, vol 30. Springer, Cham. https://doi.org/10.1007/978-3-319-53562-3_11
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