Abstract
In many actual arguments, the conclusion seems intuitively to follow from the premisses, even though we cannot show that it follows logically. The traditional approach to evaluating such arguments is to suppose that they have an unstated premiss whose explicit addition will produce an argument where the conclusion does follow logically. But there are good reasons for doubting that people so frequently leave the premisses of their arguments unstated. The inclination to suppose that they do stems from the belief that the only way in which an argument’s conclusion can follow definitely from its premisses is to follow logically. I argue that this belief is mistaken. I propose a revision of the current generic conception of logical consequence, and its variant specifications, to avoid the paradoxes of strict implication. The revised conception can then be naturally extended to include also what we might call ‘enthymematic consequence’. This concept is a kind of consequence, whose properties merit investigation.
Bibliographical note: This chapter was originally published under the same title in Argumentation 12 (1998), 15–37. © 1998 Kluwer Academic Publishers. It is republished here with permission of Springer. An earlier version was presented at the Third International Conference on Argumentation in Amsterdam in 1994 and published under the same title in Analysis and Evaluation: Proceedings of the Third ISSA Conference on Argumentation (University of Amsterdam, June 21–24, 1994), Volume II, ed. Frans H. van Eemeren, Rob Grootendorst, J. Anthony Blair, and Charles A. Willard, 113–129 (Amsterdam: International Centre for the Study of Argumentation, 1995). I thank Rolf George , John Leslie , Chris Tindale and two anonymous referees for helpful comments on earlier versions of this paper.
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Notes
- 1.
This conception does not necessarily assume that the premisses and conclusion are asserted by the author of the argument. There are suppositional arguments, in which a premiss is merely supposed to be true for the sake of the argument, and dialectical arguments, in which the author of the argument draws a conclusion from premisses which are concessions of an interlocutor.
- 2.
I think very many. Let us set aside actual arguments in which the appropriate standard of evaluation to apply is whether the premisses make the conclusion probable or offer defeasible grounds for accepting it. Of the remaining actual arguments, I suspect that well over half are enthymemes, in the sense that they have the feature I am going to describe. As a kind of test of this suspicion, I picked the above example in a haphazard (but not scientifically random) fashion from a collection of about 3000 argumentative texts discovered by my students. The first text I found was a report of someone else’s argument. The second, rather surprisingly, turned out to contain a formally valid argument. The third provided the argument here quoted. It would of course take a statistically well-designed survey to demonstrate how common enthymemes are.
- 3.
I use the term ‘follow’ in this paper in the everyday sense of that relation between conclusion and premisses which is an essential feature of a good argument. To say that a conclusion follows from certain premisses is synonymous with saying that it is a consequence of them. These concepts of following and of consequence are everyday concepts in common use; technical concepts like that of formal validity are attempts to give them theoretical precision, and should be judged with reference to ordinary usage (which is however corrigible).
- 4.
The terminology varies. The unstated premiss is variously described as missing, hidden, unexpressed, tacit, or suppressed. Of these terms, the words ‘tacit’ and ‘unexpressed’ are the least objectionable, as incorporating fewer theoretical assumptions about its status and the propriety of its non-explicitness.
- 5.
Thus Quine (1972, p. 169) writes, ‘An enthymeme is a logical inference in which one or more of the premises are omitted from mention on the ground that their truth is common knowledge and goes without saying.’ His diagnosis of the reason for the omission of a premiss, which is not essential to the standard definition, echoes Aristotle : ‘… if any of these premises [sc. of the primary syllogism] is familiar, there is no need even to mention it; for the hearer adds it himself.’ (Rhetoric I.2.1357a17–19) (Aristotle 1984, p. 2157; amended translation).
- 6.
In a careful and extensive exegetical study, Burnyeat (1994) traces how the ancient commentators on Aristotle came to attribute to him the conception found in so-called ‘traditional logic’ of an enthymeme as a syllogism with an unstated premiss, even though (according to Burnyeat) what Aristotle took to be characteristic of rhetorical ‘syllogism’ was its quasi-deductive character, its appeal to principles which hold only for the most part, or which only seem to hold for the most part, to license a definite conclusion.
- 7.
The results of such a test would not be decisive. A person who had consciously omitted a premiss in articulating an argument might not remember having done so. And a person who had not consciously omitted a premiss might be led by the test to construct such a premiss. But a widespread negative response to this test would tell strongly against the hypothesis of conscious omission of a premiss. I discuss the possibility of intentional but unconscious omission below.
- 8.
Thus, for example, there is no particular reason to expect a person who advances a disjunctive syllogism argument of the form ‘either p or q, but not p, so q’ to be conscious, even retrospectively, of having used a rule of disjunction elimination in drawing the conclusion. For this rule functions as that in accordance with which the person reasons, as procedural knowledge, rather than as that from which the person reasons, i.e. content knowledge. The oddity of the suggestion that authors of enthymemes intentionally omit a premiss is that people argue from their premisses, rather than in accordance with them, and thus could reasonably be expected to be conscious of what their premisses are.
- 9.
Speech communication theorists, who have a more nuanced conception of an enthymeme than the logic textbooks, nevertheless tend to concede that enthymemes are incomplete from a normative perspective. ‘… most enthymemes are … formally deficient.’ (Bitzer 1959, p. 404) ‘Arguments made in conversation are generally incomplete when compared to critical models.’ (Jackson and Jacobs 1980, p. 261). Conley (1984, p. 169) reports a scholarly consensus that an enthymeme is ‘not just a truncated syllogism’, that it is expressed as a truncated syllogism for practical rather than formal reasons, and that the missing premisses in an enthymeme expressed as a truncated argument are supplied by the audience. Conley himself shows that the conceptualization of enthymemes in the ancient rhetorical tradition is more complicated than even this nuanced consensus indicates.
- 10.
Van Eemeren and Grootendorst (1992) appeal to pragmatic considerations as a basis for taking one from the ‘logical minimum’ to the ‘pragmatic optimum’. I am sceptical that this approach provides a coherent and plausible basis for explicitizing what is implicit in an enthymeme’s inference. But it would take me too far afield to articulate my doubts.
- 11.
Where ‘if P then c’ is interpreted truth-functionally as logically equivalent to ‘not both P and not c’. (According to a convention introduced by Quine , there should be corner quotes rather than normal quotation marks around expressions like ‘if P then c’ where part of the expression is being used to refer to itself and part in its customary or stipulated primary usage. Sticklers for this convention are asked to make the appropriate substitutions.).
- 12.
Construed truth-functionally. As Read (1988) points out, relevant logicians do not accept modus ponens under this interpretation. But classical and intuitionist logicians do.
- 13.
I write ‘most’ rather than ‘all’, because there are some enthymemes where intuitively speaking the conclusion follows but where the conclusion is not a consequence of the stated premiss(es) in the expanded sense of ‘consequence’ I develop in this paper. See Sect. 5.4.2 below.
- 14.
Kapitan (1980) raises some counterexamples to George ’s conception, and explores in (Kapitan 1982) some alternatives. George (1983) elaborates on his earlier conception. See also Hitchcock (1985, 1987). Toulmin (1958) implicitly endorses a similar idea in his conception of a warrant; see also Toulmin et al. (1984).
- 15.
Where a is the name of an individual in the domain of discourse, x is a variable ranging over the individuals in the domain of discourse, F(x) is a formula of the system containing at least one unbound occurrence of x, and F(a) results from this formula by replacing all unbound occurrences of x in F(x) by a.
- 16.
Where p and q are sentences.
- 17.
This condition is necessary, because some relevantists have proposed an intensional (non-truth-functional) interpretation of ‘and’ in this context which does not have the two paradoxical consequences described above. See Read (1988, pp. 38–40; 1994, p. 265). I leave as an open question how to extend the concept of consequence in relevant and paraconsistent logics to enthymematic consequence.
- 18.
- 19.
The phrase ‘these species’ refers back to a previously identified set of species, and the only phrase which can be construed as identifying it is ‘most primates’. So the author evidently takes ‘most primates’ to mean ‘most species of primates’ rather than ‘most individual primates’. On the latter construal, the conclusion does not follow, so by the principle of charity we should resolve the ambiguity in favour of the former construal.
- 20.
From a radio sports broadcast. Rolf George supplied this example in his commentary on an earlier version of this paper at a conference of the Ontario Philosophical Society.
- 21.
The listener is expected to understand that ‘Detroit’, ‘Baltimore’ and ‘Toronto’ refer to professional baseball teams based in the named cities, teams which in fact belong to the same division of the same league. In North American professional baseball, standings in each division are determined each day by the number of games each team has won and lost up to that day in the given season. The leader in each division is the team with the largest positive balance of won games over lost games. If two teams in a division have won the same number of games but one has lost fewer games, the team with fewer losses is ahead of the team with more losses.
- 22.
Rolf George pointed out in his commentary on an earlier version of this paper that Euclid’s plane geometry lacks an axiom whose absence was not discovered until Hilbert’s geometry: if one draws a straight line intersecting one side of a triangle, it will also intersect one of the other two, or run through the opposite vertex. This axiom is false for some triangles in doughnut-shaped planes, and is necessary to ensure that the plane is Euclidean rather than doughnut-shaped. Thus many of Euclid ’s theorems depend on such an axiom. But George thinks Euclid’s proofs are too complex to permit the formal generation of this implicit assumption as a covering generalization. If he is right, this would be an additional exception to my claim that arguments whose conclusions intuitively follow definitely from their premisses do so in virtue of a covering generalization. Or perhaps we should say that without the axiom some of Euclid’s conclusions do not follow from his premisses, even enthymematically.
- 23.
He does recognize a class of what he calls ‘analytic arguments’ (1958, pp. 123–141). But he defines these as arguments in which checking the truth of the data and of the backing for the warrant involves checking the truth of the claim/conclusion. The warrant of such arguments is just as substantive as that of so-called ‘substantive arguments’.
- 24.
Removing the qualifiers distorts the argument. With the qualifiers, the conclusion does not follow logically. But nor does it follow in any other way, least of all in virtue of a substantive warrant. For the conclusion to follow, the author needs to remove at least one of the qualifiers on the premisses.
- 25.
For a classic and humorous demonstration of why it is unreasonable to insist on adding such purely formal inference-licensing principles as premisses, see Carroll (1895).
- 26.
There is a convenient list of these structural rules in Read (1988, pp. 42–43). Some writers take satisfaction of these rules, especially the cut rule, as a necessary condition for an acceptable conception of consequence. But if a conception of consequence is acceptable on other grounds, but satisfies only a restricted cut rule, that restriction must simply be accepted as part of that conception of consequence. Some types of consequence just are not generally transitive, or generally monotonic.
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Hitchcock, D. (2017). Does the Traditional Treatment of Enthymemes Rest on a Mistake?. In: On Reasoning and Argument. Argumentation Library, vol 30. Springer, Cham. https://doi.org/10.1007/978-3-319-53562-3_5
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