Abstract
The supposed “missing premisses” attributed to arguments are generally not premisses at all but rather statements of a rule that would license the inference as it stands. Such substantive rules of inference cannot be underwritten by substitutional or model-theoretic conceptions of consequence. They need to be understood in terms of schemata. A schema is valid if and only if the generalization corresponding to it is true or analogously acceptable in both actual and counterfactual cases, even thought there might be a case where its antecedent is true and there might be a case where its consequent is untrue. Thus an argument’s conclusion follows from its premisses if and only if a counterfactual-supporting covering generalization of the argument is non-trivially acceptable The kernel of truth in the missing premisses approach is that one sometimes needs to make explicit the universe of discourse over which a variable in an inference-licensing covering generalization ranges.
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Notes
- 1.
The 1985 publication, which is the one reprinted in the present volume, is a revision (in response to referees’ comments) of the 1987 publication, which appeared in the proceedings of the 1986 International Conference on Argumentation. The oddity of the dates is due to delayed publication of the 1985 volume of Informal Logic, which actually appeared in 1986. The proceedings of the 1986 conference appeared in 1987.
- 2.
As mentioned in note 1, the first article was written in 1986. Its publication date of 1985 is due to the late appearance of issues of the journal in which it was published.
- 3.
Strictly speaking, a contingently true assumption about the height of the Empire State Building needs to be supplied as a missing premiss. The Empire State Building is 443 m tall. It could be taken as shared background knowledge that it is less than, say, 600 m tall.
- 4.
Strictly speaking, one should add as an unstated premiss the contingently true information that the Empire State Building is 443 m tall. The necessarily true inference-licensing covering generalization would then be that any building that is less than twice the height of a building that is 443 m tall is less than 886 m tall. That generalization is true as a matter of arithmetical necessity.
- 5.
The generalization is: for all animals x, if xes have wings, then Jesus is mortal. This generalization is logically equivalent to the version above, whose meaning is easier to understand.
- 6.
I asked Tennant to confirm that he now identifies the concept of logical consequence with what is deducible in his core logic. He responded as follows:
I think the best way to answer your question is that I regard the proof system of (classical) core logic as establishing exactly those arguments that are not only truth-preserving (in the orthodox sense) but also relevantly so, in the precisely explicated sense of relevance that you will find in the attached paper (Tennant 2015). I am convinced that any attempted strengthening of that explication leads to false negatives—i.e., arguments that the strengthened explication deems non-relevant (even though valid) but which ordinary intuition tells one jolly well are relevant (in the sense that needs explication).
That having been said, I am now trying to develop an inferentialist theory of definitions, according to which the inferentialist definition of the double-turnstile of classical semantics will result in a logical consequence relation that coincides exactly with the single turnstile of the classical core proof-system. This is because the metalogic itself, within which one pursues the consequences of one’s inferentially formulated definitions, is “core-ified”. But it will be some time before I am able to offer the fruits of these labors for wider consumption! Moreover, if I fail to get this ‘inferentialist’ version of double turnstile to match my single turnstile exactly in extension, I shall be satisfied with the fall-back position described in the previous paragraph. (e-mail communication, 2016 02 16)
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Hitchcock, D. (2017). Postscript. In: On Reasoning and Argument. Argumentation Library, vol 30. Springer, Cham. https://doi.org/10.1007/978-3-319-53562-3_10
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