Abstract
This paper presents a unified, more-or-less complete, and largely pragmatic theory of indicative conditionals as they occur in natural language, which is entirely truth-functional and does not involve probability. It includes material implication as a special—and the most important—case, but not as the only case. The theory of conditional elements, as we term it, treats if-statements analogously to the more familiar and less controversial other truth-functional compounds, such as conjunction and disjunction.
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Notes
He does not say so, but then the paper was published posthumously from a manuscript.
Jackson himself does not claim to have originated this idea; see his note 2, where he cites others, particularly in discussion. What Jackson did originate is an explanation of Adams’ Thesis in terms of the truth conditions for the indicative conditional, while defending ⊃ as giving those truth conditions. All of his references are post-1963/1964, however.
We will explain later what we mean by ordinary.
It appears to matter to both the class of implicature, conventional or conversational, and the pragmatic rule by which it is derived whether iff is mediated by only-if or by if-not-then-not. See Van Canegem-Ardijns (2010) for an extensive and thorough treatment.
Cmp. Wylie’s (1979: 404): I wouldn’t marry you, if you were the last man alive.
Cmp.: I wouldn’t marry you, even if you were the last man alive. Cmp.: I wouldn’t do that, even if you paid me.
One reason why many earlier authors have denied this might be that the early literature concentrated on contrary-to-fact even if conditionals.
There is much made in the literature on whether it is the particle “if” or the whole clause that is the focus of the “even”. This may matter for generating the scale and for the type of scale, but it does not appear to me to matter as respects the truth conditions.
I owe this observation and (16) to Peter Milne.
See note 6.
Although that is not the purpose of ⊃6, the purpose being to affirm the consequent.
But Fulda is again mistaken to suggest that the conditional element, properly so-called, implicated is either ⊃2 or ⊃4; it is not: It is ⊃8, not defined there.
Cf. Brogaard and Salerno (2008) on counterfactuals.
But not a defining feature, as some of the eight combinatorially possible non-conditional elements are also transitive, although not all of them are.
There is a minor difference between the assertibility conditions for ordinary conditionals and perfected conditionals, in that it is—by definition—impossible to know the truth values of one of the antecedent and the consequent, in the case of the latter, without knowing the other. Also, Douven’s (2010) extension to active believability does not appear to apply to perfected conditionals.
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Acknowledgments
More hands have had a hand in this paper than I could possibly list; almost all of them have made it far, far better than it would otherwise be. In the rough words I saw in an acknowledgment in a recent paper I can no longer bring to mind, were I to meet these folks, some I would owe a beer, some would owe me a stiff drink. All of them have my thanks and appreciation. Two, however, stand out in particular. The first is David Sherry, whose insistence in correspondence that the first line of the truth table for material implication is just as problematic as the third and fourth led me to realize that the theory of conditional elements that I first proposed in 1999 and expanded and revised in 2009 had to be expanded still further, from four conditional elements to eight. David, you were right, and I was wrong. It was David, too, who suggested that finding a metric by which to order the conditional elements would be a worthy goal. The second is Peter Milne, with whom I have had the extraordinary good fortune to work with for the past three years. Finally, this paper was made possible, in part, by a grant from SASP from funds supplied by The Philosophical Quarterly.
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Fulda, J.S. The Full Theory of Conditional Elements: Enumerating, Exemplifying, and Evaluating Each of the Eight Conditional Elements. Acta Anal 25, 459–477 (2010). https://doi.org/10.1007/s12136-010-0097-6
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DOI: https://doi.org/10.1007/s12136-010-0097-6