Abstract
Stephen Yablo has argued for metaontological antirealism: he believes that the sentences claiming or denying the existence of numbers (or other abstract entities or mereological sums) are inapt for truth valuation, because the reference failure of a numerical singular term (or a singular term for an abstract entity or a mereological sum) would not produce a truth value gap in any sentence containing that term. At the same time, Yablo believes that nothing similar applies to singular terms that aim to refer to an entity whose existence or non-existence is a factual matter, e.g. ‘the king of France’: the failure of the presupposition that there is a unique French king makes some sentences with the term ‘the king of France’, in particular “The king of France is bald”, gappy. In this paper I will show that the sentence “The king of France is bald” must be false, and not gappy, according to Yablo’s own criteria and that, furthermore, the presupposition that the term ‘the king of France’ refers presents a fail-safe mechanism in the same way Yablo thinks abstract presuppositions do—this undermines his argument for metaontological antirealism.
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Notes
This article is a result of my research done within the project Logico-Epistemological Foundations of Science and Metaphysics (179067) supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia.
Yablo says initially that (2) and (3) strike us as false and true, or that they count as false and true, respectively (2009, p. 512), but later adds that counting as true or false is “almost the same” as being true or false and that the difference is insignificant since “φ’s counting as true (false) goes with the genuine truth (falsity) of the claim φ makes” (2009, p. 516).
One could, of course, argue that the everywhere non-catastrophic failure of the presupposition that certain entities exist presents strong grounds for denying that they do, because it would make them dispensable. Yablo seems to have sympathized with this stronger view in an earlier paper (2001), but in the more recent one, with which I am primarily concerned here, he claims that in such circumstances the answer to the ontological question with regard to these entities would be undetermined (2009).
In fact, Yablo does not demonstrate that the failure of the presupposition that there are numbers is everywhere non-catastrophic, but only gives a few examples from applied mathematics instead.
It seems that Strawson would accept the difference in truth-valuedness between (4) and (5): of (4) he says that “it is quite untrue” because “whoever the Exhibition was visited by yesterday, it was not visited by the king of France”, but adds that “we might, for example, have felt a shade more squeamish” about (5) (2004, pp. 90–91).
Had (6) not been false, we could not speak about the presupposition failure in the sentence (1) in the first place.
Earlier versions of similar ideas can be found in Lasersohn and von Fintel (von Fintel 2004, pp. 325–340).
In other words, not only is the chair unoccupied but it still might have been so if π had been true; therefore, the falsity of the considered implication is independent from the failure of π.
Clearly, for a false proposition to be π-free it is not enough that its negation be consistent with π, since the conjunction of π and (~7) does not yield a contradiction, but the claim that France has a unique king who fails to be bald; an additional theory of truth- and false-makers is needed to assess the degree to which a sentence is contaminated with its presupposition.
I deny that the fact that Mr. Hollande is the French president who fails to be bald is (8)’s false-maker. This fact is incompatible with π: had France had a unique king, it would have been a monarchy and could not have had a president. Both the fact that Mr. Hollande is the man who rules France and who is not bald and the fact that he is the French president with hair are sufficient for making (8) false, but the latter is inadmissibly specific: after all, the sentence (8) asserts nothing about the structure of the French government. If anyone claimed that the latter fact was the false-maker of (8), she would have to argue that if Mr. Hollande changed his title from the president to the king, (8)’s false-maker would be a different fact—the fact that he is the king of France who fails to be bald. And this is quite implausible, since the singular term ‘the man who rules France’ would pick out the same object after the assumed change in title as before, and, hence, the same ‘chunk of reality’—Mr. Hollande and his possession of hair—would be responsible for the falsehood of (8).
Although the expressions ‘king’ and ‘man who rules the state’ are widely used in a way which implies uniqueness, even if it were allowed for the possibility of a state with multiple kings and multiple rulers, it would not undermine my claim that (1) analytically implies (8). Had France had multiple kings—for example, if it had been a dual monarchy—it would not disprove that (8) is an analytic consequence of (1), as in this case neither π nor φ would have been true. The lapse in definedness could only occur if there were a π-world which is not a φ-world, i.e. if France were ruled by several men, only one of them a king. For instance, someone might think that France could have both a king and a president as its head; however, this case is precluded by the following analytic truths: (1) only a monarchy could be ruled by a king; (2) only a republic could have a president as its head; and (3) the monarchy and the republic are contrary forms of government. Therefore, if several men ruled France with one of them a king, the other rulers would have to be monarchs of an equal status as him: they would have to be kings themselves, which brings us back to the case with multiple kings discussed above, which does not threaten the preservation of definedness in the implication from (1) to (8).
I owe this example to Miloš Arsenijević.
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Acknowledgements
I am indebted to Miloš Arsenijević and Timothy Williamson for helpful discussions and valuable suggestions and to an anonymous reviewer for useful comments.
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Jandrić, A. “The king of France is bald” reconsidered: a case against Yablo. Philos Stud 169, 173–181 (2014). https://doi.org/10.1007/s11098-013-0164-0
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DOI: https://doi.org/10.1007/s11098-013-0164-0