Abstract
Howell Pacific Philosophical Quarterly, 89(3), 348–358 (2008) and Mizrahi and Morrow Ratio, 28(1), 1–13 (2015) offer a group of reductio arguments to rebut the CP thesis, i.e., the hypothesis that ideal conceivability entails possibility. Each of them has a conceivability premise: it is ideally conceivable that CP is false (or is necessarily false). According to the same CP, one can infer that CP’s being false (or being necessarily false) is possible, from which it follows that CP is false. In other words, CP is shown to be self-defeating and therefore false if any of these reductio arguments is proved sound. In this paper, I aim to disprove these arguments. I first show that neither Howell nor Mizrahi & Morrow provide adequate justification for their conceivability premises. I go on to argue that these reductio arguments face a dilemma: either their conceivability premises cannot be adequately justified, or they are redundant. Finally, I argue that, although this dilemma resists the reductio arguments against CP, on the other hand, it also reveals that CP lacks epistemic fruitfulness: it is of no practical use in the realm of apriority as well as necessity.
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Notes
See Chalmers (2002), p. 147.
See Chalmers (2002), p. 153. As to the notion of verification, Chalmers does not provide an explicit characterization. I will say more about it in fn. 6 of this paper.
Here, by logically possible, I mean contradiction-free, i.e., coherent. I will elaborate on the notion of logical possibility in Section 2.
See Chalmers (2002), p. 149.
See Chalmers (2002), p. 153. In this paper, I take verification as equivalent to entailment for two reasons. First, Chalmers analogizes it to entailment: ‘verification of a statement by an imagined situation is broadly analogous to an entailment of one statement by another (a priori entailment, in the central cases)’. Second, Mizrahi & Morrow read verification as entailment: to show that the falsity of CP + is ideally positively conceivable, they resort to a Spinozistic deity, whose existence ‘entails’ the falsity of CP+. Since I aim to argue against them in this paper, it will do no harm to my argument if I follow their reading. See Chalmers (2002), p. 152; Mizrahi and Morrow (2015), p. 7.
Chalmers (2002), p. 171.
Chalmers, p. 123.
Chalmers (2010), p. 191.
Chalmers (2010), p. 185.
So, a natural conclusion is that ideal negative conceivability and ideal positive conceivability are equivalent. Chalmers would like to endorse this equivalency, in most cases. He discusses three kinds of possible counterexamples and hits back, but this is an issue beyond the scope of this paper. As he writes, ‘each of these three is a distinct and substantial philosophical project, and that the investigation of each raises deep philosophical questions and promises significant philosophical rewards’. See Chalmers (2002), pp. 194–195.
Logical possibility is also called ‘conceptual possibility’ in their discussions, see Roca-Royes (2011).
Worley (2003), p. 19.
Roca-Royes (2011), p. 25.
Kripke (1980).
For more details of 2D, see Chalmers (2006).
As to how 2D works and how Chalmers addresses Kripke’s counterexamples, I follow Howell’s interpretation. See Howell (2008), pp. 349–350.
As to the term ‘H2O’, as a theoretical term in the language of physics, it behaves differently from natural kind terms like ‘water’. In any possible world, whether considered as an actual or a counterfactual world, the extension of ‘H2O’ is H2O.
Howell (2008), p. 349.
The neo-Kripkean a posteriori necessity is also called ‘strong necessity’. Discussions about it abound, many of which are mentioned in Chalmers (2010), pp.166–184.
Howell (2008), p. 351.
Howell (2008), p. 354.
Chalmers expects this potential challenge from triviality and responds to it in his paper ‘Does Conceivability Entail Possibility?’. See Chalmers (2002), p. 149.
Howell (2008), p. 353.
Chalmers (2002), p. 147.
Chalmers (2010), p. 155.
Howell (2008), p. 352.
In order for P3 to hold, Howell presupposes S5. See Howell (2008), p. 356, fn. 9. As to the questions of whether Chalmers’ theory requires S5 or whether S5 is the correct logic for metaphysical modality, I pass them over in this paper. I follow simply instead what Howell presupposes.
Notice that when Howell addresses his argument against CP, he does not consider how to vindicate his conceivability premise, but shifts the burden of proof onto the side of his opponent. I will argue in Section 3 that this move makes his argument inadequately justified.
Howell (2008), p. 353.
Ibid.
Howell (2008), p. 353.
Ibid.
So it is unclear in what sense this kind of conceivability is stronger than prima facie conceivability.
Howell (2008), p. 355.
See Howell (2008), pp. 354–355.
See Chalmers (2010), p. 185.
Howell (2008), p. 356.
Ibid.
Mizrahi and Morrow (2015), p. 7.
Mizrahi and Morrow (2015), p. 8.
In this paper, I confine my discussion to knowable propositions. Moreover, I assume that Goldbach’s conjecture is knowable. If anyone denies this assumption, I would like to replace Goldbach’s conjecture with any other mathematical proposition which is accepted as knowable and of which the truth-value is currently unknown.
In the following, I will call a proposition whose truth or falsity is necessary a ‘necessary proposition’.
In S5, ◊□q→□q and ◊¬□q→¬□q holds. It follows that in S5, □□q∨□¬□q holds. Thus, both the truth and the falsity of CP are necessary.
As I stated in fn. 45, I confine my discussion to knowable propositions in this paper. At least, friends of reductio arguments would accept that (a)–(c) are knowable. I follow suit.
References
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Acknowledgements
This paper is supported by the National Social Sciences Fund of China (Project No. 20BZX093). I am grateful to Asher Jiang, Xingming Hu, and the anonymous referee for their helpful suggestions and comments.
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Feng, S. Can reductio Arguments Defeat the Hypothesis that Ideal Conceivability Entails Possibility?. Philosophia 50, 1769–1784 (2022). https://doi.org/10.1007/s11406-022-00533-9
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DOI: https://doi.org/10.1007/s11406-022-00533-9