Abstract
My topic is moderate modal skepticism in the spirit of Peter van Inwagen. Here understood, this is a conservative version of modal empiricism that severely limits the extent to which an ordinary agent can reasonably believe “exotic” possibility claims. I offer a novel argument in support of this brand of skepticism: modal skepticism grounds an attractive (and novel) reply to Humean skepticism. Thus, I propose that modal skepticism be accepted on the basis of its theoretical utility as a tool for dissolving philosophical paradox.
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Notes
- 1.
Hume and especially Descartes are often pointed to as philosophers that embrace unconstrained conceivability techniques as a guide to possibility. Recent sophisticated advocates of conceivability techniques – such as Yablo (1993), Chalmers (2002) and, on one reading, Bealer (2002) – take great care to separate out different senses of “conceivable” and fix upon more and less promising candidates. I will relate our own discussion to some of these distinctions, often in footnotes.
- 2.
Many thanks to the editors for their constructive remarks, particularly regarding the overall focus of the present paper. Thanks to Rachael Briggs, Wesley Holliday and Krista Lawlor for reading a draft of this paper, and offering useful comments. Thanks to Robert Bassett, J.T. Chipman, Huw Duffy, Michael Fitzpatrick and Krzysztof Mierzewski for their observations in response to an early version of these ideas, which led to significant improvements.
- 3.
- 4.
See Kung (2011) for an argument against Cartesian skepticism from the perspective of modal empiricism.
- 5.
cf. Sturgeon (2010, sect. 3).
- 6.
It is not uncommon for authors to equate “metaphysical possibility” with “logical possibility” or “conceptual possibility”. As we discuss momentarily, I believe it is a dubious claim that mere “logical possibility” (i.e. mere logical consistency) guarantees that a set of sentences represent a possibility, and likewise for “conceptual possibility”. I do agree that every real possibility can be associated with a logically consistent and conceptually coherent description.
- 7.
I will characterize “conceptual possibility” more carefully in Sect. 15.9, allowing us to no longer assume this claim, but take it as a matter of definition.
- 8.
It is tempting, in the context of philosophical theorizing, to try to argue on substantive grounds that conceptual possibilities and real possibilities can be identified in some sense, in an effort to alleviate any mystery concerning what the latter are, and how it is possible to know anything about them. Nevertheless, the issues are delicate, and any such identification cannot proceed without careful qualification. For instance, a two-dimensionalist (in roughly the spirit of Chalmers 2002) might hold that ideal primary conceivability can be identified with primary possibility. In a similar vein, one might claim that a conceptual possibility given in purely qualitative terms can always be identified with a metaphysical possibility.
- 9.
Indeed, this claim is plausibly a paradigm instance of the breakdown between conceivability and possibility, since it is plausible that “all emeralds are (naturally) green” is an a posteriori necessity (or, at least, this becomes clear when we properly unpack the import of inductive reasoning).
- 10.
Our sense of the term “conceivable” may thus be taken, by a two-dimensionalist, to match that of “primarily, negatively conceivable” in Chalmers (2002). At this point, I deliberately leave our usage ambiguous between “ideal conceivability” and “prima facie conceivability”.
- 11.
As the reader has noted, throughout this essay I make use of a formal language to state formalizations of important principles and arguments. Since I freely incorporate \(\diamond \varphi\) expressions in such statements, this formal language is not to be confused with the language \(\mathcal{L}\) described above.
- 12.
We assume here that sentences can be evaluated for truth relative to possible worlds i.e. ways things could be. Note that there is a natural sense in which a sentence φ can be said to be “true” relative to a story s: namely, φ ∈ s.
- 13.
Of course, if every true necessity claim were established by a cognitively ideal agent, and that agent has a principled way of establishing that this is so (i.e. that her methods for determining necessity are exhaustive) then that agent is in a position to deduce every true possibility claim. In this case, what needs to be added to the agent’s repertoire, beyond techniques for determining necessity, is a means for determining what counts as an exhaustive set of methods for determining necessity. That the method of constructing a particular story that verifies φ is a more promising candidate (for our primary method for establishing possibility claims) rests, I think, on two observations: (i) this last method seems to better reflect our actual practice of appealing to imagined scenarios to justify possibility claims, and (ii) it is decidedly non-obvious how one might establish that a set of necessity-determining techniques is exhaustive.
- 14.
Notice that our particular usage in this essay of the term “conceivable” makes it plausible that the ideal C-P principle captures the spirit of modal rationalism in sufficient generality. For observe that the ideal C-P principle, by our lights, is equivalent to: if φ is necessary then it follows that φ is knowable a priori.
- 15.
The distinction between the ideal C-P principle and practical C-P principle is closely related to the distinction between ideal and prima facie conceivability introduced by Chalmers (2002).
- 16.
See Hanrahan (2009) for a careful discussion of the implications for modal rationalism of the practical incompleteness of the stories we can construct.
- 17.
- 18.
See Sturgeon (2010) for a careful and comprehensive evolution of positions one might take on in response to Kripkean considerations.
- 19.
- 20.
Compare Yablo’s discussion of undecidable claims in Yablo (1993, sect. XI).
- 21.
This dilemma is a generalization of that which I present for van Inwagen in Hawke (2011).
- 22.
For further discussion of the tension between conceivability techniques and de re possibility knowledge, see Roca-Royes (2011).
- 23.
That I ignored the subtleties involved with the question of combination represents a lacuna in my presentation of the safe explanation theory in Hawke (2011), one I hopefully begin to fill here.
- 24.
cf. Hawke (2011, Sect. V) and the chapter by Sonia Roca-Royes in the present volume.
- 25.
- 26.
A principle of recombination has found support in the literature, notably by David Lewis (1986, pp. 86–92) and David Armstrong (1989), though they understand the principle foremost along metaphysical lines. Of the principles of recombination I list, modest recombination is closest in statement to the principles that Lewis and Armstrong endorse, though the details of their accounts results in their versions of the principle having more elaborate consequences than I would be prepared to endorse. Lewis’ inspiration is Hume’s denial of necessary connections between distinct existences, while Armstrong’s inspiration traces to Wittgenstein’s Tractatus.
- 27.
Here is another, perhaps tempting, explanation of the coffee case. Though it is consistent with my empirical information that aliens have replaced my coffee, I can conclude on inductive grounds that this is not so: for it has never been my experience in the past that my coffee has mysteriously been replaced with another liquid before I have had a chance to drink it. Given the main contentions of the current paper – that simple enumeration is a special case of the kind of “possibility reasoning” I use to explain the case in the main text – it comes as no surprise that inductive reasoning comes to mind when considering the example. At any rate, the example is easily altered so as to be immune to an explanation via induction: consider instead the alternative that my coffee has been replaced by aliens (via teleportation), who will then (to avoid giving the game away) replace this second liquid with coffee before it reaches my lips. Simple enumeration cannot – in any straightforward way – rationalize the rejection of this alternative. For my empirical information did not verify that such a double-replacement did not occur during my past experiences of drinking coffee.
- 28.
Support for our argument against Humean skepticism (understood broadly) does not, in fact, require that the modal empiricist accept exactly the possibility-based RA principle. Suppose, for instance, that our empiricist accepts the need for an RA approach to rational belief, but is sufficiently impressed by the Goldman-Ginet barn cases in Goldman (1976) that they decide that the most plausible RA principle is the following: B φ if and only if (i) S has evidence that rules out every alternative ψ to φ such that S is reasonable to believe that ψ is a nearby possibility and (ii) S’s evidence supports that φ is a nearby possibility. Now, suppose that P1 is true – our empiricist reasonably believes that green emeralds are really possible – and that P2 is true – our empiricist does not reasonably believe that yellow are emeralds are really possible. Now, note that (plausibly) the empirical support for P1 amounts to support for a stronger claim: that our empiricist reasonably believes that there are green emeralds. It follows, by a version of the actuality principle, that she reasonably believes that green emeralds are a nearby possibility. Further, it follows from P2 that she does not reasonably believe, in particular, that yellow emeralds are a nearby possibility. Hence, our empiricist’s RA principle delivers the desired result: it is not reasonable for her to believe that there are yellow emeralds.
- 29.
Not only cursory, but patently inadequate without a fuller dialectic: the views under consideration have been developed in rich and sophisticated ways by the cited authors, and are not to be dismissed off-hand.
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Appendix 1: Hume’s Problem Is Live
Appendix 1: Hume’s Problem Is Live
I briefly address the concern that the project of replying to Hume’s problem has run its course, drawing out, in particular, some considerations that point in the direction of a solution along the lines of that in the current paper. This concern arises by accepting one of the following: (i) there is little reason to think that we actually use enumerative induction in ordinary or scientific contexts; (ii) enumerative induction is a narrow and potentially misleading special case of a broader inference method such as statistical induction or abduction; or (iii) the problem of accounting for enumerative induction has effectively already been solved.
In reply to (i): I believe that enumerative induction plays such a basic role in everyday and scientific reasoning that it is easily overlooked. I reasonably expect that when I place my coffee mug on this table that the mug will not pass through the surface of the table and smash to the floor. This belief, it seems, is not the product of, say, acceptance of a certain theory of the physics of tables and mugs. My grounds are simpler: I have had ample experience in interacting with like objects and project these lessons to future interactions. Further, we can borrow from Norton a prototypical scientific belief that is naturally ascribed to enumerative induction: “we believe all electrons have a charge of − 1. 6 × 10−19 Coulombs, simply because all electrons measured so far carry this charge” (Norton 2005, pg.12).
In reply to (ii): I delay discussion of the possibility that enumerative induction can be folded into abduction and concentrate on the exceedingly plausible claim that enumerative induction is a special case of statistical induction (or perhaps just superseded by it). Statistical reasoning has reached a level of sophistication that suggests that undue attention to universal inference might be misleading or limiting. What justifies a focus on simple enumeration?
In response, I suggest the simpler setting of universal inference brings into focus an aspect of the problem of induction that is commonly overlooked – not least in technically sophisticated discussions focused on statistics.
To illustrate: suppose we embark on a study of the color features of the actual population of emeralds. Before gathering data, we agree (for whatever reason) to take seriously three possible candidate colors: green, yellow and mauve. As it happens, we then observe a random sample of emeralds with these color-types distributed in a 70-30-0 ratio. Statistical induction directs us to project this make-up onto the entire population of emeralds, and we draw our conclusions accordingly. Altogether, our investigative methods raise two obvious questions, though the first receives less attention: what, if anything, justifies our treating green, yellow and mauve as comprising the complete set of possible candidate colors? (In particular, in retrospect, was it sensible to include mauve as a possibility to be ruled out? If so, what justified limiting ourselves to only these three colors?) And, secondly, given a set of possible candidates, what justifies projection from a sample to the whole population? (In particular, did we select enough emeralds for our sample, and use a suitable selection technique? How confident should we be in our conclusion, given the size of our sample? Should we reserve some credence for the hypothesis that some mauve emeralds are lurking out there?)
A focus on enumerative induction simplifies the statistical issues and allows us to focus better on the first, neglected question. Indeed, as should become apparent, the response to Humean skepticism I propose in this paper depends on a view as to how best to answer the first question, not the second.
In reply to (iii): ingenuity aside, there is room to feel dissatisfied with the existing major proposals for dealing with Humean skepticism. I cannot back this claim comprehensively here, so offer only cursory worries for a few promising and influential recent proposals.Footnote 29
Some propose that enumerative induction is a special case of abductive reasoning. According to the abductivist: the reason to believe that all emeralds are green – given an uninterrupted parade of observed green emeralds – is that this fact, if true, would best explain the observational data (Harman 1965). One reason to hesitate to embrace this proposal is skepticism that a happy outcome is likely for the debate concerning the nature of explanation and good explanation (van Fraassen 1989, pp. 142–148). However, even for those optimistic about securing the foundations of abduction (such as myself) there is room to doubt that abduction is the antidote to Humean skepticism. A good explanation, it is natural to presume, is one that, in some sense, generates understanding. But it is hard to see how the truth of “all emeralds are green” can by itself generate understanding as to why the emeralds I have observed are green. “All emeralds are green” entails that every emerald I observe is green, but fails to locate this fact in an “illuminating story” involving diverse (and possibly more primitive) facts, laws or entities. Or perhaps the abductivist’s claim is that we first use abduction to infer that the underlying causal-structural constitution of an emerald necessitates a green hue, then from this intermediate conclusion infer that all emeralds are green. But if an explanation citing necessitating constitutive facts is fleshed out as a detailed proposal, then it is no longer plausible that the proposed abduction captures the simplicity of enumerative induction; and if the details are left unspecified then we are again left with the question as to whether this “explanation” has genuine explanatory power. Further, the abductivist approach to enumerative induction highlights peculiar mysteries that might seem no better than (or are perhaps equivalent to) the problem of induction. For instance, if simplicity and explantory scope are offered as reasons to accept the hypothesis that all emeralds are green, then this merely provokes the question as to why these factors ought to be taken as a mark of truth.
Next consider the proposal that enumerative induction is simply a matter of subjective Bayesian inference. By subjective Bayesian lights, a rational agent is one whose degrees of belief (credences) take the form of a probability function, and who updates her beliefs by way of Bayesian conditionalization. The Bayesian may then cite a famous result due to De Finetti (1937): in the long run, so long as the agent’s prior credence function satisfies certain symmetry properties (namely, the property of exchangeability), a Bayesian agent’s credence function will eventually come to reflect the frequency information captured in the stream of her observational data. That is: if green emeralds occur with a 100 % frequency in the observations she collects, she will converge to a credence of 1 with respect to the hypothesis that all emeralds are green – essentially capturing the mechanism of enumerative induction. But this proposal again leaves room for reasonable doubt (Earman 1992). The subjective Bayesian does not typically offer reasons to think that a rational agent must have an exchangeable credence function. Nor does the typical subjective Bayesian offer much to guarantee an efficient rate of convergence to inductive conclusions. Yet, intuitively, enumerative induction is a highly efficient form of reasoning. To reasonably conclude that all electrons have a charge of − 1. 6 × 10−19 Coulombs does not, it seems, require excessive individual measurements.
Finally, consider the proposal of the formal learning theorist (Kelly 1996): there is no guarantee that the method of enumerative induction arrives at a true conclusion in the short term, but in a certain sense it is guaranteed to hit upon the truth in the long term, thereby rendering it a rational strategy for belief acceptance. For either there are only green emeralds, and so the conclusion “all emeralds are green” is true; or, if indeed there is a yellow emerald out there – and one is guaranteed to eventually observe this fact – then eventually one will come to modify one’s incorrect belief. The difficulty with this proposal is, however, two-fold. First, for ordinary agents, it is unlikely that their investigation will be so thorough as to guarantee that, if there is an exception to a universal claim, it will eventually be observed. Second, that it is in the long-run strategic to accept a certain claim does not by itself make it likely that claim is true (as the formal learning theorist admits). So it is left somewhat mysterious for the formal learning theorist why an agent should believe the conclusion of a universal inference, as opposed to merely accept it for strategic purposes.
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Hawke, P. (2017). Can Modal Skepticism Defeat Humean Skepticism?. In: Fischer, B., Leon, F. (eds) Modal Epistemology After Rationalism. Synthese Library, vol 378. Springer, Cham. https://doi.org/10.1007/978-3-319-44309-6_15
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