Abstract
The coherence of omniscience is sometimes challenged using self-referential sentences like, “No omniscient entity knows that which this very sentence expresses,” which suggest that there are truths which no omniscient entity knows. In this paper, I consider two strategies for addressing these challenges: The Common Strategy, which dismisses such self-referential sentences as meaningless, and The Conciliatory Strategy, which discounts them as quirky outliers with no impact on one’s status as being omniscient. I argue that neither strategy succeeds. The Common Strategy fails because it is both unmotivated and impotent. The Conciliatory Strategy fails because it leads to embarrassing situations in which omniscient entities are epistemically inferior to non-omniscient entities: we can, for example, devise trivia-based drinking games that force omniscient entities into an intoxicated state; and, given plausible closure principles for belief, such entities are unable to have the sorts of beliefs that give them reason to refuse to play (e.g., they are unable to believe that they can lose the game).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
Note that Milne does not straightforwardly challenge the coherence of omniscience using this sentence; rather, he uses it to argue that all omniscient entities are dialetheists. Nevertheless, his result is tangential to my present concern. Milne’s conclusion is substantive only if dialetheism is correct, and the views discussed herein presuppose classical logic. For a discussion of omni-properties within non-classical frameworks, such as dialetheism, see Cotnoir (2017) as well as Beall and Cotnoir (2017).
Swinburne (1977) and Abbruzzese (1997) are among those who say this. Jago (2018, pp. 315–316), by contrast, says that the Liar is meaningful, but nevertheless agrees that the Liar fails to express a proposition. I doubt that there is much dispute between them. They are working with different understandings of ‘meaningful’: for Jago, a sentence is meaningful only if its lexical components are meaningful and are appropriately structured; for Swinburne and Abbruzzese a sentence is meaningful only if it expresses something that is comprehensible. Here I use the latter understanding.
For theory to count these sentences as pathological is a defect rather than a benefit. Roy Cook (2002), for example, uses a sequence of sentences that resembles the Honest Disjunction to argue against Anil Gupta and Nuel Belnap’s (1993) Revision Theory of Truth on the grounds that it counts the sequence as pathological and is therefore infidelitous to the ordinary notion of truth that they aim to analyze.
What I take to be trivial, Murzi and Rossi (2018, p. 12) take to be false. Adopting a contextualist theory of truth, they replace (on p. 8) this principle with, ‘if φ is valid in a context c, then φ expresses a true proposition in context c1’ where c ≠ c1. I do not dispute their replacement. But, for two reasons, I cannot reject the principle it is meant to replace. First, I take deduction to be truth-preserving: insofar as propositions are the primary bearers of truth values, the value, true, cannot be preserved from one claim to another unless the latter expresses a proposition. And, second, rejecting Deducing-the-Deducible runs afoul classical logic: from its rejection, the conjunction, φ & ψ follows, where φ expresses no proposition; but, in a classical setting, conjunction is a truth-function, that is, φ & ψ has the value true only if φ is assigned the value, true. Taking classical logic for granted, as I do here, Deducing-the-Deducible is therefore trivial.
I borrow the label, “revenge argument” from the literature on alethic paradoxes (e.g., Beall 2007); it designates a class of arguments which reason from an alleged solution to a paradox to a new paradox that is similar to the one allegedly solved. Those who propose to solve the classic Liar, “this sentence is false,” by evaluating it as being neither true nor false, for example, face the revenge paradox, “this sentence is not true.”.
Bacon (2015) discusses these sorts of revenge paradoxes with respect to theories of truth.
We could, of course, invent theories of truth and of propositions according to which omniscience is part of their nature. We might, for example, take omniscience to be primitive and then define ‘proposition’ and ‘truth’ in terms of it: p is a proposition just in case p, or its negation, is known by an omniscient entity; p is true just in case it is known by an omniscient entity. But we must be wary of our inventions. By enslaving our logic to a metaphysics of propositions that delivers to us only the propositions we want, we can reject the existence of any proposition we find unfavorable, and, in doing so, invalidate any deductive argument raised against our beliefs despite that it conforms to rules of inference that we otherwise accept. To preserve the use of logic in rational mediation, it must be emancipated from any metaphysical theory that is not justified on independent grounds. At this time, I know of no way to justify an omniscience-based theory of proposition, or of truth, on behalf of the friend of omniscience.
They might also make this suggestion with respect to the original challenges posed by Grim’s and Milne’s sentences. As such, one might treat the charge of equivocation as an alternative strategy—call it, the contextualist strategy—for addressing those challenges. I do not treat it in this way because, in what follows, I argue that the suggestion either fails with respect to the revenge argument—and so, treating it as an alternative strategy is superfluous—or it collapses into The Conciliatory Strategy to be discussed in the next section.
For a simpler example, consider the sentence-type, “I sit upon a golden throne.” The proposition expressed by its tokens varies across contexts. But, by replacing ‘I’ with a rigidified counterpart which packs the context into the content—such as ‘I-in-c’ where c is a context in which Donald Trump is the speaker—the proposition expressed by ‘I-in-c sits upon a golden throne’ no longer varies across contexts.
The technical details of such a hierarchy can be developed in various ways, as seen in the work of Tarski (1936), Parsons (1974), Kripke (1975), Burge (1979, 1984), Anderson (1983), Barwise and Etchemendy (1989), Gaifman (1992), Koons (1992), Glanzberg (2001, 2004, 2015), and Murzi and Rossi (2018), to name only a few. Although Gaifman’s (1992) account involves an algorithmic evaluation procedure instead of a semantic hierarchy, Koons (1992) shows how to integrate it into a hierarchical approach.
Anderson (1983, p. 355) is among the friends who suggests this sort of response.
Contextualists typically make their hierarchy indefinitely extensible, which motivates the impossibility of absolutely unrestricted quantification over contexts. (Burge 1979, p. 192; Glanzberg 2001, p. 240; Rayo and Uzquiano 2006) Whether this motivation succeeds is controversial (see Gauker 2006; Grim 1988; Parsons 1974; c.f. Glanzberg 2015; Williamson 1998).
As far as I know, Grim (1990) is the only one to have considered it. Letting S be the set of all non-quirky truths known by omniscient entities, he argues that every member of S’s powerset corresponds to a non-quirky truth—e.g., that it is a member of that powerset—and so, by Cantor’s theorem, there are more non-quirky truths than there are members of S; thus, Grim concludes, there are non-quirky truths that no omniscient entity knows. His conclusion strikes me as hasty. Friends of omniscience can simply reinterpret his argument as a reductio against S’s existence; all Grim has shown, they can say, is that the knowledge possessed by an omniscient entity is among those things that, like the ordinals, cannot be collected into a set.
In this respect, The Conciliatory Strategy is analogous to theories of truth which restrict the T-schema to non-pathological, or “healthy,” cases: Healthy(φ) → (True(φ) ↔ φ). (Bacon 2015; Horwich 1998; Murzi and Rossi 2018; Williamson 1998). The main difference between The Conciliatory Strategy and these theories is that “unhealthy” cases are those for which an evaluation of truth-value leads to either contradiction or undecidability, whereas “quirky” cases like Milne’s are evaluated as being true upon pain of contradiction.
This formulation of omniscience is comparable, albeit not identical, to that given by Swinburne (1977) and Bringsjord (1989, p. 188), and to that mentioned by van Inwagen (2006; 2008). Despite the differences between (α) and their respective formulations, it is hard to see how they might reject it: letting x be their preferred omniscient entity, if (α) is false, it follows that there is a non-quirky sentence such that either (i) it expresses a truth that is knowable to someone or other but x does not know it, or (ii) x knows that it is expresses a truth, but that truth is not knowable to anyone; neither option is acceptable on their respective views. To resist The Conciliatory Strategy, then, these friends of omniscience must deny that anyone can come to know the truth of quirky sentences, despite that we can straightforwardly deduce some of them without self-defeat.
Although omniscience is classically characterized as knowledge of all truths, rather than knowledge of all that is knowable to someone or other, the conciliatory variants of these characterizations—viz. omniscience is knowledge of all non-quirky truths and (α), respectively—are materially equivalent given two assumptions made by conciliatory friends of omniscience: first, that the only truths that are neither known nor knowable to omniscient entities are those excluded by the quantifier-restriction—i.e., the quirky cases—and, second, that an omniscient entity’s knowing that P implies that P is knowable to someone or other.
Note that (β) is not merely an epistemic variant of Curry’s (1942) paradox, despite the apparent resemblance. To get anything near paradox, (β) would designate something like, “if 1 = 1, then it is not the case that this sentence is known to someone or other,” for then someone or other could deduce its truth, and assuming that its deduction suffices for knowledge of it, we then arrive at the paradox that 1 ≠ 1. But even this is hardly a paradox. Its solution is simple: deducing the epistemic Curry-sentence does not suffice for knowledge of it, upon pain of paradoxical self-defeat; so, the absurd result that 1 ≠ 1 cannot be deduced.
The alleged banality of (Ω) might be resisted on the grounds that deducing (β)’s truth requires the assumption that (β) is truth-evaluable, which, it might be argued, is too controversial to know because of its apparent similarity to the Liar Paradox. But, recall from Sect. 2, Milne-like sentences more closely resemble innocuous cases of self-reference than they do the Liar. As such, our ability to deduce (β)’s truth, without paradoxical defeat, strikes me as strong evidence for the claim that (β) is truth-evaluable—so strong that if it turns out that (β) really is truth-evaluable, as The Conciliatory Strategy concedes, then at least some of us know it to be so. In this respect, it is no more similar to the Liar than the innocuous “if all sentences are true, then this sentence is true”, of which only the most recalcitrant would claim ignorance.
Analogues of Knowing-the-Knowable involving knowledge of what is the case can fail (e.g., you might know that I know what I had for breakfast, while remaining ignorant of exactly what that was); so too can analogues involving knowledge of why something is the case (e.g., you might know that I know why I chose a particular breakfast option, while remaining ignorant of exactly why I chose it) and even analogues involving knowledge that something is the case can fail when the object of knowledge is obfuscated by a name, demonstrative, or description (e.g., you might know that I know the first proposition I came to know, without knowing that proposition yourself)..
The idea that we can gain philosophical insight by conceiving of games played against omniscient entities is well-known. We see it in R. Lance Factor’s (1978) variant of Newcomb’s puzzle, as well as in Steven Brams’ (1983, 2018) use of game-theory to draw lessons about the rationality of belief in superior beings.
We might have used (β) in place of (Ω) in Rule 2 to achieve the same result. I use (Ω) to emphasize that there are a variety of ways to construct omniscience-defeating games.
The difficulty might be due to one’s theological commitments, which make the game ethically or practically inconceivable. If one thinks that intoxication is unethical, for example, then a theological pairing of omniscience with omnibenevolence might preempt one’s ability to conceive of omniscient entities playing it; and if one’s theology takes those entities to be incorporeal, making them incapable of becoming intoxicated, then the stakes of our game might be thought to rest on a category mistake. But none of this undermines any argument given herein. Since theological commitments are not themselves conceptually necessary, the “inconceivability” of our game on such grounds is more like a refusal to conceive than a genuine impossibility to conceive. The game, after all, plays out just as well with a fun-loving genie as our would-be omniscient entity. And, albeit less fun, the stakes can be altered to align with a teetotaling conceptual scheme: stakes that nonetheless lead to embarrassment—or some other unwelcome outcome—but which avoid the concern that intoxicated omniscient entities are inconceivable because of their ethical and incorporeal natures.
It is this feature that differentiates our trivia game from other games in which omniscient players are disadvantaged, such as Steven Brams’ (1983, pp. 69–89; 2018, pp. 69–72) games of “chicken.” In such games, Brams observes, omniscient players, qua omniscient, are compelled to yield whenever their opponent refuses to yield, thereby guaranteeing their loss. But omniscient players are aware of this; and so, every conceivable circumstance in which they would lose (i.e., yield) is a circumstance in which they would have a good reason to refuse to play Bram’s game.
I take for granted that, for omniscient entities, belief is closed under known entailment: if Kx(⋄Lose(x) → Quirky(Ω)) and Bx(⋄Lose(x)), then Bx(Quirky(Ω)), where ‘Kx’ and ‘Bx’ designate x knows that and x believes that, respectively, and ‘Quirky’ designates is a quirky truth knowable only to others. Although this regimentation of the inference presumes that ‘⋄’ picks out an alethic modality, this is no reason to object to it. The same result can be obtained, albeit less straightforwardly, if one instead interprets ‘⋄x’ epistemically as, “for all x knows, it might be that…” and alters that conditional to read, “the entity knows that, as far as it knows it might lose only if as far as it knows it might be that (Ω) is a quirky truth knowable only to others”. Formally, the inference looks like: Kx(⋄xLose(x) → ⋄xQuirky(Ω)), Bx(⋄xLose(x)); thus, Bx(⋄xQuirky(Ω)). To obtain the result that the entity believes that (Ω) is quirky, i.e., Bx(Quirky(Ω)), we simply acknowledge that the entity is aware that the only cases which might, for all it knows, be quirky in fact really are quirky—i.e., Kx(⋄xQuirky(p) → Quirky(p))—and it must be aware of this since it knows the contrapositive: for every non-quirky truth, the entity knows that it is true, and since the entity’s knowing that it is true is itself non-quirky, the entity therefore knows that it is not a quirky truth knowable only to others.
The entity might, for example, refuse to play on the grounds that it believes that it is possible that it could lose. But, for it to refuse on these grounds requires that the entity believes that the relevant sense of “possibility” fails to satisfy S4 (i.e., ⋄⋄P → ⋄P): otherwise, the omniscient entity would believe that it could lose, which, as we now know, is not a belief the entity is able to have. And, without S4, the grounds are too weak to justify the claim that the entity’s refusal is conceptually necessary: to answer the question, “Are you refusing because you might lose?” with “Not at all! I refuse because it is possible that I might lose" would baffle the questioner and should not be taken to be a sensible enough reason for the entity to refuse to play in all conceivable circumstances.
Brams (1983, pp. 9–10, 2018, p. 9) suggests that a dismissive attitude towards these games could be justified by conceiving of superior beings as having natures so vastly different from ours that they are simply incapable of playing: they might, for example, lack the requisite features for reporting to us what they know. Although I, like Brams, concede that such a conception is possible, it is so far removed from the classical conception of omniscience that it strikes me as being irrelevant to the present discussion.
Note that this problem of epistemic inferiority extends to non-classical conceptions of omniscience as well. Consider a conception of omniscience which restricts omniscience to knowledge of the fundamental truths, truth-makers, or facts which ground the non-fundamental truths; or a conception like Abbruzzese’s (1997), which takes omniscience to consist in knowing a proposition which entails all others. If these conceptions validate a closure principle for knowledge, then they are equivalent to the classical conception and hence succumb to the foe’s case summarized above. And, if they do not validate it, then epistemic inferiority bites back with a vengeance: such entities might not know that I have two thumbs, despite that they know a proposition, truth-maker, or fundamental truth which entails it.
References
Abbruzzese, J. E. (1997). The coherence of omniscience: A defense. International Journal for Philosophy of Religion, 41(1), 25–34. https://doi.org/10.1023/a:1002973432493.
Anderson, C. A. (1983). The paradox of the knower. Journal of Philosophy, 80(6), 338–355.
Bacon, A. (2015). Can the classical logician avoid the revenge paradoxes? Philosophical Review, 124(3), 299–352. https://doi.org/10.1215/00318108-2895327.
Barwise, J., & Etchemendy, J. (1989). The liar: An essay on truth and circularity. New York: Oxford University Press.
Beall, J. C. (Ed.). (2007). Revenge of the liar: New essays on the paradox. New York: Oxford University Press.
Beall, J., & Cotnoir, A. J. (2017). God of the gaps: A neglected reply to God’s stone problem. Analysis, 77(4), 681–689. https://doi.org/10.1093/analys/anx069.
Brams, S. (1983). Superior beings: If they exist, how would we know?. New York: Springer.
Brams, S. J. (2018). Divine games: Game theory and the undecidability of a superior being. The MIT Press. https://doi.org/10.7551/mitpress/11683.001.0001.
Bringsjord, S. (1989). Grim on logic and omniscience. Analysis, 49(4), 186–189. https://doi.org/10.1093/analys/49.4.186.
Burge, T. (1979). Semantical paradox. Journal of Philosophy, 76(4), 169–198.
Burge, T. (1984). Epistemic paradox. Journal of Philosophy, 81(1), 5–29.
Cook, R. T. (2002). Counterintuitive consequences of the Revision Theory of Truth. Analysis, 62(1), 16–22. https://doi.org/10.1093/analys/62.1.16.
Cotnoir, A. J. (2017). Theism and dialethism. Australasian Journal of Philosophy, 96(3), 592–609. https://doi.org/10.1080/00048402.2017.1384846.
Curry, H. B. (1942). The inconsistency of certain formal logic. Journal of Symbolic Logic, 7(3), 115–117.
Factor, R. L. (1978). Newcomb’s paradox and omniscience. International Journal for Philosophy of Religion, 9(1), 30–40. https://doi.org/10.1007/BF00138728.
Gaifman, H. (1992). Pointers to truth. The Journal of Philosophy, 89(5), 223–261. https://doi.org/10.2307/2027167.
Gauker, C. (2006). Against stepping back: A critique of contextualist approaches to the semantic paradoxes. Journal of Philosophical Logic, 35(4), 393–422.
Glanzberg, M. (2001). The liar in context. Philosophical Studies, 103(3), 217–251. https://doi.org/10.1023/A:1010314719817.
Glanzberg, M. (2004). A contextual-hierarchical approach to truth and the liar paradox. Journal of Philosophical Logic, 33(1), 27–88. https://doi.org/10.1023/B:LOGI.0000019227.09236.f5.
Glanzberg, M. (2015). Complexity and hierarchy in truth predicates. In K. Fujimoto, J. Martínez Fernández, H. Galinon, & T. Achourioti (Eds.), Unifying the Philosophy of Truth. Berlin: Springer.
Grim, P. (1983). Some neglected problems of omniscience. American Philosophical Quarterly, 20(3), 265–276.
Grim, P. (1988). Truth, omniscience, and the knower. Philosophical Studies: An International Journal for Philosophy in the Analytic Tradition, 54(1), 9–41.
Grim, P. (1990). On omniscience and a “set of all truths”: A reply to Bringsjord. Analysis, 50(4), 271–276.
Grim, P. (2000). The being that knew too much. International Journal for Philosophy of Religion, 47(3), 141–154.
Gupta, A., & Belnap, N. (1993). The Revision Theory of Truth (Vol. 56). London: The MIT Press.
Horwich, P. (1998). Truth. Clarendon: Clarendon Press.
Jago, M. (2018). What truth is. Oxford: Oxford University Press.
Koons, R. C. (1992). Paradoxes of belief and strategic rationality. Cambridge: Cambridge University Press.
Kripke, S. A. (1975). Outline of a theory of truth. Journal of Philosophy, 72(19), 690–716.
Milne, P. (2007). Omniscient beings are dialetheists. Analysis, 67(3), 250–251. https://doi.org/10.1093/analys/67.3.250.
Murzi, J., & Rossi, L. (2018). Reflection principles and the liar in context. Philosophers’ Imprint, 18, 1.
Parsons, C. (1974). The liar paradox. Journal of Philosophical Logic, 3(4), 381–412.
Rayo, A., & Uzquiano, G. (Eds.). (2006). Absolute generality. New York: Oxford University Press.
Swinburne, R. (1977). The coherence of theism. Oxford: Oxford University Press.
Tarski, Alfred. (1936). The concept of truth in formalized languages. In A. Tarski (Ed.), Logic, Semantics, Metamathematics (pp. 152–278). Oxford: Oxford University Press.
van Inwagen, P. (2006). The problem of evil: The Gifford Lectures delivered in the University of St Andrews. Oxford: Oxford University Press.
van Inwagen, P. (2008). What does an omniscient being know about the future? In J. L. Kvanvig (Ed.), Oxford Studies in Philosophy of Religion (Vol. 1, pp. 216–230). Oxford: Oxford University Press.
Williamson, T. (1998). Indefinite extensibility. Grazer Philosophische Studien, 55, 1–24. https://doi.org/10.5840/gps19985512.
Acknowledgements
I thank Bernard Kobes, Steven Reynolds and Jeffrey Watson for a series of helpful conversations, as well as an anonymous reviewer for their helpful suggestions.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
McElhoes, D. The intoxicating effects of conciliatory omniscience. Philos Stud 178, 2151–2167 (2021). https://doi.org/10.1007/s11098-020-01528-6
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11098-020-01528-6