Abstract
Epistemicists claim that if it is vague whether p, it is unknowable whether p. Some contest this on epistemic grounds: vague intuitions about vague matters need not fully preclude knowledge, if those intuitions are response-dependent in some special sense of enabling vague knowledge. This paper defends the epistemicist principle that vagueness entails ignorance against such objections. I argue that not only is response-dependence an implausible characterization of actual vague matters, its mere possibility poses no threat to epistemicism and is properly accounted for by the epistemicist’s own principles.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
Other authors defend variants of Unknown. Greenough (2003) defends the existential claim that any vague predicate must have some borderline case whose status is unknowable. Wright (2001) appears to suggest the weaker claim that if something were clearly borderline F, its status would be unknowable—only clear vagueness entails ignorance. Surprisingly, nowhere does Williamson (1994) defend any explicit principle articulating the epistemic consequences of vagueness, except perhaps: “an interpretation s admits an interpretation t just in case if s were correct then speakers of the language could not know t to be incorrect. On this view, ‘definitely’ means something like ‘knowably’. Just one interpretation is correct, but speakers of the language cannot know all others to be incorrect. Vagueness is an epistemic phenomenon.” (1994: p. 164) Although Williamson’s earlier (1992) does defend a version of Unknown using classical logic, neither the argument nor the principle reappear in his later (1994).
The modal analogue of vagueness, as absence of clarity, is contingency, or the absence of necessity (in either truth or falsity). Standard presentations opt instead for a determinately or definitely operator, in place of clearly.
And reasonably so: epistemicists already identify vagueness as a special sort (or source) of epistemic uncertainty, while assuming (relatively uncontroversially) a background KT epistemic logic. Williamson’s (1994: ch. 8) logic of clarity is KTB, while Bacon (2020) argues against the B(rouwerian) principle. The defense of epistemicism offered here is free of any commitment to the controversial B principle. Since my aim is to defend Unknown on broadly epistemicist grounds, I will assume the background logic is, Bivalence and Brouwerian aside, otherwise classical.
Barnett emphasizes the semantic role of intuitions for vague terms like ‘bald’, claiming these are “mundane: their meanings seem shallow, transparent, and without environmental content. There appears to be nothing more to their meanings than would be reflected by our community-wide patterns of intuitions—elicited in good epistemic conditions, after careful consideration—regarding their conditions of application” (2010: p. 25).
Following Barnett (2010: p. 41; see also §2 of “Vagueness and Rationality” (unpublished m.s.)), I shall set aside other variants of Ambivalence—perhaps closer to views found in Peirce (1902) and Schiffer (2003)—by which, for any s who considers vague p with relevant evidence, it both seems to s that p and seems to s that ¬p. Such a reading straightforwardly rules out Response-Dependence (since it p and ¬p cannot both be known, if both seem to be).
This is notably different from “response-dependence” in the sense of Johnston (1989) and Pettit (1991). Response-dependent conditions in their sense obtain just in case they seem to obtain under normal circumstances. Redness is allegedly response-dependent* (let us call it) in this sense insofar as: an object x is red if and only if for any subject s, if s is properly situated under normal viewing conditions with respect to x, then x looks red to s.
The two notions, though distinct, are related. Following Williamson (2000: p. 95), say a condition is luminous if it can be known to obtain whenever it obtains. Consider a subject s who is properly situated toward an object x under normal viewing conditions. Assume that looking red is luminous: (i) if x looks red to s, s can know that x looks red. Assume also that being red is response-dependent* and that s, upon careful reflection over the nature of redness as well as s’s own normal viewing conditions of x, is able to know this, so that s can know: (ii) if x looks red to s, x is red. It follows by KE that: (iii) if s can know that x looks red, s can know that x is red. Together (i) and (iii) yield the relevant response-dependence conditional: if x looks red to s, then s can know that x is red.
Such reasoning is unlikely to figure into any objection against Unknown, given that luminosity is objectionable on independent grounds (see Williamson, 2000: ch. 4). Let us therefore set aside the notion of response-dependence*.
Let p mean Danny Devito is bald and s be an ordinary subject familiar with Danny Devito’s looks. By Unknown, both response-dependence conditionals—If it seems to s that p then s can know that p and If it seems to s that ¬p then s can know that ¬p—have a false consequent. By Ambivalence, both antecedents are unclear in their truth-value. At least one of the conditionals will be untrue in some circumstance on any standard account of the indicative.
On non-bivalent treatments, both antecedents—It seems to s that ¬p and It seems to s that p—will either be indeterminate in truth-value (on a trivalent logic), have some intermediate truth-value (on a many-valued logic), or have no truth-value, i.e. no fixed truth-value across all admissible precisifications (on a supervaluationist logic). Thus both conditionals will themselves either be indeterminate in truth-value (on either a strong or weak Kleene trivalent logic), have intermediate truth-value (on a Łukasiewicz many-valued logic), lack truth-value (on a Fine-Kamp supervaluationist logic), or simply get evaluated as false (on a Gödel many-valued logic). See Łukasiewicz (1920), Kleene (1938), Gödel (1932), Fine (1975), Kamp (1975).
On a bivalent treatment, so long as one of the antecedents is true, the corresponding conditional will be false. This has to be so in some circumstances, assuming that both kinds of borderline-seemings exist—cases where it seems that p but only vaguely and cases where it seems that ¬p but only vaguely. It would be ad hoc otherwise to insist that in all cases of vague intuition, it neither seems that p nor seems that ¬p, so that both conditionals must be vacuously true (disregarding “falsehood-entailing” accounts, e.g. Raffman (2005), where any borderline F is not F).
Relevant evidence may include facts about his total hair situation (hair count, head shape, hair length, hair follicle distribution, hair thickness, etc.) and how these each or collectively contribute to his overall appearance (up close or afar). It may also include facts about overall use patterns for ‘bald’, such as actual linguistic behavior or general linguistic intuitions (individual speaker dispositions, observed assent/dissent patterns, normal or idiosyncratic speaker reactions to applying ‘bald’ in various cases—paradigm, borderline, unusual—expert consensus views, etc.).
For non-supervaluationist reasons, Barnett denies that clarity distributes over disjunction: \({\text{C}}\left( {p \vee q} \right)|/ = {\text{C}}p,{\text{C}}q\).
On standard non-bivalent treatments, supplying a true antecedent and indeterminate consequent for the relevant instance of Unknown—If it is vague whether Harry is bald*, it is unknowable whether Harry is/isn’t bald*—makes the entire conditional take either an indeterminate truth-value (on either a strong or weak Kleene logic), an intermediate truth-value (on either a Łukasiewicz or Gödel many-valued logic), or no (fixed) truth-value (on a Fine-Kamp supervaluationist logic). To truly falsify a conditional with a true antecedent requires a false consequent.
She can’t be clearly ignorant (C¬Kp), otherwise by clear response-dependence: C(Np → Kp), so C(¬Kp → ¬Np) by contraposition (within ‘C’ via K), so C¬Kp → C¬Np by K, therefore C¬Np—contrary to ambivalence (INp).
These of course needn’t be Williamson’s own (idiosyncratic) version of either knowledge safety or a use theory of meaning. Importantly, neither presupposes bivalence: even if use patterns for vague terms resulted in incomplete, non-bivalent extensions, the exact range of these partial extensions would still be unknowable, for the same reasons. See Williamson (1994: ch. 8) on “meaning instability”, (2000: ch. 5) on “safe”; Sainsbury (1997) on “easily possible”.
Barnett (2010: p. 27) hastily dismisses such considerations from Williamson for failing to be “theoretically neutral”.
The relevant instance of Unknown will then already be untrue on several standard non-bivalent logics (see n. 10), although Barnett (2010), who defends bivalence elsewhere (2009: §2.1), makes no such appeals. To refute the clear truth of the conditional presumably requires at minimum a clearly true antecedent and indeterminate consequent. (Formally: Any scenario verifying {Cp, Iq} suffices to falsify C(p → q), since the latter entails Cp → Cq by K.).
Here, an indeterminate antecedent and indeterminate consequent for the relevant instance of Unknown—If it is vague whether Harry is bald*, it is unknowable whether Harry is/isn’t bald*—do guarantee the entire conditional to be untrue on certain non-bivalent treatments (a strong or weak Kleene logic), but not others (a Łukasiewicz or Gödel many-valued logic or a supervaluationist logic). Yet Barnett offers no reason why {Ip, Iq} should falsify C(p → q). Indeed, the compatibility (he affirms) between vagueness and excluded middle means this cannot in general be true: {Ip} doesn’t falsify the excluded middle instance C(¬p ∨ p), nor therefore the latter’s classical equivalent C(p → p).
E = K theorists who deny this may substitute some knowledge-neutral notion (e.g. grounds) for “evidence”. Perhaps testimony from experts with more reliable intuitions qualifies as “non-trivial evidence” in this sense. Yet such testimonial transfer of knowledge is unlikely for Zenglish speakers, whose intuitions are perfectly in sync.
As detailed below, the disjunctive epistemic consequence (either IKp or ¬IKp) owes to the disjunctive nature of claims of vague vagueness (IIp), whereby either ¬C¬Cp or ¬C¬C¬p obtains, depending on “which side” of CIp the case falls on, i.e. if C¬p is clearly ruled out (C¬C¬p) or if Cp is clearly ruled out (C¬Cp), respectively.
Wright (2003) argues against treating vagueness as a kind of “third possibility” status precluding truth or falsity.
This asymmetry between denied and hedged epistemic claims favors Unknown while distinguishing it from similar but distinct principles such as Unclear: If it is vague whether p, it is vaguely unknowable that p.
Let p mean Danny Devito is bald and s be an ordinary subject familiar with Danny Devito’s looks who considers whether Devito is bald based on the available evidence under conducive conditions (e.g. reviewing the 80s Devito film canon, red carpet photos, etc.). By Unknown, both conditionals—If s can know that p then it seems to s that ¬p and If s can know that p then it seems to s that ¬p—have a false antecedent. By Ambivalence, both consequents are unclear in their truth-value. Thus both conditionals will be true, or at worst indeterminate in truth-value, on most standard accounts of the indicative.
On non-bivalent treatments, both consequents—It seems to s that p and It seems to s that ¬p—will either be indeterminate in truth-value (on a trivalent logic), have some intermediate truth-value (on a many-valued logic), or have no truth-value (on a supervaluationist logic). Thus both conditionals will themselves either be indeterminate in truth-value (on a weak Kleene trivalent logic) or simply be true in most other systems (on a strong Kleene logic, a Łukasiewicz many-valued logic, a Fine-Kamp supervaluationist logic, or a Gödel many-valued logic).
On a bivalent treatment, both conditionals will be true, no matter the truth-values of the consequents.
That is, our ambivalence in intuitions over vague matters p prevents us from clearly knowing whether p. Assume Grounds is clearly true for p, such that C(Kp → Np). Then CKp → CNp by K, or ¬CNp →¬CKp by contraposition, so INp →¬CKp by antecedent strengthening. (Note that the explanation makes no appeal to the (nonetheless equally derivable) results ¬Np →¬Kp (via T, contraposition) and C¬Np → C¬Kp (via K, contraposition) (see below)).
Given Unknown, Ip → (¬Kp&¬K¬p). Contraposing gets ¬(¬Kp &¬K¬p) →¬Ip, or (Kp∨K¬p) →¬Ip (via de Morgan, ¬¬-intro/elim). Antecedent strengthening gets Kp →¬Ip, or Kp →¬(¬Cp &¬C¬p). Yet Kp →¬C¬p (since Kp, C¬p are inconsistent via T, TE). Therefore Kp → Cp (via &-syllogism, ¬¬-elim). Assuming the clear truth of Unknown strengthens this to be C(Kp → Cp), from which it follows that CKp → CCp (via K). Given the clear truth of Known, from C(Cp →Kp), or CCp → CKp (via K), it follows that ¬Kp →¬Cp and ¬CKp →¬CCp. But these only state (clearly) necessary, not sufficient, conditions for when ¬Kp or ¬CKp obtains.
Formally: Any scenario verifying {Cp, C¬q} suffices to clearly falsify p → q, by verifying C¬(p → q). Pf. Given Cp & C¬q, we get C(p &¬q) (since ‘C’ distributes over C(φ → (ψ → (φ&ψ))) via K), or C¬(p →q) by definition.
On many standard non-bivalent treatments, an indeterminate antecedent and false consequent for the relevant instance of Unknown—If it is vague whether Harry is bald*, it is unknowable whether Harry is/isn’t bald*—will not be enough to falsify the entire conditional, but allow it to take either an indeterminate truth-value (on either a strong or weak Kleene logic), an intermediate truth-value (on a Łukasiewicz many-valued logic), or no (fixed) truth-value (on a supervaluationist logic). To truly falsify a conditional with a false consequent requires a true antecedent. (The exception is a Gödel many-valued logic, whereby any untrue (except equally false) antecedent will do.).
That is, given Unknown, {C(Kp∨K¬p), IKp, IK¬p} is inconsistent, even if {C(p∨¬p), Ip, I¬p} is consistent.
I owe this argument for the inconsistency of {C(Cp∨C¬p), ICp, IC¬p} to an anonymous referee.
Barnett (2009: §2.2) suggests this possibility might hold of actual vague matters. Surely, this is mistaken (see §2).
Indeed, Barnett (2009: §3.1) does just this, implicitly acknowledging Greenough’s (2003) proof of equivalence for epistemic borderlineness (a weaker version of Unknown; see n. 1) with epistemic tolerance (no knowable cutoffs). Note however that the standard characterization of vagueness in terms of borderline cases—a notion we here take for granted—while backed by longstanding tradition (see Dummett 1975, Wright 1975, Fine 1975, Kamp 1975), is not without its detractors (Fine 2015).
“All” that’s required, that is, on top of satisfying e.g. basic consistency conditions: If it were to seem to one that p/p then it wouldn’t seem to one that ¬p/p. Williamson’s (1994: ch. 8) account of knowledge requires that belief remain safe even under possible changes of meaning (affecting vague predicates). In that case, the requisite notions may all be reformulated metalinguistically. Zenglish speaker intuitions about ‘bald*’ then will be robustly reliable insofar as they verify If it were to seem to one that x does/doesn’t satisfy ‘bald*’ then x does/doesn’t satisfy ‘bald*’ and robustly consistent insofar as they verify If it were to seem to one that x does/doesn’t satisfy ‘bald*’ then it wouldn’t seem to him that x doesn’t/does satisfy ‘bald*’, but not robustly sensitive in the sense of verifying If x were/weren’t to satisfy ‘bald*’ then it would seem to one that x does/doesn’t satisfy ‘bald*’.
Assume Unknown and Response-Dependence are true for p. By Unknown, Ip → ¬(Kp &¬K¬p). By Response-Dependence, Np → Kp and N¬p → K¬p. Contraposing and combining, we get Ip → (¬Np &¬N¬p).
Barnett (2010: pp. 41–42) cautions against misreporting absences of any clear intuition as absences of any intuition. It appears the real conflation lies in misrepresenting any absence of intuition as a clear absence of intuition.
References
Bacon, A. (2020). Vagueness at every order. Proceedings of the Aristotelian Society, 120(2), 165–201.
Barnett, D. (2009). Is vagueness sui generis? Australasian Journal of Philosophy, 87, 5–34.
Barnett, D. (2010). Does vagueness exclude knowledge? Philosophy and Phenomenological Research, 82, 22–45.
Bobzien, S. (2010). Higher-order vagueness, radical unclarity, and absolute agnosticism. Philosophers’ Imprint, 10(10), 1–30.
Dummett, M. (1975). Wang’s paradox. Synthese, 30(3/4), 301–324.
Fine, K. (1975). Vagueness, truth, and logic. Synthese, 30, 265–300.
Fine, K. (2015). The possibility of vagueness. Synthese, 194(10), 3699–3725.
Greenough, P. (2003). Vagueness: A minimal theory. Mind, 112, 235–281.
Johnston, M. (1989). Dispositional theories of value. Proceedings of the Aristotelian Society, 63, 139–174.
Gödel, K. (1932). Zum intuitionistischen Aussagenkalkül (On the intuitionistic propositional calculus). Anzeiger der Akademie der Wissenschaften in Wien (Mathematisch-Naturwissenschaftliche Klasse), 69, 65–66. Reprinted in S. Feferman et al. (Eds.), Collected Works, vol. 1, Oxford: Oxford University Press, 1986, pp. 222–225.
Kamp, H. (1975). Two theories about adjectives. In E. Keenan (Ed.), Formal semantics of natural language (pp. 123–155). Cambridge University Press. Reprinted in K. von Heusinger & A. ter Meulen (Eds.), Meaning and the Dynamics of Interpretation: Selected Papers of Hans Kamp, Leiden: Brill, 2013, pp. 225–61.
Kleene, S. C. (1938). On notation for ordinal numbers. Journal of Symbolic Logic, 3(4), 150–155.
Łukasiewicz, J. (1920). O logice trójwartościowej (On three-valued logic). Ruch Filozoficzny, 5, 170–171. In L. Borkowski (ed.), Selected works. Amsterdam: North-Holland Publishing Company and Warsaw: PWN, 1970.
Peirce, C. S. (1902). Vague. In J. M. Baldwin (Ed.), Dictionary of philosophy and psychology (p. 748). MacMillan.
Pettit, P. (1991). Realism and response-dependence. Mind, 100(4), 587–626.
Raffman, D. (2005). Borderline cases and bivalence. The Philosophical Review, 114, 1–31.
Sainsbury, R. M. (1997). Easy possibilities. Philosophy and Phenomenological Research, 57(4), 907–919.
Schiffer, S. (2003). The things we mean. Oxford University Press.
Williamson, T. (1992). Vagueness and ignorance. Proceedings of the Aristotelian Society, 66, 145–177.
Williamson, T. (1994). Vagueness. Routledge.
Williamson, T. (1999). The structure of higher-order vagueness. Mind, 108(429), 127–143.
Williamson, T. (2000). Knowledge and its limits. Oxford University Press.
Wright, C. (1975). On the coherence of vague predicates. Synthese, 30(3/4), 325–365.
Wright, C. (2001). On being in a quandary. Mind, 110, 45–98.
Wright, C. (2003). Vagueness: A fifth column approach. In J. C. Beall (Ed.), Liars and heaps: New essays on the semantics of paradox (pp. 84–105). Oxford University Press.
Acknowledgements
I presented an earlier version of this paper to audiences in the UT Austin Philosophy Department including for the Cogburn Foundation Philosophical Prize. Special acknowledgments to the Wangs and the Grooms for their support.
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.
This article belongs to the topical collection on “Indeterminacy and Underdetermination”, edited by Mark Bowker and Maria Baghramian.
Rights and permissions
About this article
Cite this article
Hu, I. Epistemicism and response-dependence. Synthese 199, 9109–9131 (2021). https://doi.org/10.1007/s11229-021-03196-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11229-021-03196-3