Abstract
Epistemic two-dimensional semantics (E2D), advocated by Chalmers (2006a) and Jackson (1998), among others, aims to restore the link between necessity and a priority seemingly broken by Kripke (1972/1980), by showing how armchair access to semantic intensions provides a basis for knowledge of necessary a posteriori truths (among other modal claims). The most compelling objections to E2D are that, for one or other reason, the requisite intensions are not accessible from the armchair (see, e.g., Wilson 1982; Melnyk 2008). As we substantiate here, existing versions of E2D are indeed subject to such access-based objections. But, we moreover argue, the difficulty lies not with E2D but with the typically presupposed conceiving-based epistemology of intensions. Freed from that epistemology, and given the right alternative—one where inference to the best explanation (i.e., abduction) provides the operative guide to intensions—E2D can meet access-based objections, and fulfill its promise of restoring the desirable link between necessity and a priority. This result serves as a central application of Biggs and Wilson (2016), according to which abduction is an a priori mode of inference.
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Notes
On our use, E2D does not build in any specific epistemology of the intensions at issue; hence E2D is more general than either the related view that Chalmers (2006b) calls ‘two-dimensionalism’ or the more specific view that he calls ‘epistemic two-dimensionalism’, each of which build in conceiving as the preferred epistemology of intensions. We explain our terminology in more detail in footnote 9. Chalmers (2006b) identifies Jackson (1998, 2004), Braddon-Mitchell (2004), Lewis (1994), and Wong (1996) as fellow (conceiving-based) two-dimensionalists; others whom we take to advocate relevantly similar views include, e.g., Peacocke (1993), Boghossian (1996), Henderson and Horgan (2000, 2001), and Gertler (2002). Chalmers (2006b) cites his own earlier work and Chalmers and Jackson (2001) as advocating the more specific epistemic two-dimensionalism. Advocates of a two-dimensional semantic framework who don’t endorse any version of E2D include Stalnaker (1978, 1999), Kaplan (1979, 1989), and Davies and Humberstone (1981). See Chalmers (2004, 2006b, but especially 2006a) for discussion of and further references to various interpretations of this semantic (or meta-semantic, as the case may be) framework.
We use ‘abduction’ to label inference to the best explanation for the sake of stylistic simplicity, not because we take inference to the best explanation to be Pierce’s abduction. For reasons to distinguish inference to the best explanation from Pierce’s abduction see, e.g., Minnameier (2004), Campos (2011), Plutynski (2011), and Mackonis (2013).
As per considerations highlighted by Perry (2001), there may be many aspects of meaning, reflecting variations in what is held fixed in different uses of an expression. The two-dimensional semantic framework, including E2D, can be generalized accordingly.
Those preferring a different account of the semantic facts at issue in E2D can substitute the following for the above conditionals without impacting the dialectic here: ‘if the watery stuff is actually \(\hbox {H}_{2}\hbox {O}\), then all samples of water are samples of \(\hbox {H}_{2}\hbox {O}\) in the actual world’; ‘if the watery stuff is actually XYZ, then all samples of water are samples of XYZ in the actual world’; and so on. Notice that ‘water’ no longer occurs inside quotes in the consequent of these conditionals, but the conditionals themselves are now (token) sentences, and hence, inside quotes. With some changes in form, we could even leave aside language, substituting appropriate propositions for these sentences (e.g., by removing the quotes from the above sentences)—with the result that E2D would deliver knowledge of the content of concepts/propositions, rather than the intensions of expressions.
There may be disagreement about which conditionals the primary intension encodes, of course. Perhaps the primary intension for some appropriate use of ‘water’ encodes conditionals relevant to scenarios in which the most common clear, drinkable liquid in the actual world is half water and half XYZ, or is wildly disjunctive (see Bealer 2002, p. 109 for relevant discussion, though he’s no fan of E2D). There are limits, however. One cannot hold that an ordinary use of ‘water’ refers to whatever is at the beginning of the causal chain that led to one’s acquisition of ‘water’, since ‘water’ does not refer, e.g., to an evil demon, even if the chain begins with such an entity—though see Chalmers (2005) for (at least inspiration for) an opposing view.
Our three suppositions correspond to four of what Chalmers (2006b, p. 585) calls the “[f]ive core claims of two-dimensionalism”—specifically, to his first, third, fourth, and fifth theses. We are neutral as regards his second core claim, which identifies a compositional relationship between complex and simple expressions, but see no reason to exclude this claim here.
Note that to know which world is actual is not thereby to know the extension of every token expression at the actual world. For example, scenarios understood as sets of sentences include only semantically neutral expressions, where, informally, an expression is semantically neutral if its extension in scenarios considered as counterfactual does not depend on which scenario is considered as actual (cf. Chalmers 2006a, p. 87). No ordinary use of ‘water’ is semantically neutral, since whether it refers to \(\hbox {H}_{2}\hbox {O}\) or XYZ in scenarios considered as counterfactual depends on which scenario is considered as actual. As such, to entertain a scenario s is not thereby to know the extension of ‘water’ at s, even if one can know the extension of ‘water’ at s a priori. Most names, natural kind words, and indexical words resemble ‘water’ in this respect. By contrast, many token expressions plausibly are semantically neutral. Chalmers offers ordinary uses of ‘and’, ‘philosopher’, ‘friend’, ‘consciousness’, and ‘cause’ (p. 86); other possible candidates include ‘lake’, ‘stream’, ‘clear’, ‘potable’, ‘\(\hbox {H}_{2}\hbox {O}\)’, and ‘XYZ’. By assumption, scenarios include only these sorts of expressions.
We pause to explain our decision to use the label ‘epistemic two dimensional semantics’, rather than either ‘two-dimensionalism’ or ‘epistemic two-dimensionalism’. Chalmers (2004, p. 166) distinguishes “epistemic” from “contextual” interpretations of two dimensional semantic frameworks, maintaining, as we agree, that only epistemic interpretations can fulfill E2D’s promise of restoring (to any considerable extent) the traditional link between necessity and a priority. Since we are interested only in interpretations that can fulfill this promise, we are interested in specifically epistemic interpretations; hence our moniker includes the qualifier ‘epistemic’. And since we are exploring epistemic interpretations of two-dimensional semantic frameworks, we use the label ‘epistemic two dimensional semantics’; this designation moreover serves the purpose of distinguishing our use from the specific view that Chalmers (2006b) calls ‘epistemic two-dimensionalism’, which use invokes (what we take to be) a misguided (conceiving-based) epistemology of intensions.
Though Block and Stalnaker (1999) maintain that their argument that abductive principles play an ineliminable justificatory role in assessing claims about reduction stands even if abductive principles are “as a priori as you like” (29).
One might wonder, as a referee did, if the open-texturedness of the operative notion of conceivability might stretch still further to allow all abductive considerations to enter into CEI. Perhaps, but if so, then Chalmers and Jackson, among other proponents of E2D, will have to retract not just their assumption that idealized rational reflection/positive conceivability results in conclusively justified beliefs or thoughts (hence will have to retract their usual reply to Block and Stalnaker), but also much of the argumentation they offer in response to access-based concerns with their view; for as we’ll argue down the line, on an abduction-based epistemology of intensions, many of these concerns allow for responses much different from (and better than) those that Chalmers, Jackson, and others provide.
For more on abduction and abductive principles, see Lipton (1991/2004).
One might have the following concern: given AEI, our relevant thoughts and actions are the explananda on the basis of which we should choose among competing primary intensions for any given term; CEI instructs us to make that choice on the basis of our intuitive judgments; the thoughts and actions at issue given AEI just are (or are equivalent to) the intuitive judgments at issue given CEI; so, AEI and CEI will invariably deliver the same results. Against this concern, we respond: because abduction is ampliative whereas conceiving is not, abduction can, e.g., fill out indeterminate primary intensions where conceiving cannot (since abduction can deliver extensions for expressions at scenarios where conceiving cannot). It is primarily this difference in the mode of inference itself, rather than a difference between the “input” available to abduction versus that available to conceiving, that is crucial vis-à-vis the epistemology of (here, primary) intensions.
Of course, some theories will be more difficult to express because the underlying candidate intension is more unruly—perhaps taking an \(\hbox {H}_{2}\hbox {O}\)-scenario and arbitrary world w as input and delivering all and only watery stuff at w as output, but taking an XYZ-scenario and w as input and delivering all and only XYZ at w as output.
Chalmers (2006a) uses the labels base and ordinary truths for, roughly, fundamental and derivative truths, respectively.
To be clear, we think that some objections to E2D do not hinge on which epistemology of intensions is operative, and can be overcome by E2D \(+\) CEI. We place objections from, e.g., Stalnaker (1999, 2001) and Soames (2005) in this category. For responses to these objections that we take to succeed, see Chalmers (2006a, §4) and Chalmers (2006c).
Roughly, this is the claim that deploying one’s semantic competence allows one to deduce, at any scenario s, any given truth at s from a complete list of base truths at s. As per the discussion in section 3.3, this scrutability thesis is intimately related to issues surrounding the epistemology of intensions.
In a symposium on Chalmers (2012, 2014), he suggests that he now prefers a different strategy for addressing indeterminacy, one that preserves a fully general scrutability thesis by shifting the indeterminacy at issue to scrutabilty itself. This alternative approach cannot help E2D \(+\) CEI in the present context.
One should note that Chalmers’s initial suggestion for treating Wilson’s cases, by assigning distinct intensions for each decision that the natives in fact make (albeit accidentally) is no help here, since the decisions at issue in the present cases are not the result of accident. Nor does it make sense to extend Chalmers’s original suggestion (repeated in Chalmers and Jackson 2001) by taking standards of non-demonstrative reasoning to be built into associated intensions, such that, e.g., if an appeal to fruitfulness pushes chemists to apply ‘acid’ to HCL at some scenario, then its intension includes that principle; for building abductive principles into intensions would radically multiply associated concepts, thereby eliminating most if not all substantive disagreement—and, contrary to Chalmers (2011), we see that as a serious cost. We return to this issue in Sect. 5.2.
Relatedly, we maintain that the ability to use an expression deferentially is not enough for competence. Stuck in his “Chinese Room”, Searle can use ‘
’ to refer to whatever Mandarin speakers refer to with that symbol, but Searle is not thereby competent with the associated expression.According to the main internalist alternative to dispositionalist accounts, competence with a concept C requires explicitly associating C with a definition consisting of necessary and sufficient conditions for its application. But as Chalmers and Jackson (2001, pp. 320–321) note, one can possess concepts (e.g., of knowledge) without being able to identify such conditions. One can see that Chalmers and Jackson moreover endorse a dispositional account when they take intuitive reactions (to hypothetical cases, conditionals, etc.) to reveal (and be necessary for revealing) a priori knowledge of concepts and relevant intensions.
Chalmers (2011) argues directly that disputes not expressible using basic concepts are terminological. Interestingly, since (independently of E2D) he suspects that the choice of one empirically adequate set of basic concepts over another is largely a matter of taste, it seems that there is little if any substantive disagreement, on his view of the matter. While many disputes are no doubt terminological and distinguishing substantive from terminological disputes can be quite difficult, we doubt that there is so little substantive dispute.
To prefigure, this role for experience is relevantly like its role in concept acquisition; in both cases, experience provides certain content needed to engage in epistemic deliberation, without undermining the broadly formal or structural reasons for thinking that the products of abductive deliberation are a priori.
An inferential procedure m has epistemic value if for any subject s, conclusion c, and premise(s) p: if s justifiably believes p and uses m to infer c from p, then (absent defeaters) s justifiably believes c.
The ‘can’ here and in discussion of the other roles experience might play in justifying a given belief is to be understood as ‘can, in the circumstances’. Belief in some claims (e.g., the four-color theorem) admits of both a priori and a posteriori justification, but our question here is not whether a belief that was justified, e.g., by means of a computer proof, can be justified in some different, a priori, fashion, but rather the question of whether, given the specific means by which the belief was justified, the resulting justification is a priori.
This follows Kant’s (1781/1998) take on logic. The claim that abductive inference is constitutive of human reasoning is independently plausible (cf., Gelman and Markman 1986; Feeney and Heit 2007). Incidentally, we think that abduction is the ultimate arbiter of disputes about logical principles (e.g., modus ponens) and their applications as well; but that’s a topic for a different paper.
Though Chalmers and Jackson deny that abductive principles enter into the epistemology of intensions, their reply to Block and Stalnaker offers an alternative place for such principles, as partly constitutive of individual concepts. On this view, appeal to abductive principles in the course of considering how to apply an expression would be compatible with the outcome of the deliberation’s being a priori. But as previously noted, it is a bad idea to build abductive principles into concepts, since doing so prevents there being substantive disagreement over the extensions of what are intuitively univocal expressions; see § 5.2.
Two views of the nature of cordates and renates are compatible with this result. On one, hearts and kidneys are necessarily connected because they are different components of a single kind, and so, cordate and renate are the same kind—a principle of parsimony supports this view. On the other, hearts and kidneys are necessarily connected even though they are distinct existences, and so, cordate and renate are distinct kinds even though they are inseparable (and correspondingly, even though relevant tokens of ‘cordate’ and ‘renate’ have the same modal extension). Of course, this may violate Hume’s Dictum—according to which there are no necessary connections between distinct existences—but we do not see this as a serious cost (see Wilson 2010 for discussion).
For example, given this supposition, we can build a model of a (nomologically possible) creature that has one organ for pumping blood and no organ for filtering blood because whenever the blood becomes so full of waste and excess fluid that the blood-pumping organ cannot use it, it acquires new blood (think vampires) and excretes the old, or a model of a creature that has one organ for pumping blood, but for which the filtering functions that are served by the kidneys in actual mammals are instead distributed throughout various tissues that serve multiple functions, and which collectively have no claim to being a kidney.
’ to refer to whatever Mandarin speakers refer to with that symbol, but Searle is not thereby competent with the associated expression.References
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Biggs, S., Wilson, J. Abductive two-dimensionalism: a new route to the a priori identification of necessary truths. Synthese 197, 59–93 (2020). https://doi.org/10.1007/s11229-017-1444-6
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DOI: https://doi.org/10.1007/s11229-017-1444-6