Stipulations and Requirements: Reply to Horden Louis deRosset [forthcoming in Oxford Studies in Metaphysics ] August 24, 2016 Abstract In (deRosset, 2015), I argued that there are counterexamples to the claim that the sentences analytically entailed by a claim  require nothing more of the world for their truth than does . The counterexamples involve sentences which, I argued, are analytically entailed by certain truths, but which nevertheless require more of the world for their truth. John Horden has o↵ered two interesting criticisms of this argument. First, he contends that its conclusion is inconsistent. Second, he contends that the argument faces a dilemma, depending on which of two hypotheses about the meanings of the sentences involved in the counterexamples turns out to be true. Here I reply to Horden's criticisms and briefly indicate what I take their lesson to be. In (deRosset, 2015) (henceforth, AO), I argued that there are counterexamples to each of the following two principles: DAO If P analytically entails the existence of certain things, then a theory that contains P but does not claim that those things exist is no more ontologically parsimonious than a theory that also claims that they exist. GAO If P analytically entails Q, then (P ^ Q) requires nothing more of the world than does P . John Horden has o↵ered interesting criticisms of that argument. In this short note, I reply to the criticisms and briefly indicate what I take their lesson to be. The putative counterexamples toGAO andDAO are of essentially the same sort. For the sake of simplicity, then, I will focus on a putative counterexample to GAO. In AO I asked readers to suppose that we had stipulated that 'grassgreen' 1 deRosset Stipulations and Requirements is to be a predicate that expresses the property being green if, as a matter of fact, grass is green, and not being green otherwise. To simplify the discussion, let's dispense with suppositions: I do hereby so stipulate. I trust you know enough to recognize that grass is grassgreen. Also, as you may know, the flesh of kiwi fruit, clover, and most freeway signs in the U.S. are grassgreen. Neither roses nor violets are grassgreen. My argument that this stipulation yields a counterexample to GAO relied on three premises. A My stipulation is successful, where "success" in this sense entails that, as a result of the stipulation, its content is true. B "Disquoting" the content of a successful stipulation yields an analytic truth. C Requirements for the truth of a sentence of the form '⌧ is grassgreen' are given by which individual (if any) is the referent of ⌧ and which property is expressed by 'grassgreen' in a straightforward way: the requirement is that that very individual have that very property. Given (A), we may conclude that, if grass is, as a matter of fact, green, then 'grassgreen' expresses being green, and, otherwise, 'grassgreen' expresses not being green. Application of (B) then yields the analyticity of (1) if, as a matter of fact, grass is green, then something is grassgreen i↵ it is green; and, otherwise, something is grassgreen i↵ it is not green. It is then very simple to show that (2) snow is white analytically entails (3) grass is grassgreen. Application of (C), together with the fact that grass is, as a matter of fact, green, yields the conclusion that (3) requires for its truth that grass have the property being green. Since that requirement clearly goes beyond requirements for the truth of (2), we have a counterexample to GAO. In his comment on AO, Horden o↵ers two reasons for thinking this argument unsound. First, he contends that its conclusion is inconsistent. Second, he contends that my argument faces a dilemma, depending on which of two 2 deRosset Stipulations and Requirements hypotheses about the meaning of (3) turns out to be true. I will discuss each contention in turn. Horden's charge of inconsistency is made on p. XXXXX: "If 'grass is grassgreen' is guaranteed to be actually true, no matter what colour grass actually has, then it cannot require of the actual world that grass be green. Even if we grant that the stipulation succeeds, it seems sensible to examine the semantics of the novel term 'grassgreen' a little more closely before we embrace inconsistency" (emphasis original). It is a little dicult to see what is supposed to be inconsistent here. The guarantee is epistemic, while requirements for the truth of a claim concern the metaphysical or semantic question of what the world has to be like for the claim to be true. Given (C), any residual air of inconsistency dissolves once we realize that the success of the stipulation entails that the truth of (3) requires one thing if, as a matter of fact, grass is not green and another thing if, as a matter of fact, grass is green. Horden does not explicitly say why an epistemic guarantee of the truth of a sentence is supposed to be inconsistent with there being substantial requirements for its truth. But he provides a clue when he suggests a schematic biconditional governing requirements: "a sentence  requires of the world that R i↵ (i) 'R' does not logically follow from sentences that are true entirely because of their meanings, and (ii) whichever world is actual, if  is true, this is partly because R" (p. XXXX).1 Horden only tentatively advances this biconditional, but says that his argument assumes the following consequence of its left-to-right direction (p. XXXXX): L1 if a sentence requires of the world that R, then, whichever world is actual, that sentence is true only if R. With (L1) in hand, it's pretty clear why Horden thinks the argument against GAO entangles us in inconsistency. Consider the relevant instance of (L1): L2 If (3) requires of the world that grass is green, then, whichever world is actual, (3) is true only if grass is green. If the argument from (A)-(C) is sound, then, because grass is in fact green, (3) in fact requires of the world that grass is green. However, if grass turns out as a matter of fact to be purple – if, that is, a world in which grass is purple turns 1I have benefited here from personal correspondence with Horden. 3 deRosset Stipulations and Requirements out to be actual – then the soundness of the argument implies that (3) does not require that grass be green. This would contravene (L2), which entails that (3)'s requiring of the world that grass be green be insensitive to how things turn out to be as a matter of fact. So, the contention that the argument involves us in an inconsistency can be made good if we assume (L1). But (L1) faces counterexamples. I have just flipped a coin. I hereby stipulate that 'TrueThat' is a syntactically atomic sentence that requires for its truth that grass be green if the coin landed heads, and requires for its truth that grass not be green otherwise. The stipulation passes all of the standard tests for successful stipulation. In particular, it is conservative and harmonious, and passes what in AO (pp. 141-4) I called Stevenson's constraint. I have gone on to use 'TrueThat' in conversation with my colleagues, friends, and family. As you will see, I will even be using it in this paper. Given its success, the content of my 'TrueThat' stipulation is true. So, (L1) has a false instance: L3 If 'TrueThat' requires of the world that grass is green, then, whichever world is actual, 'TrueThat' is true only if grass is green. It turns out that the coin landed heads. This provides enough information for you to recognize that TrueThat i↵ grass is green. If, however, a world in which the coin landed tails is actual, then TrueThat i↵ grass is not green. In general, we appear to be able, under the right circumstances, to successfully stipulate the requirements for the truth of new sentences. What's more, we have at our disposal devices for conditionalizing on how things are as a matter of fact in the content of such stipulations. So, (L1) appears to implausibly restrict our stipulative powers. It thus provides no reason to think that the argument from (A)-(C) against GAO entangles us in any inconsistency. Horden's second objection to the argument from (A)-(C) is that it faces a dilemma, depending on what we take (3) to mean. In AO (p. 148), I argued that the force of the putative counterexamples was independent of which of several plausible hypotheses about the meaning of, e.g., (3) turned out to be correct, and otherwise avoided explicit discussion about the meanings of my stipulated terms. A word of explanation for why we might want to avoid claims about what (3) means may, however, be appropriate. The issue is that there are a dizzying array of di↵erent semantic values that might be assigned to (3). Assume for illustration that the occurence of 'grass' in (3) is a singular term, so that (3) has 4 deRosset Stipulations and Requirements the form 'a is F ', where a is a term and F is a predicate.2 Then it is plausible to claim that the sentence expresses a russellian proposition represented by hgrass, being greeni. Certainly, a proponent of DAO is in no position to deny that sentences like (3) express such russellian propositions, given how 'russellian proposition' and related vocabulary is used in the philosophical community. But such a proponent is also in no position to deny that (3) has other semantic values, including a truth value, a carnapian intension, a character (Kaplan, 1989), or perhaps even a primary intension (Chalmers, 2002). Which, if any, of these semantic values should we hold gives the meaning of (3)? It seemed to me that nothing interesting hung on which of many plausible answers we might give to this question. Horden disagrees. Here is his dilemma. If (3) means (4) grass is green then, Horden contends, (B) is false: though the stipulation succeeds and the truth of (3) requires that grass have the property being green, (3) is not analytic. Alternatively, if (3) means (5) grass is green i↵ grass is actually green then, Horden contends, (C) is false: the requirements for the truth of (3) are trivially satisfied and so cannot include that grass have the property being green. More generally, Horden's argument here might be taken to suggest that there is no way of fixing a meaning for any sentence on which both (B) and the analogue of (C) are true. That is, there is no way of fixing a meaning for a sentence so that, like (4), it requires for its truth that grass be green, but, like (5), it is analytic. Let's consider each horn of the dilemma in turn. On the first horn, the defense of GAO would require that (3) be synthetic, even though it has what in AO (p. 158) I called the trappings of analyticity : the conventions governing the use of (3) guarantee that it is entailed by certain sentences such that failure to accept any of these sentences constitutes some measure of linguistic incompetence. For instance, one of the conventions governing the use of (3) is given by the content of my 'grassgreen' stipulation. From those conventions, instances of 2If (3) lacks such a structure, then it will express some slightly more complicated russellian singular proposition, but the point in the main text would be una↵ected. 5 deRosset Stipulations and Requirements certain disquotation principles, and a little logic, it's easy to work out that (3) is true. This certainly makes it look as if (3) is analytic, and it seems to me that there is little reason to deny that it really is analytic short of antecedent commitment to GAO. Thus, I would argue that the most plausible verdict on this horn of the dilemma is that my 'grassgreen' stipulation has fixed the meaning of (3) in such a way as to make both (B) and (C) true. Suppose, however, that I'm completely wrong about that. Suppose, that is, that appearances in this case really are misleading in the way that Horden contends: (3) has the trappings of analyticity but is not analytic. Horden's contention here is an instance of a more general strategy for defending DAO and GAO from the putative counterexamples. This defense denies that the possession of the trappings of analyticity is enough to guarantee analyticity. But the defense thereby gives up an important methodological advantage on which the philosophical applications of DAO rely. If a sentence can have the trappings of analyticity without being analytic, then we can't rely on our appreciation of the trappings of analyticity in cases like (6) If particles p1, . . . , pn are arranged table-wise in L, then there is a table in L to warrant the application of DAO. Thus, a radical ontologist who agrees that particles p1, . . . , pn are arranged table-wise in L but denies that there is a table there can admit that (6) has the trappings of analyticity while reasonably denying that it is analytic. In AO (p. 159), I concluded on this basis that, on this response, "DAO is saved, but it's rendered toothless."3 A defender of DAO and GAO might reply by distinguishing mere uninterpreted strings from meaningful expressions of an interpreted language.4 The idea is that (3) fails to be analytic because 'grassgreen' is a mere uninterpreted string: the content of my stipulation gives us reason to think that that string will be true when it acquires a meaning, but no reason to think that any meaningful interpreted sentence is true. It is only meaningful, interpreted sentences that are analytic or synthetic, so (3) is not even the right sort of thing to be analytic. This reply runs afoul of the fact that 'grassgreen' is already a term being used meaningfully (if only by me) to characterize things. In the second 3Please see AO §4.2 for more extended discussion. 4Here again I benefit from correspondence with Horden. 6 deRosset Stipulations and Requirements paragraph of this paper, for instance, I used it three times. On each occasion, I asserted something true. Perhaps you count yourself as falling short of ideal competence with the expression, but you know enough to recognize the truth of (3). So, (3) is already a meaningful sentence of an interpreted language, and the content of my stipulation provides an epistemic guarantee of its truth. It won't, then, fail to be analytic for want of semantic significance. Consider now the second horn of Horden's dilemma, on which we assume that (3) means the same thing as (5) grass is green i↵ grass is actually green. The defender of GAO holds that (5) requires nothing of the world. If this claim is granted, then, the semantic equivalence of (3) and (5) yields the falsity of (C): like (5), (3) requires nothing of the world. Horden is correct to think that (C) entails that (3) and (5) are semantically discernible. In particular, the biconditional (5) won't bear an interpretation on which its truth requires that grass have the property being green. So, if (3) and (5) were semantically indiscernible, then (C) would fail because (3), like (5), would also fail to require that grass have the property being green. I would think, however, that the claim that (3) and (5) are semantically indiscernible is independently implausible. (3) has semantic values that (5) lacks, including the russellian proposition represented by hgrass, being greeni. So, Horden is correct to contend that (C) is, plausibly, false if (3) means the same thing as (5); but it is not plausible to hold that (3) means the same thing as (5). In any case, we can tweak the argument a little to avoid this horn of the dilemma entirely, using a stipulation much like my 'TrueThat' stipulation. I hereby stipulate that 'GreenThat' is a syntactically atomic sentence that requires for its truth that grass be green if, as a matter of fact, grass is green; and that grass not be green otherwise. I have gone on to use 'GreenThat' in conversation with my colleagues, friends, and family. You know enough about grass to recognize that GreenThat i↵ grass is green, so you could use it too if you were so inclined. My stipulation passes all of the standard tests for successful stipulation. In particular, it is conservative and harmonious, and passes Stevenson's constraint. The stipulation takes the analogue of the second horn of Horden's dilemma o↵ the table. In fact, it takes the denial of the analogue of (C) o↵ the table if the success of my stipulation is granted. If the 'GreenThat' stipulation is successful, then its content is true, so it requires for its truth that 7 deRosset Stipulations and Requirements grass be green. For this reason, insofar as one is willing to countenance the idea that linguistic conventions or stipulations fix meanings for sentences, my 'GreenThat' stipulation illustrates a way to fix a meaning for a sentence on which both (B) and the analogue of (C) appear to be true. I have argued that neither the objection based on (L1) nor the dilemma ultimately threatens the cogency of the putative counterexamples to DAO and GAO. But we shouldn't let these diculties for the objections obscure the more general lessons of Horden's discussion. Horden is admirably explicit about the assumption (L1) governing requirements for the truth of a sentence on which his first objection depends. Though, as I have argued, (L1) itself is implausibly restrictive, I believe that this is a fruitful line of inquiry for the analyticity theorist to pursue. (L1) is part of Horden's proposal for a partial theory of requirements. I think (L1) itself is false, but there are other aspects of that theory that are quite attractive. For instance, on Horden's tentative proposal, the requirements for the truth of a sentence are canonically given by a specification of the form (7) Sentence S requires that . Further, the requirements for the truth of a given sentence are conceived by Horden as playing an explanatory role: they specify the conditions in virtue of which S is true (if it is). These seem like fruitful starting points for a theory of requirements. To my mind, the most promising line of defense for GAO and DAO will follow Horden's lead: first, articulate, motivate, and defend a (perhaps partial) theory of requirements; then, show that, on that theory, the proposed counterexamples fail. Moreover, the discussion of Horden's dilemma has outlined the strategy that the defense must follow. The theory of requirements on which the defense relies must be supported well enough to motivate the rejection of the otherwise plausible claim that such stipulations as the ones introducing 'grassgreen' and 'GreenThat' are successful.5 5Thanks are due to Mark Moyer and Kate Nolfi for comments on earlier drafts. Special thanks are due to John Horden for helpful correspondence. Thanks also to Amanda Lowe for help in preparing the text. 8 deRosset Stipulations and Requirements References David J. Chalmers. On Sense and Intension. In James E. Tomberlin, editor, Philosophical Perspectives: Language and Mind, volume 16, pages 135–82. Blackwell, 2002. Louis deRosset. Analyticity and Ontology. Oxford Studies in Metaphysics, 13: 129–70, 2015. David Kaplan. Demonstratives. In Joseph Almog, John Perry, and Howard Wettstein, editors, Themes From Kaplan, pages 481–563. Oxford University Press, New York, 1989.