If the world itself is metaphysically indeterminate in a specified respect, what follows? In this paper, we develop a theory of metaphysical indeterminacy answering this question.

How do thought and language manage to be 'about' aspects of the world? J. Robert G. Williams investigates how representation arises out of a fundamentally non-representational world, showing the explanatory relations between the representational properties of language, of thought, and of perception and intention.

Decisions are made under uncertainty when there are distinct outcomes of a given action, and one is uncertain to which the act will lead. Decisions are made under indeterminacy when there are distinct outcomes of a given action, and it is indeterminate to which the act will lead. This paper develops a theory of (synchronic and diachronic) decision-making under indeterminacy that portrays the rational response to such situations as inconstant. Rational agents have to capriciously and randomly choose how to resolve (...) the indeterminacy relevant to a given choice-situation, but such capricious choices once made constrain how they will choose in the future. The account is illustrated by the case of self-interested action in situations where it is indeterminate whether you yourself will survive to benefit or suffer the consequences. The conclusion emphasizes some distinctive anti-hedging predictions of the account. (shrink)

Might it be that world itself, independently of what we know about it or how we represent it, is metaphysically indeterminate? This article tackles in turn a series of questions: In what sorts of cases might we posit metaphysical indeterminacy? What is it for a given case of indefiniteness to be 'metaphysical'? How does the phenomenon relate to 'ontic vagueness', the existence of 'vague objects', 'de re indeterminacy' and the like? How might the logic work? Are there reasons for postulating (...) this distinctive sort of indefiniteness? Conversely, are there reasons for denying that there is indefiniteness of this sort? (shrink)

Inscrutability arguments threaten to reduce interpretationist metasemantic theories to absurdity. Can we find some way to block the arguments? A highly influential proposal in this regard is David Lewis’ ‘ eligibility ’ response: some theories are better than others, not because they fit the data better, but because they are framed in terms of more natural properties. The purposes of this paper are to outline the nature of the eligibility proposal, making the case that it is not ad hoc, but (...) instead flows naturally from three independently motivated elements; and to show that severe limitations afflict the proposal. In conclusion, I pick out the element of the eligibility response that is responsible for the limitations: future work in this area should therefore concentrate on amending this aspect of the overall theory. (shrink)

This article investigates the claim that some truths are fundamentally or really true — and that other truths are not. Such a distinction can help us reconcile radically minimal metaphysical views with the verities of common sense. I develop an understanding of the distinction whereby Fundamentality is not itself a metaphysical distinction, but rather a device that must be presupposed to express metaphysical distinctions. Drawing on recent work by Rayo on anti-Quinean theories of ontological commitments, I formulate a rigourous theory (...) of the notion. In the final sections, I show how this package dovetails with ' interpretationist' theories of meaning to give sober content to thought that some things — perhaps sets, or gerrymandered mereological sums — can be 'postulated into existence'. (shrink)

Lewis (1973) gave a short argument against conditional excluded middle, based on his treatment of ‘might’ counterfactuals. Bennett (2003), with much of the recent literature, gives an alternative take on ‘might’ counterfactuals. But Bennett claims the might-argument against CEM still goes through. This turns on a specific claim I call Bennett’s Hypothesis. I argue that independently of issues to do with the proper analysis of might-counterfactuals, Bennett’s Hypothesis is inconsistent with CEM. But Bennett’s Hypothesis is independently objectionable, so we should (...) resolve this tension by dropping the Hypothesis, not by dropping CEM. (shrink)

Sometimes it is indeterminate what an agent morally ought do. This generates a Decision Ought Challenge—to give moral guidance to agents in such a scenario. This article is a field guide to the options for a theory of the decision ought for cases of indeterminacy. Three categories of view are evaluated, and the best representative for each is identified.

This paper examines two puzzles of indeterminacy. The first puzzle concerns the hypothesis that there is a unified phenomenon of indeterminacy. How are we to reconcile this with the apparent diversity of reactions that indeterminacy prompts? The second puzzle focuses narrowly on borderline cases of vague predicates. How are we to account for the lack of theoretical consensus about what the proper reaction to borderline cases is? I suggest (building on work by Maudlin) that the characteristic feature of indeterminacy is (...) alethic normative silence, and use this to explain both plurality and lack of consensus. (shrink)

Worlds where things divide forever ("gunk" worlds) are apparently conceivable. The conceivability of such scenarios has been used as an argument against "nihilist" or "near-nihilist" answers to the special composition question. I argue that the mereological nihilist has the resources to explain away the illusion that gunk is possible.

Jeff Paris proves a generalized Dutch Book theorem. If a belief state is not a generalized probability then one faces ‘sure loss’ books of bets. In Williams I showed that Joyce’s accuracy-domination theorem applies to the same set of generalized probabilities. What is the relationship between these two results? This note shows that both results are easy corollaries of the core result that Paris appeals to in proving his dutch book theorem. We see that every point of accuracy-domination defines a (...) dutch book, but we only have a partial converse. (shrink)

Revisionary theories of logic or truth require revisionary theories of mind. This essay outlines nonclassically based theories of rational belief, desire, and decision making, singling out the supervaluational family for special attention. To see these nonclassical theories of mind in action, this essay examines a debate between David Lewis and Derek Parfit over what matters in survival. Lewis argued that indeterminacy in personal identity allows caring about psychological connectedness and caring about personal identity to amount to the same thing. The (...) essay argues that Lewis's treatment of two of Parfit's puzzle cases—degreed survival and fission—presuppose different nonclassical treatments of belief and desire. (shrink)

Joyce (1998) gives an argument for probabilism: the doctrine that rational credences should conform to the axioms of probability. In doing so, he provides a distinctive take on how the normative force of probabilism relates to the injunction to believe what is true. But Joyce presupposes that the truth values of the propositions over which credences are defined are classical. I generalize the core of Joyce’s argument to remove this presupposition. On the same assumptions as Joyce uses, the credences of (...) a rational agent should always be weighted averages of truth value assignments. In the special case where the truth values are classical, the weighted averages of truth value assignments are exactly the probability functions. But in the more general case, probabilistic axioms formulated in terms of classical logic are violated—but we will show that generalized versions of the axioms formulated in terms of non-classical logics are satisfied. (shrink)

Many accounts of structural rationality give a special role to logic. This paper reviews the problem case of clear-eyed logical uncertainty. An account of rational norms on belief that does not give a special role to logic is developed: doxastic probabilism.

John Hawthorne in a recent paper takes issue with Lewisian accounts of counterfactuals, when relevant laws of nature are chancy. I respond to his arguments on behalf of the Lewisian, and conclude that while some can be rebutted, the case against the original Lewisian account is strong. I develop a neo-Lewisian account of what makes for closeness of worlds. I argue that my revised version avoids Hawthorne's challenges. I argue that this is closer to the spirit of Lewis's first (non-chancy) (...) proposal than is Lewis's own suggested modification. (shrink)

This chapter defends the account of metaphysical indeterminacy of Barnes and Williams against Eklund's objections.

In the literature on supervaluationism, a central source of concern has been the acceptability, or otherwise, of its alleged logical revisionism. I attack the presupposition of this debate: arguing that when properly construed, there is no sense in which supervaluational consequence is revisionary. I provide new considerations supporting the claim that the supervaluational consequence should be characterized in a ‘global’ way. But pace Williamson (1994) and Keefe (2000), I argue that supervaluationism does not give rise to counterexamples to familiar inference-patterns (...) such as reductio and conditional proof. (shrink)

The question of the cognitive role of fictionality is this: what is the correct cognitive attitude to take to p, when it is fictional that p? We began by considering one answer to this question, implicit in the work of Kendall Walton, that the correct response to a fictional proposition is to imagine that proposition. However, this approach is silent in cases of fictional incompleteness, where neither p nor its negation are fictional. We argue that that Waltonians should embrace a (...) pluralistic account of the cognitive role of fictional incompleteness: in some cases of fictional incompleteness, we are permitted to resolve the incompleteness during our engagement with the target fiction, and in other cases, we are obliged not to resolve the incompleteness. But though pluralism is accommodated by Walton’s wider account of fictionality, it puts tension on his motivating idea that fictionality stands to the imagination as truth stands to belief. And so we develop a rival conception of the cognitive role of fictionality that is built around a different analogy: on this evidentialist approach, (known) fictionality stands to the imagination as evidence stands to credence. (shrink)

Information can be public among a group. Whether or not information is public matters, for example, for accounts of interdependent rational choice, of communication, and of joint intention. A standard analysis of public information identifies it with (some variant of) common belief. The latter notion is stipulatively defined as an infinite conjunction: for p to be commonly believed is for it to believed by all members of a group, for all members to believe that all members believe it, and so (...) forth. This analysis is often presupposed without much argument in philosophy. Theoretical entrenchment or intuitions about cases might give some traction on the question, but give little insight about why the identification holds, if it does. The strategy of this paper is to characterize a practical-normative role for information being public, and show that the only things that play that role are (variants of) common belief as stipulatively characterized. In more detail: a functional role for “taking a proposition for granted” in non-isolated decision making is characterized. I then present some minimal conditions under which such an attitude is correctly held. The key assumption links this attitude to beliefs about what is public. From minimal a priori principles, we can argue that a proposition being public among a group entails common commitment to believe among that group. Later sections explore partial converses to this result, the factivity of publicity and publicity from the perspective of outsiders to the group, and objections to the aprioricity of the result deriving from a posteriori existential presuppositions. (shrink)

We discuss arguments against the thesis that the world itself can be vague. The first section of the paper distinguishes dialectically effective from ineffective arguments against metaphysical vagueness. The second section constructs an argument against metaphysical vagueness that promises to be of the dialectically effective sort: an argument against objects with vague parts. Firstly, cases of vague parthood commit one to cases of vague identity. But we argue that Evans' famous argument against will not on its own enable one to (...) complete the reductio in the present context. We provide a metaphysical premise that would complete the reductio, but note that it seems deniable. We conclude by drawing general morals from our case study. (shrink)

Supervaluationism is often described as the most popular semantic treatment of indeterminacy. There’s little consensus, however, about how to fill out the bare-bones idea to include a characterization of logical consequence. The paper explores one methodology for choosing between the logics: pick a logic thatnorms beliefas classical consequence is standardly thought to do. The main focus of the paper considers a variant of standard supervaluational, on which we can characterizedegrees of determinacy. It applies the methodology above to focus ondegree logic. (...) This is developed first in a basic, single-premise case; and then extended to the multipremise case, and to allowdegreesof consequence. The metatheoretic properties of degree logic are set out. On the positive side, the logic is supraclassical—all classical valid sequents are degree logic valid. Strikingly, metarules such as cut and conjunction introduction fail. (shrink)

I outline and motivate a way of implementing a closest world theory of indicatives, appealing to Stalnaker's framework of open conversational possibilities. Stalnakerian conversational dynamics helps us resolve two outstanding puzzles for a such a theory of indicative conditionals. The first puzzle -- concerning so-called 'reverse Sobel sequences' -- can be resolved by conversation dynamics in a theoryneutral way: the explanation works as much for Lewisian counterfactuals as for the account of indicatives developed here. Resolving the second puzzle, by contrast, (...) relies on the interplay between the particular theory of indicative conditionals developed here and Stalnakerian dynamics. The upshot is an attractive resolution of the so-called "Gibbard phenomenon" for indicative conditionals. (shrink)

There are advantages to thrift over honest toil. If we can make do without numbers we avoid challenging questions over the metaphysics and epistemology of such entities; and we have a good idea, I think, of what a nominalistic metaphysics should look like. But minimizing ontology brings its own problems; for it seems to lead to error theory— saying that large swathes of common-sense and best science are false. Should recherche philosophical arguments really convince us to give all this up? (...) Such Moorean considerations are explicitly part of the motivation for the recent resurgence of structured metaphysics, which allow a minimal (perhaps nominalistic) fundamental ontology, while avoiding error-theory by adopting a permissive stance towards ontology that can be argued to be grounded in the fundamental. This paper evaluates the Moorean arguments, identifying key epistemological assumptions. On the assumption that Moorean arguments can be used to rule out error-theory, I examine deflationary ‘representationalist’ rivals to the structured metaphysics reaction. Quinean paraphrase, fictionalist claims about syntax and semantics are considered and criticized. In the final section, a ‘direct’ deflationary strategy is outlined and the theoretical obligations that it faces are articulated. The position advocated may have us talking a lot like a friend of structured metaphysics—but with a very different conception of what we’re up to. (shrink)

Some argue that theories of universals should incorporate structural universals, in order to allow for the metaphysical possibility of worlds of 'infinite descending complexity' ('onion worlds'). I argue that the possibility of such worlds does not establish the need for structural universals. So long as we admit the metaphysical possibility of emergent universals, there is an attractive alternative description of such cases.

Suppose you’re certain that a claim—say, ‘Frida is tall’—does not have a determinate truth value. What attitude should you take towards it? This is the question of the cognitive role of indeterminacy. This paper presents a puzzle for theories of cognitive role. Many of these theories vindicate a seemingly plausible principle: if you are fully certain that A, you are rationally required to be fully certain that A is determinate. Call this principle ‘Certainty’. We show that Certainty, in combination with (...) some minimal side premises, entails a very implausible claim: whenever you’re certain that it’s indeterminate whether A, it is rationally required that you reject A. This is a surprising result, which requires abandoning at least some intuitive views about indeterminacy and cognitive role. (shrink)

This paper outlines Lewis’s favoured foundational account of linguistic representation, and outlines and briefly evaluates variations and modifications. Section 1 gives an opinionated exegesis of Lewis’ work on the foundations of reference—his interpretationism. I look at the way that the metaphysical distinction between natural and non-natural properties came to play a central role in his thinking about language. Lewis’s own deployment of this notion has implausible commitments, so in section 2 I consider variations and alternatives. Section 3 briefly considers a (...) buck-passing strategy involving fine-grained linguistic conventions. (shrink)

In some sense, survival seems to be an intrinsic matter. Whether or not you survive some event seems to depend on what goes on with you yourself —what happens in the environment shouldn’t make a difference. Likewise, being a person at a time seems intrinsic. The principle that survival seems intrinsic is one factor which makes personal fission puzzles so awkward. Fission scenarios present cases where if survival is an intrinsic matter, it appears that an individual could survive twice over. (...) But it’s well known that standard notions of “intrinsicality” won’t do to articulate the sense in which survival is intrinsic, since ‘personhood’ appears to be a maximal property. We formulate a sense in which survival and personhood (and perhaps other maximal properties) may be almost intrinsic—a sense that would suffice, for example, to ground fission arguments. It turns out that this notion of almost-intrinsicality allows us to formulate a new version of the problem of the many. (shrink)

This essay explores the thesis that for vague predicates, uncertainty over whether a borderline instance x of red/large/tall/good is to be understood as practical uncertainty over whether to treat x as red/large/tall/good. Expressivist and quasi-realist treatments of vague predicates due to John MacFarlane and Daniel Elstein provide the stalking-horse. It examines the notion of treating/counting a thing as F , and links a central question about our attitudes to vague predications to normative evaluation of plans to treat a thing as (...) F . The essay examines how the account applies to normatively defective or contested terms. The final section raises a puzzle about the mechanics of MacFarlane’s detailed implementation for the case of gradable adjectives. (shrink)

Why should we be means-end rational? Why care whether someone’s mental states exhibit certain formal patterns, like the ones formalized in causal decision theory? This paper establishes a dominance argument for these constraints in a finite setting. If you violate the norms of causal decision theory, then your desires will be aptness dominated. That is, there will be some alternative set of desires that you could have had, which would be more apt (closer to the actual values fixed by your (...) sensibility/ what you intrinsically care about) no matter which world is actual. If we care about having apt desires, then, we should never let ourselves violate these norms of means-end rationality. This argument shares a form with now-standard accuracy arguments for probabilism, opening up a new terrain for that discussion. I show that the foundational assumptions about the shape of accuracy and of aptness required to run the arguments for means-end rationality and for probabilism run closely parallel. I show the argument is robust under different theories of subjective actual value, including nonclassical treatments of indeterminacy in actual value; I show the argument may (but need not!) be generalized to objective theories of value. The upshot is that aptness-domination arguments for decision theories should be added to the philosophical playbook. (shrink)

This chapter outlines David Lewis's favored foundational account of linguistic representation, and outlines and briefly evaluates variations and modifications. It gives an opinionated exegesis of Lewis's work on the foundations of reference: his interpretationism. The author looks at the way that the metaphysical distinction between natural and non‐natural properties came to play a central role in his thinking about language. Lewis's own deployment of this notion has implausible commitments. The chapter briefly considers a buck‐passing strategy involving fine‐grained linguistic conventions. Lewis (...) was no fan of primitive intentionality. Much of the Lewisian framework remains attractive. The overall select‐and‐project method, with its promise to deal even‐handedly with all linguistic intentionality, and its epistemic tractability, should be retained. Post‐Lewisian interpretationism results from emphasizing and retaining some of the virtues of Lewis's original proposal promises (e.g. universality and epistemic tractability), while compromising on others (e.g. metaphysical principle). (shrink)

We can use radically different reference‐schemes to generate the same truth‐conditions for the sentences of a language. In this paper, we do three things. (1) Distinguish two arguments that deploy this observation to derive different conclusions. The first argues that reference is radically indeterminate: there is no fact of the matter what ordinary terms refer to. This threat is taken seriously and most contemporary metasemantic theories come with resources intended to rebut it. The second argues for radical parochialism about reference: (...) it's a reflection of our parochial interests, rather than the nature of the subject matter, that our theorizing about language appeals to reference rather than another relation that generates the same truth‐conditions. Rebuttals of the first argument cut no ice against the second, because radical parochialism is compatible with reference being determinate. (2) Argue that radical parochialism, like radical indeterminacy, would be shocking if true. (3) Argue that the case for radical parochialism turns on the explanatory purposes of “reference”‐talk: on relatively “thin” conceptions, the argument goes through, and radical parochialism is (shockingly!) true; on richer conceptions, the argument can be blocked. We conclude that non‐revisionists must endorse, and justify, a relatively rich conception of the explanatory purposes of “reference”‐talk. (shrink)

How are permutation arguments for the inscrutability of reference to be formulated in the context of a Davidsonian truth-theoretic semantics? Davidson takes these arguments to establish that there are no grounds for favouring a reference scheme that assigns London to “Londres”, rather than one that assigns Sydney to that name. We shall see, however, that it is far from clear whether permutation arguments work when set out in the context of the kind of truth-theoretic semantics which Davidson favours. The principle (...) required to make the argument work allows us to resurrect Foster problems against the Davidsonian position. The Foster problems and the permutation inscrutability problems stand or fall together: they are one puzzle, not two. (shrink)

Taking away grains from a heap of rice, at what point is there no longer a heap? It seems small changes – removing a single grain – can’t make a difference to whether or not something is a heap; but big changes obviously do. How can this be, since big changes are nothing but small changes chained together?

Are interpersonal comparisons of desire possible? Can we give an account of how facts about desires are grounded that underpins such comparisons? This paper supposes the answer to the first question is yes, and provides an account of the nature of desire that explains how this is so. The account is a modification of the interpretationist metaphysics of representation that the author has recently been developing. The modification is to allow phenomenological affective valence into the “base facts” on which correct (...) interpretation is grounded. To use this extra resource within that theory to vindicate interpersonal comparisons, we will need to appeal rational connections between level of valence and level of desire, which this paper sets out and examines. (shrink)

In November 2016, the Council for International Organizations of Medical Sciences published its revised International Ethical Guidelines for Health-related Research Involving Humans. In relation to earlier versions, the scope of the new guidelines has been expanded to include public-health research. While successful to some extent, the document does not take into sufficient account the differences between public-health research and other types of health research. It is silent on some issues of importance to public-health research, such as its definition, health inequities (...) and novel research methodologies. Its treatment of some other issues, including the need for researchethics committee approval, consent, community involvement and dissemination of research results, are deficient in some respects. The guidelines that are particularly applicable to and useful for public-health research deal with social value, the health needs of communities and populations, community engagement, disasters and disease outbreaks, cluster randomised trials and data sharing. Much further development of the foundations and applications of public-health research ethics is needed to inform future revisions of the guidelines and of other international and national research-ethics documents. (shrink)

*This work has turned into a bigger project, and some of it is published in "Lewis on reference".* Some things, argues Lewis, are just better candidates to be referents than others. Even at the cost of attributing false beliefs, we interpret people as referring to the most interesting kinds in their vicinity. How should this be accounted for? In section 1, I look at Lewis’s interpretationism, and the reference magnetism it builds in (not just for ‘perfectly natural’ properties, but for (...) certain kinds of auxiliary apparatus). In section 2, I draw on (Field, 1975) to argue that what properties are reference magnetic may be an ultimately conventional matter—though in the Lewisian setting, there may be an objectively best conventional choice to make. But Lewis’s own account has implausible commitments, so in section 3 I consider variations and alternatives, all of which have problems. In section 4, I look in more detail at eligibility-based interpretationism that do not appeal to naturalness, arguing that there are credible metasemantic theories of this form. (shrink)

Bryne & Hajek (1997) argue that Lewis’s (1988; 1996) objections to identifying desire with belief do not go through if our notion of desire is ‘causalized’ (characterized by causal, rather than evidential, decision theory). I argue that versions of the argument go through on certain assumptions about the formulation of decision theory. There is one version of causal decision theory where the original arguments cannot be formulated—the ‘imaging’ formulation that Joyce (1999) advocates. But I argue this formulation is independently objectionable. (...) If we want to maintain the desire as belief thesis, there’s no shortcut through causalization. (shrink)

*This is a project I hope to come back to one day. It stalled, a bit, on the absence of a positive theory of update I could be satisfied with* When should we believe a indicative conditional, and how much confidence in it should we have? Here’s one proposal: one supposes actual the antecedent; and sees under that supposition what credence attaches to the consequent. Thus we suppose that Oswald did not shot Kennedy; and note that under this assumption, Kennedy (...) was assassinated by someone other than Oswald. Thus we are highly confident in the indicative: if Oswald did not kill Kennedy, someone else did. (shrink)

*This work is no longer under development* Two major themes in the literature on indicative conditionals are that the content of indicative conditionals typically depends on what is known;1 that conditionals are intimately related to conditional probabilities.2 In possible world semantics for counterfactual conditionals, a standard assumption is that conditionals whose antecedents are metaphysically impossible are vacuously true.3 This aspect has recently been brought to the fore, and defended by Tim Williamson, who uses it in to characterize alethic necessity by (...) exploiting such equivalences as: A⇔¬A A. One might wish to postulate an analogous connection for indicative conditionals, with indicatives whose antecedents are epistemically impossible being vacuously true: and indeed, the modal account of indicative conditionals of Brian Weatherson has exactly this feature.4 This allows one to characterize an epistemic modal by the equivalence A⇔¬A→A. For simplicity, in what follows we write A as KA and think of it as expressing that subject S knows that A.5 The connection to probability has received much attention. Stalnaker suggested, as a way of articulating the ‘Ramsey Test’, the following very general schema for indicative conditionals relative to some probability function P: P = P 1For example, Nolan ; Weatherson ; Gillies. 2For example Stalnaker ; McGee ; Adams. 3Lewis. See Nolan for criticism. 4‘epistemically possible’ here means incompatible with what is known. 5This idea was suggested to me in conversation by John Hawthorne. I do not know of it being explored in print. The plausibility of this characterization will depend on the exact sense of ‘epistemically possible’ in play—if it is compatibility with what a single subject knows, then can be read ‘the relevant subject knows that p’. If it is more delicately formulated, we might be able to read as the epistemic modal ‘must’. (shrink)

*Note that this project is now being developed in joint work with Rich Woodward* -/- Some things are left open by a work of fiction. What colour were the hero’s eyes? How many hairs are on her head? Did the hero get shot in the final scene, or did the jailor complete his journey to redemption and shoot into the air? Are the ghosts that appear real, or a delusion? Where fictions are open or incomplete in this way, we can (...) ask what attitudes it’s appropriate (or permissible) to take to the propositions in question, in engaging with the fiction. In Mimesis as Make-Believe (henceforth, MMB), Walton argues that just as truth norms belief, truth-in-fiction norms imagination. Granting that what is true-in-the-fiction should be imagined, and what is false-in-the-fiction is not to be imagined, there remains the question of what to say within the Waltonian framework about things that are neither true- nor false-in-the-fiction---the loci of incompleteness. (shrink)

Chancy counterfactuals are a headache. Dylan Dodd (2009) presents an interesting argument against a certain general strategy for accounting for them, instances of which are found in the appendices to Lewis (1979) and in Williams (2008). I will argue (i) that Dodd’s understates the counterintuitiveness of the conclusions he can reach; (ii) that the counterintuitiveness can be thought of as an instance of more general oddities arising when we treat vagueness and indeterminacy in a classical setting; and (iii) the underlying (...) source of discontent which animates Dodd’s complains is to be found in a certain general constraint one might impose on conditionals—what I’ll call the counterfactual Ramsey bound. Unfortunately, the counterfactual Ramsey bound is just as problematic as its famous indicative cousin. The moral is that there’s no comfortable resting place in this area; for violations of the counterfactual Ramsey bound are going to lead to prima facie surprising results. (shrink)

*These notes were folded into the published paper "Probability and nonclassical logic*. Revising semantics and logic has consequences for the theory of mind. Standard formal treatments of rational belief and desire make classical assumptions. If we are to challenge the presuppositions, we indicate what is kind of theory is going to take their place. Consider probability theory interpreted as an account of ideal partial belief. But if some propositions are neither true nor false, or are half true, or whatever—then it’s (...) far from clear that our degrees of belief in it and its negation should sum to 1, as classical probability theory requires (?, cf.). There are extant proposals in the literature for generalizing (categorical) probability theory to a non-classical setting, and we will use these below. But subjective probabilities themselves stand in functional relations to other mental states, and we need to trace the knock-on consequences of revisionism for this interrelationship (arguably, degrees of belief only count as kinds of belief in virtue of standing in these functional relationships). (shrink)