Robert Williams

*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’.

*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

*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)

According to Hegel, the true infinite is the fundamental concept of philosophy. Yet despite this fact, there is absence of consensus concerning its meaning and significance. The true infinite challenges the currently dominant non-metaphysical interpretations of Hegel, as it challenged the dominance of the Kantian framework in its own day, specifically Kant’s attack on theology and his treatment of theology as a postulate of moralit y. Kant admits that the God-postulate has only subjective necessity and validity, and is an expression of moral faith. Hegel both accepts Kant’s approach to the God-question through freedom and practical reason, but he rejects Kant’s philosophy of the postulates as incoherent, burdened with finitude and antithesis. The ought is only the beginning of the transcendence of finitude, but also essentially clings to finitude. This is the spurious infinite. In contrast to the traditional view of abstract transcendence, Hegel shows that the very attempt to separate the infinite from the finite only renders the infinite finite and levels it. The consciousness of limit (finitude) implies a transcendence of limit. The true infinite is an onto-theological principle, a social infinite that overcomes the limits imposed by abstract transcendence and the dualisms imposed by the Kantian frame. It is of vital importance for Hegel’s philosophy of religion, as both a doctrine of divine presence and absolute spirit in its community.

According to Hegel, the true infinite is the fundamental concept of philosophy. Yet despite this fact, there is absence of consensus concerning its meaning and significance. The true infinite challenges the currently dominant non-metaphysical interpretations of Hegel, as it challenged the dominance of the Kantian framework in its own day, specifically Kant’s attack on theology and his treatment of theology as a postulate of moralit y. Kant admits that the God-postulate has only subjective necessity and validity, and is an expression of moral faith. Hegel both accepts Kant’s approach to the God-question through freedom and practical reason, but he rejects Kant’s philosophy of the postulates as incoherent, burdened with finitude and antithesis. The ought is only the beginning of the transcendence of finitude, but also essentially clings to finitude. This is the spurious infinite. In contrast to the traditional view of abstract transcendence, Hegel shows that the very attempt to separate the infinite from the finite only renders the infinite finite and levels it. The consciousness of limit (finitude) implies a transcendence of limit. The true infinite is an onto-theological principle, a social infinite that overcomes the limits imposed by abstract transcendence and the dualisms imposed by the Kantian frame. It is of vital importance for Hegel’s philosophy of religion, as both a doctrine of divine presence and absolute spirit in its community.

This paper has three sections. 1) For Hegel, the true infinite is the fundamental concept of philosophy. The true infinite challenges current non-metaphysical interpretations of Hegel, as it challenged Kant’s restriction of cognition to finitude and attack on metaphysics. The consciousness of limit implies a transcendence of limit, and an infinite opposed to the finite shows itself to be finite. 2) Hegel accepts Kant’s approach to the God-question through practical reason, but rejects Kant’s postulates as incoherent. The content of the God-postulate contradicts the subject-relative form of the postulate. Kant’s moral God is a spurious infinite. The true infinite is a self-determining, self-realizing, inclusive whole which sublates the subjective ‘ought to be’ of the postulate. 3) For both Hegel and Nietzsche the moral god is dead; both pursue the question of theology after the death of God. I explore Hegel’s account of tragedy and his conception of tragic reconciliation. The latter is not a comic, but an “anguished reconciliation, a disquieted bliss in disaster.” The death of God and reconciliation include negation and suffering, and are closer to tragic reconciliation than to Dante’s Divine Comedy with its impassible absolute that lacks serious opposition

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

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.

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.

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.

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).