On the structural similarities between worlds and times

In the debate about the nature and identity of possible worlds, philosophers have neglected the parallel questions about the nature and identity of moments of time. These are not questions about the structure of time in general, but rather about the internal structure of each individual time. Times and worlds share the following structural similarities: both are maximal with respect to propositions (at every world and time, either p or ～p is true, for every p); both are consistent; both are closed (every modal consequence of a proposition true at a world is also true at that world, and every tense-theoretic consequence of a proposition true at a time is also true at that time); just as there is a unique actual world, there is a unique present moment; and just as a proposition is necessarily true iff true at all worlds, a proposition is eternally true iff true at all times. In this paper, I show that a simple extension of my theory of worlds yields a theory of times in which the above structural similarities between the two are consequences.     

What in the world are the ways things might have been?

Robert Stalnaker is an actualist who holds that merely possible worlds are uninstantiated properties that might have been instantiated. Stalnaker also holds that there are no metaphysically impossible worlds: uninstantiated properties that couldn't have been instantiated. These views motivate Stalnaker's "two dimensional" account of the necessary a posteriori on which there is no single proposition that is both necessary and a posteriori. For a (metaphysically) necessary proposition is true in all (metaphysically) possible worlds. If there were necessary a posteriori propositions, that would mean that there were propositions true in all possible worlds but which could only be known to be true by acquiring empirical evidence. Consider such a purported proposition P. The role of empirical evidence for establishing P's truth would have to be to rule out worlds in which P is false. If there were no such worlds to be ruled out, we would not require evidence for P. But by hypothesis, P is necessary and so true in all metaphysically possible worlds. And on Stalnaker's view, the metaphysically possible worlds are all the worlds there are. So there can be no proposition that is true in all possible worlds, but that we require evidence to know. In this way, the motivation for Stalnaker's two dimensional account of the necessary a posteriori rests on his denying that there are metaphysically impossible Worlds. I argue that given his view of what possible worlds are, Stalnaker has no principled reason for denying that there are metaphysically impossible worlds. If I am right, this undercuts Stalnaker's motivation for his two dimensional account of the necessary a posteriori.

General information in relevant logic

This paper sets out a philosophical interpretation of the model theory of Mares and Goldblatt (The Journal of Symbolic Logic 71, 2006). This interpretation distinguishes between truth conditions and information conditions. Whereas the usual Tarskian truth condition holds for universally quantified statements, their information condition is quite different. The information condition utilizes general propositions. The present paper gives a philosophical explanation of general propositions and argues that these are needed to give an adequate theory of general information.     

The Fundamental Theorem of World Theory

The fundamental principle of the theory of possible worlds is that a proposition p is possible if and only if there is a possible world at which p is true. In this paper we present a valid derivation of this principle from a more general theory in which possible worlds are defined rather than taken as primitive. The general theory uses a primitive modality and axiomatizes abstract objects, properties, and propositions. We then show that this general theory has very small models and hence that its ontological commitments—and, therefore, those of the fundamental principle of world theory—are minimal.     

Uncertainty and Persistence: a Bayesian Update Semantics for Probabilistic Expressions

This paper presents a general-purpose update semantics for expressions of subjective uncertainty in natural language. First, a set of desiderata are established for how expressions of subjective uncertainty should behave in dynamic, update-based semantic systems; then extant implementations of expressions of subjective uncertainty in such models are evaluated and found wanting; finally, a new update semantics is proposed. The desiderata at the heart of this paper center around the contention that expressions of subjective uncertainty express beliefs which are not persistent (i.e. beliefs that won’t necessarily survive the addition of new information that is compatible with all previous information), whereas propositions express beliefs that are persistent. I argue that if we make the move of treating updates in a dynamic semantics as Bayesian updates, i.e. as conditionalization, then expressions of subjective uncertainty will behave the way we want them to without altering the way propositions behave.     

Research note: The accuracy of group majorities for disjunctive and conjunctive decision tasks

For complex group decision tasks which can be described in terms of establishing the truth value of conjunctive (and) or disjunctive (or) composite propositions, the advantage for group judgmental accuracy of disaggregating the decision task into separate individual evaluations of the truth value of each component atomic proposition in the composite is investigated. For true propositions it is shown that disaggregation is preferable for conjunctive tasks, but not for disjunctive tasks; while the reverse is true for false propositions.     

An Impossibility Result for Coherence Rankings

If we receive information from multiple independent and partially reliable information sources, then whether we are justified to believe these information items is affected by how reliable the sources are, by how well the information coheres with our background beliefs and by how internally coherent the information is. We consider the following question. Is coherence a separable determinant of our degree of belief, i.e. is it the case that the more coherent the new information is, the more justified we are in believing the new information, ceteris paribus? We show that if we consider sets of information items of any size (Holism), and if we assume that there exists a coherence Ordering over such sets and that coherence is a function of the probability distribution over the propositions in such sets (Probabilism), then Separability fails to hold.     

Against global method safety

The global method safety account of knowledge states that an agent’s true belief that p is safe and qualifies as knowledge if and only if it is formed by method M, such that her beliefs in p and her beliefs in relevantly similar propositions formed by M in all nearby worlds are true. This paper argues that global method safety is too restrictive. First, the agent may not know relevantly similar propositions via M because the belief that p is the only possible outcome of M. Second, there are cases where there is a fine-grained belief that is unsafe and a relevantly similar coarse-grained belief (with looser truth conditions) that is safe and where both beliefs are based on the same method M. Third, the reliability of conditional reasoning, a basic belief-forming method, seems to be sensitive to fine-grained contents, as suggested by the wide variation in success rates for thematic versions of the Wason selection task.

     

Existential Import in Cartesian Semantics

The paper explores the existential import of universal affirmative in Descartes, Arnauld and Malebranche. Descartes holds, inconsistently, that eternal truths are true even if the subject term is empty but that a proposition with a false idea as subject is false. Malebranche extends Descartes’ truth-conditions for eternal truths, which lack existential import, to all knowledge, allowing only for non-propositional knowledge of contingent existence. Malebranche's rather implausible Neoplatonic semantics is detailed as consisting of three key semantic relations: illumination by which God's ideas cause mental terms, creation by which God's ideas cause material substances by a kind of ‘ontic privation’, and sensation in which brain events occasion states of mental awareness. In contrast, Arnauld distinguishes two types of propositions – necessary and contingent – with distinct truth-conditions, one with and one without existential import. Arnauld's more modern semantics is laid out as a theory of reference that substitutes earlier causal accounts with one that adapts the medieval notion of objective being. His version anticipates modern notions of intentional content and appeals in its ontology only to substances and their modes.     

Epistemic instrumentalism

According to epistemic instrumentalism, epistemically rational beliefs are beliefs that are produced in ways that are conducive to certain ends that one wants to attain. In “Epistemic Rationality as Instrumental Rationality: A Critique,” Thomas Kelly advances various objections to epistemic instrumentalism. While I agree with the general thrust of Kelly’s objections, he does not distinguish between two forms of epistemic instrumentalism. Intellectualist forms maintain that epistemically rational beliefs are beliefs arrived at in compliance with rules that are conducive to epistemic ends, such as believing true propositions and not believing false propositions. Pragmatist forms maintain that rational beliefs are those that are formed, maintained, and revised in accordance with rules that are conducive to whatever ends one wants to attain. In this paper, I argue against both forms of epistemic instrumentalism and suggest that epistemic instrumentalism grows out of a mistaken conception of what it means to say that the standards of epistemic rationality are ‘normative.’     

The new growing block theory vs presentism

It was once held to be a virtue of the growing block theory that it combines temporal dynamism with a straightforward account of in virtue of what past-tensed propositions are true, and an explanation for why some future-tensed propositions are not true (assuming they are not). This put the growing block theory ahead of its principal dynamist rival: presentism. Recently, new growing block theorists have suggested that what makes true, past-tensed propositions, is not the same kind of thing as what makes true, present-tensed propositions. They have done so in an attempt to defuse a particular epistemic objection to their view. In this paper it is argued that the new growing block theorist faces a dilemma. The more unified a strategy is for responding to the epistemic objection, the more that strategy results in the new growing block model positing truthmakers that are similar to those posited by the presentist, which erodes the purported advantage of the growing block theory over presentism. On the other hand, versions of the new growing block theory that embrace disunified strategies are better able to differentiate themselves from presentism, but are unattractive because of their disunity.     

Comparing the meanings of “if” and “all”

In this study, we compared the everyday meanings of conditionals (“if p then q”) and universally quantified statements (“all p are q”) when applied to sets of elements. The interpretation of conditionals was predicted to be directly related to the conditional probability, such that P(“if p then q”) = P(q|p). Quantified statements were assumed to have two interpretations. According to an instance-focused interpretation, quantified statements are equivalent to conditionals, such that P(“all p are q”) = P(q|p). According to a set-focused interpretation, “all p are q” is true if and only if every instance in set p is an instance of q, so that the statement would be accepted when P(q|p) = 1 and rejected when this probability was below 1. We predicted an instance-focused interpretation of “all” when the relation between p and q expressed a general law for an infinite set of elements. A set-focused interpretation of “all” was predicted when the relation between p and q expressed a coincidence among the elements of a finite set. Participants were given short context stories providing information about the frequency of co-occurrence of cases of p, q, not-p, and not-q in a population. They were then asked to estimate the probability that a statement (conditional or quantified) would be true for a random sample taken from that population. The probability estimates for conditionals were in accordance with an instance-focused interpretation, whereas the estimates for quantified statements showed features of a set-focused interpretation. The type of the relation between p and q had no effect on this outcome.     

The New View on Ignorance Undefeated

In this paper, I provide a defence of the New View, on which ignorance is lack of true belief rather than lack of knowledge. Pierre Le Morvan has argued that the New View is untenable, partly because it fails to take into account the distinction between propositional and factive ignorance. I argue that propositional ignorance is just a subspecies of factive ignorance and that all the work that needs to be done can be done by using the concept of factive ignorance. I also defend two arguments of mine in favour of the New View against Le Morvan??s criticisms. As to the Linguistic Argument, I point out that the intuitions of the adherent of the New View about cases of true belief that fall short of knowledge are really intuitions about factive rather than propositional ignorance. As to the Excuse Argument, I argue that true belief is exculpatorily relevant: a true belief in a proposition p, where disbelief that p or suspension on p would provide at least a partial excuse, is relevant in that it renders one blameworthy for one??s action, unless further excuses hold. Finally, I reply to two closely related objections that might be levelled against the New View, namely that it seems false that one can reduce one??s ignorance by arbitrarily believing as many propositions as possible and that it seems false that an intellectually conscientious and critical person is more ignorant than an intellectually sloppy and credulous person just because the latter has more true beliefs.     

Propositions: Individuation and Invirtuation

The pressure to individuate propositions more finely than intensionally—that is, hyper-intensionally—has two distinct sources. One source is the philosophy of mind: one can believe a proposition without believing an intensionally equivalent proposition. The second source is metaphysics: there are intensionally equivalent propositions, such that one proposition is true in virtue of the other but not vice versa. I focus on what our theory of propositions should look like when it's guided by metaphysical concerns about what is true in virtue of what. In this paper I articulate and defend a metaphysical theory of the individuation of propositions, according to which two propositions are identical just in case they occupy the same nodes in a network of invirtuation relations. Invirtuation is here taken to be a primitive relation of metaphysical explanation exemplified by propositions that, in conjunction with truth, defines the notion of true in virtue of. After formulating the theory, I compare it with a view that individuates propositions by cognitive equivalence, and then defend the theory from objections.     

Rationality, Justification, and the Internalism/Externalism Debate

In this paper, I argue that what underlies internalism about justification is a rationalist conception of justification, not a deontological conception of justification, and I argue for the plausibility of this rationalist conception of justification. The rationalist conception of justification is the view that a justified belief is a belief that is held in a rational way; since we exercise our rationality through conscious deliberation, the rationalist conception holds that a belief is justified iff a relevant possible instance of conscious deliberation would endorse the belief. The importance of conscious deliberation stems from its role in guiding us in acquiring true beliefs: whereas the externalist holds that if we wish to acquire true beliefs, we have to begin by assuming that some of our usual methods of belief formation generally provide us with true beliefs, the internalist holds that if we form beliefs by conscious deliberation, we can be conscious of reasons for thinking that our beliefs are true. Conscious deliberation can make us conscious of reasons because it proceeds via rational intuitions. I argue that despite the fallibility of rational intuition, rational intuitions do enable us to become conscious of reasons for belief.

The Trouble with Tarski

As a result of thinking ( pace Tarski, wrongly) that it is propositions, not sentences, that are true or false, it has been supposed (also wrongly) that propositions such as that 'Snow is white' is true if and only if snow is white are necessarily true. But changing the rules for the use of the words in a sentence has no effect on the truth of the proposition, only on what proposition it formulates. Many similar statements, e.g., that 'plus' does not mean plus, are only pragmatically contradictory: if this were true, it would be impossible to say so in these words. One should distinguish between sentences that express necessary truths, and sentences that necessarily express truths. It follows that many well known accounts of necessity are wrong, that the truth of an analytic proposition does not follow from the definitions of the words in the sentence that expresses it, that it is not helpful to define meaning in terms of truth, that truth is not relative to language, and that conventionalism is false. This paper is a move in the direction of establishing the eternity of truth.     

Propositions,Properties and Relations: Wittgenstein's “Notes on Logic” and the Tractatus

Frege famously argued that truth is not a property or relation. In the “Notes on Logic” Wittgenstein emphasised the bi‐polarity of propositions which he called their sense. He argued that “propositions by virtue of sense cannot have predicates or relations.” This led to his fundamental thought that the logical constants do not represent predicates or relations. The idea, however, has wider ramifications than that. It is not just that propositions cannot have relations to other propositions but also that they cannot have relations to anything at all. The paper explores the consequences of this insight for the way in which we should read the Tractatus. In the “Notes on Logic” the insight led to Wittgenstein's emphasis on “facts” in any attempt to understand the nature of symbolism. This emphasis is continued in the Tractatus. It is central to his view that propositions are facts which picture facts which prevent us from construing such picturing as a relation between what pictures and what is pictured. It illuminates the importance of context principle with regard to the distinction between showing and saying to which Wittgenstein attached so much importance and it underlies the non‐relational view of psychological propositions which he advocates. Finally, if propositions by virtue of sense cannot have predicates or relations the paradox at the end of a work which consist largely of propositions about propositions becomes intelligible.     

Arguments from Expert Opinion and Persistent Bias

Accounts of arguments from expert opinion take it for granted that expert judgments count as (defeasible) evidence for propositions, and so an argument that proceeds from premises about what an expert judges to a conclusion that the expert is probably right is a strong argument. In Mizrahi (Informal Log 33:57–79, 2013), I consider a potential justification for this assumption, namely, that expert judgments are significantly more likely to be true than novice judgments, and find it wanting because of empirical evidence suggesting that expert judgments under uncertainty are not significantly more likely to be true than novice judgments or even chance. In this paper, I consider another potential justification for this assumption, namely, that expert judgments are not influenced by the cognitive biases novice judgments are influenced by, and find it wanting, too, because of empirical evidence suggesting that experts are vulnerable to pretty much the same cognitive biases that novices are vulnerable to. If this is correct, then the basic assumption at the core of accounts of arguments from expert opinion, namely, that expert judgments count as (defeasible) evidence for propositions, remains unjustified.     

On the Functionalization of Pluralist Approaches to Truth

Traditional inflationary approaches that specify the nature of truth are attractive in certain ways; yet, while many of these theories successfully explain why propositions in certain domains of discourse are true, they fail to adequately specify the nature of truth because they run up against counterexamples when attempting to generalize across all domains. One popular consequence is skepticism about the efficaciousness of inflationary approaches altogether. Yet, by recognizing that the failure to explain the truth of disparate propositions often stems from inflationary approaches allegiance to alethic monism, pluralist approaches are able to avoid this explanatory inadequacy and the resulting skepticism, though at the cost of inviting other conceptual difficulties. A novel approach, alethic functionalism, attempts to circumvent the problems faced by pluralist approaches while preserving their main insights. Unfortunately, it too generates additional problems – namely, with its suspect appropriation of the multiple realizability paradigm and its platitude-based strategy – that need to be dissolved before it can constitute an adequate inflationary approach to the nature of truth.     

The grounding problem and presentist explanations

Opponents of presentism have often argued that the presentist has difficulty in accounting for what makes (presently) true past-tensed propositions (TptP) true in a way that is compatible with her metaphysical view of time and reality. The problem is quite general and concerns not only strong truth-maker principles, but also the requirement that truth be grounded in reality. In order to meet the challenge, presentists have proposed many peculiar present aspects of the world as grounds for truths concerning the past, such as uninstantiated haecceities, Meinongian non-existents, ersatz times, and dispositional and distributional properties. The main problem with all such solutions is that any explanation of what grounds a TptP that involves the past is eo ipso a better explanation than any that involves only the present. Thus, the quest for an account of grounding for TptP that is compatible with the presentist ontology and ideology is doomed to be explanatorily deficient with respect to eternalism. In a recent article, Ben Caplan and David Sanson have claimed that presentists should change their strategy and, rather than seeking for exotic grounds for TptP, should adopt a more liberal view of explanation. That is, they should allow themselves to resort to “past directed” explanations, even if they do not accept the past in their ontology and ideology. I argue that such a proposal is not compatible with the tenet that there is a substantial distinction between the ideology of such a version of presentism and that of eternalism. Therefore, the presentist cannot endorse such “deflationist” explanations as an easy way out to the problem of the grounding of TptP.