Fabio Lampert

Several theists, including Linda Zagzebski, have claimed that theism is somehow committed to nonvacuism about counterpossibles. Even though Zagzebski herself has rejected vacuism, she has offered an argument in favour of it, which Edward Wierenga has defended as providing strong support for vacuism that is independent of the orthodox semantics for counterfactuals, mainly developed by David Lewis and Robert Stalnaker. In this paper I show that argument to be sound only relative to the orthodox semantics, which entails vacuism, and give an example of a semantics for counterfactuals countenancing impossible worlds for which it fails.

Patrick Grim advances arguments meant to show that the doctrine of divine omniscience—the classical doctrine according to which God knows all truths—is false. In particular, we here have in mind to focus on two such arguments: the set theoretic argument and the semantic argument. These arguments due to Grim run parallel to, respectively, familiar paradoxes in set theory and naive truth theory. It is beyond the purview of this article to adjudicate whether or not these are successful arguments against the classical doctrine of omniscience. What we are here interested in is a way in which these arguments can be generalized. In particular, we show how generalizations of those arguments can target, explicitly, alternatives to the classical doctrine of omniscience, including what we here call 'restricted omniscience' and 'open future open theism'. As a corollary, considerations of Grim-style arguments do not support these alternatives to the classical doctrine of omniscience over the classical doctrine. We conclude that what is paradoxical is not the classical doctrine of omniscience just as such; rather, what is paradoxical is a core commitment shared by the classical doctrine and its more modest alternatives, namely, the thesis that God is a perfectly logical reasoner.

In a recent paper, Pruss proves the validity of the rule beta-2 relative to Lewis’s semantics for counterfactuals, which is a significant step forward in the debate about the consequence argument. Yet, we believe there remain intuitive counter-examples to beta-2 formulated with the actuality operator and rigidified descriptions. We offer a novel and two-dimensional formulation of the Lewisian semantics for counterfactuals and prove the validity of a new transfer rule according to which a new version of the consequence argument can be formulated. This new transfer rule is immune to the counter-examples involving the actuality operator and rigidified descriptions. However, we show that counter-examples to this new rule can also be generated, demanding that the Lewisian semantics be generalized for higher dimensions where counter-examples can always be generated.

We present a sound and complete Fitch-style natural deduction system for an S5 modal logic containing an actuality operator, a diagonal necessity operator, and a diagonal possibility operator. The logic is two-dimensional, where we evaluate sentences with respect to both an actual world (first dimension) and a world of evaluation (second dimension). The diagonal necessity operator behaves as a quantifier over every point on the diagonal between actual worlds and worlds of evaluation, while the diagonal possibility quantifies over some point on the diagonal. Thus, they are just like the epistemic operators for apriority and its dual. We take this extension of Fitch’s familiar derivation system to be a very natural one, since the new rules and labeled lines hereby introduced preserve the structure of Fitch’s own rules for the modal case.

What the rational thing to do in the face of disagreement by an epistemic peer is has been much discussed recently. Those who think that a peer’s disagreement is itself evidence against one’s belief, as many do, are committed to a special form of epistemic dependence. If such disagreement is really evidence, it seems reasonable to take it into account and to adjust one’s belief accordingly. But then it seems that the belief one ends up with depends, in part, on what someone else believes, even if one does not know why that someone believes what he does. While the practical impossibility of finding actual cases of peer disagreement has been often noted, its conceptual possibility has gone unquestioned. Here we challenge this consensus and argue, first, that, strictly speaking, peer disagreement is impossible and, second, that cases of – all-too-common – near-peer disagreement present no special puzzle and require nothing more than adhering to standard principles of sensible epistemic conduct. In particular, we argue that in such cases there is no good reason to adopt the widely accepted principle that evidence of evidence is evidence. If so, even if one takes a near-peer’s disagreement as a reason for reexamining one’s belief, one is not epistemically dependent in the sense one would be if that disagreement were evidence concerning the matter in question.

In a recent article, P. Roger Turner and Justin Capes argue that no one is, or ever was, even partly morally responsible for certain world-indexed truths. Here we present our reasons for thinking that their argument is unsound: It depends on the premise that possible worlds are maximally consistent states of affairs, which is, under plausible assumptions concerning states of affairs, demonstrably false. Our argument to show this is based on Bertrand Russell’s original ‘paradox of propositions’. We should then opt for a different approach to explain world-indexed truths whose upshot is that we may be morally responsible for some of them. The result to the effect that there are no maximally consistent states of affairs is independently interesting though, since this notion motivates an account of the nature of possible worlds in the metaphysics of modality. We also register in this article, independently of our response to Turner and Capes, and in the spirit of Russell’s aforementioned paradox and many other versions thereof, a proof of the claim that there is no set of all true propositions one can render false.

It is a widely held principle that no one is able to do something that would require the past to have been different from how it actually is. This principle of the fixity of the past has been presented in numerous ways, playing a crucial role in arguments for logical and theological fatalism, and for the incompatibility of causal determinism and the ability to do otherwise. I will argue that, assuming bivalence, this principle is in conflict with standard views about knowledge and the semantics for ‘actually’. I also consider many possible responses to the argument.

Rigidity does interesting philosophical work, with important consequences felt throughout metaphysics, epistemology, philosophy of mind, and so on. The authors’ aim in this article is to show that rigidity has yet another role to play, with surprising consequences for the problem of free will and determinism, for the phenomenon of rigidity has the upshot that some metaphysically necessary truths are up to us. The significance of this claim is shown in the context of influential arguments against free will. The authors show that some virtually indisputable inference rules employed in formulations of the Consequence Argument, as well as in fatalistic arguments, fail with a variety of counter-examples. Along the way, the authors compare the present arguments to other, similar arguments made in recent years.

In this paper we present tableau methods for two-dimensional modal logics. Although models for such logics are well known, proof systems remain rather unexplored as most of their developments have been purely axiomatic. The logics herein considered contain first-order quantifiers with identity, and all the formulas in the language are doubly-indexed in the proof systems, with the upper indices intuitively representing the actual or reference worlds, and the lower indices representing worlds of evaluation—first and second dimensions, respectively. The tableaux modulate over different notions of validity such as local, general, and diagonal, besides being general enough for several two-dimensional logics proposed in the literature. We also motivate the introduction of a new operator into two-dimensional languages and explore some of the philosophical questions raised by it concerning the relations there are between actuality, necessity, and the a priori, that seem to undermine traditional intuitive interpretations of two-dimensional operators.

Richard Feldman’s well-known principle about disagreement and evidence – usually encapsulated in the slogan, ‘evidence of evidence is evidence’, (EEE) – invites the question, what should a rational believer do when faced by such evidence, especially when the disagreement is with an epistemic peer? The question has been the subject of much controversy. However, it has been recently suggested both that the principle is subject to counterexamples and that it is trivial. If either is the case, the question of what to do in the face of evidence of evi- dence becomes less pressing. We contend that even if one or the other of these suggestions is right about (EEE) as a general principle about evidence, they leave it untouched insofar as it plays a role in the debates about the rational way to respond to disagreement and, in particular, to disagreement by an epistemic peer. This is because in such cases the evidence about which one has evidence and which is supposed to provide evidence against one's belief is the mere fact of someone’s disagreeing, rather than something that is related to the content of the proposition about which the parties disagree. We go on to argue that, so understood, the principle is false.