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A counterpossible conditional is a counterfactual with an impossible antecedent. Common sense delivers the view that some such conditionals are true, and some are false. In recent publications, Timothy Williamson has defended the view that all are true. In this paper we defend the common sense view against Williamson’s objections. [ABSTRACT FROM AUTHOR]

Sometimes a fact can play a role in a grounding explanation, but the particular content of that fact make no difference to the explanation—any fact would do in its place. I call these facts vacuous grounds. I show that applying the distinction between-vacuous grounds allows us to give a principled solution to Kit Fine and Stephen Kramer’s paradox of (reflexive) ground. This paradox shows that on minimal assumptions about grounding and minimal assumptions about logic, we can show that grounding is reflexive, contra the intuitive character of grounds. I argue that we should never have accepted that grounding is irreflexive in the first place; the intuitions that support the irreflexive intuition plausibly only require that grounding be non-vacuously irreflexive. Fine and Kramer’s paradox relies, essentially, on a case of vacuous grounding and is thus no problem for this account. [ABSTRACT FROM AUTHOR]

Our main goal is to investigate whether the infinitary rules for the quantifiers endorsed by Elia Zardini in a recent paper are plausible. First, we will argue that they are problematic in several ways, especially due to their infinitary features. Secondly, we will show that even if these worries are somehow dealt with, there is another serious issue with them. They produce a truth-theoretic paradox that does not involve the structural rules of contraction. [ABSTRACT FROM AUTHOR]

The notion of a proposition is central to philosophy. But it is subject to paradoxes. A natural response is a hierarchical account and, ever since Russell proposed his theory of types in 1908, this has been the strategy of choice. But in this paper I raise a problem for such accounts. While this does not seem to have been recognized before, it would seem to render existing such accounts inadequate. The main purpose of the paper, however, is to provide a new hierarchical account that solves the problem. [ABSTRACT FROM AUTHOR]

Epistemic utility theory seeks to establish epistemic norms by combining principles from decision theory and social choice theory with ways of determining the epistemic utility of agents' attitudes. Recently, Moss ( Mind, 120(480), 1053-69, 2011) has applied this strategy to the problem of finding epistemic compromises between disagreeing agents. She shows that the norm 'form compromises by maximizing average expected epistemic utility', when applied to agents who share the same proper epistemic utility function, yields the result that agents must form compromises by splitting the difference between their credence functions. However, this 'split the difference' norm is in conflict with conditionalization, since applications of the two norms don't commute. A common response in the literature seems to be to abandon the procedure of splitting the difference in favor of compromise strategies that avoid non-commutativity. This would also entail abandoning Moss' norm. I explore whether a different response is feasible. If agents can use epistemic utility-based considerations to agree on an order in which they will apply the two norms, they might be able to avoid diachronic incoherence. I show that this response can't save Moss' norm, because the agreements concerning the order of compromising and updating it generates are not stable over time, and hence cannot avoid diachronic incoherence. I also show that a variant of Moss' norm, which requires that the weights given to each agent's epistemic utility change in a way that ensures commutativity, cannot be justified on epistemological grounds. [ABSTRACT FROM AUTHOR]

Since Montague's work it is well known that treating a single modality as a predicate may lead to paradox. In their paper 'No Future', Horsten and Leitgeb (2001) show that if the two temporal modalities are treated as predicates paradox might arise as well. In our paper we investigate whether paradoxes of multiple modalities, such as the No Future paradox, are genuinely new paradoxes or whether they 'reduce' to the paradoxes of single modalities. In order to address this question we develop a notion of reducibility based on a version of Smoryński Diagonalized Operator Logic. We show that there are reducible multimodal paradoxes as well as irreducible paradoxes of interaction. In particular, we show the No Future paradox to be an irreducible paradox according to our notion of reducibility. [ABSTRACT FROM AUTHOR]

We discuss three aspects of the intuitionistic reformulation of Mally's deontic logic that was recently proposed (Journal of Philosophical Logic 42, 635-641, ()). First, this reformulation is more similar to Standard Deontic Logic than appears at first sight: like Standard Deontic Logic, it is Kanger reducible and Anderson reducible to alethic logic and it has a semantical interpretation that can be read in deontic terms. Second, this reformulation has an extension that provides 100% of the theorems stated by Mally himself (and that does not provide O A → A, which Mally himself did not state either). Third, it is interesting to view Mally's original deontic logic as an extension of this reformulation. [ABSTRACT FROM AUTHOR]

Several proof-theoretic notions of validity have been proposed in the literature, for which completeness of intuitionistic logic has been conjectured. We define validity for intuitionistic propositional logic in a way which is common to many of these notions, emphasizing that an appropriate notion of validity must be closed under substitution. In this definition we consider atomic systems whose rules are not only production rules, but may include rules that allow one to discharge assumptions. Our central result shows that Harrop's rule is valid under substitution, which refutes the completeness conjecture for intuitionistic logic. [ABSTRACT FROM AUTHOR]

We show that Leitgeb's dependence operator of Leitgeb ( Journal of Philosophical Logic, 34, 155-192, ) is a ${{\Pi }^{1}_{1}}$-operator and that this is best possible. [ABSTRACT FROM AUTHOR]