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Fine suggests that the possible worlds semantics for counterfactuals faces a more serious difficulty, which can't be so easily remedied or ignored. For the semantics requires that the truth-value of a counterfactual statement should be preserved under the substitution of logically equivalent antecedents. But this substitution principle is incompatible with the combination of certain intuitively compelling counterfactual judgments and certain intuitively compelling principles of reasoning. Thus adoption of the semantics forces people to make an unpalatable choice between the particular counterfactual judgments, on the one hand, and the general principles of counterfactual reasoning, on the other. He also proposes an alternative semantics, using possible states in place of possible worlds, which avoids the difficulties and which is more satisfactory than the possible worlds semantics in a number of other respects.

Since the publication of David Lewis' Counterfactuals, the standard line on subjunctive conditionals with impossible antecedents (or counterpossibles) has been that they are vacuously true. That is, a conditional of the form 'If p were the case, q would be the case' is trivially true whenever the antecedent, p, is impossible. The primary justification is that Lewis' semantics best approximates the English subjunctive conditional, and that a vacuous treatment of counterpossibles is a consequence of that very elegant theory. Another justification derives from the classical lore than if an impossibility were true, then anything goes. In this paper we defend non-vacuism, the view that counterpossibles are sometimes non-vacuously true and sometimes non-vacuously false. We do so while retaining a Lewisian semantics, which is to say, the approach we favor does not require us to abandon classical logic or a similarity semantics. It does however require us to countenance impossible worlds. An impossible worlds treatment of counterpossibles is suggested (but not defended) by Lewis (Counterfactuals. Blackwell, Oxford, 1973), and developed by Nolan (Notre Dame J Formal Logic 38:325-527, 1997), Kment (Mind 115:261-310, 2006a: Philos Perspect 20:237-302, 2006b), and Vander Laan (In: Jackson F, Priest G (eds) Lewisian themes. Oxford University Press, Oxford, 2004). We follow this tradition, and develop an account of comparative similarity for impossible worlds.

A number of recent authors (Galles and Pearl, Found Sci 3 (1):151–182, 1998; Hiddleston, Noûs 39 (4):232–257, 2005; Halpern, J Artif Intell Res 12:317–337, 2000) advocate a causal modeling semantics for counterfactuals. But the precise logical significance of the causal modeling semantics remains murky. Particularly important, yet particularly under-explored, is its relationship to the similarity-based semantics for counterfactuals developed by Lewis (Counterfactuals. Harvard University Press, 1973b). The causal modeling semantics is both an account of the truth conditions of counterfactuals, and an account of which inferences involving counterfactuals are valid. As an account of truth conditions, it is incomplete. While Lewis's similarity semantics lets us evaluate counterfactuals with arbitrarily complex antecedents and consequents, the causal modeling semantics makes it hard to ascertain the truth conditions of all but a highly restricted class of counterfactuals. I explain how to extend the causal modeling language to encompass a wider range of sentences, and provide a sound and complete axiomatization for the extended language. Extending the truth conditions for counterfactuals has serious consequences concerning valid inference. The extended language is unlike any logic of Lewis's: modus ponens is invalid, and classical logical equivalents cannot be freely substituted in the antecedents of conditionals.

A new model of persuasion is presented. A listener first announces and commits to a codex (i.e., a set of conditions). The speaker then presents a (not necessarily true) profile that must satisfy the codex in order for the listener to be persuaded. The speaker is boundedly rational in the sense that his ability to come up with a persuasive profile is limited and depends on the true profile and the content and framing of the codex. The circumstances under which the listener can design a codex that will implement his goal are fully characterized.

The traditional Lewis-Stalnaker semantics treats all counterfactuals with an impossible antecedent as trivially or vacuously true. Many have regarded this as a serious defect of the semantics. For intuitively, it seems, counterfactuals with impossible antecedents—counterpossibles—can be non-trivially true and nontrivially false. Whereas the counterpossible \"If Hobbes had squared the circle, then the mathematical community at the time would have been surprised\" seems true, \"If Hobbes had squared the circle, then sick children in the mountains of Afghanistan at the time would have been thrilled\" seems false. Many have proposed to extend the Lewis-Stalnaker semantics with impossible worlds to make room for a non-trivial or non-vacuous treatment of counterpossibles. Roughly, on the extended Lewis-Stalnaker semantics, we evaluate a counterfactual of the form \"If A had been true, then C would have been true\" by going to closest world—whether possible or impossible—in which A is true and check whether C is also true in that world. If the answer is \"yes\", the counterfactual is true; otherwise it is false. Since there are impossible worlds in which the mathematically impossible happens, there are impossible worlds in which Hobbes manages to square the circle. And intuitively, in the closest such impossible worlds, sick children in the mountains of Afghanistan are not thrilled—they remain sick and unmoved by the mathematical developments in Europe. If so, the counterpossible \"If Hobbes had squared the circle, then sick children in the mountains of Afghanistan at the time would have been thrilled\" comes out false, as desired. In this paper, I will critically investigate the extended Lewis-Stalnaker semantics for counterpossibles. I will argue that the standard version of the extended semantics, in which impossible worlds correspond to maximal, logically inconsistent entities, fails to give the correct semantic verdicts for many counterpossibles. In light of the negative arguments, I will then outline a new version of the extended Lewis-Stalnaker semantics that can avoid these problems.

According to the Principle of Conditional Non-Contradiction (CNC), conditionals of the form \"If p, q\" and \"If p, not q\" cannot both be true, unless p is inconsistent. This principle is widely regarded as an adequacy constraint on any semantics that attributes truth conditions to conditionals. Gibbard has presented an example of a pair of conditionals that, in the context he describes, appear to violate CNC. He concluded from this that conditionals lack truth conditions. We argue that this conclusion is rash by proposing a new diagnosis of what is going on in Gibbard's argument. We also provide empirical evidence in support of our proposal.

One of the most dominant approaches to semantics for relevant (and many paraconsistent) logics is the Routley-Meyer semantics involving a ternary relation on points. To some (many?), this ternary relation has seemed like a technical trick devoid of an intuitively appealing philosophical story that connects it up with conditionality in general. In this paper, we respond to this worry by providing three different philosophical accounts of the ternary relation that correspond to three conceptions of conditionality. We close by briefly discussing a general conception of conditionality that may unify the three given conceptions.

Inference versus consequence, an invited lecture at the LOGICA 1997 conference at Castle Liblice, was part of a series of articles for which I did research during a Stockholm sabbatical in the autumn of 1995. The article seems to have been fairly effective in getting its point across and addresses a topic highly germane to the Uppsala workshop. Owing to its appearance in the LOGICA Yearbook 1997, Filosofía Publishers, Prague, 1998, it has been rather inaccessible. Accordingly it is republished here with only bibliographical changes and an afterword.

In the recent paper \"Naive modus ponens\", Zardini presents some brief considerations against an approach to semantic paradoxes that rejects the transitivity of entailment. The problem with the approach is, according to Zardini, that the failure of a meta-inference closely resembling modus ponens clashes both with the logical idea of modus ponens as a valid inference and the semantic idea of the conditional as requiring that a true conditional cannot have true antecedent and false consequent. I respond on behalf of the non-transitive approach. I argue that the meta-inference in question is independent from the logical idea of modus ponens, and that the semantic idea of the conditional as formulated by Zardini is inadequate for his purposes because it is spelled out in a vocabulary not suitable for evaluating the adequacy of the conditional in semantics for non-transitive entailment. I proceed to generalize the semantic idea of the conditional and show that the most popular semantics for non-transitive entailment satisfies the new formulation.

The paper is concerned with a logical difficulty which Lionel Shapiro's deflationist theory of logical consequence (as well as the author's favoured, non-deflationist theory) gives rise to. It is argued that Shapiro's noncontractive approach to solving the difficulty, although correct in its broad outlines, is nevertheless extremely problematic in some of its specifics, in particular in its failure to validate certain intuitive rules and laws associated with the principle of modus ponens. An alternative non-contractive theory is offered which does not suffer from the same problem.