Online research in philosophy

In this paper I shall be concerned primarily with contingent subjunctive conditionals, not to analyze them, but to argue that those who attempt such an analysis employing the concept of law--an approach which I confess seems promising--are at best providing logically sufficient conditions for the truth of contingent subjunctive conditionals and are not providing a correct analysis. My argument will have two parts. I shall first argue that the more plausible attempts to analyze our concept of law without subjunctive conditionals seem to fall prey to counter-examples. Secondly, I shall argue that even if we had an independent understanding of law, it is at least questionable that such an analysis could be employed in explicating conditions which are both logically necessary and sufficient for the truth of a subjunctive conditional.

Predicate modal logics based on Kwith non-compact extra axioms are discussed and a sufficient condition for the model existence theorem is presented. We deal with various axioms in a general way by an algebraic method, instead of discussing concrete non-compact axioms one by one.

An imperative conditional is a conditional in the imperative mood (by analogy with “indicative conditional”, “subjunctive conditional”). What, in general, is the meaning and the illocutionary effect of an imperative conditional? I survey four answers: the answer that imperative conditionals are commands to the effect that an indicative conditional be true; two versions of the answer that imperative conditionals express irreducibly conditional commands; and finally, the answer that imperative conditionals express a kind of hybrid speech act between command and assertion.

It is known that indicative and subjunctive conditionals interact differently with a rigidifying "actually" operator. The paper studies this difference in an abstract setting. It does not assume the framework of possible world semantics, characterizing "actually" instead by the type of logically valid formulas to which it gives rise. It is proved that in a language with such features all sentential contexts that are congruential (in the sense that they preserve logical equivalence) are extensional (in the sense that they preserve material equivalence). For a subjunctive conditional, the natural conclusion to draw is that it is non-congruential. It is much harder to defend the claim that an indicative conditional is non-congruential. The pressure to treat the indicative conditional as truth-functional is correspondingly greater. The implications of these results for attempts to interpret the indicative conditional as an epistemic or doxastic operator are assessed.

Why are some conditionals subjunctive? It is often assumed that at least one crucial difference is that subjunctive conditionals presuppose that their antecedent is false, that they are counterfactual (Lakoff 1970). The traditional theory has apparently been refuted. Perhaps the clearest counter-example is one given by Alan Anderson (1951: 37): If Jones had taken arsenic, he would have shown just exactly those symptoms which he does in fact show. A typical place to use such a subjunctive conditional would be in the course of an argument that tries to bolster the hypothesis that Jones did in fact take arsenic. But then it would of course be self-defeating to presuppose that the hypothesis is false. Thus, something else must be going on.

Here I first raise an argument purporting to show that Lewis’ Modal Realism ends up being completely trivial. But although I reject this line, the argument reveals how difficult it is to interpret Lewis’ thesis that possibilia “exist.” Four natural interpretations are considered, yet upon reflection, none appear entirely adequate. In particular, under the three different “concretist” interpretations of ‘exist’, Modal Realism looks insufficient for genuine ontological commitment. Whereas under the “multiverse” interpretation, Modal Realism ends up being incompatible with each of axioms S5 and B. I close by entertaining a more general problem from which the present interpretive issues seem to arise.

In this essay I renew the case for Conditional Excluded Middle (CXM) in light of recent developments in the semantics of the subjunctive conditional. I argue that Michael Tooley’s recent backward causation counterexample to the Stalnaker-Lewis comparative world similarity semantics undermines the strongest argument against CXM, and I offer a new, principled argument for the validity of CXM that is in no way undermined by Tooley’s counterexample. Finally, I formulate a simple semantics for the subjunctive conditional that is consistent with both CXM and Tooley’s counterexample.

The goal of this paper is to offer a compositional semantics for subjunctive and indicative will conditionals, and to derive the projection properties of the types of conditionals we consider and in particular those of counterfactual conditionals. It is argued that subjunctive conditionals are "bare" conditional embedded under temporal and aspectural operators, which constrain the interpretation of the modal operators in the embedded conditional. Furthermore, it is argued that a theory of presupposition projection à la Heim together with the present proposal about their logical form explains the projection facts.

§0. A familiar if obscure idea: an indicative conditional presents its consequent as holding in the actual world on the supposition that its antecedent so holds, whereas a subjunctive conditional merely presents its consequent as holding in a world, typically counterfactual, in which its antecedent holds. Consider this pair.

Consider the reasonable axioms of subjunctive conditionals (1) if p q 1 and p q 2 at some world, then p (q 1 & q 2) at that world, and (2) if p 1 q and p 2 q at some world, then (p 1 ∨ p 2) q at that world, where p q is the subjunctive conditional. I show that a Lewis-style semantics for subjunctive conditionals satisfies these axioms if and only if one makes a certain technical assumption about the closeness relation, an assumption that is probably false. I will then show how Lewisian semantics can be modified so as to assure (1) and (2) even when the technical assumption fails, and in fact in one sense the semantics actually becomes simpler then.