Conditionals and Counterfactuals in Prolog

Review of Symbolic Logic, 2012

This is part B of a paper in which we defend a semantics for counterfactuals which is probabilistic in the sense that the truth condition for counterfactuals refers to a probability measure. Because of its probabilistic nature, it allows a counterfactual ‘if A then B’ to be true even in the presence of relevant ‘A and not B’-worlds, as long such exceptions are not too widely spread. The semantics is made precise and studied in different versions which are related to each other by representation theorems. Despite its probabilistic nature, we show that the semantics and the resulting system of logic may be regarded as a naturalistically vindicated variant of David Lewis’ truth-conditional semantics and logic of counterfactuals. At the same time, the semantics overlaps in various ways with the non-truth-conditional suppositional theory for conditionals that derives from Ernest Adams’ work. We argue that counterfactuals have two kinds of pragmatic meanings and come attached with two types of degrees of acceptability or belief, one being suppositional, the other one being truth based as determined by our probabilistic semantics; these degrees could not always coincide due to a new triviality result for counterfactuals, and they should not be identified in the light of their different interpretation and pragmatic purpose. However, for plain assertability the difference between them does not matter. Hence, if the suppositional theory of counterfactuals is formulated with sufficient care, our truth-conditional theory of counterfactuals is consistent with it. The results of our investigation are used to assess a claim considered by Hawthorne and Hájek, that is, the thesis that most ordinary counterfactuals are false.(Received August 10 2010)

Journal of Semantics, 2005

Kratzer (1981) discussed a naıve premise semantics of counterfactual conditionals, pointed to an empirical inadequacy of this interpretation, and presented a modification-partition semantics-which Lewis (1981) proved equivalent to version of his ordering semantics. Subsequently, proposed lumping semantics, a different modification of premise semantics, and argued it remedies empirical failings of ordering semantics as well as of naïve premise semantics. We show that lumping semantics yields truth conditions for counterfactuals that are not only different from what she claims they are, but also inferior to those of the earlier versions of premise semantics.

Synthese 289(1), 29-57 (2012).

Von Fintel (Curr Stud Linguist Ser 36:123–152, 2001) and Gillies (Linguist Philos 30(3): 329–360, 2007) have proposed a dynamic strict conditional account of counterfactuals as an alternative to the standard variably strict account due to Stalnaker (Studies in logical theory, Blackwell, London, 1968) and Lewis (Counterfactuals, Blackwell, London, 1973). Von Fintel's view is motivated largely by so-called reverse Sobel sequences, about which the standard view seems to make the wrong predictions. (The other major motivation is data surrounding so-called negative polarity items, which I do not discuss here.) More recently Moss (Noûs 46 (3):561–586, 2012) has offered a pragmatic/epistemic explanation that purports to explain the data without requiring abandonment of the standard view. So far the small amount of subsequent literature has focused primarily on the original class of cases motivating the strict conditional view. What is needed in the debate is an examination of the predictions of the dynamic strict conditional account for a broader range of data. I undertake this task here, presenting a slew of cases that are problematic for the strict conditional view but not for Moss's view, and considering some possible responses. Ultimately I take my contribution to constitute a significant blow to the dynamic strict conditional view, though not a decisive verdict against it.

Journal of semantics, 2005

This note is a reply to 'On the Lumping Semantics of Counterfactuals' by Makoto Kanazawa, Stefan Kaufmann and Stanley Peters. It shows first that the first triviality result obtained by Kanazawa, Kaufmann, and Peters is already ruled out by the constraints on admissible premise sets listed in Kratzer (1989). Second, and more importantly, it points out that the results obtained by Kanazawa, Kaufmann, and Peters are obsolete in view of the revised analysis of counterfactuals in Kratzer (1990, 2002).

Synthese, 1994

In this paper I explore the ambiguity that arises between two readings of the counterfactual construction, the n-d and the l-p, analyzed in my book A Theory of Counterfactuals. I then extend the analysis I offered there to counterfactuals with true antecedents, and offer a more precise formulation of the conception of temporal divergence points used in the 1-p interpretation. Finally, i discuss some ramifications of these issues for counterfactual analyses of knowledge. t. B A C K G R O U N D In A Theory of Counterfactuals 1 (henceforth: A TC) I discussed the two major counterfactual interpretations, the n-d and the l-p. The first applies to counterfactuals, the antecedents of which are compatible with their prior histories; the second to counterfactuals whose antecedents are incompatible with their prior histories. Together they cover counterfactuals, with premises that are factual (non-nomic), false, and logically, n , m , logically, and metaphysically possible. 2 These two are by far the most prevalent kinds of counterfactual interpretations: all counterfactuals which are not covered by these two are either esoteric or parasitic on counterfactuals which are covered by these two. (Some types of such esoteric or parasitic counterfactuals are also discussed in A TC3). After a brief survey of the n-d and t-p interpretations, I will elaborate further on the l-p interpretation and then pursue the ambiguity the two interpretations generate.

Logic, Rationality, and Interaction, 2019

The paper focuses on a recent challenge brought forward against the interventionist approach to the meaning of counterfactual conditionals. According to this objection, interventionism cannot in general account for the interpretation of right-nested counterfactuals, the problem being its strict interventionism. We will report on the results of an empirical study supporting the objection, and we will extend the well-known logic of actual causality with a new operator expressing an alternative notion of intervention that does not suffer from the problem (and thus can account for some critical examples). The core idea of the alternative approach is a new notion of intervention, which operates on the evaluation of the variables in a causal model, and not on their functional dependencies. Our result provides new insights into the logical analysis of causal reasoning.

Linguistics and Philosophy

This essay calls attention to a set of linguistic interactions between counterfactual conditionals, on one hand, and possibility modals like could have and might have, on the other. These data present a challenge to the popular variably strict semantics for counterfactual conditionals. Instead, they support a version of the strict conditional semantics in which counterfactuals and possibility modals share a unified quantificational domain. I'll argue that pragmatic explanations of this evidence are not available to the variable analysis. And putative counterexamples to the unified strict analysis, on careful inspection, in fact support it. Ultimately, the semantics of conditionals and modals must be linked together more closely than has sometimes been recognized, and a unified strict semantics for conditionals and modals is the only way to fully achieve this.

This paper investigates the metaphysics in higher-order counterfactual logic. I establish the necessity of identity and distinctness and show that the logic is committed to vacuism, which entails that all counteridenticals are true. I prove the Barcan, Converse Barcan, Being Constraint and Necessitism. I then show how to derive the Identity of Indiscernibles in counterfactual logic. I study a form of maximalist ontology which has been claimed to be so expansive as to be inconsistent. I show that it is equivalent to the collapse of the counterfactual into the material conditional---which is itself equivalent to the modal logic TRIV. TRIV is consistent, from which it follows that maximalism is, surprisingly, consistent. I close by arguing that stating the limit assumption requires a higher-order logic

Philosophical studies, 2005

This paper analyzes the logical truths as (very roughly) those truths that would still have been true under a certain range of counterfactual perturbations. What's nice is that the relevant range is characterized without relying (overtly, at least) upon the notion of logical ...

Pacific Philosophical Quarterly, 2017

In a recent paper Lee Walters criticizes a number of philosophersincluding Gundersenfor committing a 'failure in the argumentative strategy' when they attempt to amend the standard Lewis semantics for counterfactuals in order to avoid the so-called principle of Conjunction Conditionalization. In this article we defend a Gundersen-style probability-based semantics against Walter's major misgivings: that it is not logically conservative, that it is committed to the Connection Hypothesis, and that it cannot deal satisfactory with irrelevant semi-factuals.

2018

Lewis' Logic V is the fundamental logic of counterfactuals. Its proof theory is here investigated by means of two sequent calculi based on the connective of comparative plausibility. First, a labelled calculus is defined on the basis of Lewis' sphere semantics. This calculus has good structural properties and provides a decision procedure for the logic. An internal calculus, recently introduced, is then considered. In this calculus, each sequent in a derivation can be interpreted directly as a formula of V. In spite of the fundamental difference between the two calculi, a mutual correspondence between them can be established in a constructive way. In one direction, it is shown that any derivation of the internal calculus can be translated into a derivation in the labelled calculus. The opposite direction is considerably more difficult, as the labelled calculus comprises rules which cannot be encoded by purely logical rules. However, by restricting to derivations in normal fo...

Synthese, 2001

Preprint of the paper published in Synthese 127: 105–139, 2001 ABSTRACT: Many of the discussions about conditionals can best be put as follows: can those conditionals that involve an entailment relation be formulated within a formal system? The reasons for the failure of the classical approach to entailment have usually been that they ignore the meaning connection between antecedent and consequent in a valid entailment. One of the first theories in the history of logic about meaning connection resulted from the stoic discussions on tightening the relation between the If- and the Then-parts of conditionals, which in this context was called synartesis (connection). This theory gave a justification for the validity of what we today express through the formulae ~(a=>~a) and ~(~a=>a). Hugh MacColl and, more recently, Storrs McCall (from 1877 to 1906 and from 1963 to 1975 respectively) searched for a formal system in which the validity of these formulae could be expressed. Unfortunately neither of the resulting systems is very satisfactory. In this paper we introduce dialogical games with the help of a new connexive If-Then =>), the structural rules of which allow the Proponent to develop (formal) winning strategies for the above-mentioned connexive theses . Further on, we develop the corresponding tableau systems and conclude with some remarks on possible perspectives and consequences of the dialogical approach to connexivity including the loss of uniform substitution leading to a new concept of logical form.

Ms., University of Texas, Austin, 2005

Over the past twenty years, there have been numerous discoveries and theoretical pro-posals for modals in Romance and Germanic languages, as well as for conditionals and counterfactuals. But there has been little attempt to produce a compositional ac-count of ...

Synthese, 1989

This paper dwells upon formal models of changes of beliefs, or theories, which are expressed in languages containing a binary conditional connective. After defining the basic concept of a (non-trivial) belief revision model, I present a simple proof of Gärdenfors' (1986) triviality theorem. I claim that on a proper understanding of this theorem we must give up the thesis that consistent revisions ("additions") are to be equated with logical expansions. If negated or 'might' conditionals are interpreted on the basis of 'autoepistemic omniscience', or if autoepistemic modalities (Moore) are admitted, even more severe triviality results ensue. It is argued that additions cannot be philosophically construed as 'parasitic' (Levi) on expansions. In conclusion I outline some logical consequences of the fact that we must not expect 'monotonic' revisions in languages including conditionals. * This paper appeared in Synthese 81 (1989), 91-113.-I wish to thank Peter Gärdenfors for a number of helpful comments, André Fuhrmann and Wolfgang Spohn for extensive discussions of parts of this paper, and Winfred Klink for kindly checking my English.