This paper defends a counterexample to Modus Tollens, and uses it to draw some conclusions about the logic and semantics of indicative conditionals and probability operators in natural language. Along the way we investigate some of the interactions of these expressions with 'knows', and we call into question the thesis that all knowledge ascriptions have truth-conditions.

I develop a conception of expressivism according to which it is chiefly a pragmatic thesis about some fragment of discourse, one imposing certain constraints on semantics. The first half of the paper uses credal expressivism about the language of probability as a stalking-horse for this purpose. The second half turns to the question of how one might frame an analogous form of expressivism about the language of deontic modality. Here I offer a preliminary comparison of two expressivist lines. The first, (...) expectation expressivism, looks again to Bayesian modelling for inspiration: it glosses deontically modal language as characteristically serving to express decision-theoretic expectation (expected utility). The second, plan expressivism, develops the idea (due to Gibbard 2003) that this language serves to express 'plan-laden' states of belief. In the process of comparing the views, I show how to incorporate Gibbard's modelling ideas into a compositional semantics for attitudes and modals, filling a lacuna in the account. I close with the question whether and how plan expressivism might be developed with expectation-like structure. (shrink)

Epistemic modal operators give rise to something very like, but also very unlike, Moore's paradox. I set out the puzzling phenomena, explain why a standard relational semantics for these operators cannot handle them, and recommend an alternative semantics. A pragmatics appropriate to the semantics is developed and interactions between the semantics, the pragmatics, and the definition of consequence are investigated. The semantics is then extended to probability operators. Some problems and prospects for probabilistic representations of content and context are explored.

I outline and motivate a way of implementing a closest world theory of indicatives, appealing to Stalnaker's framework of open conversational possibilities. Stalnakerian conversational dynamics helps us resolve two outstanding puzzles for a such a theory of indicative conditionals. The first puzzle -- concerning so-called 'reverse Sobel sequences' -- can be resolved by conversation dynamics in a theoryneutral way: the explanation works as much for Lewisian counterfactuals as for the account of indicatives developed here. Resolving the second puzzle, by contrast, (...) relies on the interplay between the particular theory of indicative conditionals developed here and Stalnakerian dynamics. The upshot is an attractive resolution of the so-called "Gibbard phenomenon" for indicative conditionals. (shrink)

Young children spend a large portion of their time pretending about non-real situations. Why? We answer this question by using the framework of Bayesian causal models to argue that pretending and counterfactual reasoning engage the same component cognitive abilities: disengaging with current reality, making inferences about an alternative representation of reality, and keeping this representation separate from reality. In turn, according to causal models accounts, counterfactual reasoning is a crucial tool that children need to plan for the future and learn (...) about the world. Both planning with causal models and learning about them require the ability to create false premises and generate conclusions from these premises. We argue that pretending allows children to practice these important cognitive skills. We also consider the prevalence of unrealistic scenarios in children's play and explain how they can be useful in learning, despite appearances to the contrary. (shrink)

This article concerns the structure of defeasible arguments like: 'If Bob has red spots, Bob has the measles; Bob has red spots; therefore Bob has the measles.' The issue is whether such arguments have the form of modus ponens or not. Either way there is a problem. If they don't have the form of modus ponens, the common opinion to the contrary taught in leading logic textbooks is wrong. But if they do have the form of modus ponens, doubts are (...) raised about the conventional dogma that all arguments having the form of modus ponens are deductively valid. By carefully examining arguments on both sides of the issue, reasonable doubts are raised about the view that all arguments having a modus ponens form are valid. (shrink)

In this paper I explore a version of standard (expected utility) decision theory in which the probability parameter is interpreted as an objective chance believed by agents to obtain and values of this parameter are fixed by indicative conditionals linking possible actions with possible outcomes. After reviewing some recent developments centering on the common-cause counterexamples to the standard approach, I introduce and briefly discuss the key notions in my own approach. (This approach has essentially the same results as the causal (...) approach in common-cause cases.) I then discuss the Rule of Dominance and find, in the context of the present proposal, that it cannot serve as an independent source of action justification. Turning next to Newcomb''s Problem, I argue that the much discussed issue of back-tracking counterfactuals is something of a red herring for decision theory. Once the twin distractions of back-tracking counterfactuals and Dominance Reasoning are set aside the 1-box solution emerges as a natural consequence of the present proposal. It is of interest that this proposal agrees with the causal approach in the standard common-cause examples and the expected-utility approach in the Newcomb case: one can be smart and rich and keep on smoking. (shrink)

A uniform theory of conditionals is one which compositionally captures the behavior of both indicative and subjunctive conditionals without positing ambiguities. This paper raises new problems for the closest thing to a uniform analysis in the literature (Stalnaker, Philosophia, 5, 269–286 (1975)) and develops a new theory which solves them. I also show that this new analysis provides an improved treatment of three phenomena (the import-export equivalence, reverse Sobel-sequences and disjunctive antecedents). While these results concern central issues in the study (...) of conditionals, broader themes in the philosophy of language and formal semantics are also engaged here. This new analysis exploits a dynamic conception of meaning where the meaning of a symbol is its potential to change an agent’s mental state (or the state of a conversation) rather than being the symbol’s content (e.g. the proposition it expresses). The analysis of conditionals is also built on the idea that the contrast between subjunctive and indicative conditionals parallels a contrast between revising and consistently extending some body of information. (shrink)

If we overlook no consequences when we assess the act, and no relevant features when we generalize, can it matter whether we ask 'What would happen if everyone did the same?' instead of 'What would happen if this act were performed?'? David Lyons has argued that it cannot. Two examples are here articulated to show that it can. The first turns on the way consequences are identified and assessed and in particular on the treatment accorded 'threshold consequences'. The second example (...) turns on the way in which the 'social context' of the act (what others would be doing) is taken into account in the generalization. Also included is a formal theory of conditionals from which implications are drawn for utilitarianism and with which I attempt to dispel certain doubts concerning cases employed in my arguments. (shrink)

Discusses how to capture the link between the probability of indicative conditionals and conditional probability using a classical semantics for conditionals.

Thought experiments are ubiquitous in science and especially prominent in domains in which experimental and observational evidence is scarce. One such domain is the causal analysis of singular events in history. A long‐standing tradition that goes back to Max Weber addresses the issue by means of ‘what‐if’ counterfactuals. In this paper I give a descriptive account of this widely used method and argue that historians following it examine difference makers rather than causes in the philosopher’s sense. While difference making is (...) neither necessary nor sufficient for causation, to establish difference makers is more consistent with the historians’ more ultimate purposes. †To contact the author, please write to: Department of Philosophy, Erasmus University, 3000 DR Rotterdam, The Netherlands; e‐mail: [email protected]. (shrink)

Abstract There are at least eight good reasons practicing historians should concern themselves with counterfactual claims. Furthermore, four of these reasons do not even require that we are able to tell which historical counterfactuals are true and which are false. This paper defends the claim that these reasons to be concerned with counterfactuals are good ones, and discusses how each can contribute to the practice of history. Content Type Journal Article Pages 1-19 DOI 10.1007/s11098-011-9817-z Authors Daniel Nolan, School of Philosophy, (...) Australian National University, 0200 Canberra, Australia Journal Philosophical Studies Online ISSN 1573-0883 Print ISSN 0031-8116. (shrink)

Recently, von Fintel (2001) and Gillies (2007) have argued that certain sequences of counterfactuals, namely reverse Sobel sequences, should motivate us to abandon standard truth conditional theories of counterfactuals for dynamic semantic theories. I argue that we can give a pragmatic account of our judgments about counterfactuals without giving up the standard semantics. In particular, I introduce a pragmatic principle governing assertability, and I use this principle to explain a variety of subtle data concerning reverse Sobel sequences.

We show that the implicational fragment of intuitionism is the weakest logic with a non-trivial probabilistic semantics which satisfies the thesis that the probabilities of conditionals are conditional probabilities. We also show that several logics between intuitionism and classical logic also admit non-trivial probability functions which satisfy that thesis. On the other hand, we also prove that very weak assumptions concerning negation added to the core probability conditions with the restriction that probabilities of conditionals are conditional probabilities are sufficient to (...) trivialize the semantics. (shrink)

Ehring, D. 1997. Causation and Persistence. New York: Oxford University Press. Fair, D. 1979. Causation and the flow of energy. Erkenntnis 14: 219–50. Goldman, A. 1977. Perceptual objects. Synthese 35: 257–84. Lewis, D. 1986a. Causation. In Philosophical Papers Vol. 2, 159–213. New York.

This paper presents ConR (Conditional R), a logic of conditionals based on Anderson and Belnap''s system R. A Routley-Meyer-style semantics for ConR is given for the system (the completeness of ConR over this semantics is proved in E. Mares and A. Fuhrmann, A Relevant Theory of Conditionals (unpublished MS)). Moreover, it is argued that adopting a relevant theory of conditionals will improve certain theories that utilize conditionals, i.e. Lewis'' theory of causation, Lewis'' dyadic deontic logic, and Chellas'' dyadic deontic logic.

In this paper we set out a semantics for relevant (counterfactual) conditionals. We combine the Routley-Meyer semantics for relevant logic with a semantics for conditionals based on selection functions. The resulting models characterize a family of conditional logics free from fallacies of relevance, in particular counternecessities and conditionals with necessary consequents receive a non-trivial treatment.

I offer a novel solution to the problem of counterfactual skepticism: the worry that all contingent counterfactuals without explicit probabilities in the consequent are false. I argue that a specific kind of contextualist semantics and pragmatics for would- and might-counterfactuals can block both central routes to counterfactual skepticism. One, it can explain the clash between would- and might-counterfactuals as in: If you had dropped that vase, it would have broken. and If you had dropped that vase, it might have safely (...) quantum tunneled to China. Two, it can explain why counterfactuals like can be true despite the fact that quantum tunneling worlds are among the most similar worlds. I further argue that this brand of contextualism accounts for the data better than other existing solutions to the problem. (shrink)

This article is about conditionalized modal statements whose antecedents concern a preferential attitude of an agent. The focus is on anankastic conditionals or, as they are known in the philosophical literature, hypothetical imperatives. We present a linguistically-motivated analysis of anankastic and related conditionals and use it to address challenges for semantic theories of natural language conditionals motivated by certain philosophical concerns about practical reasoning and the requirements of rationality.

In this paper, I analyse a finding by Riggs and colleagues that there is a close connection between people’s ability to reason with counterfactual conditionals and their capacity to attribute false beliefs to others. The result indicates that both processes may be governed by one cognitive mechanism, though false belief attribution seems to be slightly more cognitively demanding. Given that the common denominator for both processes is suggested to be a form of the Ramsey test, I investigate whether Stalnaker’s semantic (...) theory of conditionals, which was inspired by the Ramsey test, may provide the basis for a psychologically plausible model of belief ascription. The analysis I propose will shed some new light on the developmental discrepancy between counterfactual reasoning and false belief ascription. (shrink)

We consider a paradox involving indicative conditionals (‘ifs’) and deontic modals (‘oughts’). After considering and rejecting several standard options for resolv- ing the paradox—including rejecting various premises, positing an ambiguity or hidden contextual sensitivity, and positing a non-obvious logical form—we offer a semantics for deontic modals and indicative conditionals that resolves the paradox by making modus ponens invalid. We argue that this is a result to be welcomed on independent grounds, and we show that rejecting the general validity of modus (...) ponens is compatible with vindicating most ordinary uses of modus ponens in reasoning. (shrink)

This paper discusses counterexamples to the thesis that the probabilities of conditionals are conditional probabilities. It is argued that the discrepancy is systematic and predictable, and that conditional probabilities are crucially involved in the apparently deviant interpretations. Furthermore, the examples suggest that such conditionals have a less prominent reading on which their probability is in fact the conditional probability, and that the two readings are related by a simple step of abductive inference. Central to the proposal is a distinction between (...) causal and purely stochastic dependence between variables. (shrink)

This paper surveys important work done in relevant logic in the past 10 years.

Recent accounts of actual causation are stated in terms of extended causal models. These extended causal models contain two elements representing two seemingly distinct modalities. The first element are structural equations which represent the or mechanisms of the model, just as ordinary causal models do. The second element are ranking functions which represent normality or typicality. The aim of this paper is to show that these two modalities can be unified. I do so by formulating two constraints under which extended (...) causal models with their two modalities can be subsumed under so called which contain just one modality. These two constraints will be formally precise versions of Lewissystem of weights or priorities” governing overall similarity between possible worlds. (shrink)

This book demonstrates how children's imagination makes a continuing contribution to their cognitive and emotional development.

Counterfactuals are typically thought--given the force of Sobel sequences--to be variably strict conditionals. I go the other way. Sobel sequences and (what I call) Hegel sequences push us to a strict conditional analysis of counterfactuals: counterfactuals amount to some necessity modal scoped over a plain material conditional, just which modal being a function of context. To make this worth saying I need to say just how counterfactuals and context interact. No easy feat, but I have something to say on the (...) matter. (shrink)

This paper studies the causal interpretation of counterfactual sentences using a modifiable structural equation model. It is shown that two properties of counterfactuals, namely, composition and effectiveness, are sound and complete relative to this interpretation, when recursive (i.e., feedback-less) models are considered. Composition and effectiveness also hold in Lewis's closest-world semantics, which implies that for recursive models the causal interpretation imposes no restrictions beyond those embodied in Lewis's framework. A third property, called reversibility, holds in nonrecursive causal models but not (...) in Lewis's closest-world semantics, which implies that Lewis's axioms do not capture some properties of systems with feedback. Causal inferences based on counterfactual analysis are exemplified and compared to those based on graphical models. (shrink)

I argue that the suppositional view of conditionals, which is quite popular for indicative conditionals, extends also to subjunctive or counterfactual conditionals. According to this view, conditional judgements should not be construed as factual, categorical judgements, but as judgements about the consequent under the supposition of the antecedent. The strongest evidence for the view comes from focusing on the fact that conditional judgements are often uncertain; and conditional uncertainty, which is a well-understood notion, does not function like uncertainty about matters (...) of fact. I argue that the evidence for this view is as strong for subjunctives as it is for indicatives. (shrink)

According to what is now commonly referred to as “the Equation” in the literature on indicative conditionals, the probability of any indicative conditional equals the probability of its consequent of the conditional given the antecedent of the conditional. Philosophers widely agree in their assessment that the triviality arguments of Lewis and others have conclusively shown the Equation to be tenable only at the expense of the view that indicative conditionals express propositions. This study challenges the correctness of that assessment by (...) presenting data that cast doubt on an assumption underlying all triviality arguments. (shrink)