Counterfactuals, Belief Changes, and Equilibrium Refinements

Theor Decis, 2012

We suggest a model that describes how counterfactuals are constructed and justified. The model can describe how counterfactual beliefs are updated given the unfolding of actual history. It also allows us to examine the use of counterfactuals in prediction, and to show that a logically omniscient reasoner gains nothing from using counterfactuals for prediction. * We thank Dov Samet and David Schmeidler for conversations that motivated and influenced this work. We are also grateful to Joe Altonji and Brian Hill for discussions, comments, and references. Itzhak Gilboa gratefully acknowledges ISF Grant 396/10 and ERC Grant 269754; Larry Samuelson gratefully acknowledges NSF grant SES-0850263.

Journal of Philosophical Logic, 2021

In this paper, we investigate the semantics and logic of choice-driven counterfactuals, that is, of counterfactuals whose evaluation relies on auxiliary premises about how agents are expected to act, i.e., about their default choice behavior. To do this, we merge one of the most prominent logics of agency in the philosophical literature, namely stit logic (Belnap et al. 2001; Horty 2001), with the well-known logic of counterfactuals due to Stalnaker (1968) and Lewis (1973). A key component of our semantics for counterfactuals is to distinguish between deviant and non-deviant actions at a moment, where an action available to an agent at a moment is deviant when its performance does not agree with the agent’s default choice behavior at that moment. After developing and axiomatizing a stit logic with action types, instants, and deviant actions, we study the philosophical implications and logical properties of two candidate semantics for choice-driven counterfactuals, one called rewind inspired by Lewis (Nous 13(4), 455–476 1979) and the other called independence models motivated by well-known counterexamples to Lewis’s proposal Slote (Philos. Rev. 87(1), 3–27 1978). In the last part of the paper we consider how to evaluate choice-driven counterfactuals at moments arrived at by some agents performing a deviant action.

On Counterfactual Reasoning

Counterfactual reasoning has always played a role in human life. We ask questions like, “Could it have been different?”, “Under which conditions might/would it have been different?”, “What would have happened if…?” If we don’t find an answer, i.e. what we accept as an answer, we may start reasoning. Reasoning means introducing still new information/assumptions, new questions, new answers to new questions etc. From a formal point of view, it may be compared with stepwise moving towards a destination in a path-system, in which you never fully have an overview. In this way, reasoning is an activity, with its own rationale, which will be studied from the agent’s own perspective. Questions include: What are the conditions where asking that specific question, or introducing this information/assumption, etc. will count as a reasonable step or progress towards the answer of the initial question? What makes this step more reasonable than another?

2006

We offer a novel theory of information that differs from traditional accounts in two respects:(i) it explains information in terms of counterfactuals rather than conditional probabilities, and (ii) it does not make essential reference to doxastic states of subjects, and consequently allows for the sort of objective, reductive explanations of various notions in epistemology and philosophy of mind that many have wanted from an account of information.

Journal of Philosophy, 109(3), pp. 221-46 (2012)

2002

This article should be read in conjunction with its companion, "Counterfactual Reasoning (Philosophical Aspects)-Qualitative". Here, after a general introduction and historical overview, we emphasize the role of counterfactual reasoning within the quantitative frameworks of probability theory, decision theory, and game theory.

Mind, 2006

On the received view, counterfactuals are analyzed using the concept of closeness between possible worlds: ‘if it had been that p, then it would have been the case that q’ is true at world w just in case q is true at all the possible p-worlds closest to w. The degree of closeness between two worlds is usually thought to be determined by weighting different respects of similarity between them. The question I consider in the paper is which weights attach to different respects of similarity. I start by considering Lewis’s answer to the question and argue against it by presenting several counterexamples. I use the same examples to motivate a general principle about closeness: If a fact obtains in both of two worlds, then this similarity is relevant to the closeness between them if and only if the fact has the same explanation in the two worlds. I use this principle and some ideas of Lewis’s to formulate a general account of counterfactuals, and I argue that this account can explain the asymmetry of counterfactual dependence. The paper concludes with a discussion of some examples that cannot be accommodated by the present version of the account and therefore necessitate further work on the details.

Linguistics and Philosophy, 2018

Based on a crowdsourced truth value judgment experiment, we provide empirical evidence challenging two classical views in semantics, and we develop a novel account of counterfactuals that combines ideas from inquisitive semantics and causal reasoning. First, we show that two truth-conditionally equivalent clauses can make different semantic contributions when embedded in a counterfactual antecedent. Assuming compositionality, this means that the meaning of these clauses is not fully determined by their truth conditions. This finding has a clear explanation in inquisitive semantics: truth-conditionally equivalent clauses may be associated with diierent propositional alternatives, each of which counts as a separate counterfactual assumption. Second, we show that our results contradict the common idea that the interpretation of a counterfactual involves minimizing change with respect to the actual state of affairs. We propose to replace the idea of minimal change by a distinction between foreground and background for a given counterfactual assumption: the background is held fixed in the counterfactual situation, while the foreground can be varied without any minimality constraint.

Journal of Economic Theory, 1999

The epistemic analysis of solution concepts for dynamic games involves statements about the players' beliefs conditional upon different histories of play, their conditional beliefs about each other's conditional beliefs, etc. To represent such statements, we construct a space of infinite (coherent) hierarchies of conditional probability systems, defined with respect to a fixed collection of relevant hypotheses concerning an external state (e.g. the strategy profile being played.) As an application, we derive results about common certainty of the opponent's rationality conditonal on an arbitrary collection of histories in multistage games with observed actions and (possibly) incomplete information. Journal of Economic Literature Classification Numbers: C72, D82.

1999

The epistemic analysis of solution concepts for dynamic games involves statements about the players' beliefs conditional upon different histories of play, their conditional beliefs about each other's conditional beliefs, etc. To represent such statements, we construct a space of infinite (coherent) hierarchies of conditional probability systems, defined with respect to a fixed collection of relevant hypotheses concerning an external state (e.g. the strategy profile being played.) As an application, we derive results about common certainty of the opponent's rationality conditonal on an arbitrary collection of histories in multistage games with observed actions and (possibly) incomplete information.