The standard backward-induction reasoning in a game like the centipede assumes that the players maintain a common belief in rationality throughout the game. But that is a dubious assumption. Suppose the first player X didn't terminate the game in the first round; what would the second player Y think then? Since the backwards-induction argument says X should terminate the game, and it is supposed to be a sound argument, Y might be entitled to doubt X's rationality. Alternatively, Y might (...) doubt that X believes Y is rational, or that X believes Y believes X is rational, or Y might have some higher-order doubt. X’s deviant first move might cause a breakdown in common belief in rationality, therefore. Once that goes, the entire argument fails. The argument also assumes that the players act rationally at each stage of the game, even if this stage could not be reached by rational play. But it is also dubious to assume that past irrationality never exerts a corrupting influence on present play. However, the backwards-induction argument can be reconstructed for the centipede game on a more secure basis.1 It may be implausible to assume a common belief in rationality throughout the game, however the game might go, but the argument requires less than this. The standard idealisations in game theory certainly allow us to assume a common belief in rationality at the beginning of the game. They also allow us to assume this common belief persists so long as no one makes an irrational move. That is enough for the argument to go through. (shrink)

The ‘structural injustice’ framework is an increasingly influential way of thinking about historical injustice. Structural injustice theorists argue against reparations for historical injustice on the grounds that our focus should be on forward-looking responsibility for contemporary structural injustice. Through the use of a case study – the Caribbean Community 10-Point Plan for reparations from 2014 – I argue that this reasoning is flawed. Backward-looking reparations can be justified on the basis of state liability over time. The value of backward-looking reparations (...) is that they ensure that historical perpetrators do not evade their reparative obligations and that affected communities are taken seriously. However, I argue that this backward-looking approach should be supplemented by a forward-looking structural injustice approach and the ‘social connection model’ of responsibility, which can expand the scope of responsible agents and forms of injustice that warrant repair and explain how citizens living now can be expected to pay for crimes of the past. (shrink)

In this letter, we argue against a recurring idea that early word learning in infants is related to the low-level capacity for backward associations—a notion that suggests a cognitive gap with other animal species. Because backward associations entail the formation of bidirectional associations between sequentially perceived stimulus pairs, they seemingly mirror the label-referent bidirectional mental relations underlying the lexicon of natural language. This appealing but spurious resemblance has led to various speculations on language acquisition, in particular regarding early word learning, (...) which we deconstruct here. (shrink)

The backward induction argument purports to show that rational and suitably informed players will defect throughout a finite sequence of prisoner's dilemmas. It is supposed to be a useful argument for predicting how rational players will behave in a variety of interesting decision situations. Here, I lay out a set of assumptions defining a class of finite sequences of prisoner's dilemmas. Given these assumptions, I suggest how it might appear that backward induction succeeds and why it is actually fallacious. Then, (...) I go on to consider the consequences of adopting a stronger set of assumptions. Focusing my attention on stronger sets that, like the original, obey the informedness condition, I show that any supplementation of the original set that preserves informedness does so at the expense of forcing rational participants in prisoner's dilemma situations to have unexpected beliefs, ones that threaten the usefulness of backward induction. (shrink)

Philosophers dispute whether an effect can be earlier than its cause (i.e. whether backwards causation can occur). For example, could a trainwreck cause a psychic to have earlier knowledge of it? Max Black tried to show backwards causation to be impossible but he failed to do so, or so I will argue. Nonetheless, his famous article can still teach us something important about certain cases of backwards causation.

It is an open question whether we ever successfully explain earlier states by appealing to later ones, and, further, whether this is even possible. Typically, these two questions are answered in the same way: if we give and accept ‘backwards explanations,’ they must be possible; if they are impossible, we are right to reject them. I argue that backwards explanations are brittle—they fail if the future event does not occur—and this is part of the reason they are not (...) accepted about the actual world. This does not mean, however, that they must be rejected entirely. I argue that backwards explanations are possible for certain systems. This shields unificationism about scientific explanation from some recent criticisms. (shrink)

A cornerstone of game theory is backward induction, whereby players reason backward from the end of a game in extensive form to the beginning in order to determine what choices are rational at each stage of play. Truels, or three-person duels, are used to illustrate how the outcome can depend on (1) the evenness/oddness of the number of rounds (the parity problem) and (2) uncertainty about the endpoint of the game (the uncertainty problem). Since there is no known endpoint in (...) the latter case, an extension of the idea of backward induction is used to determine the possible outcomes. The parity problem highlights the lack of robustness of backward induction, but it poses no conflict between foundational principles. On the other hand, two conflicting views of the future underlie the uncertainty problem, depending on whether the number of rounds is bounded (the players invariably shoot from the start) or unbounded (they may all cooperate and never shoot, despite the fact that the truel will end with certainty and therefore be effectively bounded). Some real-life examples, in which destructive behavior sometimes occurred and sometimes did not, are used to illustrate these differences, and some ethical implications of the analysis are discussed. (shrink)

We propose an analysis of backward causation in terms of interventionism that can avoid several problems typically associated with backward causation. Its main advantage over other accounts is that it allows for reducing the problematic task of supporting backward causal claims to the unproblematic task of finding evidence for several ordinary forward directed causal hypotheses.

This research parallels Tongan academic Hūfanga ‘Okusitino Māhina’s assertions in the 1994 Contemporary Pacific article Our Sea of Islands, that ‘People are thought to walk forward into the past and walk backward into the future, both taking place in the present, where the past and the future are constantly mediated in the ever-transforming present’ alongside those of Professor Terry Irwin and fellow Transition Designers in which they discuss the use of Indigenous Wisdom to enable designing for the Long Now as (...) defined by Brand in his 1999 book The Clock for the Long Now: Time and Responsibility. In the 2015 Transition Design Monograph Irwin asserts that, ‘Transition Design draws on knowledge and wisdom from the past to conceive solutions in the present with future generations in mind’. This paper draws on the pre-industrial wisdom of indigenous knowledge, specifically that of the Pacific regions, Moana, who have lived and designed sustainably in-place for generations to illustrate the value it holds for the formulation of sustainable and sustaining futures. (shrink)

Bell’s theorem requires the assumption that hidden variables are independent of future measurement settings. This independence assumption rests on surprisingly shaky ground. In particular, it is puzzlingly time-asymmetric. The paper begins with a summary of the case for considering hidden variable models which, in abandoning this independence assumption, allow a degree of ‘backward causation’. The remainder of the paper clarifies the physical significance of such models, in relation to the issue as to whether quantum mechanics provides a complete description of (...) physical reality. (shrink)

I argue that the past can be objectively chancy in cases of backwards causation, and defend a view of chance that allows for this. Using a case, I argue against the popular temporal view of chance, according to which chances are defined relative to times, and all chancy events must lie in the future. I then state and defend the causal view of chance, according to which chances are defined relative to causal histories, and all chancy events must lie (...) causally downstream. The causal view replicates the intuitively correct results of the temporal view in cases of ordinary forwards causation, while correctly handling cases of backwards causation. I conclude that objective chance is more closely related to the direction of causation than it is to the direction of time. (shrink)

ABSTRACT Backwards-looking operators Saarinen, E. [1979. “Backwards-Looking Operators in Tense Logic and in Natural Language.” In Essays on Mathematical and Philosophical Logic, edited by J. Hintikka, I. Niiniluoto, and E. Saarinen, 341–367. Dordrecht: Reidel] that have the material in their scope depend on higher intensional operators, are known to increase the expressivity of some intensional languages and have thus played a central role in debates about approaches to intensionality in terms of implicit parameters vs. variables explicitly quantifying over (...) them. The current contribution takes a look at these operators from a type-logical perspective. It is shown that extending Gallin's translation from intensional type logic to two-sorted type theory so as to include a version of Yanovich's backwards-looking operators, does not increase the expressive power of formulae with exclusively intensional parameters. The result, which makes use of a theorem by Zimmermann : 65–77]), is illustrated by pertinent examples from the literature. The paper closes by indicating alternative strategies of incorporating backwards-looking operators. (shrink)

argues that the success of the backward causation hypothesis in quantum mechanics would provide strong support for a version of Reichenbach's account of the direction of causal processes, which takes the direction of causation to rest on the fork asymmetry. He also criticises my perspectival account of the direction of causation, which takes causal asymmetry to be a projection of our own temporal asymmetry as agents. In this reply I take issue with Dowe's argument at three main points: his claim (...) that the backward causation hypothesis in QM is incompatible with my perspectival approach to the direction of causation; his defence of the fork asymmetry approach against a general criticism of mine based on the time-symmetry of microphysics; and his application of his preferred account of the direction of causal processes to the relevant cases in QM. (shrink)

The backward induction controversy in game theory flared up and then practically ended within a decade – the 1990s. The protagonists, however, did not converge on an agreement about the source of the controversy. Why was this the case, if opposing sides had access to the same modelling techniques and empirical facts? In this paper I offer an explanation for this controversy and its unsettled end. The answer is not to be found in the modelling claims made by the opposing (...) protagonists, but in the tacit metaphors they operate under. Aristotle defined metaphor as giving a 'thing a name that belongs to something else' (Poetica, 1457b). The meaning of metaphors has not changed much since then – in contrast to models which are comparatively new, and still not well-understood, scientific tools. The controversy of backward induction in game theory provides a test bed for the explanatory power of metaphors. This paper frames the controversy in terms of metaphor choice to provide a common framework for the protagonists. This results in the identification of three different domains – mathematical logic, game theory and the world – each connected to the other via different metaphors. The controversy around backward induction is placed in, and tentatively explained by, this framework. (shrink)

The empirical study of language is a young field in contemporary linguistics. This being the case, and following a natural development process, the field is currently at a stage where different research methods and experimental approaches are being put into question in terms of their validity. Without pretending to provide an answer with respect to the best way to conduct linguistics related experimental research, in this article we aim at examining the process that researchers follow in the design and implementation (...) of experimental linguistics research with a goal to validate specific theoretical linguistic analyses. First, we discuss the general challenges that experimental work faces in finding a compromise between addressing theoretically relevant questions and being able to implement these questions in a specific controlled experimental paradigm. We discuss the Granularity Mismatch Problem (Poeppel and Embick, 2005 ) which addresses the challenges that research that is trying to bridge the representations and computations of language and their psycholinguistic/neurolinguistic evidence faces, and the basic assumptions that interdisciplinary research needs to consider due to the different conceptual granularity of the objects under study. To illustrate the practical implications of the points addressed, we compare two approaches to perform linguistic experimental research by reviewing a number of our own studies strongly grounded on theoretically informed questions. First, we show how linguistic phenomena similar at a conceptual level can be tested within the same language using measurement of event-related potentials (ERP) by discussing results from two ERP experiments on the processing of long-distance backward dependencies that involve coreference and negative polarity items respectively in Dutch. Second, we examine how the same linguistic phenomenon can be tested in different languages using reading time measures by discussing the outcome of four self-paced reading experiments on the processing of in-situ wh -questions in Mandarin Chinese and French. Finally, we review the implications that our findings have for the specific theoretical linguistics questions that we originally aimed to address. We conclude with an overview of the general insights that can be gained from the role of structural hierarchy and grammatical constraints in processing and the existing limitations on the generalization of results. (shrink)

We discuss explanation of an earlier event by a later event, and argue that prima facie cases of backwards event explanation are ubiquitous. Some examples: (1) I am tidying my flat because my brother is coming to visit tomorrow. (2) The scarlet pimpernels are closing because it is about to rain. (3) The volcano is smoking because it is going to erupt soon. We then look at various ways people might attempt to explain away these prima facie cases by (...) arguing that in each case the 'real' explanation is something else. We argue that none of the explaining-away strategies are successful, and so any plausible account of explanation should either make room for backwards explanation, or have a good story to tell about why it doesn't have to. (shrink)

According to a familiar argument, iterated prisoner's dilemmas of known finite lengths resolve for ideally rational and well-informed players: They would defect in the last round, anticipate this in the next to last round and so defect in it, and so on. But would they anticipate defections even if they had been cooperating? Not necessarily, say recent critics. These critics "lose" the backward-induction paradox by imposing indicative interpretations on rationality and information conditions. To regain it I propose subjunctive interpretations. To (...) solve it I stress that implications for ordinary imperfect players are limited. (shrink)

Gian Aldo Antonelli and Cristina Bicchieri. Backwards Forwards Induction.

This paper proposes a cognitive linguistic explanation of the unusual narrative construal of time as moving backwards. It shows that backwards time in narrative involves setting up an alternative space in which a second narrative is constructed simultaneously, resulting in a viewpoint hierarchy which postulates four viewpoints on each discourse statement. The paper draws together research on conceptual metaphor, mental spaces theory and viewpoint multiplicity, bringing it to bear on discourse fragments. The majority of these are taken from (...) Martin Amis’s Time’s Arrow (Amis, Martin. 2003 [1991]. Time’s Arrow. London: Vintage.) (a logically consistent and linguistically revealing text), but the discussion is contextualised with further examples. It is argued that the causal construal implied by narrative is not limited by our phenomenological experience, as other studies (e.g., Evans, Vyvyan. 2013. Language and time: A cognitive linguistics approach. Cambridge: Cambridge University Press.) might suggest, but is instead prompted by conceptual re-interpretation of deictic markers in the discourse. The analysis focuses on causal construal, negation (especially causal catachresis), and alternativity. It shows how linguistic features at the sentential level generate top-down reorganization of both episodic structure and discourse meaning, and how this relies on multiplicity of viewpoint and a conceptual “zooming out” prompting the perception of irony. (shrink)

A large class of games is that of non-cooperative, extensive form games of perfect information. When the length of these games is finite, the method used to reach a solution is that of a backward induction. Working from the terminal nodes, dominated strategies are successively deleted and what remains is a unique equilibrium. Game theorists have generally assumed that the informational requirement needed to solve these games is that the players have common knowledge of rationality. This assumption, however, has given (...) rise to several problems and paradoxes. Most notably, it has been shown that the common knowledge assumption makes the theory of the game inconsistent at some information set. The present paper shows that a) no common knowledge of rationality need be assumed for the backward induction solution to hold. Rather, it is sufficient that the players have a number of levels of knowledge proportional to the length of the game, and b) it is also necessary that the number of levels of knowledge is finite and proportional to the length of the game. For a higher number of levels of knowledge, inconsistencies arise. (shrink)

We present Backward Clock, an original counterexample to Robert Nozick’s truth-tracking analysis of propositional knowledge, which works differently from other putative counterexamples and avoids objections to which they are vulnerable. We then argue that four ways of analysing knowledge in terms of safety, including Duncan Pritchard’s, cannot withstand Backward Clock either.

Sometimes also called retro causation. A common feature of our world seems to be that in all cases of causation, the cause and the effect are placed in time so that the cause precedes its effect temporally. Our normal understanding of causation assumes this feature to such a degree that we intuitively have great difficulty imagining things differently. The notion of backward causation, however, stands for the idea that the temporal order of cause and effect is a mere contingent feature (...) and that there may be cases where the cause is causally prior to its effect but where the temporal order of the cause and effect is reversed with respect to normal causation, i.e. there may be cases where the effect temporally, but not causally, precedes its cause. (shrink)

Backward induction has been the standard method of solving finite extensive-form games with perfect information, notwithstanding the fact that this procedure leads to counter-intuitive results in various games. However, beginning in the late eighties, the method of backward induction became an object of criticism. It is claimed that the assumptions needed for its defence are quite implausible, if not incoherent. It is therefore natural to ask for the justification of backward induction: Can one show that rational players who know the (...) structure of the game, have trust in each other's practical rationality and reason correctly, will act in accordance in backward induction? Several researchers have tried a justification of this kind, but the argument presented in Robert Aumann's paper from 1995 is perhaps the most well-known and influential attempt to provide such a justification. Clausing provides a sustained discussion of the justification problem for backward induction. It is an excellent work and the criticism I will present below does not detract from this evaluation: the issues discussed by the author are complex and it is difficult to get everything right. Furthermore, I hope that the criticism to be presented may be instructive; Even though it has not been Clausing's intention, his logical reconstruction of Aumann's defence of backward induction allows us to see very clearly what is wrong with that argument. It also provides us with * This paper was presented at workshops in Lund and in Uppsala, in the Fall of 1999. I am indebted to the participants for their useful comments. The work on the paper was supported by a generous research grant from The Bank of Sweden Tercentenary Foundation. (shrink)

The problem of finding sufficient doxastic conditions for backward induction in games of perfect information is analyzed in a syntactic framework with subjunctive conditionals. This allows to describe the structure of the game by a logical formula and consequently to treat beliefs about this structure in the same way as beliefs about rationality. A backward induction and a non-Nash equilibrium result based on higher level belief in rationality and the structure of the game are derived.

Philosophy says that life must be understood backwards. But . . . it must be lived forward. . , , It is more and more evident that life can never be really understood in Time. It was a pleasure to read Jason Thompson’s serious and thought-provoking piece, and I am grateful to the editors for giving me a chance to comment. The idea that the self is revealed in narrative is a popular one among different schools of psychotherapy, both (...) in terms of technique and theory; and my response addresses both these issues in turn. As a clinician, I have always liked people’s stories. As a junior psychiatrist, I used to love the moment when I first met someone and could say to them, ‘You were born; and then what .. (shrink)

Here are some intuitions we have about the nature of space and time. There is something fundamentally different about the past, present, and future. What is definitive of the past is that the past events are fixed. What is definitive of the future is that future events are not fixed. What is definitive of the present is that it marks the objective ontological border between the past and the future and, by doing so, instantiates a particularly salient phenomenological property of (...) nowness. Call the combination of these intuitions according to which there exists an objective present, a fixed past, and an open future, the intuitive view. I argue that, given the intuitive view, the possibility of backwards causation—and hence, for instance, backwards time travel—is problematic. (shrink)

Whereas many philosophers take backwards causation to be impossible, the few who maintain its possibility either take it to be absent from the actual world or else confined to theoretical physics. Here, however, I argue that backwards causation is not only actual, but common, though occurring in the context of our social institutions. After juxtaposing my cases with a few others in the literature and arguing that we should take seriously the reality of causal cases in these contexts, (...) I consider several objections. These objections involve whether the cases should be reinterpreted, whether they are properly within the institution, whether they involve necessitation or else Cambridge changes, whether and how they involve changing the past, and whether this should call us to question institutional reality. I end by suggesting that it is a virtue of our institutions that they allow backwards causation, that this is a kind of technology that they are often built to incorporate. (shrink)

In our world we never observe an effect which is earlier than its cause. All of our experience is of future-directed causation. But many have thought that backwards causation is at least logically or metaphysically possible. Max Black famously argued against this thought. I think his argument fails, but it’s still instructive. The correct rejoinder to Black teaches us what backwards causation must be like in a world of free agents, and implies that we can never have reason (...) to bring about past events. (shrink)

In their Introduction to Logic, Copi and Cohen suggest that students construct a formal proof by "working backwards from the conclusion by looking for some statement or statements from which it can be deduced and then trying to deduce those intermediate statements from the premises. What follows is an elaboration of this suggestion. I describe an almost mechanical procedure for determining from which statement(s) the conclusion can be deduced and the rules by which the required inferences can be made. (...) This method is designed to forestall the quandary in which many beginners find themselves: not knowing how to get started. (shrink)

Climate change involves changes in the climate system caused by polluting human activities and the social and natural effects of these changes. The historical and anthropogenic grounds of climate change play an important role in climate justice claims. Many climate justice scholars believe that principles of climate justice should account for the historical and anthropogenic sources of climate change. Two main backward-looking principles have been proposed: the polluter pays principle (PPP) and the beneficiary pays principle (BPP). The BPP emerged in (...) the literature on climate justice in response to certain objections raised against the PPP. In this paper, I focus on two of these objections: the causation objection and the excusable ignorance objection. Defenders of the BPP have traditionally assumed that this principle is not vulnerable to those objections, which renders the BPP superior to the PPP. In this paper, I challenge this underlying assumption. My argument here is simple: moving from the PPP to the BPP in response to any of these objections might be unjustified because the BPP is affected by at least some of the considerations giving rise to these objections. (shrink)

An important approach to game theory is to examine the consequences of beliefs that agents may have about each other. This paper investigates respect for public preferences. Consider an agent A who believes that B strictly prefers an option a to an option b. Then A respects B’s preference if A assigns probability 1 to the choice of a given that B chooses a or b. Respect for public preferences requires that if it is common belief that B prefers a (...) to b, then it is common belief that all other agents respect that preference. Along the lines of Blume, Brandenburger and Dekel [3] and Asheim [1], I treat respect for public preferences as a constraint on lexicographic probability systems. The main result is that given respect for public preferences and perfect recall, players choose in accordance with Iterated Backward Inference. Iterated Backward Inference is a procedure that generalizes standard backward induction reasoning for games of both perfect and imperfect information. From Asheim’s characterization of proper rationalizability [1] it follows that properly rationalizable strategies are consistent with respect for public preferences; hence strategies eliminated by Iterated Backward Inference are not properly rationalizable. (shrink)

There are two curious features about the backward induction argument (BIA) to the effect that repeated non-cooperation is the rational solution to the finite iterated prisoner’s dilemma (FIPD). First, however compelling the argument may seem, one remains hesitant either to recommend this solu- tion to players who are about to engage in cooperation or to explain cooperation as a deviation from rational play in real-life FIPD’s. Second, there seems to be a similarity between the BIA for the FIPD and the (...) surprise exam paradox (SEP) and one cannot help but wonder whether the former is indeed no more than an instance of the latter. I argue that there is an important difference between the BIA for the FIPD and the SEP, but that a comparison to the SEP can help us understand why the conclusion of the BIA for the FIPD strikes us as a counterintuitive solution to real-life FIPD’s. (shrink)

Whether we’re reading H.G. Wells, Robert Heinlein, Ray Bradbury, or Kurt Vonnegut, time travel is a wonderful narrative trick, freeing a story from the normal ‘one damn thing after another’ progression of time. But many philosophers claim it can never be more than that because backwards causation in general, and time travel in particular, are logically impossible.In this paper I examine one type of argument commonly given for this disappointing conclusion: the time travel paradoxes. Happily for science fiction fans, (...) these arguments fall far short of showing what they are intended to show. Why they fail can be better understood in the light of an analogy between these arguments and some arguments libertarians offer against determinism. (shrink)

Backward induction has been the standard method of solving finite extensive-form games with perfect information, notwithstanding the fact that this procedure leads to counter-intuitive results in various games. However, beginning in the late eighties, the method of backward induction became an object of criticism. It is claimed that the assumptions needed for its defence are quite implausible, if not incoherent. It is therefore natural to ask for the justification of backward induction: Can one show that rational players who know the (...) structure of the game, have trust in each other's practical rationality and reason correctly, will act in accordance in backward induction? Several researchers have tried a justification of this kind, but the argument presented in Robert Aumann's paper from 1995 is perhaps the most well-known and influential attempt to provide such a justification. Clausing provides a sustained discussion of the justification problem for backward induction. It is an excellent work and the criticism I will present below does not detract from this evaluation: the issues discussed by the author are complex and it is difficult to get everything right. Furthermore, I hope that the criticism to be presented may be instructive; Even though it has not been Clausing's intention, his logical reconstruction of Aumann's defence of backward induction allows us to see very clearly what is wrong with that argument. It also provides us with * This paper was presented at workshops in Lund and in Uppsala, in the Fall of 1999. I am indebted to the participants for their useful comments. The work on the paper was supported by a generous research grant from The Bank of Sweden Tercentenary Foundation. (shrink)

According to David Albert, there are certain situations where we can cause events that lie in our past. In response to a well-known objection that we never observe backward causation, he argues that there are good reasons why we can’t tell when it obtains. However, I identify another difficulty with Albert’s view: at face value, it has the unattractive consequence that backward causation is not just possible, but rife. In this article, I show how this implication can be blocked. I (...) then use my analysis to defend Albert’s account from a second well-known objection, namely, that it allows us to control the past. (shrink)