There are three questions associated with Simpson’s Paradox (SP): (i) Why is SP paradoxical? (ii) What conditions generate SP?, and (iii) What should be done about SP? By developing a logic-based account of SP, it is argued that (i) and (ii) must be divorced from (iii). This account shows that (i) and (ii) have nothing to do with causality, which plays a role only in addressing (iii). A counterexample is also presented against the causal account. Finally, the causal and logic-based (...) approaches are compared by means of an experiment to show that SP is not basically causal. (shrink)

You should rather play hide-and-seek against someone who cannot predict where you hide than against someone who can, as the article illustrates in connection with a high-stakes example. Causal Decision Theory denies this. So Causal Decision Theory is false.

This essay develops a joint theory of rational (all-or-nothing) belief and degrees of belief. The theory is based on three assumptions: the logical closure of rational belief; the axioms of probability for rational degrees of belief; and the so-called Lockean thesis, in which the concepts of rational belief and rational degree of belief figure simultaneously. In spite of what is commonly believed, this essay will show that this combination of principles is satisfiable (and indeed nontrivially so) and that the principles (...) are jointly satisfied if and only if rational belief is equivalent to the assignment of a stably high rational degree of belief. Although the logical closure of belief and the Lockean thesis are attractive postulates in themselves, initially this may seem like a formal “curiosity”; however, as will be argued in the rest of the essay, a very reasonable theory of rational belief can be built around these principles that is not ad hoc and that has various philosophical features that are plausible independently. In particular, this essay shows that the theory allows for a solution to the Lottery Paradox, and it has nice applications to formal epistemology. The price that is to be paid for this theory is a strong dependency of belief on the context, where a context involves both the agent's degree of belief function and the partitioning or individuation of the underlying possibilities. But as this essay argues, that price seems to be affordable. (shrink)

Biological knowledge does not fit the image of science that philosophers have developed. Many argue that biology has no laws. Here I criticize standard normative accounts of law and defend an alternative, pragmatic approach. I argue that a multidimensional conceptual framework should replace the standard dichotomous law/ accident distinction in order to display important differences in the kinds of causal structure found in nature and the corresponding scientific representations of those structures. To this end I explore the dimensions of stability, (...) strength, and degree of abstraction that characterize the variety of scientific knowledge claims found in biology and other sciences. (shrink)

Disagreement is a hot topic in epistemology. A fast-growing literature centers around a dispute between the ‘steadfast’ view, on which one may maintain one’s beliefs even in the light of disagreement with epistemic peers who have all the same evidence, and the ‘conciliationist’ view, on which such disagreement requires a revision of attitudes. In this paper, however, I argue that there is less separating the main rivals in the debate about peer disagreement than is commonly thought. The extreme versions of (...) both views are clearly indefensible, while more moderate versions of the views converge on the idea that how much revision of belief is called for by an instance of peer disagreement varies from case to case. Those tempted by this diagnosis are sometimes pessimistic about the prospects for giving a unified account which clearly predicts when more or less extensive revisions will be called for. By contrast, in this paper I give an account that aspires to such unity and predictive power, centering on the notion of the net resilience of your estimate of your own reliability against your estimate of your interlocutor’s reliability. The view I present thus amounts to a new, moderate theory of how one should respond to disagreement. I argue that ultimately, when we weaken conciliationism and the steadfast view to account for exception cases and to make them adequately plausible, they end up converging on the moderate view I present. Much of the seeming disagreement about disagreement is, then, illusory. (shrink)

Ordinary Language Philosophy has largely fallen out of favour, and with it the belief in the primary importance of analyses of ordinary language for philosophical purposes. Still, in their various endeavours, philosophers not only from analytic but also from other backgrounds refer to the use and meaning of terms of interest in ordinary parlance. In doing so, they most commonly appeal to their own linguistic intuitions. Often, the appeal to individual intuitions is supplemented by reference to dictionaries. In recent times, (...) Internet search engine queries for expressions of interest have become quite popular. Apparently, philosophers attempt to surpass the limits of their own linguistic intuitions by appealing to experts or to factual uses of language. I argue that this attempt is commendable but that its execution is wanting. Instead of appealing to dictionaries or Internet queries, philosophers should employ computer-based linguistic corpora in order to confirm or falsify hypotheses about the factual use of language. This approach also has some advantages over methods employed by experimental philosophers. If the importance of ordinary language is stressed, the use of linguistic corpora is hardly avoidable. (shrink)

I argue that there are at least two concepts of law of nature worthy of philosophical interest: strong law and weak law. Strong laws are the laws investigated by fundamental physics, while weak laws feature prominently in the “special sciences” and in a variety of non-scientific contexts. In the first section, I clarify my methodology, which has to do with arguing about concepts. In the next section, I offer a detailed description of strong laws, which I claim satisfy four criteria: (...) (1) If it is a strong law that L then it also true that L; (2) strong laws would continue to be true, were the world to be different in some physically possible way; (3) strong laws do not depend on context or human interest; (4) strong laws feature in scientific explanations but cannot be scientifically explained. I then spell out some philosophical consequences: (1) is incompatible with Cartwright’s contention that “laws lie” (2) with Lewis’s “best-system” account of laws, and (3) with contextualism about laws. In the final section, I argue that weak laws are distinguished by (approximately) meeting some but not all of these criteria. I provide a preliminary account of the scientific value of weak laws, and argue that they cannot plausibly be understood as ceteris paribus laws. (shrink)

The weather report says that the chance of a hurricane arriving later today is 90%. Forewarned is forearmed: expecting a hurricane, before leaving home you pack your hurricane lantern.

Counterexamples are constructed for classical decision theory, turning on the fact that actions must often be chosen in groups rather than individually, i.e., the objects of rational choice are plans. It is argued that there is no way to define optimality for plans that makes the finding of optimal plans the desideratum of rational decision-making. An alternative called “locally global planning” is proposed as a replacement for classical decision theory. Decision-making becomes a non-terminating process without a precise target rather than (...) a terminating search for an optimal solution. (shrink)

There are two central questions concerning probability. First, what are its formal features? That is a mathematical question, to which there is a standard, widely (though not universally) agreed upon answer. This answer is reviewed in the next section. Second, what sorts of things are probabilities---what, that is, is the subject matter of probability theory? This is a philosophical question, and while the mathematical theory of probability certainly bears on it, the answer must come from elsewhere. To see why, observe (...) that there are many things in the world that have the mathematical structure of probabilities---the set of measurable regions on the surface of a table, for example---but that one would never mistake for being probabilities. So probability is distinguished by more than just its formal characteristics. The bulk of this essay will be taken up with the central question of what this “more” might be. (shrink)

Causal decision theory defines a rational action as the one that tends to cause the best outcomes. If we adopt counterfactual or probabilistic theories of causation, then we may face problems in overdetermination cases. Do such problems affect Causal decision theory? The aim of this work is to show that the concept of causation that has been fundamental in all versions of causal decision theory is not the most intuitive one. Since overdetermination poses problems for a counterfactual theory of causation, (...) one can think that a version of causal decision theory based on counterfactual dependence may also be vulnerable to such scenarios. However, only when an intuitive, not analyzed notion of causation is presupposed as a ground for a more plausible version of causal decision theory, overdetermination turns problematic. The first interesting consequence of this is that there are more reasons to dismiss traditional theories of causation (and to accept others). The second is to confirm that traditional causal decision theory is not based on our intuitive concept of the causal relation. (shrink)

Normative theories can be useful in developing descriptive theories, as when normative subjective expected utility theory is used to develop descriptive rational choice theory and behavioral game theory. “Ought” questions are also the essence of theories of moral reasoning, a domain of higher mental processing that could not survive without normative considerations.

The concept of evidence is among the central concerns of epistemology broadly construed. As such, it has long engaged the intellectual energies of both philosophers of science and epistemologists of a more traditional variety. Here I briefly survey some of the more important ideas to have emerged from this tradition of reflection. I then look somewhat more closely at an issue that has recently come to the fore, largely as a result of Williamson's Knowledge and Its Limits: that of whether (...) one's evidence supervenes on one's non-factive mental states. (shrink)

We pose and resolve several vexing decision theoretic puzzles. Some are variants of existing puzzles, such as 'Trumped' (Arntzenius and McCarthy 1997), 'Rouble trouble' (Arntzenius and Barrett 1999), 'The airtight Dutch book' (McGee 1999), and 'The two envelopes puzzle' (Broome 1995). Others are new. A unified resolution of the puzzles shows that Dutch book arguments have no force in infinite cases. It thereby provides evidence that reasonable utility functions may be unbounded and that reasonable credence functions need not be countably (...) additive. The resolution also shows that when infinitely many decisions are involved, the difference between making the decisions simultaneously and making them sequentially can be the difference between riches and ruin. Finally, the resolution reveals a new way in which the ability to make binding commitments can save perfectly rational agents from sure losses. (shrink)

The essay presents a novel counterexample to Causal Decision Theory (CDT). Its interest is that it generates a case in which CDT violates the very principles that motivated it in the first place. The essay argues that the objection applies to all extant formulations of CDT and that the only way out for that theory is a modification of it that entails incompatibilism. The essay invites the reader to find this consequence of CDT a reason to reject it.

Recently, it has been debated as to whether understanding is a species of explanatory knowledge. Those who deny this claim frequently argue that understanding, unlike knowledge, can be lucky. In this paper I argue that current arguments do not support this alleged compatibility between understanding and epistemic luck. First, I argue that understanding requires reliable explanatory evaluation, yet the putative examples of lucky understanding underspecify the extent to which subjects possess this ability. In the course of defending this claim, I (...) also provide a new account of the kind of ‘grasping’ taken to be central to understanding. Second, I show that putative examples of lucky understanding unwittingly deploy a kind of luck that is compatible with knowledge. Finally, appealing to a number of works on explanation and its attendant epistemology, I argue that alleged instances of lucky understanding that overcome these two obstacles will invariably violate certain norms of explanatory inquiry – our paradigmatic understanding-oriented practice. By contrast, knowledge of the same information is immune to these criticisms. Consequently, if understanding is environmentally lucky, it is always inferior to the understanding that a corresponding case of knowledge would provide. (shrink)

This paper focuses on the view that rationality requires that our credences be regular. I go through different formulations of the requirement, and show that they face several problems. I then formulate a version of the requirement that solves most of, if not all, these problems. I conclude by showing that an argument thought to support the requirement as traditionally formulated actually does not; if anything, the argument, slightly modified, supports my version of the requirement.Send article to KindleTo send this (...) article to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle. Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply. Find out more about the Kindle Personal Document Service.REGULARITY REFORMULATEDVolume 9, Issue 4Weng Hong TangDOI: https://doi.org/10.1017/epi.2012.23Your Kindle email address Please provide your Kindle [email protected]@kindle.com Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Dropbox To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Dropbox. REGULARITY REFORMULATEDVolume 9, Issue 4Weng Hong TangDOI: https://doi.org/10.1017/epi.2012.23Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Google Drive To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Google Drive. REGULARITY REFORMULATEDVolume 9, Issue 4Weng Hong TangDOI: https://doi.org/10.1017/epi.2012.23Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Export citation Request permission. (shrink)

I formulate a counterfactual version of the notorious 'Ramsey Test'. Whereas the Ramsey Test for indicative conditionals links credence in indicatives to conditional credences, the counterfactual version links credence in counterfactuals to expected conditional chance. I outline two forms: a Ramsey Identity on which the probability of the conditional should be identical to the corresponding conditional probabihty/expectation of chance; and a Ramsey Bound on which credence in the conditional should never exceed the latter.Even in the weaker, bound, form, the counterfactual (...) Ramsey Test makes counterfactuals subject to the very argument that Lewis used to argue against the indicative version of the Ramsey Test. I compare the assumptions needed to run each, pointing to assumptions about the time-evolution of chances that can replace the appeal to Bayesian assumptions about credence update in motivating the assumptions of the argument.I finish by outlining two reactions to the discussion: to indicativize the debate on counterfactuals; or to counterfactualize the debate on indicatives. (shrink)

Some of the information we receive comes to us in an explicitly conditional form. It is an open question how to model the accommodation of such information in a Bayesian framework. This paper presents data suggesting that there may be no strictly Bayesian account of updating on conditionals. Specifically, the data seem to indicate that such updating at least sometimes proceeds on the basis of explanatory considerations, which famously have no home in standard Bayesian epistemology. The paper also proposes a (...) still broadly Bayesian model of updating on conditionals that explicitly factors in explanation. The model is shown to have clear empirical content and thus to be open to empirical testing. (shrink)

Reasons transmit. If one has a reason to attain an end, then one has a reason to effect means for that end: reasons are transmitted from end to means. I argue that the likelihood ratio (LR) is a compelling measure of reason transmission from ends to means. The LR measure is superior to other measures, can be used to construct a condition specifying precisely when reasons transmit, and satisfies intuitions regarding end-means reason transmission in a broad array of cases.

This paper explores the idea that laws express relationships between properties or universals as defended in Michael Tooley's recent book Causation: A Realist Approach. I suggest that the most plausible version of realism will take a different form than that advocated by Tooley. According to this alternative, laws are grounded in facts about the capacities and powers of particular systems, rather than facts about relations between universals. The notion of lawfulness is linked to the notion of invariance, rather than to (...) the metaphysical notion of a necessary connection. (shrink)

The so-called ‘Adams’ Thesis’ is often understood as the claim that the assertibility of an indicative conditional equals the corresponding conditional probability—schematically: $${({\rm AT})}\qquad\qquad\quad As(A\rightarrow B)=P({B|A}),{\rm provided}\quad P(A)\neq 0.$$ The Thesis is taken by many to be a touchstone of any theorizing about indicative conditionals. Yet it is unclear exactly what the Thesis is . I suggest some precise statements of it. I then rebut a number of arguments that have been given in its favor. Finally, I offer a new (...) argument against it. I appeal to an old triviality result of mine against ‘Stalnaker’s Thesis’ that the probability of a conditional equals the corresponding conditional probability. I showed that for all finite-ranged probability functions, there are strictly more distinct values of conditional probabilities than there are distinct values of probabilities of conditionals, so they cannot all be paired up as Stalnaker’s Thesis promises. Conditional probabilities are too fine-grained to coincide with probabilities of conditionals across the board. If the assertibilities of conditionals are to coincide with conditional probabilities across the board, then assertibilities must be finer-grained than probabilities. I contend that this is implausible—it is surely the other way round. I generalize this argument to other interpretations of ‘ As ’, including ‘acceptability’ and ‘assentability’. I find it hard to see how any such figure of merit for conditionals can systematically align with the corresponding conditional probabilities. (shrink)

Many philosophers have become worried about the use of standard real numbers for the probability function that represents an agent's credences. They point out that real numbers can't capture the distinction between certain extremely unlikely events and genuinely impossible ones—they are both represented by credence 0, which violates a principle known as “regularity.” Following Skyrms 1980 and Lewis 1980, they recommend that we should instead use a much richer set of numbers, called the “hyperreals.” This essay argues that this popular (...) view is the result of two mistakes. The first mistake, which this essay calls the “numerical fallacy,” is to assume that a distinction that isn't represented by different numbers isn't represented at all in a mathematical representation. In this case, the essay claims that although the real numbers do not make all relevant distinctions, the full mathematical structure of a probability function does. The second mistake is that the hyperreals make too many distinctions. They have a much more complex structure than credences in ordinary propositions can have, so they make distinctions that don't exist among credences. While they might be useful for generating certain mathematical models, they will not appear in a faithful mathematical representation of credences of ordinary propositions. (shrink)

Examples involving common causes — most prominently, examples involving genetically influenced choices — are analytically equivalent not to standard Newcomb Problems — in which the Predictor genuinely predicts the agent's decision — but to non-standard Newcomb Problems — in which the Predictor guarantees the truth of her predictions by interfering with the agent's decision to make the agent choose as it was predicted she would. When properly qualified, causal and epistemic decision theories diverge only on standard — not on non-standard (...) — Newcomb Problems, and thus not on examples involving common causes. (shrink)

Genic selectionism holds that all selection can be understood as operating on particular genes. Critics (and conventional biological wisdom) insist that this misrepresents the actual causal structure of selective phenomena at higher levels of biological organization, but cannot convincingly defend this intuition. I argue that the real failing of genic selectionism is pragmatic – it prevents us from adopting the most efficient corpus of causal laws for predicting and intervening in the course of affairs – and I offer a Pragmatic (...) account of causation itself which ultimately bears out the claim that genic selectionism misrepresents the causal structure of selective contexts. (shrink)

It is plausible that Newcomb problems in which causal maximizers and evidential maximizers would do different things would not be possible for ideal maximizers who are attentive to metatickles. An objection to Eells's first argument for this makes welcome a second. Against it I argue that even ideal evidential and causal maximizers would do different things in some non-dominance Newcomb problems; and that they would hope for different things in some third-person and non-action problems, which is relevant if a good (...) theory of rational choices of acts should fit smoothly into a good theory of rational desires for facts. (shrink)

Conventional wisdom has it that many intriguing features of indicative conditionals aren’t shared by subjunctive conditionals. Subjunctive morphology is common in discussions of wishes and wants, however, and conditionals are commonly used in such discussions as well. As a result such discussions are a good place to look for subjunctive conditionals that exhibit features usually associated with indicatives alone. Here I offer subjunctive versions of J. L. Austin’s ‘biscuit’ conditionals—e.g., “There are biscuits on the sideboard if you want them”—and subjunctive (...) versions of Allan Gibbard’s ‘stand-off’ or ‘Sly Pete’ conditionals, in which speakers with no relevant false beliefs can in the same context felicitously assert conditionals with the same antecedents and contradictory consequents. My cases undercut views according to which the indicative/subjunctive divide marks a great difference in the meaning of conditionals. They also make trouble for treatments of indicative conditionals that cannot readily be generalized to subjunctives. (shrink)

The brain is often taken to be a paradigmatic example of a signaling system with semantic and representational properties, in which neurons are senders and receivers of information carried in action potentials. A closer look at this picture shows that it is not as appealing as it might initially seem in explaining the function of the brain. Working from several sender-receiver models within the teleosemantic framework, I will first argue that two requirements must be met for a system to support (...) genuine semantic information: 1. The receiver must be competent —that is, it must be able to extract rewards from its environment on the basis of the signals that it receives. 2. The receiver must have some flexibility of response relative to the signal received. In the second part of the paper, this initial framework will be applied to neural processes, pointing to the surprising conclusion that signaling at the single-neuron level is only weakly semantic at best. Contrary to received views, neurons will have little or no access to semantic information (though their patterns of activity may carry plenty of quantitative, correlational information) about the world outside the organism. Genuine representation of the world requires an organism - level receiver of semantic information, to which any particular set of neurons makes only a small contribution. (shrink)

This article discusses how the concept of a fair finite lottery can best be extended to denumerably infinite lotteries. Techniques and ideas from non-standard analysis are brought to bear on the problem.

The explanatory role of natural selection is one of the long-term debates in evolutionary biology. Nevertheless, the consensus has been slippery because conceptual confusions and the absence of a unified, formal causal model that integrates different explanatory scopes of natural selection. In this study we attempt to examine two questions: (i) What can the theory of natural selection explain? and (ii) Is there a causal or explanatory model that integrates all natural selection explananda? For the first question, we argue that (...) five explananda have been assigned to the theory of natural selection and that four of them may be actually considered explananda of natural selection. For the second question, we claim that a probabilistic conception of causality and the statistical relevance concept of explanation are both good models for understanding the explanatory role of natural selection. We review the biological and philosophical disputes about the explanatory role of natural selection and formalize some explananda in probabilistic terms using classical results from population genetics. Most of these explananda have been discussed in philosophical terms but some of them have been mixed up and confused. We analyze and set the limits of these problems. (shrink)

According to Nancy Cartwright, a causal law holds just when a certain probabilistic condition obtains in all test situations which in turn satisfy a set of background conditions. These background conditions are shown to be inconsistent and, on separate account, logically incoherent. I offer a corrective reformulation which also incorporates a strategy for problems like Hesslow's thrombosis case. I also show that Cartwright's recent argument for modifying the condition to appeal to singular causes fails.Proposed modifications of the theory's probabilistic condition (...) to handle effects with extreme probabilities (0 or 1) are found unsatisfactory. I propose a unified solution which also handles extreme causes. Undefined conditional probabilities give rise to three good, but non-equivalent, ways of formulating the theory. Various formulations appear in the literature. I give arguments to eliminate all but one candidate. Finally, I argue for a crucial new condition clause, and show how to extend the results beyond a simple probabilistic framework. (shrink)

Examples growing out of the Newcomb problem have convinced many people that decision theory should proceed in terms of some kind of causal probability. I endorse this view and define and investigate a variety of causal probability. My definition is related to Skyrms' definition, but proceeds in terms of objective probabilities rather than subjective probabilities and avoids taking causal dependence as a primitive concept.

The starting point in the development of probabilistic analyses of token causation has usually been the naïve intuition that, in some relevant sense, a cause raises the probability of its effect. But there are well-known examples both of non-probability-raising causation and of probability-raising non-causation. Sophisticated extant probabilistic analyses treat many such cases correctly, but only at the cost of excluding the possibilities of direct non-probability-raising causation, failures of causal transitivity, action-at-a-distance, prevention, and causation by absence and omission. I show that (...) an examination of the structure of these problem cases suggests a different treatment, one which avoids the costs of extant probabilistic analyses. (shrink)

Traditional theories construe approximate truth or truthlikeness as a measure of closeness to facts, singular facts, and idealization as an act of either assuming zero of otherwise very small differences from facts or imagining ideal conditions under which scientific laws are either approximately true or will be so when the conditions are relaxed. I first explain the serious but not insurmountable difficulties for the theories of approximation, and then argue that more serious and perhaps insurmountable difficulties for the theory of (...) idealization force us to sever its close tie to approximation. This leads to an appreciation of lawlikeness as a measure of closeness to laws, which I argue is the real measure of idealization whose main purpose is to carve nature at its joints. (shrink)

Weighted averaging is a method for aggregating the totality of information, both regimented and unregimented, possessed by an individual or group of individuals. The application of such a method may be warranted by a theorem of the calculus of probability, simple conditionalization, or Jeffrey's formula for probability kinematics, all of which average in terms of the prior probability of evidence statements. Weighted averaging may, however, be applied as a method of rational aggregation of the probabilities of diverse perspectives or persons (...) in cases in which the weights cannot be articulated as the prior probabilities of statements of evidence. The method is justified by Wagner's Theorem exhibiting that any method satisfying the conditions of the Irrelevance of Alternatives and Zero Unanimity must, when applied to three or more alternatives, be weighted averaging. (shrink)