Probabilities of counterfactuals and counterfactual probabilities

Probabilities figure centrally in much of the literature on the semantics of conditionals. I find this surprising: it accords a special status to conditionals that other parts of language apparently do not share. I critically discuss two notable ‘probabilities first’ accounts of counterfactuals, due to Edgington and Leitgeb. According to Edgington, counterfactuals lack truth values but have probabilities. I argue that this combination gives rise to a number of problems. According to Leitgeb, counterfactuals have truth conditions-roughly, a counterfactual is true when the corresponding conditional chance is sufficiently high. I argue that problems arise from the disparity between truth and high chance, between approximate truth and high chance, and from counterfactuals for which the corresponding conditional chances are undefined. However, Edgington, Leitgeb and I can unite in opposition to Stalnaker and Lewis-style ‘similarity’ accounts of counterfactuals.     

Deterministic probability: neither chance nor credence

Some have argued that chance and determinism are compatible in order to account for the objectivity of probabilities in theories that are compatible with determinism, like Classical Statistical Mechanics (CSM) and Evolutionary Theory (ET). Contrarily, some have argued that chance and determinism are incompatible, and so such probabilities are subjective. In this paper, I argue that both of these positions are unsatisfactory. I argue that the probabilities of theories like CSM and ET are not chances, but also that they are not subjective probabilities either. Rather, they are a third type of probability, which I call counterfactual probability. The main distinguishing feature of counterfactual-probability is the role it plays in conveying important counterfactual information in explanations. This distinguishes counterfactual probability from chance as a second concept of objective probability.     

Common Knowledge and Reductionism about Shared Agency

Most reductionist accounts of intentional joint action include a condition that it must be common knowledge between participants that they have certain intentions and beliefs that cause and coordinate the joint action. However, this condition has typically simply been taken for granted rather than argued for. The condition is not necessary for ensuring that participants are jointly responsible for the action in which each participates, nor for ensuring that each treats the others as partners rather than as social tools. It is thus something of a mystery why the condition is so widely accepted. By rejecting three arguments that could potentially support it, I argue that reductionists should get rid of the condition. I show that two of the arguments fail. While the third argument is intuitively compelling, it builds on key premises that are unavailable to the reductionist.     

The Reduction of Causal Processes

The principle that causes always render their effects more likely is fundamental to the enterprise of reducing facts of causation to facts about (objective) chances. This reductionist enterprise faces famous difficulties in accommodating common-sense intuitions about causal processes, if it insists on cashing out causal processes in terms of streams of events in which every event that belongs to the stream is a cause of the adjoining event downstream of it. I shall propose modifications to this way of cashing out causal processes, still well within the reductionist faith. These modifications will allow the reductionist to handle processes successfully, on the assumption that the reductionist proposal is itself otherwise satisfactory. I shall then argue that the reductionist enterprise lies squarely behind the Theory of Relativity, and so has all the confirmatory weight of Relativity behind it. However this is not all good news for reductionists. For throughout I shall simply assume that the reductionist proposal, to the effect that causes are just chance-raisers, is correct. AndI shall sidestep problems with that proposal as such. And so I shall show that, if in the end we find the reductionist proposal unsatisfactory, it cannot be on grounds of its treatment of causal processes as such. Thus, while I shall argue that causal processes pose no extra trouble for redutionists, I shall be making a case that all the action between reductionists and their opponents should be focused upon the proposal to reduce the two-term causal relation itself to relations amongst probabilities.     

Self-Awareness without a Self: Buddhism and the Reflexivity of Awareness

In this paper, I show that a robust, reflexivist account of self-awareness (such as was defended by Dignāga and Dharmakīrti, most phenomenologists, and others) is compatible with reductionist view of persons, and hence with a rejection of the existence of a substantial, separate self. My main focus is on the tension between Buddhist reflexivism and the central Buddhist doctrine of no-self. In the first section of the paper, I give a brief sketch of reflexivist accounts of self-awareness, using the Buddhist philosopher Dharmakīrti as my example. In the next section, I examine reductionism as it relates to accounts of the self. I then, in the third section, argue that a reductionist account of persons can account for the unique features of first-person contents and our deep and multi-layered sense of self.     

How chance explains

What explains the outcomes of chance processes? We claim that their setups do. Chances, we think, mediate these explanations of outcome by setup but do not feature in them. Facts about chances do feature in explanations of a different kind: higher-order explanations, which explain how and why setups explain their outcomes. In this paper, we elucidate this 'mediator view' of chancy explanation and defend it from a series of objections. We then show how it changes the playing field in four metaphysical disputes concerning chance. First, it makes it more plausible that even low chances can have explanatory power. Second, it undercuts a circularity objection against reductionist theories of chance. Third, it redirects the debate about a prominent argument against epistemic theories of chance. Finally, it sheds light on potential chancy explanations of the Universe's origin.     

More than 50% or Less than 70% Chance: Pragmatic Implications of Single‐Bound Probability Estimates

Probability estimates can be given as ranges or uncertainty intervals, where often only one of the interval bounds (lower or upper) is specified. For instance, a climate forecast can describe La Niña as having “more than 70% chance” or “less than 90% chance” of occurring. In three experiments, we studied how research participants perceived climate‐related forecasts expressed with lower‐bound (“over X% chance”) or upper‐bound (“under Y% chance”) probability statements. Results indicate that such single‐bound statements give pragmatic information in addition to the numeric probabilities they convey. First, the studies show that these statements are directional, leading the listeners' attention in opposite directions. “Over” statements guide attention towards the possible occurrence of the event and are explained by reasons for why it might happen, while “under” statements direct attention to its possible non‐occurrence and are more often explained by reasons for why the target event might not appear, corresponding to positive (it is possible) versus negative (it is uncertain) verbal probabilities. Second, boundaries were found to reveal the forecaster's beliefs and could be perceived as indicative of an increasing or a decreasing trend. Single‐bound probability estimates are therefore not neutral communications of probability level but might “leak” information about the speaker's expectations and about past and future developments of the forecast. Copyright © 2017 John Wiley & Sons, Ltd.     

Are Dispositions Reducible?

The traditional analysis of dispositions as conditionals is subject to in-superable difficulties. Recently David Lewis has offered a new, reformed analysis intended to meet objections to the old accounts while remaining reductionist about causal powers. I argue that it succeeds in meeting only some of the objections to its predecessors. For the reductionist programme to succeed, more is needed than the correct analysis of dispositions. If dispositional properties are to be reduced, then the world must contain a reduction base. Prima facie this is not the case: the dispositions of medium-sized objects are only reducible to dispositional properties of the structural parts of the objects. The physically ultimate constituents of matter, sub-atomic particles, are simple, and have no properties that could serve as the grounding of their dispositions. Reductionists make three major responses to this argument, which I evaluate. I conclude that the world does not contain anything to which dispositions could be reduced.     

Toward an integrative approach of cognitive neuroscientific and evolutionary psychological studies of art

This paper examines explanations for human artistic behavior in two reductionist research programs, cognitive neuroscience and evolutionary psychology. Despite their different methodological outlooks, both approaches converge on an explanation of art production and appreciation as byproducts of normal perceptual and motivational cognitive skills that evolved in response to problems originally not related to art, such as the discrimination of salient visual stimuli and speech sounds. The explanatory power of this reductionist framework does not obviate the need for higher-level accounts of art from the humanities, such as aesthetics, art history or anthropology of art.     

Taming Chance: Social Science and Everyday Narratives

Although the impacts of chance occurrences play an important role in some of our everyday narratives, they are rarely discussed in social science accounts of the life cycle. The discrepancy between chance's relative significance in each of these portrayals is partly attributable to the highlighting of the unusual and unexpected in order to make our narratives interesting. The difference is also based in social sciences' attempt to tame chance using stochastic models enriched by recent nonlinear dynamic systems approaches. A critical factor affecting our accounts, whether in everyday life or in the search for robust general laws of behavior, is our commitment to prediction and control.     

How incidental values from the environment affect decisions about money, risk, and delay

How different are ￡0.50 and ￡1.50, "a small chance" and "a good chance," or "three months" and "nine months"? Our studies show that people behave as if the differences between these values are altered by incidental everyday experiences. Preference for a ￡1.50 lottery rather than a ￡0.50 lottery was stronger among individuals exposed to intermediate supermarket prices than among those exposed to lower or higher prices. Preference for "a good chance" rather than "a small chance" of winning a lottery was stronger among participants who predicted intermediate probabilities of rain than among those who predicted lower or higher chances of rain. Preference for consumption in "three months" rather than "nine months" was stronger among participants who planned for an intermediate birthday than among participants who planned for a sooner or later birthday. These fluctuations directly challenge economic accounts that translate monies, risks, and delays into subjective equivalents with stable functions. The decision-by-sampling model-in which subjective values are rank positions constructed from comparisons with samples-predicts these effects and indicates a primary role for sampling in decision making.     

Can membership-functions capture the directionality of verbal probabilities?

Verbal probabilities are a common mean for communicating risk and uncertainties in many decision-making settings (e.g., finance, medicine, military). They are considered directional because they elicit a focus on either the outcome occurrence (e.g., there is a chance) or on its non-occurrence (e.g., it is unlikely). According to a quantitative perspective, directionality is dependent on the vague probabilistic meaning conveyed by verbal probabilities—e.g., p(outcome) > .50 = > focus on outcome occurrence. In contrast a more qualitative perspective suggests that directionality depends on contextual factors. The present study tested whether the directionality of verbal probabilities was determined by their vague probabilistic meaning, by contextually manipulated variables (i.e., representativeness and base rate), or by a combination of both. Participants provided their own expressions to describe the guilt of a suspect and then assessed the vague probabilistic meaning and directionality associated with those expressions. Results showed that directionality was mainly determined by the vague probabilistic meaning but also by the base rate of guilt. Although attention focus on the occurrence or the non-occurrence of the target outcome is dependent on vague probabilistic meaning, it cannot be fully accounted for by it.     

Rewording the Rules on Disjunctive Probability

Logic is a central and highly useful part of philosophy. Its value is particularly evident when it comes to keeping our thinking about disjunctive probabilities clear. Because of the two meanings of “or” (“just one of these statements is true,” “at least one of these statements is true”), logic can show how the likelihood of a disjunction being true can be determined quite easily. To gauge the chance that one of two or more exclusive alternatives is true, one need only sum up their respective likelihoods. And to know the chance that at least one of two or more compatible alternatives is true, one simply has to figure the chance that it is false that all of them are false!     

Human agency and weakness of will: A neo-Thomist discussion

Contemporary neo-Thomist writers offer an alternative to reductionist accounts of human agency. I argue that to do so plausibly they will have to show (a) their accounts do not entail a simple dualism of reason over desire; and (b) how they account for weakness of will. McCabe argues that for living organisms perception is a matter of receiving “intentionally”, allowing for a degree of voluntariness, and that by virtue of the human capacity for language, and insertion into a culture, the human animal can direct itself by means of its grasp of good reasons for action. In partial disagreement, Shutte clarifies the non-material nature of this human capacity as referring to our capacity for self-enactment—which gives rise to, or finds expression in, language and culture. The further problem of weakness of will is explained by Farrer as a question of the quality of one’s willingness, one’s ability to be persuaded—mistakenly thought of as a matter of the correct knowledge of the good taken out of the context of deliberation about action. Furthermore, the logic of growth in the breadth of one’s willingness is unpacked by Shutte by means of the guru-novice model of interpersonal transaction. I conclude that framing our understanding of agency in terms of a philosophical anthropology is eminently reasonable.     

On the a priori and a posteriori assessment of probabilities

We argue that in spite of their apparent dissimilarity, the methodologies employed in the a priori and a posteriori assessment of probabilities can both be justified by appeal to a single principle of inductive reasoning, viz., the principle of symmetry. The difference between these two methodologies consists in the way in which information about the single-trial probabilities in a repeatable chance process is extracted from the constraints imposed by this principle. In the case of a posteriori reasoning, these constraints inform the analysis by fixing an a posteriori determinant of the probabilities, whereas, in the case of a priori reasoning, they imply certain claims which then serve as the basis for subsequent probabilistic deductions. In a given context of inquiry, the particular form which a priori or a posteriori reason may take depends, in large part, on the strength of the underlying symmetry assumed: the stronger the symmetry, the more information can be acquired a priori and the less information about the long-run behavior of the process is needed for an a posteriori assessment of the probabilities. In the context of this framework, frequency-based reasoning emerges as a limiting case of a posteriori reasoning, and reasoning about simple games of chance, as a limiting case of a priori reasoning. Between these two extremes, both a priori and a posteriori reasoning can take a variety of intermediate forms.     

A direct assessment of the role of expectation in inhibition of return

An object hidden among distractors can be found more efficiently if previously searched locations are not reinspected. The inhibition-of-return (IOR) phenomenon indexes the tendency to avoid reinspections. Two accounts of IOR, that it is due to inhibition and that it is due to expectation, are generally regarded as incompatible. The relevant evidence to date, however, has been indirect: Inhibition or expectation has been inferred from response times or similar indirect measures. This article reports the first direct measure of IOR, obtained by asking observers to predict the location of the next target in a display containing eight possible locations on an imaginary circle. On any given trial, the previously cued location was chosen less frequently (impairment)--and the opposite location was chosen more frequently (facilitation)--than chance (choice of all other locations was at chance). The impairment is consistent with both inhibition and expectation accounts; the facilitation is consistent only with expectation accounts. This work also shows that inhibition and expectation are not necessarily incompatible: Implementing expectations may entail inhibiting previously cued locations.     

Who they are and what de se: Burge on quasi-memory

Tyler Burge has recently argued that quasi-memory-based psychological reductionist accounts of diachronic personal identity are deeply problematic. According to Burge, these accounts either fail to include appropriately de se elements or presuppose facts about diachronic personal identity—facts of the very kind that the accounts are supposed to explain. Neither of these objections is compelling. The first is based in confusion about the version of reductionism to which it putatively applies. The second loses its force when we recognize that reductionism is a metaphysical thesis, not an epistemological one.

What Chance‐Credence Norms Should Not Be

A chance‐credence norm states how an agent's credences in propositions concerning objective chances ought to relate to her credences in other propositions. The most famous such norm is the Principal Principle (PP), due to David Lewis. However, Lewis noticed that PP is too strong when combined with many accounts of chance that attempt to reduce chance facts to non‐modal facts. Those who defend such accounts of chance have offered two alternative chance‐credence norms: the first is Hall's and Thau's New Principle (NP); the second is Ismael's General Recipe (IP). Thus, the question arises: Should we adopt NP or IP or both? In this paper, I argue that IP has unacceptable consequences when coupled with reductionism, so we must accept NP alone.