We investigate the connection between interference and computational power within the operationally defined framework of generalised probabilistic theories. To compare the computational abilities of different theories within this framework we show that any theory satisfying four natural physical principles possess a well-defined oracle model. Indeed, we prove a subroutine theorem for oracles in such theories which is a necessary condition for the oracle model to be well-defined. The four principles are: causality, purification, strong symmetry, and informationally consistent composition. Sorkin (...) has defined a hierarchy of conceivable interference behaviours, where the order in the hierarchy corresponds to the number of paths that have an irreducible interaction in a multi-slit experiment. Given our oracle model, we show that if a classical computer requires at least n queries to solve a learning problem, because fewer queries provide no information about the solution, then the corresponding “no-information” lower bound in theories lying at the kth level of Sorkin’s hierarchy is \. This lower bound leaves open the possibility that quantum oracles are less powerful than general probabilistic oracles, although it is not known whether the lower bound is achievable in general. Hence searches for higher-order interference are not only foundationally motivated, but constitute a search for a computational resource that might have power beyond that offered by quantum computation. (shrink)

Recent studies indicate that indicative conditionals like "If people wear masks, the spread of Covid-19 will be diminished" require a probabilistic dependency between their antecedents and consequents to be acceptable (Skovgaard-Olsen et al., 2016). But it is easy to make the slip from this claim to the thesis that indicative conditionals are acceptable only if this probabilistic dependency results from a causal relation between antecedent and consequent. According to Pearl (2009), understanding a causal relation involves multiple, hierarchically organized (...) conceptual dimensions: prediction, intervention, and counterfactual dependence. In a series of experiments, we test the hypothesis that these conceptual dimensions are differentially encoded in indicative and counterfactual conditionals. If this hypothesis holds, then there are limits as to how much of a causal relation is captured by indicative conditionals alone. Our results show that the acceptance of indicative and counterfactual conditionals can become dissociated. Furthermore, it is found that the acceptance of both is needed for accepting a causal relation between two co-occurring events. The implications that these findings have for the hypothesis above, and for recent debates at the intersection of the psychology of reasoning and causal judgment, are critically discussed. Our findings are consistent with viewing indicative conditionals as answering predictive queries requiring evidential relevance (even in the absence of direct causal relations). Counterfactual conditionals in contrast target causal relevance, specifically. Finally, we discuss the implications our results have for the yet unsolved question of how reasoners succeed in constructing causal models from verbal descriptions. (shrink)

In our former works, for a given concept of reduction, we study the following hypothesis: “For a random oracle A, with probability one, the degree of the one-query tautologies with respect to A is strictly higher than the degree of A.” In our former works (Suzuki in Kobe J. Math. 15, 91–102, 1998; in Inf. Comput. 176, 66–87, 2002; in Arch. Math. Logic 44, 751–762), the following three results are shown: The hypothesis for p-T (polynomial-time Turing) reduction is equivalent (...) to the assertion that the probabilistic complexity class R is not equal to NP; The hypothesis for p-tt (polynomial-time truth-table) reduction implies that P is not NP; The hypothesis holds for each of the following: disjunctive reduction, conjunctive reduction, and p-btt (polynomial-time bounded-truth-table) reduction. In this paper, we show the following three results: (1) Let c be a positive real number. We consider a concept of truth-table reduction whose norm is at most c times size of input, where for a relativized propositional formula F, the size of F denotes the total number of occurrences of propositional variables, constants and propositional connectives. Then, our main result is that the hypothesis holds for such tt-reduction, provided that c is small enough. How small c can we take so that the above holds? It depends on our syntactic convention on one-query tautologies. In our setting, the statement holds for all c < 1. (2) The hypothesis holds for monotone truth-table reduction (also called positive reduction). (3) Dowd (in Inf. Comput. 96, 65–76, 1992) shows a polynomial upper bound for the minimum sizes of forcing conditions associated with a random oracle. We apply the above result (1), and get a linear lower bound for the sizes. (shrink)

The sampling-based motion planner is the mainstream method to solve the motion planning problem in high-dimensional space. In the process of exploring robot configuration space, this type of algorithm needs to perform collision query on a large number of samples, which greatly limits their planning efficiency. Therefore, this paper uses machine learning methods to establish a probabilistic model of the obstacle region in configuration space by learning a large number of labeled samples. Based on this, the high-dimensional samples’ (...) rapid collision query is realized. The influence of number of Gaussian components on the fitting accuracy is analyzed in detail, and a self-adaptive model training method based on Greedy expectation-maximization algorithm is proposed. At the same time, this method has the capability of online updating and can eliminate model fitting errors due to environmental changes. Finally, the model is combined with a variety of sampling-based motion planners and is validated in multiple sets of simulations and real world experiments. The results show that, compared with traditional methods, the proposed method has significantly improved the planning efficiency. (shrink)

This paper presents an effort to induce a Bayesian belief network (BBN) from crime data, namely the national crime victimization survey (NCVS). This BBN defines a joint probability distribution over a set of variables that were employed to record a set of crime incidents, with particular focus on characteristics of the victim. The goals are to generate a BBN to capture how characteristics of crime incidents are related to one another, and to make this information available to domain specialists. The (...) novelty associated with the study reported in this paper lies in the use of a Bayesian network to represent a complex data set to non-experts in a way that facilitates automated analysis. Validation of the BBN’s ability to approximate the joint probability distribution over the set of variables entailed in the NCVS data set is accomplished through a variety of sources including mathematical techniques and human experts for appropriate triangulation. Validation results indicate that the BBN induced from the NCVS data set is a good joint probability model for the set of attributes in the domain, and accordingly can serve as an effective query tool. (shrink)

1 Boolean retrieval 1 2 The term vocabulary and postings lists 19 3 Dictionaries and tolerant retrieval 49 4 Index construction 67 5 Index compression 85 6 Scoring, term weighting and the vector space model 109 7 Computing scores in a complete search system 135 8 Evaluation in information retrieval 151 9 Relevance feedback and query expansion 177 10 XML retrieval 195 11 Probabilistic information retrieval 219 12 Language models for information retrieval 237 13 Text classification and Naive (...) Bayes 253 14 Vector space classification 289 15 Support vector machines and machine learning on documents 319 16 Flat clustering 349 17 Hierarchical clustering 377 18 Matrix decompositions and latent semantic indexing 403 19 Web search basics 421 20 Web crawling and indexes 443 21 Link analysis 461.. (shrink)

Newton’s earliest publications contained scandalous epistemological claims: not only did he aim for certainty; he also claimed success. Some commentators argue that Newton ultimately gave up claims of certainty in favor of a high degree of probability. I argue that no such shift occurred. I examine the evidence of a probabilistic shift: a passage from query 23/31 of the Opticks and rule 4 of the Principia. Neither passage supports a probabilistic approach to natural philosophy. The aim of (...) certainty, then, was an enduring feature of Newton’s methodology. (shrink)

We present a new framework for combining logic with probability, and demonstrate the application of this framework to breast cancer prognosis. Background knowledge concerning breast cancer prognosis is represented using logical arguments. This background knowledge and a database are used to build a Bayesian net that captures the probabilistic relationships amongst the variables. Causal hypotheses gleaned from the Bayesian net in turn generate new arguments. The Bayesian net can be queried to help decide when one argument attacks another. The (...) Bayesian net is used to perform the prognosis, while the argumentation framework is used to provide a qualitative explanation of the prognosis. (shrink)

We present an information-theoretic interpretation of quantum formalism based on a Bayesian framework and devoid of any extra axiom or principle. Quantum information is construed as a technique for analyzing a logical system subject to classical constraints, based on a question-and-answer procedure. The problem is posed from a particular batch of queries while the constraints are represented by the truth table of a set of Boolean functions. The Bayesian inference technique consists in assigning a probability distribution within a real-valued probability (...) space to the joint set of queries in order to satisfy the constraints. The initial query batch is not unique and alternative batches can be considered at will. They are enabled mechanically from the initial batch, quite simply by transcribing the probability space into an auxiliary Hilbert space. It turns out that this sole procedure leads to exactly rediscover the standard quantum information theory and thus provides an information-theoretic rationale to its technical rules. In this framework, the great challenges of quantum mechanics become simple platitudes: Why is the theory probabilistic? Why is the theory linear? Where does the Hilbert space come from? In addition, most of the paradoxes, such as uncertainty principle, entanglement, contextuality, nonsignaling correlation, measurement problem, etc., become straightforward features. In the end, our major conclusion is that quantum information is nothing but classical information processed by a mature form of Bayesian inference technique and, as such, consubstantial with Aristotelian logic. (shrink)

Indirect negative evidence is clearly an important way for learners to constrain overgeneralisation, and yet a good learning theoretic analysis has yet to be provided for this, whether in a PAC or a probabilistic identification in the limit framework. In this paper we suggest a theoretical analysis of indirect negative evidence that allows the presence of ungrammatical strings in the input and also accounts for the relationship between grammaticality/acceptability and probability. Given independently justified assumptions about lower bounds on the (...) probabilities of grammatical strings, we establish that a limited number of membership queries of some strings can be probabilistically simulated. (shrink)

In a first part I present the results of the philosophy of scientific explanation with an attempt to apply them to the case of the theory of evolution. Then I observe that the requirements of modelization of phenomena with the help of inductive logic do not capture efficiently the pertinent factors and fail just as much to exclude those which end up being neutral as explanatory premises. I then query in the direction of confirmation theory, and show that (...) class='Hi'>probabilistic reasoning does not possess the syntactic means of testing evolutionary hypotheses in a way that would rely on a valid mode of inference. In a second part, I try to show how biology has oscillated between two privileged modes of explanation, the first one being through form of which I suggest here that it has never been replaced and that it has known a forgotten vitality in the middle and latter part of the 19th Century, and the second one being through function here evaluated critically alongside that of tinkering. Finally, some limits are seen to hold against the pretence to epistemological exclusivism of those two outlooks on the biological object. (shrink)

Decision makers often rely on expert opinion when making forecasts under uncertainty. In doing so, they confront two methodological challenges: the elicitation problem, which requires them to extract meaningful information from experts; and the aggregation problem, which requires them to combine expert opinion by resolving disagreements. Linear averaging is a justifiably popular method for addressing aggregation, but its robust simplicity makes two requirements on elicitation. First, each expert must offer probabilistically coherent forecasts; second, each expert must respond to all our (...) queries. In practice, human judges (even experts) may be incoherent, and may prefer to assess only the subset of events about which they are comfortable offering an opinion. In this paper, a new methodology is developed for combining expert assessment of chance. The method retains the conceptual and computational simplicity of linear averaging, but generalizes the standard approach by relaxing the requirements on expert elicitation. The method also enjoys provable performance guarantees, and in experiments with real-world forecasting data is shown to offer both computational efficiency and competitive forecasting gains as compared to rival aggregation methods. This paper is relevant to the practice of decision analysis, for it enables an elicitation methodology in which judges have freedom to choose the events they assess. (shrink)

Several authors have investigated the question of whether canonical logic-based accounts of belief revision, and especially the theory of AGM revision operators, are compatible with the dynamics of Bayesian conditioning. Here we show that Leitgeb's stability rule for acceptance, which has been offered as a possible solution to the Lottery paradox, allows to bridge AGM revision and Bayesian update: using the stability rule, we prove that AGM revision operators emerge from Bayesian conditioning by an application of the principle of maximum (...) entropy. In situations of information loss, or whenever the agent relies on a qualitative description of her information state - such as a plausibility ranking over hypotheses, or a belief set - the dynamics of AGM belief revision are compatible with Bayesian conditioning; indeed, through the maximum entropy principle, conditioning naturally generated AGM revision operators. This mitigates an impossibility theorem of Lin and Kelly for tracking Bayesian conditioning with AGM revision, and suggests an approach to the compatibility problem that highlights the information loss incurred by acceptance rules in passing from probabilistic to qualitative representations of beliefs. (shrink)

We investigate a basic probabilistic dynamic semantics for a fragment containing conditionals, probability operators, modals, and attitude verbs, with the aim of shedding light on the prospects for adding probabilistic structure to models of the conversational common ground.

Words are the essence of communication: They are the building blocks of any language. Learning the meaning of words is thus one of the most important aspects of language acquisition: Children must first learn words before they can combine them into complex utterances. Many theories have been developed to explain the impressive efficiency of young children in acquiring the vocabulary of their language, as well as the developmental patterns observed in the course of lexical acquisition. A major source of disagreement (...) among the different theories is whether children are equipped with special mechanisms and biases for word learning, or their general cognitive abilities are adequate for the task. We present a novel computational model of early word learning to shed light on the mechanisms that might be at work in this process. The model learns word meanings as probabilistic associations between words and semantic elements, using an incremental and probabilistic learning mechanism, and drawing only on general cognitive abilities. The results presented here demonstrate that much about word meanings can be learned from naturally occurring child-directed utterances (paired with meaning representations), without using any special biases or constraints, and without any explicit developmental changes in the underlying learning mechanism. Furthermore, our model provides explanations for the occasionally contradictory child experimental data, and offers predictions for the behavior of young word learners in novel situations. (shrink)

Suppose several individuals (e.g., experts on a panel) each assign probabilities to some events. How can these individual probability assignments be aggregated into a single collective probability assignment? This article reviews several proposed solutions to this problem. We focus on three salient proposals: linear pooling (the weighted or unweighted linear averaging of probabilities), geometric pooling (the weighted or unweighted geometric averaging of probabilities), and multiplicative pooling (where probabilities are multiplied rather than averaged). We present axiomatic characterisations of each class of (...) pooling functions (most of them classic, but one new) and argue that linear pooling can be justified procedurally, but not epistemically, while the other two pooling methods can be justified epistemically. The choice between them, in turn, depends on whether the individuals' probability assignments are based on shared information or on private information. We conclude by mentioning a number of other pooling methods. (shrink)

In this paper I expound an argument which seems to establish that probabilism and special relativity are incompatible. I examine the argument critically, and consider its implications for interpretative problems of quantum theory, and for theoretical physics as a whole.

Four important arguments for probabilism—the Dutch Book, representation theorem, calibration, and gradational accuracy arguments—have a strikingly similar structure. Each begins with a mathematical theorem, a conditional with an existentially quantified consequent, of the general form: if your credences are not probabilities, then there is a way in which your rationality is impugned. Each argument concludes that rationality requires your credences to be probabilities. I contend that each argument is invalid as formulated. In each case there is a mirror-image theorem and (...) a corresponding argument of exactly equal strength that concludes that rationality requires your credences not to be probabilities. Some further consideration is needed to break this symmetry in favour of probabilism. (shrink)

The postwar welfare state provides social insurance against economic, health, and related risks in an uncertain world. Because everyone can envision themselves to be among the unfortunate, social insurance fuses self-interest and solidarism in a normative principle Friedman (2020) calls probabilistic justice. But there is a competing principle of status defense, where the aim is to erect boundaries between socioeconomic strata and discourage cross-class mobility. We argue that this principle dominates when inequality is high and uncertainty low. The current (...) moment is one of high inequality and high uncertainty, which results in intense status anxiety, yet does not rule out solidaristic solutions. Our contributions are to diagnose the causes of our current malaise, and to theorize the normative bases for the political choice facing contemporary western democracies. (shrink)

Are special relativity and probabilism compatible? Dieks argues that they are. But the possible universe he specifies, designed to exemplify both probabilism and special relativity, either incorporates a universal "now" (and is thus incompatible with special relativity), or amounts to a many world universe (which I have discussed, and rejected as too ad hoc to be taken seriously), or fails to have any one definite overall Minkowskian-type space-time structure (and thus differs drastically from special relativity as ordinarily understood). Probabilism and (...) special relativity appear to be incompatible after all. What is at issue is not whether "the flow of time" can be reconciled with special relativity, but rather whether explicitly probabilistic versions of quantum theory should be rejected because of incompatibility with special relativity. (shrink)

Traditional philosophical discussions of knowledge have focused on the epistemic status of full beliefs. In this book, Moss argues that in addition to full beliefs, credences can constitute knowledge. For instance, your .4 credence that it is raining outside can constitute knowledge, in just the same way that your full beliefs can. In addition, you can know that it might be raining, and that if it is raining then it is probably cloudy, where this knowledge is not knowledge of propositions, (...) but of probabilistic contents. -/- The notion of probabilistic content introduced in this book plays a central role not only in epistemology, but in the philosophy of mind and language as well. Just as tradition holds that you believe and assert propositions, you can believe and assert probabilistic contents. Accepting that we can believe, assert, and know probabilistic contents has significant consequences for many philosophical debates, including debates about the relationship between full belief and credence, the semantics of epistemic modals and conditionals, the contents of perceptual experience, peer disagreement, pragmatic encroachment, perceptual dogmatism, and transformative experience. In addition, accepting probabilistic knowledge can help us discredit negative evaluations of female speech, explain why merely statistical evidence is insufficient for legal proof, and identify epistemic norms violated by acts of racial profiling. Hence the central theses of this book not only help us better understand the nature of our own mental states, but also help us better understand the nature of our responsibilities to each other. (shrink)

The debate on probabilistic measures of coherence flourishes for about 15 years now. Initiated by papers that have been published around the turn of the millennium, many different proposals have since then been put forward. This contribution is partly devoted to a reassessment of extant coherence measures. Focusing on a small number of reasonable adequacy constraints I show that (i) there can be no coherence measure that satisfies all constraints, and that (ii) subsets of these adequacy constraints motivate two (...) different classes of coherence measures. These classes do not coincide with the common distinction between coherence as mutual support and coherence as relative set-theoretic overlap. Finally, I put forward arguments to the effect that for each such class of coherence measures there is an outstanding measure that outperforms all other extant proposals. One of these measures has recently been put forward in the literature, while the other one is based on a novel probabilistic measure of confirmation. (shrink)

Richard Jeffrey espoused an antifoundationalist variant of Bayesian thinking that he termed ‘Radical Probabilism’. Radical Probabilism denies both the existence of an ideal, unbiased starting point for our attempts to learn about the world and the dogma of classical Bayesianism that the only justified change of belief is one based on the learning of certainties. Probabilistic judgment is basic and irreducible. Bayesian conditioning is appropriate when interaction with the environment yields new certainty of belief in some proposition but leaves (...) one’s conditional beliefs untouched (the ‘Rigidity’ condition). Although Richard Jeffrey denied the general applicability of this condition, one of his main contributions to probabilistic thinking is a form of belief updating—now typically called ‘Jeffrey conditioning’ or ‘probability kinematics’—that is appropriate in circumstances in which Rigidity is satisfied, but where the interaction causes one to reevaluate one’s probability judgments over some partition of the possibility space without conferring certainty on any particular element. The most familiar occasion for Jeffrey conditioning is receipt of uncertain evidence: things partially perceived or remembered. But it also serves to illuminate belief updating occasioned by a change in one’s degrees of conditional belief, a kind of belief change largely ignored by classical Bayesianism. I argue that such changes in conditional belief can also be basic (in the sense of not being analyzable as a consequence of conditioning on factual information) and offer a kinematical model for a particular kind change in conditional belief. Both are applied to changes in preference. Finally, I argue that Rigidity can fail when changes of belief give inferential grounds for changes in conditional belief (and vice versa). These failures show that conditioning methods are properly regarded, not as valid rules of inference, but as tools in the ‘art of judgment’. (shrink)

'The Probabilistic Mind' is a follow-up to the influential and highly cited 'Rational Models of Cognition'. It brings together developments in understanding how, and how far, high-level cognitive processes can be understood in rational terms, and particularly using probabilistic Bayesian methods.

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)

In this important book, Ellery Eells explores and refines philosophical conceptions of probabilistic causality. In a probabilistic theory of causation, causes increase the probability of their effects rather than necessitate their effects in the ways traditional deterministic theories have specified. Philosophical interest in this subject arises from attempts to understand population sciences as well as indeterminism in physics. Taking into account issues involving spurious correlation, probabilistic causal interaction, disjunctive causal factors, and temporal ideas, Professor Eells advances the (...) analysis of what it is for one factor to be a positive causal factor for another. A salient feature of the book is a theory of token level probabilistic causation in which the evolution of the probability of a later event from an earlier event is central. This will be a book of crucial significance to philosophers of science and metaphysicians; it will also prove stimulating to many economists, psychologists, and physicists. (shrink)

Probabilism is the view that a rational agent's credences should always be probabilistically coherent. It has been argued that Probabilism follows, given the assumption that an epistemically rational agent ought to try to have credences that represent the world as accurately as possible. The key claim in this argument is that the goal of representing the world as accurately as possible is best served by having credences that are probabilistically coherent. This essay shows that this claim is false. In certain (...) cases, the goal of having accurate credences is best served by being probabilistically incoherent. Assuming that an epistemically rational agent ought to try to have credences that are as accurate as possible, it follows that in certain cases a rational agent ought to have probabilistically incoherent credences. (shrink)

Are probabilism and special relativity compatible? Dieks argues that they are. But the possible universe he specifies, designed to exemplify both probabilism and special relativity, either incorporates a universal “now”, or amounts to a many world universe, or fails to have any one definite overall Minkowskian-type space-time structure. Probabilism and special relativity appear to be incompatible after all. What is at issue is not whether “the flow of time” can be reconciled with special relativity, but rather whether explicitly probabilistic (...) versions of quantum theory should be rejected because of incompatibility with special relativity. (shrink)

D. M. Armstrong famously claims that deterministic laws of nature are contingent relations between universals and that his account can also be straightforwardly extended to irreducibly probabilistic laws of nature. For the most part, philosophers have neglected to scrutinize Armstrong’s account of probabilistic laws. This is surprising precisely because his own claims about probabilistic laws make it unclear just what he takes them to be. We offer three interpretations of what Armstrong-style probabilistic laws are, and argue (...) that all three interpretations are incompatible either with some feature of Armstrong’s broader metaphysics or with essential features of his account of laws (or both). (shrink)

I put forward a micro realistic, probabilistic version of quantum theory, which specifies the precise nature of quantum entities thus solving the quantum wave/particle dilemma, and which both reproduces the empirical success of orthodox quantum theory, and yields predictions that differ from orthodox quantum theory for as yet unperformed experiments.

After clarifying the probabilistic conception of causality suggested by Good (1961-2), Suppes (1970), Cartwright (1979), and Skyrms (1980), we prove a sufficient condition for transitivity of causal chains. The bearing of these considerations on the units of selection problem in evolutionary theory and on the Newcomb paradox in decision theory is then discussed.

The aim of the paper is to develop general criteria of argumentative validity and adequacy for probabilistic arguments on the basis of the epistemological approach to argumentation. In this approach, as in most other approaches to argumentation, proabilistic arguments have been neglected somewhat. Nonetheless, criteria for several special types of probabilistic arguments have been developed, in particular by Richard Feldman and Christoph Lumer. In the first part (sects. 2-5) the epistemological basis of probabilistic arguments is discussed. With (...) regard to the philosophical interpretation of probabilities a new subjectivist, epistemic interpretation is proposed, which identifies probabilities with tendencies of evidence (sect. 2). After drawing the conclusions of this interpretation with respect to the syntactic features of the probability concept, e.g. one variable referring to the data base (sect. 3), the justification of basic probabilities (priors) by judgements of relative frequency (sect. 4) and the justification of derivative probabilities by means of the probability calculus are explained (sect. 5). The core of the paper is the definition of '(argumentatively) valid derivative probabilistic arguments', which provides exact conditions for epistemically good probabilistic arguments, together with conditions for the adequate use of such arguments for the aim of rationally convincing an addressee (sect. 6). Finally, some measures for improving the applicability of probabilistic reasoning are proposed (sect. 7). (shrink)

How can different individuals' probability assignments to some events be aggregated into a collective probability assignment? Classic results on this problem assume that the set of relevant events -- the agenda -- is a sigma-algebra and is thus closed under disjunction (union) and conjunction (intersection). We drop this demanding assumption and explore probabilistic opinion pooling on general agendas. One might be interested in the probability of rain and that of an interest-rate increase, but not in the probability of rain (...) or an interest-rate increase. We characterize linear pooling and neutral pooling for general agendas, with classic results as special cases for agendas that are sigma-algebras. As an illustrative application, we also consider probabilistic preference aggregation. Finally, we compare our results with existing results on binary judgment aggregation and Arrovian preference aggregation. This paper is the first of two self-contained, but technically related companion papers inspired by binary judgment-aggregation theory. (shrink)

In this essay, I attempt to provide answers to the following four queries concerning the metaphysics of early human embryogenesis. (1) Following its first cellular fission, is it coherent to claim that one and only one of two “blastomeric” twins of a human zygote is identical with that zygote? (2) Following the fusion of two human pre-embryos, is it coherent to claim that one and only one pre-fusion pre-embryo is identical with that postfusion pre-embryo? (3) Does a live human being (...) come into existence only when its brain comes into existence? (4) At implantation, does a pre-embryo become a mere part of its mother? I argue that either if things have quidditative properties or if criterialism is false, then queries (1) and (2) can be answered in the affirmative; that in light of recent developments in theories of human death and in light of a more “functional” theory of brains, query (3) can be answered in the negative; and that plausible mereological principles require a negative answer to query (4). (shrink)

The notion of a “query” occurred in legal, medical, theological and scientific writings during the early modern period. Whereas the “questionary” (from c. 1400s) sought replies from within a doctrine (such as Galenic medicine), in the 1600s the query posed open-ended inquiries, seeking empirical information from travellers, explorers and others. During the 1660s in Britain, three versions of the query (and lists of queries) emerged. Distinctions need to be made between queries seeking information via observation and those (...) asking for experimentation, and between those aiming to keep theory to one side and those that framed theoretical conjectures. My examples are drawn from the work of the Royal Society of London (founded 1660) and from some of its leading members, especially Robert Boyle, Robert Hooke and Isaac Newton. (shrink)

“Probabilistic Causation” designates a group of theories that aim to characterize the relationship between cause and effect using the tools of probability theory. The central idea behind these theories is that causes change the probabilities of their effects. This article traces developments in probabilistic causation, including recent developments in causal modeling. A variety of issues within, and objections to, probabilistic theories of causation will also be discussed.

Robert Brandom’s normative-pragmatic theory is intended to represent the minimal set of practical abilities whose exhibition qualifies creatures as speaking a language. His model of a minimally discursive practice (MDP) is one in which participants, devoid of logical vocabulary, are only capable of making assertions and drawing inferences. This paper argues that Brandom’s purely assertional practices are not MDPs and that speech acts of asking questions (queries) must be included in any practice that counts as an MDP. The upshot of (...) the argument is support for the claim that the normative pragmatic analysis of assertions requires a corresponding analysis of queries and vice versa. (shrink)

This work concerns itself with characterising the different types of contents that arise from uses of interrogative sentences, describing what meanings get associated with particular interrogative sentences, and explaining how these get put together compositionally on the basis of the meaning of their constituents, with particular attention to the meaning of interrogative phrases. ;Within most recent work in linguistic semantics, questions, the contents of query uses of interrogatives, have been analysed reductively as higher order propositional objects. The current work (...) argues against such an analysis. In its stead a view of questions is offered wherein these constitute the subclass of singular propositional entities, unresolved states-of-affairs , those that contain one or more argument roles of the propositional entity with whom no entity is associated. This view provides for an inherently richer notion of answerhood that is at the same time based on entities that are more plausibly available to cognitive agents engaged in querying. The need for a richer notion of answerhood is prompted by our demonstration that the class of answers to any given question--contents that can be conveyed by acceptable responses--has been considerably under-recognized in past work. An important gain made by the proposed approach is that it reveals and provides a simple account of systematic and cross-linguistically stable contrasts in the ability of a predicate to take an interrogative meaning as an argument. ;Our proposal for characterising the meaning of interrogative expressions argues that there exist three independent classes of uses which interrogative phrases can undergo, which we dub independent, dependent, and reprise uses. We argue extensively against an assumption common to most past work that interrogatives should be viewed as quantifiers on either syntactic or semantic grounds. We propose that dependent and reprise uses of interrogative expressions are each particular instances of use-types applicable to non-interrogative expressions. Dependent uses include bound variable anaphora as an instance. Reprise uses comprehend quotative uses of declarative sentences. We show how combining the general characteristics of each use type with the characterisation of independent interrogative uses we provide enables the defining conditions pertaining to these additional interrogative uses to be derived. This allows for a simple and comprehensive account of the available interrogative meanings. (shrink)

We study probabilistic logic under the viewpoint of the coherence principle of de Finetti. In detail, we explore how probabilistic reasoning under coherence is related to model- theoretic probabilistic reasoning and to default reasoning in System . In particular, we show that the notions of g-coherence and of g-coherent entailment can be expressed by combining notions in model-theoretic probabilistic logic with concepts from default reasoning. Moreover, we show that probabilistic reasoning under coherence is a generalization (...) of default reasoning in System . That is, we provide a new probabilistic semantics for System , which neither uses infinitesimal probabilities nor atomic bound (or big-stepped) probabilities. These results also provide new algorithms for probabilistic reasoning under coherence and for default reasoning in System , and they give new insight into default reasoning with conditional objects. (shrink)

We argue that a conflict between two conceptions of “quantity of matter” employed in a corollary to proposition 6 of Book III of the Principia illustrates a deeper conflict between Newton’s view of the nature of extended bodies and the concept of mass appropriate for the theoretical framework of the Principia. We trace Newton’s failure to recognize the conflict to the fact that he allowed for the justification of natural philosophical claims by two types of a posteriori, empiricist methodologies. Newton's (...) thoughts on these methodologies demonstrate that his natural philosophy continued to develop after the publication of the first edition of Principia and that De Grav should be understood as an early, and not necessarily representative, text. (shrink)

Probabilistic methods are providing new explanatory approaches to fundamental cognitive science questions of how humans structure, process and acquire language. This review examines probabilistic models defined over traditional symbolic structures. Language comprehension and production involve probabilistic inference in such models; and acquisition involves choosing the best model, given innate constraints and linguistic and other input. Probabilistic models can account for the learning and processing of language, while maintaining the sophistication of symbolic models. A recent burgeoning of (...) theoretical developments and online corpus creation has enabled large models to be tested, revealing probabilistic constraints in processing, undermining acquisition arguments based on a perceived poverty of the stimulus, and suggesting fruitful links with probabilistic theories of categorization and ambiguity resolution in perception. (shrink)

We provide self-contained proof of a theorem relating probabilistic coherence of forecasts to their non-domination by rival forecasts with respect to any proper scoring rule. The theorem recapitulates insights achieved by other investigators, and clarifi es the connection of coherence and proper scoring rules to Bregman divergence.