Coping with uncertainty is a necessary part of ordinary life and is crucial to an understanding of how the mind works. For example, it is a vital element in developing artificial intelligence that will not be undermined by its own rigidities. There have been many approaches to the problem of uncertain inference, ranging from probability to inductive logic to nonmonotonic logic. Thisbook seeks to provide a clear exposition of these approaches within a unified framework. The principal market for (...) the book will be students and professionals in philosophy, computer science, and AI. Among the special features of the book are a chapter on evidential probability, which has not received a basic exposition before; chapters on nonmonotonic reasoning and theory replacement, matters rarely addressed in standard philosophical texts; and chapters on Mill's methods and statistical inference that cover material sorely lacking in the usual treatments of AI and computer science. (shrink)

Kyburg’s opposition to the subjective Bayesian theory, and in particular to its advocates’ indiscriminate and often questionable use of Dutch Book arguments, is documented and much of it strongly endorsed. However, it is argued that an alternative version, proposed by both de Finetti at various times during his long career, and by Ramsey, is less vulnerable to Kyburg’s misgivings. This is a logical interpretation of the formalism, one which, it is argued, is both more natural and also avoids other, widely-made (...) objections to Bayesianism. (shrink)

This paper develops a trivalent semantics for the truth conditions and the probability of the natural language indicative conditional. Our framework rests on trivalent truth conditions first proposed by Cooper (1968) and Belnap (1973) and it yields two logics of conditional reasoning: (i) a logic C of certainty-preserving inference; and (ii) a logic U for uncertain reasoning that preserves the probability of the premises. We show systematic correspondences between trivalent and probabilistic representations of inferences in either framework, and (...) we use the distinction between the two systems to cast light on the validity of inferences such as Modus Ponens, Or-To-If, and Conditional Excluded Middle. Specifically, the conditional behaves monotonically in C, but non-monotonically in U; Modus Ponens is valid in C, but valid in U only for non-nested conditionals. The result is a unified account of the semantics and epistemology of indicative conditionals that can be fruitfully applied to analyzing the validity of conditional inferences. (shrink)

Systems of logico-probabilistic reasoning characterize inference from conditional assertions that express high conditional probabilities. In this paper we investigate four prominent LP systems, the systems _O, P_, _Z_, and _QC_. These systems differ in the number of inferences they licence _. LP systems that license more inferences enjoy the possible reward of deriving more true and informative conclusions, but with this possible reward comes the risk of drawing more false or uninformative conclusions. In the first part of the paper, (...) we present the four systems and extend each of them by theorems that allow one to compute almost-tight lower-probability-bounds for the conclusion of an inference, given lower-probability-bounds for its premises. In the second part of the paper, we investigate by means of computer simulations which of the four systems provides the best balance of reward versus risk. Our results suggest that system _Z_ offers the best balance. (shrink)

We reflect on lessons that the lottery and preface paradoxes provide for the logic of uncertain inference. One of these lessons is the unreliability of the rule of conjunction of conclusions in such contexts, whether the inferences are probabilistic or qualitative; this leads us to an examination of consequence relations without that rule, the study of other rules that may nevertheless be satisfied in its absence, and a partial rehabilitation of conjunction as a ‘lossy’ rule. A second lesson (...) is the possibility of rational inconsistent belief; this leads us to formulate criteria for deciding when an inconsistent set of beliefs may reasonably be retained. (shrink)

We chart the ways in which closure properties of consequence relations for uncertain inference take on different forms according to whether the relations are generated in a quantitative or a qualitative manner. Among the main themes are: the identification of watershed conditions between probabilistically and qualitatively sound rules; failsafe and classicality transforms of qualitatively sound rules; non-Horn conditions satisfied by probabilistic consequence; representation and completeness problems; and threshold-sensitive conditions such as `preface' and `lottery' rules.

It has recently been argued that a non-Bayesian probabilistic version of inference to the best explanation (IBE*) has a number of advantages over Bayesian conditionalization (Douven [2013]; Douven and Wenmackers [2017]). We investigate how IBE* could be generalized to uncertain evidential situations and formulate a novel updating rule IBE**. We then inspect how it performs in comparison to its Bayesian counterpart, Jeffrey conditionalization (JC), in a number of simulations where two agents, each updating by IBE** and JC, respectively, (...) try to detect the bias of a coin while they are only partially certain what side the coin landed on. We show that IBE** more often prescribes high probability to the actual bias than JC. We also show that this happens considerably faster, that IBE** passes higher thresholds for high probability, and that it in general leads to more accurate probability distributions than JC. (shrink)

Brit. J. Phil. Sci. 0, 1–25. Published 14 March 2018.

The certainties which once underpinned Christian belief have crumbled in a world where science sets the standard for what is true. A rational case for belief must therefore be constructed out of uncertainties. Probability theory provides the tools for measuring and combining uncertainties and is thus the key to progress. This book examines four much debated topics where the logic of uncertain inference can be brought to bear. These are: miracles, the paranormal, God's existence, and the Bible. Given (...) the great diversity of evidence, it is not surprising that opposite conclusions have been drawn by supposedly rational people. An assessment of the state of argument from a probabilistic perspective is overdue. In this book Professor Bartholomew examines and refutes some of the more extravagent claims, evaluates the weight of some of the quantitive evidence, and provides an answer to the fundamental question: is it rational to be a Christian? (shrink)

Despite decades of focused philosophical investigation, Inference to the Best Explanation still lacks a precise articulation and compelling defense. The primary reason for this is that it is not at all clear what it means for a hypothesis to be the best available explanation of the evidence. This paper first seeks to rectify this problem by developing a formal explication of the explanatory virtue of power. A resulting account of IBE is then evaluated as a form of uncertain (...) inference. Overall, this paper offers a precise account and novel defense of one important version of IBE. (shrink)

ABSTRACTThe new paradigm in the psychology of reasoning redirects the investigation of deduction conceptually and methodologically because the premises and the conclusion of the inferences are assumed to be uncertain. A probabilistic counterpart of the concept of logical validity and a method to assess whether individuals comply with it must be defined. Conceptually, we used de Finetti's coherence as a normative framework to assess individuals' performance. Methodologically, we presented inference schemas whose premises had various levels of probability that (...) contained non-numerical expressions and, as a control, sure levels. Depending on the inference schemas, from 60% to 80% of the participants produced coherent conclusions when the premises were uncertain. The data also show that except for schemas involving conjunction, performance was consistently lower with certain than uncertain premises, the rate of conjunction fallacy was consistently low (not exceeding 20%,.. (shrink)

Oaksford & Chater (O&C) begin in the halfway Bayesian house of assuming that minor premises in conditional inferences are certain. We demonstrate that this assumption is a serious limitation. They additionally suggest that appealing to Jeffrey's rule could make their approach more general. We present evidence that this rule is not limited enough to account for actual probability judgements.

Bayesian accounts are currently popular in the field of inductive reasoning. This commentary briefly reviews the limitations of one such account, the Rational Model (Anderson 1991b), in explaining how inferences are made about objects whose category membership is uncertain. These shortcomings are symptomatic of what Jones & Love (J&L) refer to as Bayesian approaches.

Our knowledge forms a highly interconnected and dynamically changing body of propositions. One obviously important way that knowledge changes is via rational inference, based either upon new insight into the content of what we already know or upon new knowledge provided by the senses. The most obvious codification of the acceptability of inference driven knowledge growth is the so-called known entailment closure principle, the principle that if S knows that p and knows that p implies q then S (...) knows that q, or, more formally. (shrink)

This monograph is an in-depth and engaging discourse on the deeply cognitive roots of human scientific quest. The process of making scientific inferences is continuous with the day-to-day inferential activity of individuals, and is predominantly inductive in nature. Inductive inference, which is fallible, exploratory, and open-ended, is of essential relevance in our incessant efforts at making sense of a complex and uncertain world around us, and covers a vast range of cognitive activities, among which scientific exploration constitutes the (...) pinnacle. Inductive inference has a personal aspect to it, being rooted in the cognitive unconscious of individuals, which has recently been found to be of paramount importance in a wide range of complex cognitive processes. One other major aspect of the process of inference making, including the making of scientific inferences, is the role of a vast web of beliefs lodged in the human mind, as also of a huge repertoire of heuristics, that constitute an important component of ‘unconscious intelligence’. Finally, human cognitive activity is dependent in a large measure on emotions and affects, that operate mostly at an unconscious level. Of special importance in scientific inferential activity is the process of hypothesis making, which is examined in this book, along with the above aspects of inductive inference, at considerable depth. The book focuses on the inadequacy of the viewpoint of naive realism in understanding the contextual nature of scientific theories, where a cumulative progress towards an ultimate truth about Nature appears to be too simplistic a generalization. It poses a critique to the commonly perceived image of science which is seen as the last word in logic and objectivity, the latter in the double sense of being independent of individual psychological propensities and, at the same time, approaching a correct understanding of the workings of a mind-independent nature. Adopting the naturalist point of view, it examines the essential tension between the cognitive endeavours of individuals and scientific communities, immersed in belief systems and cultures, on the one hand, and the engagement with a mind-independent reality on the other. In the end, science emerges as an interpretation of nature, which is perceived by us only contextually, as successively emerging cross-sections of limited scope and extent. Successive waves of theory building in science appear as episodic and kaleidoscopic changes in perspective as certain in-built borders are crossed, rather than as a cumulative progress towards some ultimate truth. While written in an informal and conversational style, the book raises a number of deep and intriguing questions located at the interface of cognitive psychology and philosophy of science, meant for both the general lay reader and the specialist. Of particular interest is the way it explores the role of belief (aided by emotions and affects) in making the process of inductive inference possible since belief is a subtle though all-pervasive cognitive factor not adequately investigated in the current literature. (shrink)

We investigate uncertain reasoning with quantified sentences of the predicate calculus treated as the limiting case of maximum entropy inference applied to finite domains.

This thesis consists of a collection of five papers on naturalized formal epistemology of uncertain reasoning. In all papers I apply coherence based probability logic to make fundamental epistemological questions precise and propose new solutions to old problems. I investigate the rational evaluation of uncertain arguments, develop a new measure of argument strength, and explore the semantics of uncertain indicative conditionals. Specifically, I study formally and empirically the semantics of negated apparently selfcontradictory conditionals (Aristotle’s theses), resolve a (...) number of paradoxes of the material conditional in a purely semantical way without employing pragmatics and investigate the psychological plausibility of the proposed semantics. Moreover, I defend the formalization of defeasible inferences within a probabilistic framework of nonmonotonic reasoning and empirically justify the formalizations by a series of psychological experiments. I investigate general properties of uncertain argument forms and the interrelations among logical validity, Adams’ p-validity and probabilistic informativeness. (shrink)

Conditionals are central to inference. Before people can draw inferences about a natural language conditional, they must interpret its meaning. We investigated interpretation of uncertain conditionals using a probabilistic truth table task, focussing on (i) conditional event, (ii) material conditional, and (iii) conjunction interpretations. The order of object (shape) and feature (color) in each conditional's antecedent and consequent was varied between participants. The conditional event was the dominant interpretation, followed by conjunction, and took longer to process than conjunction (...) (mean di erence 500 ms). Material conditional responses were rare. The proportion of conditional event responses increased from around 40% at the beginning of the task to nearly 80% at the end, with 55% of participants showing a qualitative shift of interpretation. Shifts to the conditional event occurred later in the feature-object order than in the object-feature order. We discuss the results in terms of insight and suggest implications for theories of interpretation. (shrink)

Four experiments investigated uncertainty about a premise in a deductive argument as a function of the expertise of the speaker and of the conversational context. The procedure mimicked everyday reasoning in that participants were not told that the premises were to be treated as certain. The results showed that the perceived likelihood of a conclusion was greater when the major or the minor premise was uttered by an expert rather than a novice (Experiment 1). The results also showed that uncertainty (...) about the conclusion was higher when the major premise was uttered by a novice and an alternative premise by an expert, compared to when the major premise was uttered by an expert and the alternative by a novice (Experiment 2). Similarly, the believability of a conclusion was considerably lower when the minor premise was uttered by a novice and denied by an expert, as opposed to when an expert uttered the minor premise and a novice denied it (Experiment 3). Experiment 4 showed that the nature of the uncertainty induced by a denial of the minor premise depended on whether or not the context was a conversation. These results pose difficult problems for current theories of reasoning, as current theories are based on the results of experiments in which the premises are treated as certain. Our discussion of the results emphasises the importance of pragmatics in reasoning, namely, the role of general knowledge about the world in assessing the probability of a premise uttered by an expert or a novice and the role of interpretations of the premise based on pragmatic inferences in revising these initial probabilities. (shrink)

. Prediction of crop yield is significant in order to accurately meet market requirements and proper administration of agricultural activities directed towards enhancement in yield. Several parameters such as weather, pests, biophysical and physio morphological features merit their consideration while determining the yield. However, these parameters are uncertain in their nature, thus making the determined amount of yield to be approximate. It is exactly here that the fuzzy logic comes into play. This paper elaborates an attempt to develop fuzzy (...) inference systems for crop yield prediction. Physio morphological features of Sorghum were considered. A huge database of physio morphological features such as days of 50 percent flowering, dead heart percentage, plant height, panicle length, panicle weight and number of primaries and the corresponding yield were considered for the development of the model. In order to find out the sensitivity of parameters, one-to-one, two-to-one and three-to-one combinations of input and output were considered. The results have clearly shown that panicle length contributes for the yield as the lone parameter with almost one-to-one matching between predicted yield and actual value while panicle length and panicle weight in combination seemed to play a decisive role in contributing for the yield with the prediction accuracy reflected by very low RMS value. (shrink)

Recent advances in philosophy, artificial intelligence, mathematical psychology, and the decision sciences have brought a renewed focus to the role and interpretation of probability in theories of uncertain reasoning. Henry E. Kyburg, Jr. has long resisted the now dominate Bayesian approach to the role of probability in scientific inference and practical decision. The sharp contrasts between the Bayesian approach and Kyburg's program offer a uniquely powerful framework within which to study several issues at the heart of scientific (...) class='Hi'>inference, decision, and reasoning under uncertainty. The commissioned essays for this volume take measure of the scope and impact of Kyburg's views on probability and scientific inference, and include several new and important contributions to the field. Contributors: Gert de Cooman, Clark Glymour, William Harper, Isaac Levi, Ron Loui, Enrique Miranda, John Pollock, Teddy Seidenfeld, Choh Man Teng, Mariam Thalos, Gregory Wheeler, Jon Williamson, and Henry E. Kyburg, Jr. (shrink)

Heuristics are efficient cognitive processes that ignore information. In contrast to the widely held view that less processing reduces accuracy, the study of heuristics shows that less information, computation, and time can in fact improve accuracy. We review the major progress made so far: the discovery of less-is-more effects; the study of the ecological rationality of heuristics, which examines in which environments a given strategy succeeds or fails, and why; an advancement from vague labels to computational models of heuristics; the (...) development of a systematic theory of heuristics that identifies their building blocks and the evolved capacities they exploit, and views the cognitive system as relying on an “adaptive toolbox;” and the development of an empirical methodology that accounts for individual differences, conducts competitive tests, and has provided evidence for people’s adaptive use of heuristics. Homo heuristicus has a biased mind and ignores part of the available information, yet a biased mind can handle uncertainty more efficiently and robustly than an unbiased mind relying on more resource-intensive and general-purpose processing strategies. (shrink)

“Decisions from experience” (DFE) refers to a body of work that emerged in research on behavioral decision making over the last decade. One of the major experimental paradigms employed to study experienced-based choice is the “sampling paradigm”, which serves as a model of decision making under limited knowledge about the statistical structure of the world. In this paradigm respondents are presented with two payoff distributions, which, in contrast to standard approaches in behavioral economics, are specified not in terms of explicit (...) outcome-probability information, but by the opportunity to sample outcomes from each distribution without economic consequences. Participants are encouraged to explore the distributions until they feel confident enough to decide from which they would prefer to draw from in a final trial involving real monetary payoffs. One commonly employed measure to characterize the behavior of participants in the sampling paradigm is the sample size, that is, the number of outcome draws which participants choose to obtain from each distribution prior to terminating sampling. A natural question that arises in this context concerns the “optimal” sample size, which could be used as a normative benchmark to evaluate human sampling behavior in DFE. In this theoretical manuscript, we relate the DFE sampling paradigm to the classical statistical decision theoretic literature and, under a probabilistic inference assumption, evaluate optimal sample sizes for decisions from experience. In our treatment we go beyond analytically established results by showing how the classical statistical decision theoretic framework can be used to derive optimal sample sizes under arbitrary, but numerically evaluable, constraints. Finally, we critically evaluate the value of deriving optimal sample sizes under this framework as testable predictions for the experimental study of sampling behavior in DFE. (shrink)

This article tests human inference rationality when dealing with default rules. To study human rationality, psychologists currently use classical models of logic or probability theory as normative models for evaluating human ability to reason rationally. Our position is that this approach is convincing, but only manages to capture a specific case of inferential ability with little regard to conditions of everyday reasoning. We propose that the most general case to be considered is inference with imperfect knowledge - in (...) the present case restricted to uncertain knowledge - and that a natural framework for testing the rationality of plausible reasoning is System P. This system provides rational postulates for nonmonotonic inference. The semantic of the nonmonotonic inference is given by a possibilistic constraint introduced by Dubois and Prade (1991). This constraint states that a rule p ( q is a plausible rule if "the degree to which p ( q is possible" is greater than "the degree to which p ( (q is possible". Given the choice of this constraint, we study two supplementary postulates of rationality. Eighty-eight subjects participated in an experiment whose results confirm - provided that reflexivity and left logical equivalence would be tested in a further experiment - the rationality of human nonmonotonic inference according to the rational postulates of System P. (shrink)

Bayes’ formula is a fundamental statistical method for inference judgments in uncertain situations used by both laymen and professionals. However, since people often fail in situations where Bayes’ formula can be applied, how to improve their performance in Bayesian situations is a crucial question. We based our research on a widely accepted beneficial strategy in Bayesian situations, representing the statistical information in the form of natural frequencies. In addition to this numerical format, we used five visualizations: a 2×2-table, (...) a unit square, an icon array, a tree diagram, and a double-tree diagram. In an experiment with 688 undergraduate students, we empirically investigated the effectiveness of three graphical properties of visualizations: area-proportionality, use of discrete and countable statistical entities, and graphical transparency of the nested-sets structure. We found no additional beneficial effect of area-proportionality. In contrast, the representation of discrete objects seems to be beneficial. Furthermore, our results show a strong facilitating effect of making the nested-sets structure of a Bayesian situation graphically transparent. Our results contribute to answering the questions of how and why a visualization could facilitate judgment and decision making in situations of uncertainty. (shrink)

This paper is a sequel to an earlier result of the authors that in making inferences from certain probabilistic knowledge bases the maximum entropy inference process, ME, is the only inference process respecting “common sense.” This result was criticized on the grounds that the probabilistic knowledge bases considered are unnatural and that ignorance of dependence should not be identified with statistical independence. We argue against these criticisms and also against the more general criticism that ME is representation dependent. (...) In a final section, however, we provide a criticism of our own of ME, and of inference processes in general, namely that they fail to satisfy compactness. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Insight and Inference: Descartes's Founding Principle and Modern PhilosophyTom SorellMurray Miles. Insight and Inference: Descartes's Founding Principle and Modern Philosophy. Toronto: University of Toronto Press, 1999. Pp. xviii + 564. Cloth, $120.00.This book reopens the question of the correct interpretation of 'cogito, ergo sum,' and considers the significance of Descartes's first principle for Western philosophy up to and including the twentieth century. The gist of Miles's (...) interpretation is captured in the first three words of his title. The cogito is both insight and inference. How is it an inference, exactly? In the course of a process of selective attention to elements of thought, the cogito brings each person to the explicit knowledge of the fact of his or her existence (49). We have an implicit grasp of what the cogito makes explicit; and the passage from implicit to explicit knowledge amounts to a kind of inference. It is like an Aristotelian induction (cf. chapter 20).Inference is the topic of Part Three. Part Two concerns certainty. The cogito is certain in Meditation Two not in the light of the thought that God is veracious, but in the light solely of reflection on one's actually occurring thoughts (47). As for what Cartesian thoughts are, Miles seems to suggest that they are rather like what Husserl gets out of his phenomenological reduction: "intentionally-structured or object-directed acts of thinking" that are the sole immediate objects of consciousness (45). Miles rejects, correctly I think, the attribution to Descartes of any of the usual forms of representationalism.The diagnosis in Part Two of the certainty of the cogito seemed to me to be plausible on its face. It is in line with, although much more elaborate than, some reasonably familiar "psychologistic" interpretations clearing Descartes of the charge of circularity in the reasoning from clarity and distinctness to God's existence and nature and back again. (See A. Kenny, Descartes: A Study of his Philosophy [New York: Random House, 1968], chapter 8, and J. Tlumak, "Certainty and Cartesian Method" in M. Hooker, ed., Descartes: Critical and Interpretive Essays [Baltimore: Johns Hopkins University Press, 1978], 40-73. See also L. Loeb's article on the Cartesian Circle in J. Cottingham, ed., The Cambridge Companion to Descartes [New York, Cambridge University Press, 1992], 200-235.) To the extent that Miles departs from these interpretations, it seems to be by trying to base the authority of the cogito on the immutability of God (215-18). But this move seems ill-advised. Not only does it land Descartes in difficulties over the interpretation of pieces of scripture in which God changes his mind; it may also be in tension with the idea of omnipotence. On the whole, however, there is much in Part Two to admireófrom the interpretation of the simple natures (chapter 10), to the differences between scientia, persuasio, and notitia (chapter 11).Part One is less satisfactory, because Miles seems intent on reading Descartes through Husserl. Although he does not evade the objection that this approach is anachronistic (91-93), Miles does reinforce the impression, already created in the 55-page introduction, that he is unsure which interpretive perspective to use to control the book. Is he writing primarily as a twentieth century reader attracted to phenomenology, or is he someone who is keen to penetrate the seventeenth century and earlier and let the meanings of the early modern period infuse the text? Miles leaves the reader uncertain. In Part One we have a Husserlian Descartes. In the Introduction, the sixteenth and seventeenth century perspectives supply the preferred interpretation of [End Page 122] Descartes's metaphysics as something more or less traditional—concerned with the most certain, most universal, and the highest kind of being, the kind of being studied by theology.It is hard not to be put off by Miles's very swift dismissals of mainstream Anglo-American interpretations of Descartes's metaphysics as having some special connection with his physics (27ff). Can this line of interpretation really be refuted by quoting passages in which Descartes says that metaphysics is more basic and more certain than physics? Surely not. In choosing the formulation... (shrink)

This book uses the psychological literature on rationality to weigh in on the recent debate between virtue epistemologists and epistemic situationists. It argues that both sides have misconstrued the literature and that an interactionist framework is needed to square epistemic theory with empirical facts about reasoning and inference. The explosion of empirical literature on human rationality has led to seismic shifts across a multitude of academic disciplines. This book considers its implications for epistemology. In particular, it critically evaluates the (...) treatment of the rationality literature within the recent controversy between virtue epistemologists, who attempt to ground knowledge in stable epistemic virtues, and epistemic situationists, who claim that such a project is doomed by empirical evidence of widespread irrationality. It links this foundational controversy to two of the most important debates in psychology: the Rationality Wars and the person-situation debate. The book argues that both virtue theorists and epistemic situationists have misunderstood the implications of these debates, leading them to focus exclusively on personal dispositions and situational factors as two independent sources of epistemic success, failure, and improvement. A more accurate reading of the empirical literature implies that interactions between epistemic agents and their social, informational, and institutional environments are the fundamental drivers of both rational and irrational behaviour. An interactionist framework motivated by this insight conceives of epistemic virtues and vices as both responsive to and responsible for the environments in which they're manifested and cultivated. The central aim of this book is to present and defend this novel type of virtue epistemology. Rationality in Context will be of interest to scholars and advanced students working in epistemology, philosophy of science, philosophy of psychology, cognitive psychology, and social psychology. (shrink)

ABSTRACTTo build a process model of the understanding of conditionals we extract a common core of three semantics of if-then sentences: the conditional event interpretation in the coherencebased probability logic, the discourse processingtheory of Hans Kamp, and the game-theoretical approach of Jaakko Hintikka. The empirical part reports three experiments in which each participant assessed the probability of 52 if-then sentencesin a truth table task. Each experiment included a second task: An n-back task relating the interpretation of conditionals to working memory, (...) a Bayesian bookbag and poker chip task relating the interpretation of conditionals to probability updating, and a probabilistic modus ponens task relating the interpretation of conditionals to a classical inference task. Data analysis shows that the way in which the conditionals are interpreted correlates with each of the supplementary tasks. The results are discussed within the process model proposed in the introduction. (shrink)

According to probabilistic theories of reasoning in psychology, people's degree of belief in an indicative conditional `if A, then B' is given by the conditional probability, P(B|A). The role of language pragmatics is relatively unexplored in the new probabilistic paradigm. We investigated how consequent relevance a ects participants' degrees of belief in conditionals about a randomly chosen card. The set of events referred to by the consequent was either a strict superset or a strict subset of the set of events (...) referred to by the antecedent. We manipulated whether the superset was expressed using a disjunction or a hypernym. We also manipulated the source of the dependency, whether in long-term memory or in the stimulus. For subset-consequent conditionals, patterns of responses were mostly conditional probability followed by conjunction. For superset-consequent conditionals, conditional probability responses were most common for hypernym dependencies and least common for disjunction dependencies, which were replaced with responses indicating inferred consequent irrelevance. Conditional probability responses were also more common for knowledge-based than stimulus-based dependencies. We suggest. (shrink)

In this article I present some characteristics of logics and semantics of an uncertain world. I confront two-valued and fuzzy logic. I use Kafka’s novel Process as an example, which is designed as an uncertain context with words which are rigid designators without rigid meaning. That produces an uncertain world of logical and semantical relations. In presentation of problems I introduce basic concepts of Frege’s, Wittgenstein’s, Tarsky’s, Searle’s, Quine’s and Davidson’s philosophy of language. I differ the logical (...) and semantical identification of identity. I differ reference and inference, or representation and identification as two components which are fundamental for the identification of identity. I found this difference on the role of logical unification and granulation of predicates in the structure of thought and semantical unification and granulation of attributes in the structure of statements and their relation to ontology of context. Through the confrontation of the logical and semantical unification and granulation I find that the limits of logic are not also the limits of language. The semantical unification goes over the highest genre and below the lowest species. That enables the extra-logical, non-scientifical, con-fessional, pro-phetical, artistic, and ordinary use of language. (shrink)

The explanation of the suppression of Modus Ponens inferences within the framework of linguistic pragmatics and of plausible reasoning (i.e., deduction from uncertain premises) is defended. First, this approach is expounded, and then it is shown that the results of the first experiment of Byrne, Espino, and Santamar a (1999) support the uncertainty explanation but fail to support their counterexample explanation. Second, two experiments are presented. In the first one, aimed to refute one objection regarding the conclusions observed, the (...) additional conditional premise ( if N, C ) was replaced with a statement of uncertainty ( it is not certain that N ); the answers produced by the participants remained qualitatively and quantitatively similar in both conditions. In the second experiment, a fine-grained analysis of the responses to and justifications for an evaluation task was performed. The results of both experiments strongly supported the uncertainty explanation. (shrink)

Science is about evaluation, persuasion and logic. In scientific debate, scientists collectively evaluate theories by persuading each other in regard to epistemological qualities such as deduction and fact. There is, however, a flaw intrinsic to evaluation-by-persuasion: an individual can attempt and even succeed in persuading others by asserting that their reasoning is logical when it is not. This is a problem since, from an epistemological perspective, it is not always transparent nor obvious when a persuasive assertion is actually deductively warranted. (...) Empirical research upon reasoning, indeed, supports the notion that assertions are often strongly persuasive for reasons other than their logic. The unreliability of the link between persuasion and logic raises an important methodological issue: how do scientists debate in a manner such that claimed but false “logical” arguments are ignored, and only warranted arguments get to determine theory preference? This need for soundness in debate is a particularly important epistemological concern in cases where the deductive qualities of persuasive argument are not overt, and so cannot be directly checked --such as when they are founded upon Bayesianism probabilistic coherence. The argument presented here is that scientists make the qualities of probabilistic and nonprobabilistic inference sound (and so warranted) through how they organize their debate. Scientists, I argue, abide by “epistemological quality control practices” that limit the persuasive power of unsound arguments upon theory evaluation. Examples of such debate quality control practices are publicness, clarity, openness to criticism, and the collective promotion of attempts at theory conjecture and refutation. Methodologically, these quality control practices are extralogical since they do not directly provide scientific inferences with additional logical warrantedness. They function instead in science to generate an epistemological evaluative environment in which persuasiveness is due, and only due, to logic (i.e. sound). Their methodological role is therefore to make what is warranted de papyri (in our principles of rationality – epistemologically competence) also what is persuasive in evaluation and debate de cognitio (in our exercise of such principles – epistemologically performance). Several limitations exist upon the soundness of Bayesian inferential coherence – surreptitious revision, logical omniscience, uncertain evidence, old evidence, and new hypotheses. Bayesianism, as a result, can only exist if it is pursued in a debate that is regulated by quality control practices over its inferences (for instance, practices that ensure there is autonomy of inference, diligence of inference, probity of evidence, auditability of inference and assiduousness of conjecture). In this context, one can reinterpret Popper’s concern with criticism, openness, refutation and conjecture, as deriving not (as he thought) directly from the needs of logic, but, indirectly, from the need of scientists to create epistemological soundness. (shrink)

This paper describes a cubic water tank equipped with a movable partition receiving various amounts of liquid used to represent joint probability distributions. This device is applied to the investigation of deductive inferences under uncertainty. The analogy is exploited to determine by qualitative reasoning the limits in probability of the conclusion of twenty basic deductive arguments (such as Modus Ponens, And-introduction, Contraposition, etc.) often used as benchmark problems by the various theoretical approaches to reasoning under uncertainty. The probability bounds imposed (...) by the premises on the conclusion are derived on the basis of a few trivial principles such as "a part of the tank cannot contain more liquid than its capacity allows", or "if a part is empty, the other part contains all the liquid". This stems from the equivalence between the physical constraints imposed by the capacity of the tank and its subdivisions on the volumes of liquid, and the axioms and rules of probability. The device materializes de Finetti's coherence approach to probability. It also suggests a physical counterpart of Dutch book arguments to assess individuals' rationality in probability judgments in the sense that individuals whose degrees of belief in a conclusion are out of the bounds of coherence intervals would commit themselves to executing physically impossible tasks. (shrink)

This paper examines precursors and consequents of perceived relevance of a proposition A for a proposition C. In Experiment 1, we test Spohn's assumption that ∆P = P − P is a good predictor of ratings of perceived relevance and reason relations, and we examine whether it is a better predictor than the difference measure − P). In Experiment 2, we examine the effects of relevance on probabilistic coherence in Cruz, Baratgin, Oaksford, and Over's uncertain “and-to-if” inferences. The results (...) suggest that ∆P predicts perceived relevance and reason relations better than the difference measure and that participants are either less probabilistically coherent in “and-to-if” inferences than initially assumed or that they do not follow P = P. Results are discussed in light of recent results suggesting that the Equation may not hold under conditions of irrelevance or negative relevance. (shrink)

This paper introduces a novel perspective on Agentive Cognitive Construction Grammar (AgCCxG) by examining the intricate interplay between mind and language through the lens of both Active Inference and Peircean semiotics. AgCCxG emphasizes the impact of intention and purpose on linguistic choices as a cognitive imperative to balance the symbolic Self (Intelligent Agent) with the dynamics of the environment. Among other things, the paper posits that linguistic constructions, particularly Constructional Attachment Patterns (CAPs), like argument structure constructions, embody experienced interactions (...) with the world through reenactment routines via the integration of multisensory channels. Unlike traditional usage-based approaches (e.g., construction grammars), AgCCxG embraces a robust theory of signs that reveals human representation as a continuous process of semiotic hybridization for the creative prediction of uncertain scenarios. Importantly, the paper challenges the notion of the mind as a unified, rational, uncertainty-reducing machine by asserting that physical processes governing open biological systems profoundly influence the linguistic sign system. Intelligent agents’ adaptability in expressing incongruous realities thus highlights the role of semiotic hybridization in preserving an agent’s autonomy and semiotic boundary. (shrink)

Inferences made from endocasts of fossil skulls cannot provide information on the function of particular neocortical areas or the subcortical pathways to prefrontal cortex that form part of the neural substrate for speech, syntax, and certain aspects of cognition. The neural bases of syntax cannot be disassociated from “communication.” Manual motor control was probably a preadaptive factor in the evolution of humansyntactic ability, but neurophysiological data on living humans show that speech motor control and syntax are more closely linked. The (...) evolution of fully modern speech occurred fairly recently; thoughHomo habilismay have had some degree of speech and syntactic ability, it was not fully modern. Stone tools are uncertain indices of language or cognition. (shrink)

This contribution aims at providing an argumentative method to account for epistemic modality and evidentiality. I claim that these two linguistic categories can work as semantic components of defeasible argumentative schemes based on classification processes. This kind of approximate reasoning is, in fact, frequently indicated by appearance verbs which signal that the inferred standpoint is conceived by the speaker as uncertain due to the deceiving nature of perceptual data. Drawing from an analysis at the semantic-argumentative interface, the way in (...) which prototype theory sheds light on the processes of meaning construction underlying defeasible arguments from definition is also shown. (shrink)

The use of evidence to resolve uncertainties is key to many endeavours, most conspicuously science and law. Despite this, the logic of uncertainty is seldom taught explicitly, and often seems misunderstood. Traditional educational practice even fails to encourage students to identify uncertainty when they express knowledge, though mark schemes that reward the identification of reliable and uncertain responses have long been shown to encourage more insightful understanding. In our information-rich society the ability to identify uncertainty is often more important (...) than the possession of knowledge itself. In both science and law there are fundamentally different kinds of uncertainty at issue. There is uncertainty whether a particular hypothesis is correct, and there is uncertainty about observable data that may be generated if a particular hypothesis is correct. Both are expressed in terms of probabilities. Each has its own domain of application and its own logic, but the inter-relationship is complex and sometimes misunderstood. Hypothesis probabilities are always open to error through possible failure to take account of realistic alternatives, while the proper inferences that can be drawn from data probabilities (often in the context of significance testing) are quite limited and easily over-interpreted. When considering these two kinds of probability in a court of law it is possible to interpret the phrase 'reasonable doubt' in different ways. It can be seen as addressing data uncertainty: whether such incriminating evidence might with reasonable probability arise to confront an innocent person. Or (the more conventional view) it can be seen as some sort of threshold level on the probability that the defendant is guilty (a hypothesis probability). Each typically involves elements of subjective judgement, but fewer issues and uncertainties arise when considering the data probability and it is argued that this is often the more critical and proper issue for a jury to address. This has particular repercussions for cases involving identification of a suspect through trawl of a DNA or other database. (shrink)

In this article I present some characteristics of logics and semantics of an uncertain world. I confront two-valued and fuzzy logic. I use Kafka’s novel Process as an example, which is designed as an uncertain context with words which are rigid designators without rigid meaning. That produces an uncertain world of logical and semantical relations. In presentation of problems I introduce basic concepts of Frege’s, Wittgenstein’s, Tarsky’s, Searle’s, Quine’s and Davidson’s philosophy of language. I differ the logical (...) and semantical identification of identity. I differ reference and inference, or representation and identification as two components which are fundamental for the identification of identity. I found this difference on the role of logical unification and granulation of predicates in the structure of thought and semantical unification and granulation of attributes in the structure of statements and their relation to ontology of context. Through the confrontation of the logical and semantical unification and granulation I find that the limits of logic are not also the limits of language. The semantical unification goes over the highest genre and below the lowest species. That enables the extra-logical, non-scientifical, con-fessional, pro-phetical, artistic, and ordinary use of language. (shrink)

Learning is fundamentally about action, enabling the successful navigation of a changing and uncertain environment. The experience of pain is central to this process, indicating the need for a change in action so as to mitigate potential threat to bodily integrity. This review considers the application of Bayesian models of learning in pain that inherently accommodate uncertainty and action, which, we shall propose are essential in understanding learning in both acute and persistent cases of pain.

Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem directly. Expressive languages like higher-order logic are ideally suited for representing and reasoning about structured knowledge. Uncertain knowledge can be modeled by using graded probabilities rather than binary truth-values. The main technical problem studied in this paper is the following: Given a set of sentences, each having some probability (...) of being true, what probability should be ascribed to other (query) sentences? A natural wish-list, among others, is that the probability distribution (i) is consistent with the knowledge base, (ii) allows for a consistent inference procedure and in particular (iii) reduces to deductive logic in the limit of probabilities being 0 and 1, (iv) allows (Bayesian) inductive reasoning and (v) learning in the limit and in particular (vi) allows confirmation of universally quantified hypotheses/sentences. We translate this wish-list into technical requirements for a prior probability and show that probabilities satisfying all our criteria exist. We also give explicit constructions and several general characterizations of probabilities that satisfy some or all of the criteria and various (counter) examples. We also derive necessary and sufficient conditions for extending beliefs about finitely many sentences to suitable probabilities over all sentences, and in particular least dogmatic or least biased ones. We conclude with a brief outlook on how the developed theory might be used and approximated in autonomous reasoning agents. Our theory is a step towards a globally consistent and empirically satisfactory unification of probability and logic. (shrink)

In a quiet London office, a software designer muses on the algorithms that will make possible the risk flags to be visualized on the screens of border guards from Heathrow to St Pancras International. There is, he says, ‘real time decision making’ – to detain, to deport, to secondarily question or search – but there is also the ‘offline team who run the analytics and work out the best set of rules’. Writing the code that will decide the association rules (...) between items of data, prosaic and mundane – flight route, payment type, passport – the analysts derive a novel preemptive security measure. This paper proposes the analytic of the data derivative – a visualized risk flag or score drawn from an amalgam of disaggregated fragments of data, inferred from across the gaps between data and projected onto an array of uncertain futures. In contrast to disciplinary and enclosed techniques of collecting data to govern population, the data derivative functions via ‘differential curves of normality’, imagining a range of potential futures through the association rule, thus ‘opening up to let things happen’. In some senses akin to the risk orientation of the financial derivative, itself indifferent to actual underlying people, places or events by virtue of modulated norms, the contemporary security derivative is not centred on who we are, nor even on what our data say about us, but on what can be imagined and inferred about who we might be – on our very proclivities and potentialities. (shrink)

Bayesian paradigm has been widely acknowledged as a coherent approach to learning putative probability model structures from a finite class of candidate models. Bayesian learning is based on measuring the predictive ability of a model in terms of the corresponding marginal data distribution, which equals the expectation of the likelihood with respect to a prior distribution for model parameters. The main controversy related to this learning method stems from the necessity of specifying proper prior distributions for all unknown parameters of (...) a model, which ensures a complete determination of the marginal data distribution. Even for commonly used models, subjective priors may be difficult to specify precisely, and therefore, several automated learning procedures have been suggested in the literature. Here we introduce a novel Bayesian learning method based on the predictive entropy of a probability model, that can combine both subjective and objective probabilistic assessment of uncertain quantities in putative models. It is shown that our approach can avoid some of the limitations of the earlier suggested objective Bayesian methods. (shrink)

Policy-makers face an uncertain world. One way of getting a handle on decision-making in such an environment is to rely on evidence. Despite the recent increase in post-fact figures in politics, evidence-based policymaking takes centre stage in policy-setting institutions. Often, however, policy-makers face large volumes of evidence from different sources. Robustness analysis can, prima facie, handle this evidential diversity. Roughly, a hypothesis is supported by robust evidence if the different evidential sources are in agreement. In this thesis, I strengthen (...) the case for the use of robustness analysis in evidence-based policymaking by answering open research questions about this inference technique. First, I argue that existing taxonomies miss a fruitful category of robustness reasoning, that is predictive stability. Second, I claim that derivational robustness analysis – the investigation of whether the results of different models are in agreement – can yield interesting insights even if not the entire relevant model space is covered by available models or if the model results are only partially in agreement. Third, I claim that expert knowledge is necessary to address questions that arise when one applies measurement robustness analysis – the investigation into whether multiple means of measurement yield the same result. Finally, I argue that, in situations where evidence from different measurements is not in agreement, it can be advisable to no longer take all of the evidence into account. This can be done in a rationally defensible way by choosing the most adequate theory or model underlying parts of the evidence set. I discuss examples from climate, medical, and economic policy-making to establish my claims. (shrink)

According to the Bayesian paradigm in the psychology of reasoning, the norms by which everyday human cognition is best evaluated are probabilistic rather than logical in character. Recently, the Bayesian paradigm has been applied to the domain of argumentation, where the fundamental norms are traditionally assumed to be logical. Here, we present a major generalisation of extant Bayesian approaches to argumentation that utilizes a new class of Bayesian learning methods that are better suited to modelling dynamic and conditional inferences than (...) standard Bayesian conditionalization, is able to characterise the special value of logically valid argument schemes in uncertain reasoning contexts, greatly extends the range of inferences and argumentative phenomena that can be adequately described in a Bayesian framework, and undermines some influential theoretical motivations for dual function models of human cognition. We conclude that the probabilistic norms given by the Bayesian approach to rationality are not necessarily at odds with the norms given by classical logic. Rather, the Bayesian theory of argumentation can be seen as justifying and enriching the argumentative norms of classical logic. (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)

Around 97% of climate scientists endorse anthropogenic global warming (AGW), the theory that human activities are partly responsible for recent increases in global average temperatures. Clearly, this widespread endorsement of AGW is a reason for non-experts to believe in AGW. But what is the epistemic significance of the fact that some climate scientists do not endorse AGW? This paper contrasts expert unanimity, in which virtually no expert disagrees with some theory, with expert consensus, in which some non-negligible proportion either rejects (...) or is uncertain about the theory. It is argued that, from a layperson’s point of view, an expert consensus is often stronger evidence for a theory’s truth than unanimity. Several lessons are drawn from this conclusion, e.g. concerning what laypeople should infer from expert pronouncements, how journalists should report on scientific theories, and how working scientists should communicate with the public. (shrink)