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)

Savage denied that Bayesian decision theory applies in large worlds. This paper proposes a minimal extension of Bayesian decision theory to a large-world context that evaluates an event E\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E$$\end{document} by assigning it a number π\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi $$\end{document} that reduces to an orthodox probability for a class of measurable events. The Hurwicz criterion evaluates π\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi $$\end{document} (...) as a weighted arithmetic mean of its upper and lower probabilities, which we derive from the measurable supersets and subsets of E\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E$$\end{document}. The ambiguity aversion reported in experiments on the Ellsberg paradox is then explained by assigning a larger weight to the lower probability of winning than to the upper probability. However, arguments are given here that would make anything but equal weights irrational when using the Hurwicz criterion. The paper continues by embedding the Hurwicz criterion in an extension of expected utility theory that we call expectant utility. (shrink)

Autobiographical memories typically give rise either to memory reports (“I remember going swimming”) or to first person past-tense judgements (“I went swimming”). This article focuses on first person past-tense judgements that are (epistemically) based on autobiographical memories. Some of these judgements have the IEM property of being immune to error through misidentification. This article offers an account of when and why first person past-tense judgements have the IEM property.

Intelligence can be understood as a form of rationality, in the sense that an intelligent system does its best when its knowledge and resources are insufficient with respect to the problems to be solved. The traditional models of rationality typically assume some form of sufficiency of knowledge and resources, so cannot solve many theoretical and practical problems in Artificial Intelligence (AI). New models based on the Assumption of Insufficient Knowledge and Resources (AIKR) cannot be obtained by minor revisions or extensions (...) of the traditional models, and have to be established fully according to the restrictions and freedoms provided by AIKR. The practice of NARS, an AI project, shows that such new models are feasible and promising in providing a new theoretical foundation for the study of rationality, intelligence, consciousness, and mind. (shrink)

There is a debate in Bayesian confirmation theory between subjective and non-subjective accounts of evidence. Colin Howson has provided a counterexample to our non-subjective account of evidence: the counterexample refers to a case in which there is strong evidence for a hypothesis, but the hypothesis is highly implausible. In this article, we contend that, by supposing that strong evidence for a hypothesis makes the hypothesis more believable, Howson conflates the distinction between confirmation and evidence. We demonstrate that Howson’s counterexample fails (...) for a different pair of hypotheses. (shrink)

We introduce a distinction, unnoticed in the literature, between four varieties of objective Bayesianism. What we call ' strong objective Bayesianism' is characterized by two claims, that all scientific inference is 'logical' and that, given the same background information two agents will ascribe a unique probability to their priors. We think that neither of these claims can be sustained; in this sense, they are 'dogmatic'. The first fails to recognize that some scientific inference, in particular that concerning evidential relations, is (...) not (in the appropriate sense) logical, the second fails to provide a non-question-begging account of 'same background information'. We urge that a suitably objective Bayesian account of scientific inference does not require either of the claims. Finally, we argue that Bayesianism needs to be fine-grained in the same way that Bayesians fine-grain their beliefs. (shrink)

Nelson Goodman has constructed two theories of simplicity: one of predicates; one of hypotheses. I offer a simpler theory by generalization and abstraction from his. Generalization comes by dropping special conditions Goodman imposes on which unexcluded extensions count as complicating and which excluded extensions count as simplifying. Abstraction is achieved by counting only nonisomorphic models and subinterpretations. The new theory takes into account all the hypotheses of a theory in assessing its complexity, whether they were projected prior to, or result (...) from, projection of a given hypothesis. It assigns simplicity post-projection priority over simplicity pre-projection. It better orders compound conditionals than does the theory of simplicity of hypotheses, and it does not inherit an anomaly of the theory of simplicity of predicates — its failure to order the ordering relations. Drop Goodman's special conditions, and the problems fall away with them. (shrink)

Two powerful arguments have famously dominated the realism debate in philosophy of science: The No Miracles Argument (NMA) and the Pessimistic Meta-Induction (PMI). A standard response to the PMI is selective scientific realism (SSR), wherein only the working posits of a theory are considered worthy of doxastic commitment. Building on the recent debate over the NMA and the connections between the NMA and the PMI, I here consider a stronger inductive argument that poses a direct challenge for SSR: Because it (...) is sometimes exactly the working posits which contradict each other, i.e., that which is directly responsible for empirical success, SSR cannot deliver a general explanation of scientific success. (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)

We explore which types of probabilistic updating commute with convex IP pooling. Positive results are stated for Bayesian conditionalization, imaging, and a certain parameterization of Jeffrey conditioning. This last observation is obtained with the help of a slight generalization of a characterization of externally Bayesian pooling operators due to Wagner :336–345, 2009). These results strengthen the case that pooling should go by imprecise probabilities since no precise pooling method is as versatile.

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)

The justification of induction is of central significance for cross-cultural social epistemology. Different ‘epistemological cultures’ do not only differ in their beliefs, but also in their belief-forming methods and evaluation standards. For an objective comparison of different methods and standards, one needs (meta-)induction over past successes. A notorious obstacle to the problem of justifying induction lies in the fact that the success of object-inductive prediction methods (i.e., methods applied at the level of events) can neither be shown to be universally (...) reliable (Hume's insight) nor to be universally optimal. My proposal towards a solution of the problem of induction is meta-induction. The meta-inductivist applies the principle of induction to all competing prediction methods that are accessible to her. By means of mathematical analysis and computer simulations of prediction games I show that there exist meta-inductive prediction strategies whose success is universally optimal among all accessible prediction strategies, modulo a small short-run loss. The proposed justification of meta-induction is mathematically analytical. It implies, however, an a posteriori justification of object-induction based on the experiences in our world. In the final section I draw conclusions about the significance of meta-induction for the social spread of knowledge and the cultural evolution of cognition, and I relate my results to other simulation results which utilize meta-inductive learning mechanisms. (shrink)

This paper argues that chance (risk or opportunity) discovery is challenging, from a reasoning point of view, because it represents a dilemma for inductive reasoning. Chance discovery shares many features with the grue paradox. Consequently, Bayesian approaches represent a potential solution. The Bayesian solution evaluates alternative models generated using a temporal logic planner to manage the chance. Surprise indices are used in monitoring the conformity of the real world and the assessed probabilities. Game theoretic approaches are proposed to deal with (...) multi-agent interaction in chance management. (shrink)

The volume analyses and develops David Makinson’s efforts to make classical logic useful outside its most obvious application areas. The book contains chapters that analyse, appraise, or reshape Makinson’s work and chapters that develop themes emerging from his contributions. These are grouped into major areas to which Makinsons has made highly influential contributions and the volume in its entirety is divided into four sections, each devoted to a particular area of logic: belief change, uncertain reasoning, normative systems and the resources (...) of classical logic. Among the contributions included in the volume, one chapter focuses on the “inferential preferential method”, i.e. the combined use of classical logic and mechanisms of preference and choice and provides examples from Makinson’s work in non-monotonic and defeasible reasoning and belief revision. One chapter offers a short autobiography by Makinson which details his discovery of modern logic, his travels across continents and reveals his intellectual encounters and inspirations. The chapter also contains an unusually explicit statement on his views on the role of logic in philosophy. (shrink)

A probability forecast scored ex post using a probability scoring rule (e.g. Brier) is analogous to a risky financial security. With only superficial adaptation, the same economic logic by which securities are valued ex ante – in particular, portfolio theory and the capital asset pricing model (CAPM) – applies to the valuation of probability forecasts. Each available forecast of a given event is valued relative to each other and to the “market” (all available forecasts). A forecast is seen to be (...) more valuable the higher its expected score and the lower the covariance of its score with the market aggregate score. Forecasts that score highly in trials when others do poorly are appreciated more than those with equal success in “easy” trials where most forecasts score well. The CAPM defines economically rational (equilibrium) forecast prices at which forecasters can trade shares in each other’s ex post score – or associated monetary payoff – thereby balancing forecast risk against return and ultimately forming optimally hedged portfolios. Hedging this way offers risk averse forecasters an “honest” alternative to the ruse of reporting conservative probability assessments. (shrink)

The (recent, Bayesian) cognitive science literature on The Wason Task (WT) has been modeled largely after the (not-so-recent, Bayesian) philosophy of science literature on The Paradox of Confirmation (POC). In this paper, we apply some insights from more recent Bayesian approaches to the (POC) to analogous models of (WT). This involves, first, retracing the history of the (POC), and, then, reexamining the (WT) with these historico-philosophical insights in mind.

outlined. This account is partly inspired by the work of C.S. Peirce. When we want to consider how degree of confirmation varies with changing I show that a large class of quantitative Bayesian measures of con-.

During the past decades several philosophers of science and social scientists have been interested in the problems of causation. Recently attention has been given to probabilistic causation in dichotomous causal systems. The paper uses the basic features of probabilistic causation to argue that the causal modeling approaches developed by such researchers as Blalock and Duncan can provide, when an additional assumption is added, adequate qualitative measures of one variableś causal influence upon another. Finally, some of the difficulties and issues involved (...) in developing adequate quantitative measures are discussed, and it is concluded that the causal modeling measures cannot provide adequate quantitative measures. (shrink)

Bayesian models typically assume that agents are rational, logically omniscient and opinionated. The last of these has little descriptive or normative appeal, however, and limits our ability to describe how agents make up their minds (as opposed to changing them) or how they can suspend or withdraw their opinions. To address these limitations this paper represents the attitudinal states of non-opinionated agents by sets of (permissible) probability and desirability functions. Several basic ways in which such states of mind can be (...) changed are then characterised and compared with those found in AGM style models of attitude revision. Finally these models are employed to describe how agents make up their mind when deliberating. (shrink)

Simulation evidence obtained within a Bayesian model of price-setting in a betting market, where anonymous gamblers queue to bet against a risk-neutral bookmaker, suggests that a gambler who wants to maximize future profits should trade on the advice of the analyst cum probability forecaster who records the best probability score, rather than the highest trading profits, during the preceding observation period. In general, probability scoring rules, specifically the log score and better known “Brier” (quadratic) score, are found to have higher (...) probability of ranking rival analysts in predetermined “correct” order than either (i) the more usual method of counting categorical forecast errors (misclassifications), or (ii) an economic measure of forecasting success, described here as the “Kelly score” and defined as the trading profits accumulated by making log optimal bets (i.e. Kelly betting) against the market maker based on the probability forecasts of the analyst being assessed. This runs counter to the conventional wisdom that financial forecasts are more aptly evaluated in terms of their financial consequences than by an abstract non-monetary measure of statistical accuracy such as the number of misclassifications or a probability score. (shrink)

In my dissertation I define historical disciplines as disciplines that aim to give a historical interpretation of the evidence. Phylogenetic systematics is a historical discipline and therefore in my definition phylogenies should be thought of as historical interpretations of relationships between taxa.