Weak Bayesian coherentism

Recent results in probability theory have cast doubt on coherentism, purportedly showing (a) that coherence among a set of beliefs cannot raise their probability unless individual beliefs have some independent credibility, and (b) that no possible measure of coherence makes coherence generally probability-enhancing. I argue that coherentists can reject assumptions on which these theorems depend, and I derive a general condition under which the concurrence of two information sources lacking individual credibility can raise the probability of what they report.     

Absence of evidence and evidence of absence: evidential transitivity in connection with fossils,fishing, fine-tuning,and firing squads

“Absence of evidence isn’t evidence of absence” is a slogan that is popular among scientists and nonscientists alike. This article assesses its truth by using a probabilistic tool, the Law of Likelihood. Qualitative questions (“Is E evidence about H?”) and quantitative questions (“How much evidence does E provide about H?”) are both considered. The article discusses the example of fossil intermediates. If finding a fossil that is phenotypically intermediate between two extant species provides evidence that those species have a common ancestor, does failing to find such a fossil constitute evidence that there was no common ancestor? Or should the failure merely be chalked up to the imperfection of the fossil record? The transitivity of the evidence relation in simple causal chains provides a broader context, which leads to discussion of the fine-tuning argument, the anthropic principle, and observation selection effects.     

Reasoning Dialogues

When people argue with others in conversation, they make a variety of conversational moves: They make claims, ask for justification of others' claims, attack claims, and attack claims' justifications. The arrangement of these moves gives argumentation its characteristic shape. This article illustrates a proposed format for conversations of this type, and it reviews some findings about the way people understand and evaluate these conversations. The findings suggest that judgments of the arguers' burden depend not only on the content of their claims, but also on the conversation's structure. In addition, judgments of the strength of a justification—an arguer's evidence or explanation—are a function of the argument's setting.     

Reasoning about the future: Doom and Beauty

According to the Doomsday Argument we have to rethink the probabilities we assign to a soon or not so soon extinction of mankind when we realize that we are living now, rather early in the history of mankind. Sleeping Beauty finds herself in a similar predicament: on learning the date of her first awakening, she is asked to re-evaluate the probabilities of her two possible future scenarios. In connection with Doom, I argue that it is wrong to assume that our ordinary probability judgements do not already reflect our place in history: we justify the predictive use we make of the probabilities yielded by science (or other sources of information) by our knowledge of the fact that we live now, a certain time before the possible occurrence of the events the probabilities refer to. Our degrees of belief should change drastically when we forget the date—importantly, this follows without invoking the “Self Indication Assumption”. Subsequent conditionalization on information about which year it is cancels this probability shift again. The Doomsday Argument is about such probability shifts, but tells us nothing about the concrete values of the probabilities—for these, experience provides the only basis. Essentially the same analysis applies to the Sleeping Beauty problem. I argue that Sleeping Beauty “thirders” should be committed to thinking that the Doomsday Argument is ineffective; whereas “halfers” should agree that doom is imminent—but they are wrong.     

Williamson on justification

Timothy Williamson has a marvelously precise account of epistemic justification in terms of knowledge and probability. I argue that the account runs aground on certain cases involving the probability values 0 and 1.     

Adding possibilities can reduce the Gambler's Fallacy: A naïve-probability paradox

This paper reports a novel paradox of intuitive probabilistic reasoning detected in naïve reasoners’ responses in two separate experiments where we manipulated the number of sets (or possibilities) of the problem keeping constant the probability of the critical set. Experiment 1 showed that the incidence of the Gambler's Fallacy (GF) was reduced when the number of sets was increased. In Experiment 2, a reduction of the GF also occurred but, more importantly, the percentage of correct responses of the participants increased when three sets of possibilities instead of two were used. Therefore, both Experiments 1 and 2 demonstrated that an increase in the extensional complexity of a problem can, under certain circumstances, lead to facilitation. These results support the importance of the extensional features in solving chance problems and are consistent with the model theory of reasoning.     

The big bad bug bites anti-realists about chance

David Lewis’s ‘Humean Supervenience’ (henceforth ‘HS’) combines realism about laws, chances, and dispositions with a sparse ontology according to which everything supervenes on the overall spatiotemporal distribution of non-dispositional properties (Lewis 1986a, Philosophical papers: Volume II, pp. ix–xvii, New York: Oxford Univesity Press, 1994, Mind 103:473–490). HS faces a serious problem—a “big bad bug” (Lewis 1986a, p. xiv): it contradicts the Principal Principle, a seemingly obvious norm of rational credence. Two authors have tried to rescue Lewis’s ontology from the ‘big bad bug’ (henceforth ‘the Bug’) by rejecting realism about laws, chances, and dispositions (Halpin 1994, Aust J Phil 72:317–338, 1998, Phil Sci 65:349–360; Ward 2005, Phil Sci 71:241–261). I will argue that this strategy cannot possibly work: it is the ontology, not the realist thesis, that lies at the root of the problem.     

Reasoning about highly emotional topics: Syllogistic reasoning in a group of war veterans

Previous studies have generally found that emotion impairs logical reasoning. However, laboratory experiments have typically involved relatively mild levels of emotion where affect is not linked to personal experience. In this study we examined how army veterans reasoned about syllogisms of three types: neutral, generally emotional, and combat-related emotional. We also measured intensity of combat experience. Veterans were more likely to provide logically accurate answers when reasoning about combat-related compared to neutral problems. Participants with more intense combat experiences showed a reduced advantage in reasoning about combat-related emotional problems.     

Reasoning serves argumentation in children

The argumentative theory of reasoning (Mercier & Sperber, in press-c) claims that reasoning evolved for argumentation: to find and evaluate arguments in dialogic contexts. The theory has drawn most of its supportive evidence from work with adults, leaving open the possibility that argumentive features of reasoning are in fact entirely learned. Evidence is reviewed here suggesting that the special relation between reasoning and argumentation holds at all ages. More specifically, it is argued that (a) children possess at least rudimentary argument skills, (b) they are able to reap the benefits of social reasoning from very early on, (c) confirmation bias is present as soon as they start to argue, and (d) children can be victims of the same biases that affect adults when they use reasoning in the wrong contexts. These claims strengthen the argumentative theory of reasoning and support a call for more research on the interactive features of reasoning in both adults and children.     

Reasoning with conditionals: a test of formal models of four theories

The four dominant theories of reasoning from conditionals are translated into formal models: The theory of mental models (Johnson-Laird, P. N., & Byrne, R. M. J. (2002). Conditionals: a theory of meaning, pragmatics, and inference. Psychological Review, 109, 646-678), the suppositional theory (Evans, J. S. B. T., & Over, D. E. (2004). If. Oxford: Oxford University Press), a dual-process variant of the model theory (Verschueren, N., Schaeken, W., & d'Ydewalle, G. (2005). A dual-process specification of causal conditional reasoning. Thinking &Reasoning, 11, 278-293), and the probabilistic theory (Oaksford, M., Chater, N., & Larkin, J. (2000). Probabilities and polarity biases in conditional inference. Journal of Experimental Psychology: Learning, Memory, and Cognition, 26, 883-899). The first three theories are formalized as multinomial models. The models are applied to the frequencies of patterns of acceptance or rejection across the four basic inferences modus ponens, acceptance of the consequent, denial of the antecedent, and modus tollens. Model fits are assessed for two large data sets, one representing reasoning with abstract, basic conditionals, the other reflecting reasoning with pseudo-realistic causal and non-causal conditionals. The best account of the data was provided by a modified version of the mental-model theory, augmented by directionality, and by the dual-process model.     

From Bayesian epistemology to inductive logic

Inductive logic admits a variety of semantics (Haenni et al. (2011) [7, Part 1]). This paper develops semantics based on the norms of Bayesian epistemology (Williamson, 2010 [16, Chapter 7]). Section 1 introduces the semantics and then, in Section 2, the paper explores methods for drawing inferences in the resulting logic and compares the methods of this paper with the methods of Barnett and Paris (2008) [2]. Section 3 then evaluates this Bayesian inductive logic in the light of four traditional critiques of inductive logic, arguing (i) that it is language independent in a key sense, (ii) that it admits connections with the Principle of Indifference but these connections do not lead to paradox, (iii) that it can capture the phenomenon of learning from experience, and (iv) that while the logic advocates scepticism with regard to some universal hypotheses, such scepticism is not problematic from the point of view of scientific theorising.     

Reasoning about geography

To understand the nature and etiology of biases in geographical judgments, the authors asked people to estimate latitudes (Experiments 1 and 2) and longitudes (Experiments 3 and 4) of cities throughout the Old and New Worlds. They also examined how people's biased geographical judgments change after they receive accurate information ("seeds") about actual locations. Location profiles constructed from the pre- and postseeding location estimates conveyed detailed information about the representations underlying geography knowledge, including the subjective positioning and subregionalization of regions within continents; differential seeding effects revealed between-region dependencies. The findings implicate an important role for conceptual knowledge and plausible-reasoning processes in tasks that use subjective geographical information.     

Reasoning about relations

Inferences about spatial, temporal, and other relations are ubiquitous. This article presents a novel model-based theory of such reasoning. The theory depends on 5 principles. (a) The structure of mental models is iconic as far as possible. (b) The logical consequences of relations emerge from models constructed from the meanings of the relations and from knowledge. (c) Individuals tend to construct only a single, typical model. (d) They spontaneously develop their own strategies for relational reasoning. (e) Regardless of strategy, the difficulty of an inference depends on the process of integration of the information from separate premises, the number of entities that have to be integrated to form a model, and the depth of the relation. The article describes computer implementations of the theory and presents experimental results corroborating its main principle.     

Reasoning about visibility

We consider properties of sequences of spatial regions, as seen from a viewpoint. In particular, we concentrate on two types of regions: (1) general domains in which a region is any subset of the space, and (2) axis-parallel domains, where the regions are boxes in an N-dimensional space. We introduce binary relations allowing to express properties of these sequences and present two approaches to process them. First, we show that constraints on these relations can be solved in polynomial time for general domain and that the same problem is NP-complete in the axis-parallel case. Second, we introduce a modal logic on these relations, called Visibility Logic, and show that model-checking on a finite sequence of regions can be done in polynomial time (both in the general and axis-parallel cases). Finally, we present applications to image processing and firewall filtering.     

Some Aspects of Polyadic Inductive Logic

We give a brief account of some de Finetti style representation theorems for probability functions satisfying Spectrum Exchangeability in Polyadic Inductive Logic, together with applications to Non-splitting, Language Invariance, extensions with Equality and Instantial Relevance.     

Reasoning about update logic

Logical frameworks for analysing the dynamics of information processing abound [4, 5, 8, 10, 12, 14, 20, 22]. Some of these frameworks focus on the dynamics of the interpretation process, some on the dynamics of the process of drawing inferences, and some do both of these. Formalisms galore, so it is felt that some conceptual streamlining would pay off.This paper is part of a larger scale enterprise to pursue the obvious parallel between information processing and imperative programming. We demonstrate that logical tools from theoretical computer science are relevant for the logic of information flow. More specifically, we show that the perspective of Hoare logic [13, 18] can fruitfully be applied to the conceptual simplification of information flow logics.