Why does coherence appear truth-conducive?

This paper aims to reconcile (i) the intuitively plausible view that a higher degree of coherence among independent pieces of evidence makes the hypothesis they support more probable, and (ii) the negative results in Bayesian epistemology to the effect that there is no probabilistic measure of coherence such that a higher degree of coherence among independent pieces of evidence makes the hypothesis they support more probable. I consider a simple model in which the negative result appears in a stark form: the prior probability of the hypothesis and the individual vertical relations between each piece of evidence and the hypothesis completely determine the conditional probability of the hypothesis given the total evidence, leaving no room for the lateral relation (such as coherence) among the pieces of evidence to play any role. Despite this negative result, the model also reveals that a higher degree of coherence is indirectly associated with a higher conditional probability of the hypothesis because a higher degree of coherence indicates stronger individual supports. This analysis explains why coherence appears truth-conducive but in such a way that it defeats the idea of coherentism since the lateral relation (such as coherence) plays no independent role in the confirmation of the hypothesis. An earlier version of this paper was presented at the workshop Coherence: Interpreting the Impossibility Results held in Lund, Sweden. I would like to thank the participants of the workshop, especially Erik J. Olsson who subsequently sent me written comments. I would also like to thank Ken Akiba for comments on precursors of this paper     

On the alleged impossibility of coherence

If coherence is to have justificatory status, as some analytical philosophers think it has, it must be truth-conducive, if perhaps only under certain specific conditions. This paper is a critical discussion of some recent arguments that seek to show that under no reasonable conditions can coherence be truth-conducive. More specifically, it considers Bovens and Hartmann’s and Olsson’s “impossibility results,” which attempt to show that coherence cannot possibly be a truth-conducive property. We point to various ways in which the advocates of a coherence theory of justification may attempt to divert the threat of these results.     

The evidential support theory of conditionals

According to so-called epistemic theories of conditionals, the assertability/acceptability/acceptance of a conditional requires the existence of an epistemically significant relation between the conditional’s antecedent and its consequent. This paper points to some linguistic data that our current best theories of the foregoing type appear unable to explain. Further, it presents a new theory of the same type that does not have that shortcoming. The theory is then defended against some seemingly obvious objections.     

Violations of coherence in subjective probability: a representational and assessment processes account

Coherent judgment is a cardinal feature of rational cognition. Six experiments revealed systematic violations of coherence in probability judgment in which participants assigned different probabilities to mathematically equiprobable events. Experiments 1-5 revealed a strict refocusing effect: Compared to an occurrence frame, a non-occurrence frame resulted in higher estimates if base-rate evidence favored occurrence, lower estimates if evidence favored non-occurrence, and similar estimates if evidence supported indifference. Moreover, Experiments 5 and 6 revealed a pessimistic bias in which the less favorable of two equiprobable events was assigned greater probability. The findings support a Representational and Assessment Processes account (RAP) in which subjective probability is influenced by the perceived compatibility between representations of focal events and representations of evidence.     

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.     

Category coherence and category-based property induction

One important property of human object categories is that they define the sets of exemplars to which newly observed properties are generalized. We manipulated the causal knowledge associated with novel categories and assessed the resulting strength of property inductions. We found that the theoretical coherence afforded to a category by inter-feature causal relationships strengthened inductive projections. However, this effect depended on the degree to which the exemplar with the to-be-projected predicate manifested or satisfied its category's causal laws. That is, the coherence that supports inductive generalizations is a property of individual category members rather than categories. Moreover, we found that an exemplar's coherence was mediated by its degree of category membership. These results were obtained across a variety of causal network topologies and kinds of categories, including biological kinds, non-living natural kinds, and artifacts.     

Ways in which coherence is confirmation conducive

Recent works in epistemology show that the claim that coherence is truth conducive – in the sense that, given suitable ceteris paribus conditions, more coherent sets of statements are always more probable – is dubious and possibly false. From this, it does not follows that coherence is a useless notion in epistemology and philosophy of science. Dietrich and Moretti (Philosophy of science 72(3): 403–424, 2005) have proposed a formal of account of how coherence is confirmation conducive—that is, of how the coherence of a set of statements facilitates the confirmation of such statements. This account is grounded in two confirmation transmission properties that are satisfied by some of the measures of coherence recently proposed in the literature. These properties explicate everyday and scientific uses of coherence. In his paper, I review the main findings of Dietrich and Moretti (2005) and define two evidence-gathering properties that are satisfied by the same measures of coherence and constitute further ways in which coherence is confirmation conducive. At least one of these properties vindicates important applications of the notion of coherence in everyday life and in science.     

Measuring coherence using LP-models

This paper introduces a technique for measuring the degree of (in)coherence of inconsistent sets of propositional formulas. The coherence of these sets of formulas is calculated using the minimal models of those sets in G. Priest's Logic of Paradox. The compatibility of the information expressed by a set of formulas with the background or domain knowledge can also be measured with this technique. In this way, Hunter's objections to many-valued paraconsistent logics as instruments for measuring (in)coherence are addressed.     

Personality and the coherence of psychotherapy narratives

The stories people construct about themselves and their social worlds are key aspects of their identities [Bruner, J. S. (1990). Acts of meaning. Cambridge, MA: Harvard University Press; McAdams, D. P. (2001). The psychology of life stories. Review of General Psychology, 5, 100–122]. Whereas certain expected life experiences (e.g., leaving home, getting a job) may be relatively easy to narrate, more unexpected and difficult events, such as undergoing psychotherapy, may pose a challenge to successful narration. Yet it is especially important to successfully narrate one’s experience in psychotherapy in order to maintain the gains from treatment [Frank, J. D. (1961). Persuasion and healing: A comprehensive study of psychotherapy. Baltimore, MD: Johns Hopkins University Press; Spence, D. P. (1982). Narrative truth and historical truth: Meaning and interpretation in psychoanalysis. New York: W.W. Norton]. The present study collected psychotherapy narratives from 76 adult former clients and coded them for the fundamental story criterion of coherence [Baerger, D. R., & McAdams, D. P. (1999). Life story coherence and its relation to psychological well-being. Narrative Inquiry, 9, 69–96]. Former clients that were high in trait Openness to experience and those at higher stages of ego development told more coherent stories about therapy. The relationship between ego development and narrative coherence remained significant even when controlling for Openness. The findings suggest that high ego development may provide narrators with the kind of sophisticated frameworks for meaning-making that are especially well-suited for the important task of making good sense of psychotherapy.     

Assertion,Moore, and Bayes

It is widely believed that the so-called knowledge account of assertion best explains why sentences such as “It’s raining in Paris but I don’t believe it” and “It’s raining in Paris but I don’t know it” appear odd to us. I argue that the rival rational credibility account of assertion explains that fact just as well. I do so by providing a broadly Bayesian analysis of the said type of sentences which shows that such sentences cannot express rationally held beliefs. As an interesting aside, it will be seen that these sentences also harbor a lesson for Bayesian epistemology itself.

Inference and coherence in causal-based artifact categorization

In four experiments, we tested conditions under which artifact concepts support inference and coherence in causal categorization. In all four experiments, participants categorized scenarios in which we systematically varied information about artifacts’ associated design history, physical structure, user intention, user action and functional outcome, and where each property could be specified as intact, compromised or not observed. Consistently across experiments, when participants received complete information (i.e., when all properties were observed), they categorized based on individual properties and did not show evidence of using coherence to categorize. In contrast, when the state of some property was not observed, participants gave evidence of using available information to infer the state of the unobserved property, which increased the value of the available information for categorization. Our data offers answers to longstanding questions regarding artifact categorization, such as whether there are underlying causal models for artifacts, which properties are part of them, whether design history is an artifact’s causal essence, and whether physical appearance or functional outcome is the most central artifact property.     

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.     

On the alleged impossibility of Bayesian Coherentism

The success of Bovens and Hartmann’s recent “impossibility result” against Bayesian Coherentism relies upon the adoption of a specific set of ceteris paribus conditions. In this paper, I argue that these conditions are not clearly appropriate; certain proposed coherence measures motivate different such conditions and also call for the rejection of at least one of Bovens and Hartmann’s conditions. I show that there exist sets of intuitively plausible ceteris paribus conditions that allow one to sidestep the impossibility result. This shifts the debate from the merits of the impossibility result itself to the underlying choice of ceteris paribus conditions.

A General Structure for Legal Arguments About Evidence Using Bayesian Networks

A Bayesian network (BN) is a graphical model of uncertainty that is especially well suited to legal arguments. It enables us to visualize and model dependencies between different hypotheses and pieces of evidence and to calculate the revised probability beliefs about all uncertain factors when any piece of new evidence is presented. Although BNs have been widely discussed and recently used in the context of legal arguments, there is no systematic, repeatable method for modeling legal arguments as BNs. Hence, where BNs have been used in the legal context, they are presented as completed pieces of work, with no insights into the reasoning and working that must have gone into their construction. This means the process of building BNs for legal arguments is ad hoc, with little possibility for learning and process improvement. This article directly addresses this problem by describing a method for building useful legal arguments in a consistent and repeatable way. The method complements and extends recent work by Hepler, Dawid, and Leucari (2007) on object‐oriented BNs for complex legal arguments and is based on the recognition that such arguments can be built up from a small number of basic causal structures (referred to as idioms). We present a number of examples that demonstrate the practicality and usefulness of the method.     

Global coherence in younger and older adults: Influence of cognitive processes and discourse type

The purpose of the present research was to examine the influence of cognitive processes on discourse global coherence ability measured across different discourse tasks and collected from younger (n = 40; 20–39 years) and older (n = 40; 70–87 years) cognitively healthy adults. Study participants produced oral language samples in response to five commonly used discourse elicitation tasks and they were analyzed for maintenance of global coherence. Participants also completed memory and attention measures. Group differences on the global coherence scale were found for only one type of discourse—recounts. Across discourse elicitation tasks the lowest global coherence scores were found for recounts compared to the other discourse elicitation tasks. The influence of cognitive processes on maintenance of global coherence differed for the two age groups. For the younger group, there were no observed significant relationships. For the older group, cognitive measures were related to global coherence of stories and procedures.     

Referential cohesion and logical coherence of narration after closed head injury

A group with closed head injury was compared to neurologically intact controls regarding the referential cohesion and logical coherence of narrative production. A sample of six stories was obtained with tasks of cartoon-elicited story-telling and auditory-oral retelling. We found deficits in the clinical group with respect to referential cohesion, logical coherence, and accuracy of narration. The occurrence of deficits depended on the condition of narrative production and, to some extent, on the particular story used. The primary implications of this study pertain to the attention given by researchers to the feature of discourse production being studied and processing demands of the task.     

What Are the “True” Statistics of the Environment?

A widespread assumption in the contemporary discussion of probabilistic models of cognition, often attributed to the Bayesian program, is that inference is optimal when the observer's priors match the true priors in the world—the actual “statistics of the environment.” But in fact the idea of a “true” prior plays no role in traditional Bayesian philosophy, which regards probability as a quantification of belief, not an objective characteristic of the world. In this paper I discuss the significance of the traditional Bayesian epistemic view of probability and its mismatch with the more objectivist assumptions about probability that are widely held in contemporary cognitive science. I then introduce a novel mathematical framework, the observer lattice, that aims to clarify this issue while avoiding philosophically tendentious assumptions. The mathematical argument shows that even if we assume that “ground truth” probabilities actually do exist, there is no objective way to tell what they are. Different observers, conditioning on different information, will inevitably have different probability estimates, and there is no general procedure to determine which one is right. The argument sheds light on the use of probabilistic models in cognitive science, and in particular on what exactly it means for the mind to be “tuned” to its environment.     

Non-bayesian inference: causal structure trumps correlation

The study tests the hypothesis that conditional probability judgments can be influenced by causal links between the target event and the evidence even when the statistical relations among variables are held constant. Three experiments varied the causal structure relating three variables and found that (a) the target event was perceived as more probable when it was linked to evidence by a causal chain than when both variables shared a common cause; (b) predictive chains in which evidence is a cause of the hypothesis gave rise to higher judgments than diagnostic chains in which evidence is an effect of the hypothesis; and (c) direct chains gave rise to higher judgments than indirect chains. A Bayesian learning model was applied to our data but failed to explain them. An explanation-based hypothesis stating that statistical information will affect judgments only to the extent that it changes beliefs about causal structure is consistent with the results.     

Objective Bayesianism with predicate languages

Objective Bayesian probability is often defined over rather simple domains, e.g., finite event spaces or propositional languages. This paper investigates the extension of objective Bayesianism to first-order logical languages. It is argued that the objective Bayesian should choose a probability function, from all those that satisfy constraints imposed by background knowledge, that is closest to a particular frequency-induced probability function which generalises the λ = 0 function of Carnap’s continuum of inductive methods.     

When sounds look right and images sound correct: Cross-modal coherence enhances claims of pattern presence

How do people decide whether a stimulus contains a pattern? One possibility is that they rely on a global, non-specific signal of coherence. Interestingly, this signal might reflect a combination of different stimulus sources. Consequently, the coherence of one stimulus might influence decisions about coherence of a second, unrelated stimulus. We explored this possibility in three experiments in which participants judged the presence of a pattern in targets from one sensory modality, while being exposed in the background to incidental coherent and incoherent stimuli in a different modality (visual → auditory, auditory → visual). Across all three experiments, using a variety of judgments, coherence of incidental background cross-modal patterns enhanced claims of pattern presence. These findings advance our understanding of how people judge order in the structured as well as in the unstructured world.