Is evidential support transitive? The answer is negative when evidential support is understood as confirmation so that X evidentially supports Y if and only if p(Y | X) > p(Y). I call evidential support so understood “support” (for short) and set out three alternative ways of understanding evidential support: support-t (support plus a sufficiently high probability), support-t* (support plus a substantial degree of support), and support-tt* (support plus both a sufficiently high probability and a substantial degree of support). I also (...) set out two screening-off conditions (under which support is transitive): SOC1 and SOC2. It has already been shown that support-t is non-transitive in the general case (where it is not required that SOC1 holds and it is not required that SOC2 holds), in the special case where SOC1 holds, and in the special case where SOC2 holds. I introduce two rather weak adequacy conditions on support measures and argue that on any support measure meeting those conditions it follows that neither support-t* nor support-tt* is transitive in the general case, in the special case where SOC1 holds, or in the special case where SOC2 holds. I then relate some of the results to Douven’s evidential support theory of conditionals along with a few rival theories. (shrink)

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

We show that as a chain of confirmation becomes longer, confirmation dwindles under screening-off. For example, if E confirms H1, H1 confirms H2, and H1 screens off E from H2, then the degree to which E confirms H2 is less than the degree to which E confirms H1. Although there are many measures of confirmation, our result holds on any measure that satisfies the Weak Law of Likelihood. We apply our result to testimony cases, relate it to the Data-Processing Inequality (...) in information theory, and extend it in two respects so that it covers a broader range of cases. (shrink)

The Linda paradox is a key topic in current debates on the rationality of human reasoning and its limitations. We present a novel analysis of this paradox, based on the notion of verisimilitude as studied in the philosophy of science. The comparison with an alternative analysis based on probabilistic confirmation suggests how to overcome some problems of our account by introducing an adequately defined notion of verisimilitudinarian confirmation.

There are two distinct approaches to Bayesian modelling in cognitive science. Black-box approaches use Bayesian theory to model the relationship between the inputs and outputs of a cognitive system without reference to the mediating causal processes; while mechanistic approaches make claims about the neural mechanisms which generate the outputs from the inputs. This paper concerns the relationship between these two approaches. We argue that the dominant trend in the philosophical literature, which characterizes the relationship between black-box and mechanistic approaches to (...) Bayesian cognitive science in terms of the dichotomy between instrumentalism and realism, is misguided. We propose that the two distinctions are orthogonal: black-box and mechanistic approaches to Bayesian modelling can each be given either an instrumentalist or a realist interpretation. We argue that the current tendency to conflate black-box approaches with instrumentalism and mechanistic approaches with realism stems from unwarranted assumptions about the nature of scientific explanation, the ontological commitments of scientific theories, and the role of abstraction and idealization in scientific models. We challenge each of these assumptions to reframe the debates over Bayesian modelling in cognitive science. (shrink)

The Abrahamic traditions regard God as the world’s author. But what kind of author? A novelist? A playwright? Perhaps a composer of classical music? I will argue that it is best to regard God as like an improvisational play director or the leader of a jazz ensemble. Each determines the broad melodic contours or coarse-grained plot beforehand, while allowing their musicians or actors, and chance, to fill in the more fine-grained details. This analogy allows us to regard God as the (...) ultimate author of this world, while allowing us to be, while less than co-authors, more than mere enactors of a pre-written piece. These metaphors are particularly well-suited to illustrate and flesh out an Open Theistic view of things. (shrink)

Should you always be certain about what you should believe? In other words, does rationality demand higher-order certainty? First answer: Yes! Higher-order uncertainty can’t be rational, since it breeds at least a mild form of epistemic akrasia. Second answer: No! Higher-order certainty can’t be rational, since it licenses a dogmatic kind of insensitivity to higher-order evidence. Which answer wins out? The first, I argue. Once we get clearer about what higher-order certainty is, a view emerges on which higher-order certainty does (...) not, in fact, license any kind of insensitivity to higher-order evidence. The view as I will describe it has plenty of intuitive appeal. But it is not without substantive commitments: it implies a strong form of internalism about epistemic rationality, and forces us to reconsider standard ways of thinking about the nature of evidential support. Yet, the view put forth promises a simple and elegant solution to a surprisingly difficult problem in our understanding of rational belief. (shrink)

What sort of evidence can confer the strongest support to a hypothesis? A natural answer is that the evidence entails the hypothesis. Roush claims that the likelihood ratio measure of degree of incremental support can deliver this intuitively natural result, and regards it as unifying “[the] account of induction and deduction in the only way that makes sense”. In this paper, we highlight a difficulty in the treatment of this case, and question the great significance that is attached to this (...) measure and its alleged capacity to accommodate the logicality requirement. We contrast the likelihood ratio measure with other measures, and argue that problems still emerge in light of tensions with plausible requirements for confirmation measures more generally. (shrink)

The epistemic probability of A given B is the degree to which B evidentially supports A, or makes A plausible. This paper is a first step in answering the question of what determines the values of epistemic probabilities. I break this question into two parts: the structural question and the substantive question. Just as an object’s weight is determined by its mass and gravitational acceleration, some probabilities are determined by other, more basic ones. The structural question asks what probabilities are (...) not determined in this way—these are the basic probabilities which determine values for all other probabilities. The substantive question asks how the values of these basic probabilities are determined. I defend an answer to the structural question on which basic probabilities are the probabilities of atomic propositions conditional on potential direct explanations. I defend this against the view, implicit in orthodox mathematical treatments of probability, that basic probabilities are the unconditional probabilities of complete worlds. I then apply my answer to the structural question to clear up common confusions in expositions of Bayesianism and shed light on the “problem of the priors.”. (shrink)

We explore the grammar of Bayesian confirmation by focusing on some likelihood principles, including the Weak Law of Likelihood. We show that none of the likelihood principles proposed so far is satisfied by all incremental measures of confirmation, and we argue that some of these measures indeed obey new, prima facie strange, antilikelihood principles. To prove this, we introduce a new measure that violates the Weak Law of Likelihood while satisfying a strong antilikelihood condition. We conclude by hinting at some (...) relevant links between the likelihood principles considered here and other properties of Bayesian confirmation recently explored in the literature. (shrink)

Bayesian confirmation theory is rife with confirmation measures. Zalabardo focuses on the probability difference measure, the probability ratio measure, the likelihood difference measure, and the likelihood ratio measure. He argues that the likelihood ratio measure is adequate, but each of the other three measures is not. He argues for this by setting out three adequacy conditions on confirmation measures and arguing in effect that all of them are met by the likelihood ratio measure but not by any of the other (...) three measures. Glass and McCartney, hereafter “G&M,” accept the conclusion of Zalabardo’s argument along with each of the premises in it. They nonetheless try to improve on Zalabardo’s argument by replacing his third adequacy condition with a weaker condition. They do this because of a worry to the effect that Zalabardo’s third adequacy condition runs counter to the idea behind his first adequacy condition. G&M have in mind confirmation in the sense of increase in probability: the degree to which E confirms H is a matter of the degree to which E increases H’s probability. I call this sense of confirmation “IP.” I set out four ways of precisifying IP. I call them “IP1,” “IP2,” “IP3,” and “IP4.” Each of them is based on the assumption that the degree to which E increases H’s probability is a matter of the distance between p and a certain other probability involving H. I then evaluate G&M’s argument in light of them. (shrink)

This paper offers a probabilistic treatment of the conditions for argument cogency as endorsed in informal logic: acceptability, relevance, and sufficiency. Treating a natural language argument as a reason-claim-complex, our analysis identifies content features of defeasible argument on which the RSA conditions depend, namely: change in the commitment to the reason, the reason’s sensitivity and selectivity to the claim, one’s prior commitment to the claim, and the contextually determined thresholds of acceptability for reasons and for claims. Results contrast with, and (...) may indeed serve to correct, the informal understanding and applications of the RSA criteria concerning their conceptual dependence, their function as update-thresholds, and their status as obligatory rather than permissive norms, but also show how these formal and informal normative approachs can in fact align. (shrink)

Bayesian confirmation theory is rife with confirmation measures. Many of them differ from each other in important respects. It turns out, though, that all the standard confirmation measures in the literature run counter to the so-called “Reverse Matthew Effect” (“RME” for short). Suppose, to illustrate, that H1 and H2 are equally successful in predicting E in that p(E | H1)/p(E) = p(E | H2)/p(E) > 1. Suppose, further, that initially H1 is less probable than H2 in that p(H1) < p(H2). (...) Then by RME it follows that the degree to which E confirms H1 is greater than the degree to which it confirms H2. But by all the standard confirmation measures in the literature, in contrast, it follows that the degree to which E confirms H1 is less than or equal to the degree to which it confirms H2. It might seem, then, that RME should be rejected as implausible. Festa (2012), however, argues that there are scientific contexts in which RME holds. If Festa’s argument is sound, it follows that there are scientific contexts in which none of the standard confirmation measures in the literature is adequate. Festa’s argument is thus interesting, important, and deserving of careful examination. I consider five distinct respects in which E can be related to H, use them to construct five distinct ways of understanding confirmation measures, which I call “Increase in Probability”, “Partial Dependence”, “Partial Entailment”, “Partial Discrimination”, and “Popper Corroboration”, and argue that each such way runs counter to RME. The result is that it is not at all clear that there is a place in Bayesian confirmation theory for RME. (shrink)

In this paper I critically discuss and, in the end, reject Morgan’s Canon, a popular principle in comparative psychology. According to this principle we should always prefer explanations of animal behavior in terms of lower psychological processes over explanations in terms of higher psychological processes, when alternative explanations are possible. The validity of the principle depends on two things, a clear understanding of what it means for psychological processes to be higher or lower relative to each other and a justification (...) of a general preference for explanations that refer to lower psychological abilities. However, I argue that we cannot spell out the idea of a psychological scale in a way that claim is satisfied. I start with the discussion of different interpretations of the notion of a psychological scale. In Sect. 3, I discuss different possible strategies to justify any of those interpretations and argue that all of them fail. Finally, in Sect. 4, I generalize the argument for all possible interpretations of Morgan’s Canon and propose an alternative strategy: We should base our interpretations of animal behavior on more general principles such as evidential support and explanatory power, as followed in other scientific domains. (shrink)

The problem of perception is the problem of explaining how perceptual knowledge is possible. The skeptic has a simple solution: it is not possible. I analyze the weaknesses of one type of skeptical reasoning by making explicit a dynamic epistemic principle from dynamic epistemic logic that is implicitly used in debating the problem, with the aim of offering a novel diagnosis to this skeptical argument. I argue that prominent modest foundationalist responses to perceptual skepticism can be understood as rejecting the (...) dynamic assumption made by the skeptic, that there are independent reasons to doubt the truth of such a principle in the context of skeptical reasoning, and that making the dynamic principle explicit allows for a better understanding of at least one objection to modest foundationalism. (shrink)

This paper discusses a novel kind of argument for assessing the moral significance of acts of lying and misleading. It is based on considerations about valuable social norms that might be eroded by these actions, because these actions function as signals. Given that social norms can play an important role in supporting morality, individuals have a responsibility to preserve such norms and to prevent ‘cultural slopes’ that erode them. Depending on whether there are norms against lying, misleading, or both, and (...) how likely it is that they might be eroded, these actions can thus have different moral significance. In cases in which the rule ‘do not lie’, as a relatively simple rule, functions as a ‘focal point’, acts of misleading are often morally preferable. In other words, in such cases the possibility of ‘cultural slopes’ can ground a context-dependent slippery slope argument for a moral difference between lying and misleading. (shrink)

How can we determine the adequacy of a probabilistic coherence measure? A widely accepted approach to this question besides formulating adequacy constraints is to employ paradigmatic test cases consisting of a scenario providing a joint probability distribution over some specified set of propositions coupled with a normative coherence assessment for this set. However, despite the popularity of the test case approach, a systematic evaluation of the proposed test cases is still missing. This paper’s aim is to change this. Using a (...) custom written computer program for the necessary probabilistic calculations a large number of coherence measures in an extensive collection of test cases is examined. The result is a detailed overview of the test case performance of any probabilistic coherence measures proposed so far. It turns out that none of the popular coherence measures such as Shogenji’s, Glass’ and Olsson’s, Fitelson’s or Douven and Meijs’ but two rather unnoticed measures perform best. This, however, does not mean that the other measures can be rejected straightforwardly. Instead, the results presented here are to be understood as a contribution among others to the project of finding adequate probabilistic coherence measures. (shrink)

This (brief) note is about the (evidential) “favoring” relation. Pre-theoretically, favoring is a three-place (epistemic) relation, between an evidential proposition E and two hypotheses H1 and H2. Favoring relations are expressed via locutions of the form: E favors H1 over H2. Strictly speaking, favoring should really be thought of as a four-place relation, between E, H1, H2, and a corpus of background evidence K. But, for present purposes (which won't address issues involving K), I will suppress the background corpus, so (...) as to simplify our discussion. Moreover, the favoring relation is meant to be a propositional epistemic relation, as opposed to a doxastic epistemic relation. That is, the favoring relation is not meant to be restricted to bodies of evidence that are possessed (as evidence) by some actual agent(s), or to hypotheses that are (in fact) entertained by some actual agent(s). In this sense, favoring is analogous to the relation of propositional justification — as opposed to doxastic justification (Conee 1980). In order to facilitate a comparison of Likelihoodist vs Bayesian explications of favoring, I will presuppose the following bridge principle, linking favoring and evidential support: • E favors H1 over H2 iff E supports H1 more strongly than E supports H2.1 Finally, I will only be discussing instances of the favoring relation involving contingent, empirical claims. So, it is to be understood that “favoring” will not apply if any of E, H1, or H2 are non-contingent (and/or non-empirical). With this background in place, we're ready to begin. (shrink)

Is logical consistency required for a set of beliefs or propositions to be categorically coherent? An affirmative answer is often assumed by mainstream epistemologists, and yet it is unclear why. Cases like the lottery and the preface call into question the assumption that beliefs must be consistent in order to be epistemically rational. And thus it is natural to wonder why all inconsistent sets of propositions are incoherent. On the other hand, Easwaran and Fitelson have shown that particular kinds of (...) inconsistency entail the epistemically ‘irrationality’ of holding certain sets of beliefs. In cases of the latter kind of inconsistency, it seems more reasonable to insist that such sets of beliefs or propositions are categorically incoherent. What the precise relationship is between coherence and consistency depends on the nature of the coherence relation. We shall examine recent attempts to explicate the coherence relation in terms of probabilistic measures of confirmation or agreement to see what they can teach us about the relationship between coherence and consistency. We shall show that some probabilistic measures of coherence allow for inconsistent sets to be categorically coherent, while satisfying plausible epistemic rationality constraints. Other probabilistic measures of coherence impose very strong logical consistency requirements, and some measures are tolerant of most forms of inconsistency. As we try to understand what distinguishes coherence measures in this respect, we will also draw some important lessons about Bayesian confirmation measures and differences in the way that they treat contradictory propositions. (shrink)

This paper presents a new argument for the likelihood ratio measure of confirmation by showing that one of the adequacy criteria used in another argument can be replaced by a more plausible and better supported criterion which is a special case of the weak likelihood principle. This new argument is also used to show that the likelihood ratio measure is to be preferred to a measure that has recently received support in the literature.

Conditionalization is a norm that governs the rational reallocation of credence. I distinguish between factive and non-factive formulations of Conditionalization. Factive formulations assume that the conditioning proposition is true. Non-factive formulations allow that the conditioning proposition may be false. I argue that non-factive formulations provide a better foundation for philosophical and scientific applications of Bayesian decision theory. I furthermore argue that previous formulations of Conditionalization, factive and non-factive alike, have almost universally ignored, downplayed, or mishandled a crucial causal aspect of (...) Conditionalization. To formulate Conditionalization adequately, one must explicitly address the causal structure of the transition from old credences to new credences. I offer a formulation of Conditionalization that takes these considerations into account, and I compare my preferred formulation with some prominent formulations found in the literature. (shrink)