Conditional Random Quantities and Compounds of Conditionals

In this paper we consider conditional random quantities (c.r.q.’s) in the setting of coherence. Based on betting scheme, a c.r.q. X|H is not looked at as a restriction but, in a more extended way, as \({XH + \mathbb{P}(X|H)H^c}\) ; in particular (the indicator of) a conditional event E|H is looked at as EH +  P(E|H)H ^c . This extended notion of c.r.q. allows algebraic developments among c.r.q.’s even if the conditioning events are different; then, for instance, we can give a meaning to the sum X|H + Y|K and we can define the iterated c.r.q. (X|H)|K. We analyze the conjunction of two conditional events, introduced by the authors in a recent work, in the setting of coherence. We show that the conjoined conditional is a conditional random quantity, which may be a conditional event when there are logical dependencies. Moreover, we introduce the negation of the conjunction and by applying De Morgan’s Law we obtain the disjoined conditional. Finally, we give the lower and upper bounds for the conjunction and disjunction of two conditional events, by showing that the usual probabilistic properties continue to hold.     

“That is just what they want you to believe”: A modest defence of Marxist paranoia

This essay defends a rational reconstruction of a genealogical debunking argument that begins with the premise “that's just what the economic elite want you to believe” and ends in the conclusion “you should lower your confidence in your belief.” The argument is genealogical because it includes a causal explanation of your beliefs; it is debunking because it claims that the contingencies uncovered by the genealogy undermine your beliefs. The essay begins by defending a plausible causal explanation of your belief in terms of the wants of the elite. Then a number of recent objections to genealogical debunking arguments are considered. It is argued that the genealogy offered in the first part constitutes evidence that a testimony‐based belief is not safe and therefore does not constitute knowledge if the economic elite wants you to believe it.     

Appearances,Rationality, and Justified Belief

One might think that its seeming to you that p makes you justified in believing that p. After all, when you have no defeating beliefs, it would be irrational to have it seem to you that p but not believe it. That view is plausible for perceptual justification, problematic in the case of memory, and clearly wrong for inferential justification. I propose a view of rationality and justified belief that deals happily with inference and memory. Appearances are to be evaluated as ‘sound’ or ‘unsound.’ Only a sound appearance can give rise to a justified belief, yet even an unsound appearance can ‘rationally require’ the subject to form the belief. Some of our intuitions mistake that rational requirement for the belief’s being justified. The resulting picture makes it plausible that there are also unsound perceptual appearances. I suggest that to have a sound perceptually basic appearance that p, one must see that p.     

Direct phenomenal beliefs,cognitive significance,and the specious present

Chalmers (The character of consciousness, 2010) argues for an acquaintance theory of the justification of direct phenomenal beliefs. A central part of this defense is the claim that direct phenomenal beliefs are cognitively significant. I argue against this. Direct phenomenal beliefs are justified within the specious present, and yet the resources available with the present ‘now’ are so impoverished that it barely constrains the content of a direct phenomenal belief. I argue that Chalmers’s account does not have the resources for explaining how direct phenomenal beliefs support the inference from ‘this _E is R’ to ‘that was R.’     

The corroboration paradox

Evidentiary propositions E ₁ and E ₂, each p-positively relevant to some hypothesis H, are mutually corroborating if p(H|E ₁ ∩ E ₂) > p(H|E _i ), i = 1, 2. Failures of such mutual corroboration are instances of what may be called the corroboration paradox. This paper assesses two rather different analyses of the corroboration paradox due, respectively, to John Pollock and Jonathan Cohen. Pollock invokes a particular embodiment of the principle of insufficient reason to argue that instances of the corroboration paradox are of negligible probability, and that it is therefore defeasibly reasonable to assume that items of evidence positively relevant to some hypothesis are mutually corroborating. Taking a different approach, Cohen seeks to identify supplementary conditions that are sufficient to ensure that such items of evidence will be mutually corroborating, and claims to have identified conditions which account for most cases of mutual corroboration. Combining a proposed common framework for the general study of paradoxes of positive relevance with a simulation experiment, we conclude that neither Pollock’s nor Cohen’s claims stand up to detailed scrutiny. I am quite prepared to be told…”oh, that is an extreme case: it could never really happen!” Now I have observed that this answer is always given instantly, with perfect confidence, and without any examination of the proposed case. It must therefore rest on some general principle: the mental process being something like this—“I have formed a theory. This case contradicts my theory. Therefore, this is an extreme case, and would never occur in practice.” Rev. Charles L. Dodgson      

Knowledge in Action

This paper argues that the role of knowledge in the explanation and production of intentional action is as indispensable as the roles of belief and desire. If we are interested in explaining intentional actions rather than intentions or attempts, we need to make reference to more than the agent's beliefs and desires. It is easy to see how the truth of your beliefs, or perhaps, facts about a setting will be involved in the explanation of an action. If you believe you can stop your car by pressing a pedal, then, if your belief is true, you will stop. If it is false, you will not. By considering cases of unintentional actions, actions involving luck and cases of deviant causal chains, I show why knowledge is required. By looking at the notion of causal relevance, I argue that the connection between knowledge and action is causal and not merely conceptual.
"What knowledge adds to belief is not psychologically relevant." ¹ —Stephen Stich     

The pseudodiagnosticity trap: Should participants consider alternative hypotheses?

The pseudodiagnosticity task has been used as an example of the tendency on the part of participants to incorrectly assess Bayesian constraints in assessing data, and as a failure to consider alternative hypotheses in a probabilistic inference task. In the task, participants are given one value, the anchor value, corresponding to P(D1|H) and may choose one other value, either P(D1|¬!H), P(D2|H), or P(D2|not;!H). Most participants select P(D2|H), or P(D2|¬!H) which have been considered inappropriate (and called pseudodiagnostic) because only P(D1|¬!H) allows use of Bayes' theorem. We present a new analysis based on probability intervals and show that selection of either P(D2|H), or P(D2|¬!H) is in fact pseudodiagnostic, whereas choice of P(D1|¬!H) is diagnostic. Our analysis shows that choice of the pseudodiagnostic values actually increases uncertainty regarding the posterior probability of H, supporting the original interpretation of the experimental findings on the pseudodiagnosticity task. The argument illuminates the general proposition that evolutionarily adaptive heuristics for Bayesian inference can be misled in some task situations.     

Intolerance of Uncertainty Mediates the Relation Between Generalized Anxiety Disorder Symptoms and Anger

Previous research has shown that individuals with generalized anxiety disorder (GAD) report elevated anger compared with nonanxious individuals; however, the pathways linking GAD and anger are currently unknown. We hypothesized that negative beliefs about uncertainty, negative beliefs about worry and perfectionism dimensions mediate the relationship between GAD symptoms and anger variables. We employed multiple mediation with bootstrapping on cross-sectional data from a student sample (N = 233) to test four models assessing potential mediators of the association of GAD symptoms to inward anger expression, outward anger expression, trait anger and hostility, respectively. The belief that uncertainty has negative personal and behavioural implications uniquely mediated the association of GAD symptoms to inward anger expression (confidence interval [CI] = .0034, .1845, P_M = .5444), and the belief that uncertainty is unfair and spoils everything uniquely mediated the association of GAD symptoms to outward anger expression (CI = .0052, .1936, P_M = .4861) and hostility (CI = .0269, .2427, P_M = .3487). Neither negative beliefs about worry nor perfectionism dimensions uniquely mediated the relation of GAD symptoms to anger constructs. We conclude that intolerance of uncertainty may help to explain the positive connection between GAD symptoms and anger, and these findings give impetus to future longitudinal investigations of the role of anger in GAD.     

Propositional Reasoning that Tracks Probabilistic Reasoning

This paper concerns the extent to which uncertain propositional reasoning can track probabilistic reasoning, and addresses kinematic problems that extend the familiar Lottery paradox. An acceptance rule assigns to each Bayesian credal state p a propositional belief revision method ${\sf B}_{p}$ , which specifies an initial belief state ${\sf B}_{p}(\top)$ that is revised to the new propositional belief state ${\sf B}(E)$ upon receipt of information E. An acceptance rule tracks Bayesian conditioning when ${\sf B}_{p}(E) = {\sf B}_{p|_{E}}(\top)$ , for every E such that p(E)?>?0; namely, when acceptance by propositional belief revision equals Bayesian conditioning followed by acceptance. Standard proposals for uncertain acceptance and belief revision do not track Bayesian conditioning. The ??Lockean?? rule that accepts propositions above a probability threshold is subject to the familiar lottery paradox (Kyburg 1961), and we show that it is also subject to new and more stubborn paradoxes when the tracking property is taken into account. Moreover, we show that the familiar AGM approach to belief revision (Harper, Synthese 30(1?C2):221?C262, 1975; Alchourrón et al., J Symb Log 50:510?C530, 1985) cannot be realized in a sensible way by any uncertain acceptance rule that tracks Bayesian conditioning. Finally, we present a plausible, alternative approach that tracks Bayesian conditioning and avoids all of the paradoxes. It combines an odds-based acceptance rule proposed originally by Levi (1996) with a non-AGM belief revision method proposed originally by Shoham (1987).     

Our Vision and our Mission: Bulishit,Assertion and Belief

Given ht as the hypothesis of theism, hm as the hypothesis of materialism, and e as the evidence of a complex life-bearing universe, Richard Swinburne presents these arguments in The Existence of God: (1) that this ordered universe is a priori improbable, given the stringent requirements for life and the Second Law of Thermodynamics; (2) that this universe's structure is evidence for theism, and that theism therefore explains this universe; Swinburne argues that because P(e|ht) > P(e|hm), it follows that P(ht|e)>P(hm|e); and (3) a theistic explanation for the universe is more probable because it is simpler; therefore it is more likely that God exists than not. As I have addressed (3) in a prior paper, this paper will address the Bayesian argument that Swinburne offers in (2), i.e. that P(e|ht)>P(e). In the paper I draw a number of conclusions, most pertinently, that Hacking's Total Probability Rule (TPR) for cases of mutually exclusive hypotheses [ht vs hm] and evidence e entails that ht can only be confirmed if P(e|～ht) is low. I also conclude that if we follow the TPR for Swinburne's argument, we achieve the result that theism is at best slightly improbable, or equiprobable with materialism.     

Irrelevant Influences

We often hear such casual accusations: you just believe that because you are a liberal, a Christian, an American, a woman… When such charges are made they are meant to sting—not just emotionally, but epistemically. But should they? It can be disturbing to learn that one's beliefs reflect the influence of such irrelevant factors. The pervasiveness of such influence has led some to worry that we are not justified in many of our beliefs. That same pervasiveness has led others to doubt whether there is any worry here at all. I argue that evidence of irrelevant belief influence is sometimes, but not always, undermining. My proposal picks out ordinary, non‐skeptical cases in which we get evidence of error. It says that, in those cases, evidence of irrelevant influence is epistemically significant. It shows how respecting evidence of error is compatible with the epistemic lives we see ourselves living. We are fallible creatures, yes, but we are also capable and intelligent ones. We can recognize and correct for our own error so as to improve our imperfect, yet nevertheless robust, epistemic lives.     

Irrational Beliefs and Attention Bias Towards Symptoms-Related Stimuli in Maintaining Gastrointestinal Symptoms: Results from a Pilot Study

Recent etiopathogenic theories of gastrointestinal conditions state that information processing biases can be a possible major factor involved in the aetiology and maintenance of these conditions. This exploratory study investigated the role of attention biases (AB) towards symptoms-related cues in gastrointestinal patients with respect to symptom maintenance, simultaneously taking into consideration the role of irrational beliefs. We included 32 patients diagnosed with gastrointestinal conditions. Patients completed a battery of psychological tests and an experimental task aimed to measure the preferential attention processing of linguistic stimuli related to gastrointestinal symptoms when they compete for attention resources with neutral stimuli. AB was positively related to irrational beliefs [r(31) = .376, p = .037] and analgesics use [r(32) = .518, p = .002], but not to self-report gastrointestinal symptoms [r(30) = ?.165, p = .382]. Irrational beliefs correlated with pain catastrophizing [r(31) = .373, p = .039], but not to gastrointestinal symptoms, pain intensity, visceral sensitivity or negative emotions; however, pain catastrophizing correlated with all of these. Taken together, our results suggest that core irrational beliefs action as general vulnerability factors that trigger specific implicit and explicit cognitive mechanisms (i.e., AB, pain catastrophizing) involved in the onset and maintenance of symptoms. Future experimental studies should test the robustness of these results in larger samples and aim to further advance our understanding of how cognitive factors interact and potentiate each other in generating and maintaining debilitating suffering.     

Justified inference

This paper proposes a general account of the epistemological significance of inference. This account rests on the assumption that the concept of a ??justified?? belief or inference is a normative concept. It also rests on a conception of belief that distinguishes both (a) between conditional and unconditional beliefs and (b) between enduring belief states and mental events of forming or reaffirming a belief, and interprets all of these different kinds of belief as coming in degrees. Conceptions of ??rational coherence?? and ??competent inference?? are then formulated, in terms of the undefeated instances of certain rules of inference. It is proposed that (non-accidental) rational coherence is a necessary and sufficient condition of justified enduring belief states, while competent inference always results in a justified mental event of some kind. This proposal turns out to tell against the view that there are any non-trivial cases of ??warrant transmission failure??. Finally, it is explained how these proposals can answer the objections that philosophers have raised against the idea that justified belief is ??closed?? under competent inference.     

A theory-based epistemology of modality

We have some justified beliefs about modal matters. A modal epistemology should explain what’s involved in our having that justification. Given that we’re realists about modality, how should we expect that explanation to go? In the first part of this essay, I suggest an answer to this question based on an analogy with games. Then, I outline a modal epistemology that fits with that answer. According to a theory-based epistemology of modality, you justifiably believe that p if (a) you justifiably believe a theory that says that p and (b) you believe p on the basis of that theory.     

Beliefs About God and Mental Health Among American Adults

This study examines the association between beliefs about God and psychiatric symptoms in the context of Evolutionary Threat Assessment System Theory, using data from the 2010 Baylor Religion Survey of US Adults (N = 1,426). Three beliefs about God were tested separately in ordinary least squares regression models to predict five classes of psychiatric symptoms: general anxiety, social anxiety, paranoia, obsession, and compulsion. Belief in a punitive God was positively associated with four psychiatric symptoms, while belief in a benevolent God was negatively associated with four psychiatric symptoms, controlling for demographic characteristics, religiousness, and strength of belief in God. Belief in a deistic God and one’s overall belief in God were not significantly related to any psychiatric symptoms.     

Reasoning defeasibly about probabilities

In concrete applications of probability, statistical investigation gives us knowledge of some probabilities, but we generally want to know many others that are not directly revealed by our data. For instance, we may know prob(P/Q) (the probability of P given Q) and prob(P/R), but what we really want is prob(P/Q&;R), and we may not have the data required to assess that directly. The probability calculus is of no help here. Given prob(P/Q) and prob(P/R), it is consistent with the probability calculus for prob(P/Q&;R) to have any value between 0 and 1. Is there any way to make a reasonable estimate of the value of prob(P/Q&;R)? A related problem occurs when probability practitioners adopt undefended assumptions of statistical independence simply on the basis of not seeing any connection between two propositions. This is common practice, but its justification has eluded probability theorists, and researchers are typically apologetic about making such assumptions. Is there any way to defend the practice? This paper shows that on a certain conception of probability—nomic probability—there are principles of “probable probabilities” that license inferences of the above sort. These are principles telling us that although certain inferences from probabilities to probabilities are not deductively valid, nevertheless the second-order probability of their yielding correct results is 1. This makes it defeasibly reasonable to make the inferences. Thus I argue that it is defeasibly reasonable to assume statistical independence when we have no information to the contrary. And I show that there is a function Y(r, s, a) such that if prob(P/Q) = r, prob(P/R) = s, and prob(P/U) = a (where U is our background knowledge) then it is defeasibly reasonable to expect that prob(P/Q&;R) = Y(r, s, a). Numerous other defeasible inferences are licensed by similar principles of probable probabilities. This has the potential to greatly enhance the usefulness of probabilities in practical application.     

Justified Belief from Unjustified Belief

Under what conditions is a belief inferentially justified? A partial answer is found in Justification from Justification (JFJ): a belief is inferentially justified only if all of the beliefs from which it is essentially inferred are justified. After reviewing some important features of JFJ, I offer a counterexample to it. Then I outline a positive suggestion for how to think about inferentially justified beliefs while still retaining a basing condition. I end by concluding that epistemologists need a model of inferentially justified belief that is more permissive and more complex than JFJ.     

Williamson on Knowledge and Psychological Explanation

According to many philosophers, psychological explanation canlegitimately be given in terms of belief and desire, but not in termsof knowledge. To explain why someone does what they do (so the common wisdom holds) you can appeal to what they think or what they want, but not what they know. Timothy Williamson has recently argued against this view. Knowledge, Williamson insists, plays an essential role in ordinary psychological explanation.Williamson's argument works on two fronts.First, he argues against the claim that, unlike knowledge, belief is``composite' (representable as a conjunction of a narrow and a broadcondition). Belief's failure to be composite, Williamson thinks, undermines the usual motivations for psychological explanation in terms of belief rather than knowledge.Unfortunately, we claim, the motivations Williamson argues against donot depend on the claim that belief is composite, so what he saysleaves the case for a psychology of belief unscathed.Second, Williamson argues that knowledge can sometimes provide abetter explanation of action than belief can.We argue that, in the cases considered, explanations that cite beliefs(but not knowledge) are no less successful than explanations that citeknowledge. Thus, we conclude that Williamson's arguments fail both coming andgoing: they fail to undermine a psychology of belief, and they fail tomotivate a psychology of knowledge.     

A puzzle about epistemic akrasia

In this paper I will present a puzzle about epistemic akrasia, and I will use that puzzle to motivate accepting some non-standard views about the nature of epistemological judgment. The puzzle is that while it seems obvious that epistemic akrasia must be irrational, the claim that epistemic akrasia is always irrational amounts to the claim that a certain sort of justified false belief—a justified false belief about what one ought to believe—is impossible. But justified false beliefs seem to be possible in any domain, and it’s hard to see why beliefs about what one ought to believe should be an exception. I will argue that when we get clearer about what sort of psychological state epistemic akrasia is, we can resolve the puzzle in favor of the intuitive view that epistemic akrasia is always irrational.