Facilitating normative judgments of conditional probability: frequency or nested sets?

Recent probability judgment research contrasts two opposing views. Some theorists have emphasized the role of frequency representations in facilitating probabilistic correctness; opponents have noted that visualizing the probabilistic structure of the task sufficiently facilitates normative reasoning. In the current experiment, the following conditional probability task, an isomorph of the "Problem of Three Prisoners" was tested. "A factory manufactures artificial gemstones. Each gemstone has a 1/3 chance of being blurred, a 1/3 chance of being cracked, and a 1/3 chance of being clear. An inspection machine removes all cracked gemstones, and retains all clear gemstones. However, the machine removes 1/2 of the blurred gemstones. What is the chance that a gemstone is blurred after the inspection?" A 2 x 2 design was administered. The first variable was the use of frequency instruction. The second manipulation was the use of a roulette-wheel diagram that illustrated a "nested-sets" relationship between the prior and the posterior probabilities. Results from two experiments showed that frequency alone had modest effects, while the nested-sets instruction achieved a superior facilitation of normative reasoning. The third experiment compared the roulette-wheel diagram to tree diagrams that also showed the nested-sets relationship. The roulette-wheel diagram outperformed the tree diagrams in facilitation of probabilistic reasoning. Implications for understanding the nature of intuitive probability judgments are discussed.     

Wunder’s probability objection

Tyler Andrew Wunder, in his article, “Alvin Plantinga on Paul Draper’s evolutionary atheology: implications of theism’s non-contingency (Wunder in International Journal for the Philosophy of Religion 74: 67–75 2013),” argues that Plantinga makes a serious error regarding probabilities in his critique of Draper. Properly modified, Wunder believes the argument “works,” but only in a trivial sense. This paper argues that Wunder’s objection, based on an assumed probability calculus, is merely asserted; whereas, there are other competing axiomatic systems consistent with Plantinga’s treatment of probability. As to the modified argument, it is demonstrated that Wunder mistakenly concludes that two key propositions are contradictory. The consequence of this is not that Plantinga’s argument “works” in a trivial sense, but rather that the argument becomes incoherent. Lastly, this paper will explore the consequences of both Wunder’s and Plantinga’s assumptions concerning conditional probability for Draper’s evidentiary argument and Plantiga’s Evolutionary Argument Against Naturalism.     

Other People’s Errors

The question of when other people’s bad acts belong on our moral ledger arises in a number of different scenarios. Each scenario has received some philosophical attention, but no one has noted the structural similarities of these various scenarios or the implications of a proposed approach to one for how the others should be approached. That is the ambition of this article. In it, seemingly disparate moral phenomena—blunt rules, preemptive restrictions, moral blackmail, complicity, retreat and proportional response, and the duty to rescue from a peril one has caused—are shown to have similar structures and thus to require similar moral approaches.     

Ranking judgments in Arrow’s setting

In this paper, I investigate the relationship between preference and judgment aggregation, using the notion of ranking judgment introduced in List and Pettit (Synthese 140(1–2):207–235, 2004). Ranking judgments were introduced in order to state the logical connections between the impossibility theorem of aggregating sets of judgments proved in List and Pettit (Economics and Philosophy 18:89–110, 2002) and Arrow’s theorem (Arrow, Social choice and individual values, 1963). I present a proof of the theorem concerning ranking judgments as a corollary of Arrow’s theorem, extending the translation between preferences and judgments defined in List and Pettit (Synthese 140(1–2):207–235, 2004) to the conditions on the aggregation procedure.     

Kant’s virtue theory

By focusing on human virtues rather than the general morality of rational beings, Kant’s virtue theory presents systematic arguments from the perspectives of reason and experiential emotion, norms and disposition, spirituality and humanity, etc., which is of great significance to an overall understanding of Kantian ethics, thus clarifying misunderstandings from the past decades.     

Developmental trends in children’s typicality judgments

Category typicality norms from 12 natural language categories are presented for kindergarten, third-grade, sixth-grade, and college students. Subjects first selected examples of familiar word concepts and rated them on a 3-point scale in terms of category typicality. Age differences in the percentage of items included as category members were found primarily for the less typical items, with inclusion rates varying as a function of both age and typicality level. The absolute level of typicality judgments increased with age, although correlations between the children’s and college students’ ratings were generally significant for all three children’s groups, with average correlations increasing somewhat with age. It was suggested that the rating data would be useful to developmental investigators interested in children’s processing of category information.     

Causing People to Exist and Saving People’s Lives

Most people are skeptical of the claim that the expectation that a person would have a life that would be well worth living provides a reason to cause that person to exist. In this essay I argue that to cause such a person to exist would be to confer a benefit of a noncomparative kind and that there is a moral reason to bestow benefits of this kind. But this conclusion raises many problems, among which is that it must be determined how the benefits conferred on people by causing them to exist weigh against comparable benefits conferred on existing people. In particular, might the reason to cause people to exist ever outweigh the reason to save the lives of existing people?     

Sosa’s theory of knowledge

Synthese - This paper is a critical discussion of Ernest Sosa’s recent analysis of reflective knowledge.     

There’s no ball without noise: cats’ prediction of an object from noise

We used an expectancy violation procedure to ask whether cats could use a causal rule to infer the presence of an unseen object on hearing the noise it made inside a container and predict its appearance when the container was turned over. We presented cats with either an object dropping out of an opaque container or no object dropping out (turning-over phase) after producing either a rattling sound by shaking the container with the object inside, or no sound (shaking phase). The cats were then allowed to freely explore the experimental environment (exploration phase). The relation between the sound and the object matched with physical laws in half of the trials (congruent condition) and mismatched in the other half (incongruent condition). Inferring the presence of an unseen object from the noise was predicted to result in longer looking time in the incongruent condition. The prediction was supported by the cats’ behavior during the turning-over phase. The results suggest that cats used a causal-logical understanding of auditory stimuli to predict the appearance of invisible objects. The ecology of cats’ natural hunting style may favor the ability for inference on the basis of sounds.     

Arrow’s theorem and theory choice

In a recent paper (Okasha, Mind 120:83–115, 2011), Samir Okasha uses Arrow’s theorem to raise a challenge for the rationality of theory choice. He argues that, as soon as one accepts the plausibility of the assumptions leading to Arrow’s theorem, one is compelled to conclude that there are no adequate theory choice algorithms. Okasha offers a partial way out of this predicament by diagnosing the source of Arrow’s theorem and using his diagnosis to deploy an approach that circumvents it. In this paper I explain why, although Okasha is right to emphasise that Arrow’s result is the effect of an informational problem, he is not right to locate this problem at the level of the informational input of a theory choice rule. Once the informational problem is correctly located, Arrow’s theorem may be dismissed as a problem.     

Hume’s naturalistic theory of representation

Hume is a naturalist in many different respects and about many different topics; this paper argues that he is also a naturalist about intentionality and representation. It does so in the course of answering four questions about his theory of mental representation: (1) Which perceptions represent? (2) What can perceptions represent? (3) Why do perceptions represent at all? (4) Howdo perceptions represent what they do? It appears that, for Hume, all perceptions except passions can represent; and they can represent bodies, minds, and persons, with their various qualities. In addition, ideas can represent impressions and other ideas. However, he explicitly rejects the view that ideas are inherently representational, and he implicitly adopts a view according to which things (whether mental or non-mental) represent in virtue of playing, through the production of mental effects and dispositions, a significant part of the causal and/or functional role of what they represent. It is in virtue of their particular functional roles that qualitatively identical ideas are capable of representing particulars or general kinds; substances or modes; relations; past, present, or future; and individuals or compounds.     

Note on Crozier’s Neural-Availability theory

Two implications of Crozier’s Availability theory are developed. First, the population of elements of neural effect is shown to have a minimum size. Second, intensity discrimination must be mediated by progressively smaller increments in neural effect as stimulus intensity is increased-an improbable state of affairs.     

Hume’s theory of justice and Vanderschraaf’s vulnerablity objection

Philosophical Studies -     

The Mystery of Chinese People’s Happiness

The great improvement in economic wealth and social welfare over the decade doesn’t promote the Chinese people’s happiness. We construct a theoretical framework which covers economic wealth, social welfare, individual functional capability to explore the impact factors and determinants of the Chinese people’s happiness. Based on a national wide questionnaire survey in China, we test and modify the framework by the method of structural equation model. The empirical findings indicate that there are direct and indirect effects on the formation of happiness. For the direct effect, both the increasing of economic wealth and social welfare improves the national happiness, while the individual functional capability reduces it. For the indirect effect, the individual functional capability also reduces happiness by negatively affecting economic wealth and social welfare. The negative effect that played by individual functional capability overwhelms the positive effect played by economic wealth and social welfare. This causes the Chinese people’s happiness goes down while the economic wealth and social welfare are improving. Finally, we conclude that the Chinese people’s happiness is more about individual functional capability rather than social welfare or economic wealth.     

Counterfactual thinking about one’s birth enhances well-being judgments

Previous research demonstrates that thinking counterfactually about life experiences facilitates meaning making about those events. Two studies extend this work into the well-being domain by examining the effects of writing factually or counterfactually about one’s birth on well-being. In Study 1, participants (N?=?252) were randomly assigned to write factually or counterfactually about their births or the election of Barack Obama and then completed measures of meaning in life and life satisfaction. Writing counterfactually about one’s birth led to higher evaluations of life relative to all other groups. In Study 2, (N?=?98) participants wrote factually or counterfactually about their births and again completed well-being measures. Fate attributions, probability estimates, and feelings of luck were explored as potential mediators. The effect on well-being from Study 1 replicated, but was not driven by any of the measured variables. Implications for existential psychology and well-being research are discussed.     

Beyond sympathy: Smith’s rejection of Hume’s moral theory

Adam Smith’s Theory of Moral Sentiments (TMS) has long been recognized as importantly influenced by, and in part responding to, David Hume’s earlier ethical theory. With regard to Smith’s account of the foundations of morals in particular, recent scholarly attention has focused on Smith’s differences with Hume over the question of sympathy. Whilst this is certainly important, disagreement over sympathy in fact represents only the starting point of Smith’s engagement with – and eventual attempted rejection of – Hume’s core moral theory. We can see this by recognizing the TMS’s account of moral foundations as predicated upon a rejection of Hume’s distinction between the natural and artificial virtues. Smith is in turn revealed as generating a major break with Hume – a break which, if based on a superior theory of moral foundations (as Smith thought it to be) has important consequences for how we treat Smith and Hume in both the history of philosophy and contemporary moral theory.     

The impact of emotional expressions on children’s trust judgments

Research on the development of selective trust has shown that young children do not indiscriminately trust all potential informants. They are likely to seek and endorse information from individuals who have proven competent or benign in the past. However, research on trust among adults raises the possibility that children might also be influenced by the emotions expressed by potential informants. In particular, they might trust individuals expressing more positive emotion. Indeed, young children’s trust in particular informants based on their past behaviour might be undermined by their currently expressed emotions. To examine this possibility, we tested the selective trust of fifty 4- and 5-year-olds in two steps. We first confirmed that children are likely to invest more trust in individuals expressing more positive emotion. We then showed that even if children have already formed an impression of two potential informants based on their behavioural record, their choices about whose claims to trust are markedly influenced by the degree of positive emotion currently expressed by the two informants. By implication, the facial emotions expressed by potential informants can undermine young children’s selective trust based on the behavioural record of those informants.