Bets and Boundaries: Assigning Probabilities to Imprecisely Specified Events

Uncertainty and vagueness/imprecision are not the same: one can be certain about events described using vague predicates and about imprecisely specified events, just as one can be uncertain about precisely specified events. Exactly because of this, a question arises about how one ought to assign probabilities to imprecisely specified events in the case when no possible available evidence will eradicate the imprecision (because, say, of the limits of accuracy of a measuring device). Modelling imprecision by rough sets over an approximation space presents an especially tractable case to help get one’s bearings. Two solutions present themselves: the first takes as upper and lower probabilities of the event X the (exact) probabilities assigned X’s upper and lower rough-set approximations; the second, motivated both by formal considerations and by a simple betting argument, is to treat X’s rough-set approximation as a conditional event and assign to it a point-valued (conditional) probability. With rough sets over an approximation space we get a lot of good behaviour. For example, in the first construction mentioned the lower probabilities are n-monotone, for every . When we examine other models of approximation/imprecision/vagueness, and in particular, proximity spaces, we lose a lot of that good behaviour. In the literature there is not (even) agreement on the definition of upper and lower approximations for events (subsets) in the underlying domain. Betting considerations suggest one choice and, again, ways to assign upper and lower and point-valued probabilities, but nothing works well. Special Issue on Vagueness Edited by Rosanna Keefe and Libor Bêhounek     

Interpretation bias and social anxiety: does interpretation bias mediate the relationship between trait social anxiety and state anxiety responses?

Two studies aimed to examine whether high socially anxious individuals are more likely to negatively interpret ambiguous social scenarios and facial expressions compared to low socially anxious individuals. We also examined whether interpretation bias serves as a mediator of the relationship between trait social anxiety and state anxiety responses, in particular current state anxiety, bodily sensations, and perceived probability and cost of negative evaluation pertaining to a speech task. Study 1 used ambiguous social scenarios and Study 2 used ambiguous facial expressions as stimuli to objectively assess interpretation bias. Undergraduate students with high and low social anxiety completed measures of state anxiety responses at three time points: baseline, after the interpretation bias task, and after the preparation for an impromptu speech. Results showed that high socially anxious individuals were more likely to endorse threat interpretations for ambiguous social scenarios and to interpret ambiguous faces as negative than low socially anxious individuals. Furthermore, negative interpretations mediated the relationship between trait social anxiety and perceived probability of negative evaluation pertaining to the speech task in Study 1 but not Study 2. The present studies provide new insight into the role of interpretation bias in social anxiety.     

Visual impressions of penetration in the perception of objects in motion

Observers viewed visual stimuli in which one object moved to a position of partial occlusion by another. The objects were presented as two-dimensional profiles moving in an undefined space, so the partial occlusion supports several different physical interpretations. In fact some stimuli reliably gave rise to a perceptual impression that the moving object penetrated or pierced the stationary one. This kind of interaction impression has not previously been reported. The impression was maximized by rapid deceleration to a halt with minimal occlusion. If the object decelerated more slowly, so that it was completely occluded or projected from the far side of the stationary object, it was perceived as moving behind the stationary object. The shape of the moving object and its speed prior to occlusion had significant but small effects.     

Indicative conditionals,conditional probabilities,and the “defective truth-table”: A request for more experiments

While there is now considerable experimental evidence that, on the one hand, participants assign to the indicative conditional as probability the conditional probability of consequent given antecedent and, on the other, they assign to the indicative conditional the “defective truth-table” in which a conditional with false antecedent is deemed neither true nor false, these findings do not in themselves establish which multi-premise inferences involving conditionals participants endorse. A natural extension of the truth-table semantics pronounces as valid numerous inference patterns that do seem to be part of ordinary usage. However, coupled with something the probability account gives us—namely that when conditional-free ? entails conditional-free ψ, “if ? then ψ” is a trivial, uninformative truth—we have enough logic to derive the paradoxes of material implication. It thus becomes a matter of some urgency to determine which inference patterns involving indicative conditionals participants do endorse. Only thus will we be able to arrive at a realistic, systematic semantics for the indicative conditional.     

A connectionist implementation of the theory of planned behavior: association of beliefs with exercise intention.

The theory of planned behavior suggests attitudes are a product of salient beliefs. This study examined whether aggregating salient beliefs was plausible within a more biologically centered information-processing environment. A neural network was used to examine associations among beliefs relating to exercise intention. Data on intentions and behavioral, normative, and control beliefs from 114 respondents were used to train (by error backpropagation) a neural network to associate beliefs with intention. The R-sup-2 between the network's estimated and self-reported intention was.66. The network's representation comprised 6 belief profiles associated with high, moderate, or low behavioral intention. The neural network accommodated complex relationships among beliefs and belief-intention associations and indicated how high-level constructs such as attitudes may be viewed as the best fit (compromise state) between aroused beliefs.     

Temporality and the Lyotardian Sublime: Kant between Husserl and Freud

ABSTRACT

While Lyotard's first book was an introduction to phenomenology, most of the work that follows can be said to openly challenge the limits of phenomenological analysis. This is particularly evident in the well-known writings on the Kantian sublime, which Lyotard reads as a “temporal crisis” that undoes the conscious knowing subject and escapes “experience” in the phenomenological sense. Nonetheless, if this allows him to relate the sublime to Freud's “unconscious affect,” this “crisis” only becomes visible in contrast to a figure of subjective temporalization the model of which, I argue, is broadly Husserlian. Approaching the sublime as a temporal crisis thus allows not only for a clearer view of the import of Lyotard's late work on the affect with regard to subjectivity, knowledge, and experience; it also reveals what that work continues to owe to a certain phenomenological analysis.     

Predicting garden path sentences

This work is an investigation into part of the human sentence parsing mechanism (HSPM). The major test of the psychological validity of any model of the HSPM is that it fail on precisely those sentences that humans find to be garden paths. It is hypothesized that the HSPM consists of at least two processes. We call the first process the syntactic processor, and the second will be known as the semantic processor. It is hypothesized that the syntactic processor is unconscious, deterministic and fast, but limited. While most ambiguities are resolved on the basis of syntactic information, when the syntactic processor can no longer guarantee a correct analysis, semantic information is used to help resolve the ambiguity. This model leads to a better prediction and explanation of which sentences will cause people to garden path.     

II—What is the Normative Role of Logic?

In making assertions one takes on commitments to the consistency of what one asserts and to the logical consequences of what one asserts. Although there is no quick link between belief and assertion, the dialectical requirements on assertion feed back into normative constraints on those beliefs that constitute one's evidence. But if we are not certain of many of our beliefs and that uncertainty is modelled in terms of probabilities, then there is at least prima facie incoherence between the normative constraints on belief and the probability-like structure of degrees of belief. I suggest that the norm-governed practice relating to degrees of belief is the evaluation of betting odds.