Patterns in the Philosophy of Mathematics

Books reviewed in this article:
Michael D. Resnik, Mathematics as a Science of Patterns
Penelope Maddy, Naturalism in Mathematics
Jerrold J. Katz, Realistic Rationalism
Jaakko Hintikka, The Principles of Mathematics Revisited     

Saving the worst for last: The effect of time horizon on the efficiency of negotiating benefits and burdens

Three experiments explored the effect of outcome delays—longer time horizons for the realization of outcomes—on the efficiency of negotiated agreements. We hypothesized that there would be a positive relationship between a longer temporal distance to the consequences of negotiated agreements and the efficiency of those agreements. Outcome delays did increase the efficiency of the negotiated agreements. In addition, type of resource, burden or benefit, moderated this relationship. Because negotiating for burdens is more difficult than negotiating for benefits in the present, the salutary discounting effects of outcome delays were greater for burdens. The multifaceted effects of time on negotiations are discussed.     

Inequity/Iniquity: Card on Balancing Injustice and Evil

Card argues that we should not give injustice priority over evil. I agree. But I think Card sets us up for some difficult balances, for example of small evils against middle‐sized injustices. I suggest some ways of staying off the tightrope.     

Modulation of cognitive flexibility by hunger and desire

Knowing when to persevere with a plan and knowing when to ditch it and change strategy is highly adaptive and breaks down in several frontal and striatal disorders. Cognitive flexibility is also susceptible to tonic influences of neuromodulators (such as dopamine) and so may be influenced by everyday fluctuations in processes known to depend upon them (such as motivation). The current study employed an attentional shifting paradigm to examine the influence of changes in food-related motivational state in healthy volunteers. Hunger was induced through fasting (physiological manipulation) or through the presentation of appetitive food cues prior to testing (desire manipulation). The desire manipulation produced a stronger effect than fasting by inducing errors when participants were attempting to shift. The results suggest that everyday fluctuations in appetite and desire can produce a significant impact on cognition, highlighting implications for our understanding of excessive motivational control including maladaptive eating behaviour.     

From Self‐Respect to Respect for Others

The leading accounts of respect for others usually assume that persons have a rational nature, which is a marvelous thing, so they should be respected like other objects of ‘awesome’ value. Kant's views about the ‘value’ of humanity, which have inspired contemporary discussions of respect, have been interpreted in this way. I propose an alternative interpretation in which Kant proceeds from our own rational self‐regard, through our willingness to reciprocate with others, to duties of respect for others. This strategy, which shares some similarities with moral contractualism, offers a way to justify other‐regarding moral requirements from self‐regarding rational dispositions.     

A DUAL-IDENTITY FRAMEWORK FOR UNDERSTANDING LESBIAN EXPERIENCE

The diverse life experiences of contemporary lesbians are shaped by women's differing ties to two social worlds, the majority heterosexual society and the minority subculture of the lesbian or sexual-minority world. This article presents a detailed conceptual analysis of a dual-identity framework that emphasizes lesbians' simultaneous affiliations with both lesbian and mainstream/heterosexual communities. The usefulness of this approach is discussed, with emphasis on implications for understanding individual differences in exposure to gay-related stress and mental health. Results from a survey of 116 lesbians showed that scores on measures of Lesbian Identity and Mainstream Identity were not significantly correlated with each other. Both lesbian and mainstream identities were significantly related to lesbians' reported experiences of discrimination, feelings of internalized homophobia, and life satisfaction. Limitations of the dual-identity framework and suggestions for future research are considered.     

The mean-integral representation of rectangles

To assess perceptual interaction between the height and width of rectangles, we used an accuracy variant of the Garner paradigm. We measured the discriminability of height and width (baseline tasks) and size and shape (correlated tasks). From thed′ values in these conditions, we estimated perceptual distances and inferred amean-integral representation in which height and width corresponded to nonindependent dimensions in a perceptual space. This model accounted well for performance in these two-stimulus conditions, and it also explained 70% –80% of the decline in performance in selective and divided attention. In a second experiment, conducted for purposes of comparison with the rectangle discrimination Experiment, we studied the discrimination of horizontal and vertical line segments connected in an L-shape. In size discrimination, observers were equally good with line pairs and rectangles, suggesting holistic perception; but in shape discrimination, they appeared to combine information from the two line-pair components of the rectangle independently. The mean-integral model was again successful in relating performance in the Garner tasks quantitatively.     

Comments on “markovian processes with identifiable states: General considerations and applications to all-or-none learning”

When knowledge of the response sequence permits one to specify the sequence of theoretical states that occurred, we propose to say that the theory has observable states. Our earlier usage of identifiable conflicts with established usage in econometrics. We also present a revised definition of implication between theories that avoids a technical flaw in the earlier definition, and we correct a mistake in an example in our earlier paper.