An Inferential Conception of the Application of Mathematics

A number of people have recently argued for a structural approach to accounting for the applications of mathematics. Such an approach has been called “the mapping account”. According to this view, the applicability of mathematics is fully accounted for by appreciating the relevant structural similarities between the empirical system under study and the mathematics used in the investigation of that system. This account of applications requires the truth of applied mathematical assertions, but it does not require the existence of mathematical objects. In this paper, we discuss the shortcomings of this account, and show how these shortcomings can be overcome by a broader view of the application of mathematics: the inferential conception.     

Skepticism,naturalism, pyrrhonism

Skepticism and naturalism bear important connections with one another. Do they conflict or are they different sides of the same coin? In this paper, by considering the ways in which Sextus and Hume have examined these issues, I offer a Pyrrhonian response to Penelope Maddy's attempt to reject skepticism within the form of naturalism that she calls “second philosophy” (Maddy, 2007, 2017) and to Timothy Williamson's attempt to avoid skepticism from emerging within his knowledge-first approach (Williamson, 2000). Some lessons about Pyrrhonism result.     

Time flies with music whatever its emotional valence

The present study used a temporal bisection task to investigate whether music affects time estimation differently from a matched auditory neutral stimulus, and whether the emotional valence of the musical stimuli (i.e., sad vs. happy music) modulates this effect. The results showed that, compared to sine wave control music, music presented in a major (happy) or a minor (sad) key shifted the bisection function toward the right, thus increasing the bisection point value (point of subjective equality). This indicates that the duration of a melody is judged shorter than that of a non-melodic control stimulus, thus confirming that “time flies” when we listen to music. Nevertheless, sensitivity to time was similar for all the auditory stimuli. Furthermore, the temporal bisection functions did not differ as a function of musical mode.     

Efectos de los cambios cognitivos y del esfuerzo de procesamiento sobre los juicios de duración prospectivos y retrospectivos

Resumen

El objetivo de esta investigación ha sido someter a prueba en un mismo diseño las variables representativas de cada uno de los tres principales modelos contemporáneos que tratan de explicar la experiencia humana sobre la duración. Además, se ha efectuado una comparación entre los paradigmas experimentales prospectivo y retrospectivo igualados en el tiempo que transcurre hasta la realización del juicio, así como una medición directa mediante un índice independiente del esfuerzo cognitivo involucrado en la realización de las tareas experimentales. El experimento realizado ha sido aplicado a 192 estudiantes de Psicología de la Universidad de Salamanca. Los resultados muestran que cuando se atiende de forma intencional al tiempo, los cambios ocurridos en el contexto cognitivo son utilizados como los indicios primordiales para la configuración de los juicios de tiempo más precisos. Sin embargo, cuando la atención al tiempo es tan sólo incidental, el esfuerzo cognitivo es el factor que mejor explica la estimación temporal mediante una relación inversa con el tamaño de la reproducción efectuada.     

A Defense of Second-Order Logic

Second-order logic has a number of attractive features, in particular the strong expressive resources it offers, and the possibility of articulating categorical mathematical theories (such as arithmetic and analysis). But it also has its costs. Five major charges have been launched against second-order logic: (1) It is not axiomatizable; as opposed to first-order logic, it is inherently incomplete. (2) It also has several semantics, and there is no criterion to choose between them (Putnam, J Symbol Logic 45:464–482, 1980). Therefore, it is not clear how this logic should be interpreted. (3) Second-order logic also has strong ontological commitments: (a) it is ontologically committed to classes (Resnik, J Phil 85:75–87, 1988), and (b) according to Quine (Philosophy of logic, Prentice-Hall: Englewood Cliffs, 1970), it is nothing more than “set theory in sheep’s clothing”. (4) It is also not better than its first-order counterpart, in the following sense: if first-order logic does not characterize adequately mathematical systems, given the existence of non-isomorphic first-order interpretations, second-order logic does not characterize them either, given the existence of different interpretations of second-order theories (Melia, Analysis 55:127–134, 1995). (5) Finally, as opposed to what is claimed by defenders of second-order logic [such as Shapiro (J Symbol Logic 50:714–742, 1985)], this logic does not solve the problem of referential access to mathematical objects (Azzouni, Metaphysical myths, mathematical practice: the logic and epistemology of the exact sciences, Cambridge University Press, Cambridge, 1994). In this paper, I argue that the second-order theorist can solve each of these difficulties. As a result, second-order logic provides the benefits of a rich framework without the associated costs.     

French categorization norms for 70 semantic categories and comparison with Van Overschelde et al.’s (2004) English norms

The present methodological note provides categorization norms for 70 semantic categories collected from 200 participants. The categories were mainly derived from a French translation of the Van Overschelde, Rawson, and Dunlosky (2004) inductor terms including a large set of semantic categories. Our study also extends recent French norms (Léger, Boumlak, & Tijus, 2008; Marchal & Nicolas, 2003) and tests their stability. These 70 categories constitute the widest French categorization norms to date and will be of use to studies in the fields of both linguistics and psycholinguistics. A cross-linguistic comparison, with both quantitative and qualitative results, is also performed, which should prove useful for bilingual and/or cross-linguistic studies. The norms collected for all 70 categories are available for download as supplemental materials from http://brm.psychonomic-journals.org/content/supplemental.     

Are conditioned stimuli determinants of oriented exploratory behavior in the rat?

To test Bindra and Palfai's hypothesis about enhancing and inhibitory motivational effects of a conditioned stimulus on exploratory behavior, rats in a first experiment were submitted to pairings of a tone with (a) water, (b) intermittent deliveries of water after a period of constant pairing. In a control condition, the tone was presented alone. The tone was subsequently presented during oriented exploration of a novel stimulus, in the conditioning context. There was no difference in exploratory performance between conditions. In a second experiment with another kind of stimulus change and a larger number of training trials, exploration did not increase when occurring during CS presentation. The lack of facilitation which is possibly the product of competition between exploration and magazine-directed responses, can also be interpreted as indicating that the effects of a conditioned stimulus are reinforcer specific and that the diffuse activity it generates in a situation different from the training one is not equivalent, as concerns the processes involved, to oriented exploratory behavior.     

Present mood states in Brazilian night nurses

Variations in the state of momentary emotions of Brazilian hospital nurses on day and night shifts were recorded. Ten graduate nurses working on day and night shifts in the clinical ward of hospitals completed the Present Mood States List of Engelmann at the beginning and end of the first and last days of each shift. Analysis indicated (a) nurses had a stable emotional profile, present at the working shift, and (b) variations in present mood states related to specific effects of shift work were observed when comparisons were made between the present mood states at the beginning and end of each shift duty.     

Troubles with Theoretical Virtues: Resisting Theoretical Utility Arguments in Metaphysics

In this paper we examine theoretical utility arguments in metaphysics. While philosophers claim a procedural continuity with science when using such arguments, we argue that examining famous instances from the history of science expose their fundamental flaws. We find that arguments from theoretical utility invoke considerations that are not truth conducive and that justifications for claims that a theory possesses theoretical virtues often assume the truth of the theory such virtues are supposed to support. We conclude that theoretical utility arguments provide no epistemic grounds for metaphysical inquiry.