This book contains an introduction to mathematical proofs, including fundamental material on logic, proof methods, set theory, number theory, relations, functions, cardinality, and the real number system. The book is divided into approximately fifty brief lectures. Each lecture corresponds rather closely to a single class meeting.

We agree with Branigan & Pickering that structural priming experiments should supplant grammaticality judgments for testing linguistic representation. However, B&P overlook a vast linguistic literature that converges with – but extends – the experimental findings. B&P conclude that syntax is functionally independent of the lexicon. We argue that a broader approach to priming reveals cracks in the façade of syntactic autonomy.

Acoustical changes in the prosody of mothers’ speech to infants are distinct and near universal. However, less is known about the visible properties of mothers’ infant-directed (ID) speech, and their relation to speech acoustics. Mothers’ head movements were tracked as they interacted with their infants using ID speech, and compared to movements accompanying their adult-directed (AD) speech. Movement measures along three dimensions of head translation, and three axes of head rotation were calculated. Overall, more head movement was found for ID (...) than AD speech, suggesting that mothers exaggerate their visual prosody in a manner analogous to the acoustical exaggerations in their speech. Regression analyses examined the relation between changing head position and changing acoustical pitch ( F0 ) over time. Head movements and voice pitch were more strongly related in ID speech than in AD speech. When these relations were examined across time windows of different durations, stronger relations were observed for shorter time windows (< 5 sec). However, the particular form of these more local relations did not extend or generalize to longer time windows. This suggests that the multimodal correspondences in speech prosody are variable in form, and occur within limited time spans. (shrink)

This article examines Abu Nasr al-Farabı (c. 872–950/1) on the topic of intentionality, with particular focus on how intentionality is integral for the constitution of the intellect within his psychology. Unfortunately, targeted study of al-Farabı’s doctrine of intentionality has been largely neglected since Kwame Gyekye’s 1971 essay, The Terms ‘Prima Intentio’ and ‘Secunda Intentio’ in Arabic Logic. Gyekye showed that the Arabic (and thus the Latin) doctrine of first and second intention originated within the texts of al-Farabı,not the texts of (...) Avicenna, as had been previously thought. In response, this article aims to show three things. First, while the doctrine of first and second intention appears in al-Farabı’s texts, it is not as clearly developed or defined as is presented in Gyekye’s 1971 article. al-Farabı both lacks consistent technical terminology for the doctrine (as he discusses it across disparate sciences, in unrelated contexts) and develops it far too little to fully flesh out his doctrine. Second, even given the fact that al-Farabı’s discussion of intentionality is underdeveloped, Gyekye was right to credit the doctrine to him. And third, al-Farabı’s doctrine of first and second intention is not merely important to understand his positions regarding signification and universals; they play a pivotal role in the constitution of the human intellect. (shrink)

Researchers have proposed that blocking facial feedback via glabellar-region botulinum toxin injections can reduce depression. Random-effects meta-analyses of studies that administered GBTX...

An experiment examined goal understanding and how perceivers’ suspiciousness was associated with the accuracy, valence, and certainty of their inferences about a pursuer’s goal. In initial interactions, one dyad member was randomly assigned as the pursuer, and the other was the perceiver. The congruency of the perceiver’s and the pursuer’s conversation goals and the perceiver’s cognitive busyness were manipulated. Results confirmed that accuracy decreased as perceivers’ suspiciousness increased only for not-busy perceivers in the goal-discord condition because perceivers’ inferences were negatively (...) valenced. Results also supported the hypotheses that certainty decreased as perceivers’ suspiciousness increased only for not-busy perceivers in the goal-discord condition and that certainty increased as perceivers’ suspiciousness increased both for not-busy perceivers in the identical-goal condition and for busy perceivers in the goal-discord condition. (shrink)

Proper conduct of an AIDS vaccine trial in Africa must be informed not only by the epidemiology and biology of HIV infection in African settings, but also by the ethical norms and cultural constraints prevailing in African settings.

Acoustical changes in the prosody of mothers’ speech to infants are distinct and near universal. However, less is known about the visible properties of mothers’ infant-directed speech, and their relation to speech acoustics. Mothers’ head movements were tracked as they interacted with their infants using ID speech, and compared to movements accompanying their adult-directed speech. Movement measures along three dimensions of head translation, and three axes of head rotation were calculated. Overall, more head movement was found for ID than AD (...) speech, suggesting that mothers exaggerate their visual prosody in a manner analogous to the acoustical exaggerations in their speech. Regression analyses examined the relation between changing head position and changing acoustical pitch over time. Head movements and voice pitch were more strongly related in ID speech than in AD speech. When these relations were examined across time windows of different durations, stronger relations were observed for shorter time windows. However, the particular form of these more local relations did not extend or generalize to longer time windows. This suggests that the multimodal correspondences in speech prosody are variable in form, and occur within limited time spans. (shrink)

Acoustical changes in the prosody of mothers’ speech to infants are distinct and near universal. However, less is known about the visible properties of mothers’ infant-directed speech, and their relation to speech acoustics. Mothers’ head movements were tracked as they interacted with their infants using ID speech, and compared to movements accompanying their adult-directed speech. Movement measures along three dimensions of head translation, and three axes of head rotation were calculated. Overall, more head movement was found for ID than AD (...) speech, suggesting that mothers exaggerate their visual prosody in a manner analogous to the acoustical exaggerations in their speech. Regression analyses examined the relation between changing head position and changing acoustical pitch over time. Head movements and voice pitch were more strongly related in ID speech than in AD speech. When these relations were examined across time windows of different durations, stronger relations were observed for shorter time windows. However, the particular form of these more local relations did not extend or generalize to longer time windows. This suggests that the multimodal correspondences in speech prosody are variable in form, and occur within limited time spans. (shrink)

Opponents of abortion are commonly said to be inconsistent in their beliefs or actions, and to fail in their obligations to prevent the deaths of embryos and fetuses from causes other than induced...

Freedom to smoke is part and parcel of overall freedom. The former cannot be abrogated without violating the latter. The present paper applies this insight to the regulations placed on the tobacco industry and smoking in general. We find that government interventions into people’s lives regarding smoking are highly incompatible with libertarian principles. We examine many regulations such as prohibiting youths from smoking, preventing second hand smoke, restrictions on advertising, taxing the industry, and liability issues.

"A complete and unified account of Plato's epistemology... scholarly, historically sensitive, and philosophically sophisticated. Above all it is sensible.... White's strength is that he places Plato's preoccupation in careful historical perspective, without belittling the intrinsic difficulties of the problems he tackled.... White's project is to find a continuous argument running through Plato's various attacks on epistemological problems. No summary can do justice to his remarkable success." --Ronald B. De Sousa, University of Toronto, in Phoenix.

Can a person privileged in some respect understand what it is like to be disprivileged in that respect? Some say yes; some say no. I argue that both positions are correct, because ‘understand what it is like to be disprivileged’ is ambiguous. Sometimes, it means grasp of the character of particular experiences of disprivileged people. Privileged people can achieve this. Sometimes, it means grasp of the general character shared by experiences of disprivileged people. Privileged people cannot achieve this. However, there (...) is a general kind of understanding that they can achieve: understanding of why individual experiences have their character, in relation to privilege and disprivilege. This understanding is a skill, not knowledge. It is difficult and discomforting for the privileged to acquire and is easily conflated with knowledge of general experiential character. Distinguishing and characterizing these kinds of understanding clarifies whether, and how, the privileged might understand what it is like to be disprivileged. (shrink)

This Element is a concise, high-level introduction to the philosophy of physical symmetry. It begins with the notion of `physical representation' (the kind of empirical representation of nature that we effect in doing physics), and then lays out the historically and conceptually central case of physical symmetry that frequently falls under the rubric of 'the Relativity Principle', or 'Galileo's Ship. This material is then used as a point of departure to explore the key hermeneutic challenge concerning physical symmetry in the (...) last century, namely understanding the physical significance of the notion of 'local' gauge symmetry. The approach taken stresses both the continuity with historically important themes such as the Relativity Principle, as well as novel insights earned by working with contemporary media such as the covariant phase space and derived critical locus formalisms. (shrink)