-/- Continuous first-order logic has found interest among model theorists who wish to extend the classical analysis of “algebraic” structures (such as fields, group, and graphs) to various natural classes of complete metric structures (such as probability algebras, Hilbert spaces, and Banach spaces). With research in continuous first-order logic preoccupied with studying the model theory of this framework, we find a natural question calls for attention. Is there an interesting set of axioms yielding a completeness result? -/- The primary purpose (...) of this article is to show that a certain, interesting set of axioms does indeed yield a completeness result for continuous first-order logic. In particular, we show that in continuous first-order logic a set of formulae is (completely) satisfiable if (and only if) it is consistent. From this result it follows that continuous first-order logic also satisfies an approximated form of strong completeness, whereby Σ⊧φ (if and) only if Σ⊢φ ∸2−n for all n < ω. This approximated form of strong completeness asserts that if Σ⊧φ, then proofs from Σ, being finite, can provide arbitrarily better approximations of the truth of φ. -/- Additionally, we consider a different kind of question traditionally arising in model theory—that of decidability. When is the set of all consequences of a theory (in a countable, recursive language) recursive? Say that a complete theory T is decidable if for every sentence φ, the value φ T is a recursive real, and moreover, uniformly computable from φ. If T is incomplete, we say it is decidable if for every sentence φ the real number φ T o is uniformly recursive from φ, where φ T o is the maximal value of φ consistent with T. As in classical first-order logic, it follows from the completeness theorem of continuous first-order logic that if a complete theory admits a recursive (or even recursively enumerable) axiomatization then it is decidable. (shrink)

© 2016 Elsevier LtdJumping spiders are famous for their visually driven behaviors [1]. Here, however, we present behavioral and neurophysiological evidence that these animals also perceive and respond to airborne acoustic stimuli, even when the distance between the animal and the sound source is relatively large and with stimulus amplitudes at the position of the spider of ∼65 dB sound pressure level. Behavioral experiments with the jumping spider Phidippus audax reveal that these animals respond to low-frequency sounds by freezing—a common (...) anti-predatory behavior characteristic of an acoustic startle response. Neurophysiological recordings from auditory-sensitive neural units in the brains of these jumping spiders showed responses to low-frequency tones —recordings that also represent the first record of acoustically responsive neural units in the jumping spider brain. Responses persisted even when the distances between spider and stimulus source exceeded 3 m and under anechoic conditions. Thus, these spiders appear able to detect airborne sound at distances in the acoustic far-field region, beyond the near-field range often thought to bound acoustic perception in arthropods that lack tympanic ears [2]. Furthermore, direct mechanical stimulation of hairs on the patella of the foreleg was sufficient to generate responses in neural units that also responded to airborne acoustic stimuli—evidence that these hairs likely play a role in the detection of acoustic cues. We suggest that these auditory responses enable the detection of predators and facilitate an acoustic startle response. Video. (shrink)

Continuous first-order logic has found interest among model theorists who wish to extend the classical analysis of “algebraic” structures to various natural classes of complete metric structures. With research in continuous first-order logic preoccupied with studying the model theory of this framework, we find a natural question calls for attention. Is there an interesting set of axioms yielding a completeness result?The primary purpose of this article is to show that a certain, interesting set of axioms does indeed yield a completeness (...) result for continuous first-order logic. In particular, we show that in continuous first-order logic a set of formulae is satisfiable if it is consistent. From this result it follows that continuous first-order logic also satisfies an approximated form of strong completeness, whereby Σ⊨φ only if Σ⊢φ∸ 2-n for all n < ω. This approximated form of strong completeness asserts that if Σ⊨φ, then proofs from Σ, being finite, can provide arbitrarily better approximations of the truth of φ.Additionally, we consider a different kind of question traditionally arising in model theory—that of decidability. When is the set of all consequences of a theory recursive? Say that a complete theory T is decidable if for every sentence φ, the value φT is a recursive real, and moreover, uniformly computable from φ. If T is incomplete, we say it is decidable if for every sentence φ the real number φT∘ is uniformly recursive from φ, where φT∘is the maximal value of φ consistent with T. As in classical first-order logic, it follows from the completeness theorem of continuous first-order logic that if a complete theory admits a recursive axiomatization then it is decidable. (shrink)

The impact of Nietzsche's engagement with the Greek skeptics has never before been systematically explored in a book-length work - an inattention that belies the interpretive weight scholars otherwise attribute to his early career as a professor of classical philology and to the fascination with Greek literature and culture that persisted throughout his productive academic life. Jessica N. Berry fills this gap in the literature on Nietzsche by demonstrating how an understanding of the Pyrrhonian skeptical tradition illuminates Nietzsche's own reflections (...) on truth, knowledge, and ultimately, the nature and value of philosophic inquiry. This entirely new reading of Nietzsche's epistemological and ethical views promises to make clear and render coherent his provocative but often opaque remarks on the topics of truth and knowledge and to grant us further insight into his ethics-since the Greek skeptics, like Nietzsche, take up the position they do as a means of promoting well-being and psychological health. In addition, it allows us to recover a portrait of Nietzsche as a philologist and philosophical psychologist that has been too often obscured by commentaries on his thought. "The book addresses a number of central issues in Nietzsche's philosophy, including perspectivism and his conception of truth. The idea that his views in these areas owe much to the ancient Pyrrhonists casts them in an important new light, and is well supported by the texts. A lot of people from a lot of different areas in philosophy will have good reason to take notice." - Richard Bett, Johns Hopkins University. (shrink)

Study of Śivasvarodaya, work on yoga; includes original Sanskrit text with English translation.

Dictionary of Nyaya terminology ; English and Sanskrit interpretation.

Savīyahʹhā-yi maʻrifatʹāfarīn-i nafs -- Falsafah-yi Ṣadrā -- Falsafahʹī barā-yi zīstan-i safar-i ʻishq.

This edition presents the first complete English translation of N.N. Ladygina-Kohts' journal chronicling her pioneering work with the chimpanzee, Joni. The journal entries describe and compare the instincts, emotions, play, and habits of her son Rudy and Joni as each develops.

Context: Technology has not only changed the way we teach mathematical concepts but also the nature of knowledge, and thus what is possible to learn. While geometric transformations are recognized to be foundational to the formation of students’ geometric conceptions, little research has focused on how these notions can be introduced in elementary schooling. Problem: This project addressed the need for development of students’ reasoning about and with geometric transformations in elementary school. We investigated the nature of students’ understandings of (...) translations, rotations, scaling, and stretching in two dimensions in the context of use of the software application Graphs ’n Glyphs. More specifically, we explored the question “What is the nature of elementary students’ reasoning of geometric transformations when instruction exploits the technological tool Graphs ’n Glyphs?” Method: Using a design research perspective, we present the conduct of a teaching experiment with one pair of fourth-graders, studying translation and rotation. The project investigated how and to what extent activity using Graphs ’n Glyphs can elicit students’ reasoning about geometric transformations, and explored the constraints and affordances of Graphs ’n Glyphs for thinking-in-change about geometric transformations. Results: The students proved adept using the software with carefully designed tasks to explore the behavior of two-dimensional shapes, distinguish among transformations, and develop predictions. In relation to varied conditions of transformations, they formed generalizations about the way a shape behaves, including the use of referent points in predicting outcomes of translations, and recognizing the role of the center of rotation. Implications: The generalizations that the students developed are foundational for developing an understanding of the properties of transformations in the later years of schooling. Dynamic technological approaches to geometry may prove as valuable to elementary students’ understanding of geometry as it is for older students. Constructivist content: This study contributes to ongoing constructivism/constructionism conversations by concentrating on the transformation of ideas when engaging learners in activity through particular contexts and tools. Key Words: Geometry, transformations, constructionist technologies. (shrink)