We survey the history of Shelah’s conjecture on strongly dependent fields, give an equivalent formulation in terms of a classification of strongly dependent fields and prove that the conjecture implies that every strongly dependent field has finite dp-rank.

In this paper, the notion of sustainability as a general regulative idea is distinguished from sustainable development as a more concrete concept leading to practical actions. After that, different economic meanings of sustainable development are discussed, and a concept of critical sustainability is proposed especially with respect to the problem of climate change. Maintaining critical crash barriers and bottlenecks presupposes, however, demanding, continuous improvements in energy efficiency. After discussing problems of decision theory in cases of uncertainty, which is constitutive for (...) climate change, the links between intragenerational and intergenerational justice are analyzed, and by using Barry's notion of justice and Goodin's concept of vulnerability, two possible positions of the general idea of fairness inherent in sustainable development are presented. We conclude by shortly sketching the notion of sufficiency as an additional supplementary sustainability strategy in cases where efficiency improvements based on innovation are less than sufficient for securing the (energetic) fundaments of economic activity and human life. (shrink)

Argument“The problem of university courses on infinitesimal calculus and their demarcation from infinitesimal calculus in high schools” is the published version of an address Otto Toeplitz delivered at a meeting of the German Mathematical Society held in Düsseldorf in 1926. It contains the most detailed exposition of Toeplitz's ideas about mathematics education, particularly his thinking about the role of the history of mathematics in mathematics education, which he called the “genetic method” to teaching mathematics. The tensions and assumptions about mathematics, (...) history of mathematics, and historiography revealed in this piece dedicated to educational ideas are what make Toeplitz's text interesting in the study of historiography of mathematics. In general, the ways historiography of mathematics and teaching of mathematics, even without an immediate concern for history, are deeply entangled and, in our view, worth attention both in historical and educational research. (shrink)

We initiate the study of definable [Formula: see text]-topologies and show that there is at most one such [Formula: see text]-topology on a [Formula: see text]-henselian NIP field. Equivalently, we show that if [Formula: see text] is a bi-valued NIP field with [Formula: see text] henselian, then [Formula: see text] and [Formula: see text] are comparable. As a consequence, Shelah’s conjecture for NIP fields implies the henselianity conjecture for NIP fields. Furthermore, the latter conjecture is proved for any field admitting (...) a henselian valuation with a dp-minimal residue field. We conclude by showing that Shelah’s conjecture is equivalent to the statement that any NIP field not contained in the algebraic closure of a finite field is [Formula: see text]-henselian. (shrink)

Concept of Avidyā in the Vedānta philosophy of Śaṅkarācārya; a study.

Study of Vedāntasiddhāntamuktāvalī, treatise on Hindu Advaita (non-dualistic) Vedanta philosophy, by Prakāśānanda, 16th cent.

On philosophy; transcript of the 1978-1979 Śāradā-vyākhyāna-mālā lecture, under the auspices of Sri Lal Bahadur Shastri Rashtriya Vidyapeeth, New Delhi.

Singularity Hypotheses: A Scientific and Philosophical Assessment offers authoritative, jargon-free essays and critical commentaries on accelerating technological progress and the notion of technological singularity. It focuses on conjectures about the intelligence explosion, transhumanism, and whole brain emulation. Recent years have seen a plethora of forecasts about the profound, disruptive impact that is likely to result from further progress in these areas. Many commentators however doubt the scientific rigor of these forecasts, rejecting them as speculative and unfounded. We therefore invited prominent (...) computer scientists, physicists, philosophers, biologists, economists and other thinkers to assess the singularity hypotheses. Their contributions go beyond speculation, providing deep insights into the main issues and a balanced picture of the debate. (shrink)

Mikhail Psel i vizantiĭskii︠a︡t khumanizŭm na XI vek -- Palamitskite sporove.

Study of Suddhadvaita philosophy with reference to other system of Hindu philosophy.

The articles included in this Volume represent a broad and highly qualified view on the present state of general relativity, quantum gravity, and their cosmological and astrophysical implications. As such, it may serve as a valuable source of knowledge and inspiration for experts in these fields, as well as an advanced source of information for young researchers. The occasion to gather together so many leading experts in the field was to celebrate the centenary of Einstein's stay in Prague in 1911-1912. (...) It was in fact during his stay in Prague that Einstein started in earnest to develop his ideas about general relativity that fully developed in his paper in 1915. Approaching soon the centenary of his famous paper, this volume offers a precious overview of the path done by the scientific community in this intriguing and vibrant field in the last century, defining the challenges of the next 100 years. The content is divided into four broad parts: (i) Gravity and Prague, (ii) Classical General Relativity, (iii) Cosmology and Quantum Gravity, and (iv) Numerical Relativity and Relativistic Astrophysics. (shrink)