In this paper, we give an example of a complete computable infinitary theory T with countable models ${\mathcal{M}}$ and ${\mathcal{N}}$ , where ${\mathcal{N}}$ is a proper computable infinitary extension of ${\mathcal{M}}$ and T has no uncountable model. In fact, ${\mathcal{M}}$ and ${\mathcal{N}}$ are (up to isomorphism) the only models of T. Moreover, for all computable ordinals α, the computable ${\Sigma_\alpha}$ part of T is hyperarithmetical. It follows from a theorem of Gregory (JSL 38:460–470, 1972; Not Am Math Soc 17:967–968, 1970) (...) that if T is a Π 1 1 set of computable infinitary sentences and T has a pair of models ${\mathcal{M}}$ and ${\mathcal{N}}$ , where ${\mathcal{N}}$ is a proper computable infinitary extension of ${\mathcal{M}}$ , then T would have an uncountable model. (shrink)

'This book is a masterpiece of theoretical thought. It anticipates the actual achievements of much of what we now call sociolinguistics.

Several researchers have recently established that for every Turing degree \, the real closed field of all \-computable real numbers has spectrum \. We investigate the spectra of real closed fields further, focusing first on subfields of the field \ of computable real numbers, then on archimedean real closed fields more generally, and finally on non-archimedean real closed fields. For each noncomputable, computably enumerable set C, we produce a real closed C-computable subfield of \ with no computable copy. Then we (...) build an archimedean real closed field with no computable copy but with a computable enumeration of the Dedekind cuts it realizes, and a computably presentable nonarchimedean real closed field whose residue field has no computable presentation. (shrink)

Ocherk 1. Voprosy ontologii -- Ocherk 2. Voprosy ėtiki i ėstetiki -- Ocherk 3. Voprosy gnoseologii i aksiologii.

Because the techno-economic paradigm of contemporary conceptualizations of innovation is often taken for granted in the literature, this chapter opens up this self-evident notion. First, the chapter consults the work of Joseph Schumpeter, who can be seen as the founding father of the current conceptualization of innovation as technological and commercial. Second, we open up the concept by reflecting on two aspects of Schumpeter’s conceptualization of innovation, namely its destructive and its constructive aspect, based on findings in the history of (...) innovation. Finally, we synthesize our findings and propose an ontic-ontological conceptualization of innovation as ontogenetic process and outcome with six dimensions—newness, political dimension, economic dimension, temporal dimension, human dimension and risk—that moves beyond its technological and commercial orientation. (shrink)

Research on brain or cognitive/affective processes, culture, social interaction, and structural analysis are overlapping but often independent ways humans have attempted to understand the origins of their evolution, historical, and contemporary development. Each level seeks to employ its own theoretical concepts and methods for depicting human nature and categorizing objects and events in the world, and often relies on different sources of evidence to support theoretical claims. Each level makes reference to different temporal bandwidths (milliseconds, seconds, minutes, hours, days, months, (...) years, decades, and centuries) and focuses on different spatio-temporal activities and controlled and non-controlled stimulus conditions. Biological mechanisms and environmental pressures for survival simultaneously created a gradual intersection and enhancement of cognitive/affective skills, cultural practices, and changes in collaborative social interaction and communicative skills. The evolution of a given level of analysis is assumed to have been incremental and overlapping. These innovative and independent ways humans have learned to characterize their brain or cognitive/affective and social/economic/political life often depend on unexamined, representational re-descriptions or cognitive/affective and socio-cultural devices and forms of communication that facilitate the depiction of practices and beliefs we attribute to respondents or subjects and research colleagues. (shrink)

Russkai︠a︡ t︠erkovʹ i drugie statʹi -- V temnykh religioznykh luchakh.

The "mathematization" of knowledge is a historically inevitable process governed by two circumstances. In the first place there is the need for the further extension of knowledge in all areas of human activity, whether it be the study of natural phenomena or the theory of taking decisions in the economic or social sphere. Marx pointed out long ago that a science reaches its highest levels only when it succeeds in making use of mathematics. The second circumstance rendering the process of (...) deepening and broadening the mathematization of knowledge not only necessary but possible lies in the constant development both of mathematics itself and of the technical means broadening the sphere of its application. (shrink)

On verbal epistemology of the neo-Nyaya school in Indic philosophy; includes Sanskrit text, Apūrvavāda from Nyāyasiddhāntadīpa of Śaśadhara.

T. 1. Opytʺ psikhologicheskoĭ istorīi i kritiki osnovnykhʺ voprosovʺ zhizni. 3. izd. 1905.--T. 2. Metafizika zhizni i khrīstianskoe otkrovenīe. 2. izd. 1906.

В книге очерки Владимира Брагинского в жанре ироничного эссе о любви.