We analyse the connection between the computability and continuity of functions in the case of homomorphisms between topological algebraic structures. Inspired by the Pour-El and Richards equivalence theorem between computability and boundedness for closed linear operators on Banach spaces, we study the rather general situation of partial homomorphisms between metric partial universal algebras. First, we develop a set of basic notions and results that reveal some of the delicate algebraic, topological and effective properties of partial algebras. Our main computability concepts (...) are based on numerations and include those of effective metric partial algebras and effective partial homomorphisms. We prove a general equivalence theorem that includes a version of the Pour-El and Richards Theorem, and has other applications. Finally, the Pour-El and Richards axioms for computable sequence structures on Banach spaces are generalised to computable partial sequence structures on metric algebras, and we prove their equivalence with our computability model based on numerations. (shrink)

We analyse the connection between the computability and continuity of functions in the case of homomorphisms between topological algebraic structures. Inspired by the Pour-El and Richards equivalence theorem between computability and boundedness for closed linear operators on Banach spaces, we study the rather general situation of partial homomorphisms between metric partial universal algebras. First, we develop a set of basic notions and results that reveal some of the delicate algebraic, topological and effective properties of partial algebras. Our main computability concepts (...) are based on numerations and include those of effective metric partial algebras and effective partial homomorphisms. We prove a general equivalence theorem that includes a version of the Pour-El and Richards Theorem, and has other applications. Finally, the Pour-El and Richards axioms for computable sequence structures on Banach spaces are generalised to computable partial sequence structures on metric algebras, and we prove their equivalence with our computability model based on numerations. (shrink)

This volume features in-depth philosophical analyses of major Japanese Confucian philosophers as well as themes and topics addressed in their writings. Its main historical focus is the early-modern period (1600-1868), when much original Confucian philosophizing occurred. Written by scholars from the United States, Canada, Europe, Australia, Japan, and China and eclectic in methodology and disciplinary approach, this anthology seeks to advance new multidimensional studies of Japanese Confucian philosophy for English language readers. It presents essays that focus on Japanese Confucianism, while (...) including topics related to Buddhism, Shintō, Nativism, and even Andō Shōeki (1703-1762), one of the most vehement critics of Confucianism in all of East Asia. The book builds on the premise that Japanese Confucian philosophy consists in the ongoing engagement in critical, self-reflective discussions of and speculative theorizing about ethics, epistemology, metaphysics, political theory, and spiritual problems, as well as aesthetics, cosmology, and ontology. (shrink)

Volume one. History -- volume two. Philosophy -- volume three. Religion -- volume four. Translations.

: Most discussions of Yamaga Soko's philosophical development as a Confucian scholar in Tokugawa Japan suggest that in his later years he moved away from Confucianism and toward a religio-philosophical celebration of Japan's supposed uniqueness. It is shown here, however, that Soko's nativism, set forth in his Chucho jijitsu, was later eclipsed by his final philosophical work, the Gengen hakki, wherein he articulated a kind of naturalistic numerology, based vaguely on the Yijing. This shift in Soko's thought can be viewed (...) as a return to Neo-Confucianism, the earliest philosophical paradigm that he had embraced. Moreover, the successive shifts in his thinking can be understood in terms of the vicissitudes of his life, first in his exile to the Kansai area, near the ancient imperial capital of Kyoto, and then later in his pardon and return to Edo, the shogun's capital. Perhaps most importantly, this final shift in Soko's thought reveals that this prominent early modern thinker did reach his philosophical climax not in defiant opposition to Neo-Confucianism, nor in a sustained celebration of Japan's political traditions and their superlative nature, but instead in a return to modes of metaphysics akin to those typically deployed by Neo- Confucians themselves in their attempts to understand the changing nature of the cosmos and their political place within its flux. (shrink)

Earlier, we have studied computations possible by physical systems and by algorithms combined with physical systems. In particular, we have analysed the idea of using an experiment as an oracle to an abstract computational device, such as the Turing machine. The theory of composite machines of this kind can be used to understand (a) a Turing machine receiving extra computational power from a physical process, or (b) an experimenter modelled as a Turing machine performing a test of a known physical (...) theory T.Our earlier work was based upon experiments in Newtonian mechanics. Here we extend the scope of the theory of experimental oracles beyond Newtonian mechanics to electrical theory. First, we specify an experiment that measures resistance using a Wheatstone bridge and start to classify the computational power of this experimental oracle using non-uniform complexity classes. Secondly, we show that modelling an experimenter and experimental procedure algorithmically imposes a limit on our ability to measure resistance by the Wheatstone bridge.The connection between the algorithm and physical test is mediated by a protocol controlling each query, especially the physical time taken by the experimenter. In our studies we find that physical experiments have an exponential time protocol; this we formulate as a general conjecture. Our theory proposes that measurability in Physics is subject to laws which are co-lateral effects of the limits of computability and computational complexity. (shrink)

Earlier, we have studied computations possible by physical systems and by algorithms combined with physical systems. In particular, we have analysed the idea of using an experiment as an oracle to an abstract computational device, such as the Turing machine. The theory of composite machines of this kind can be used to understand (a) a Turing machine receiving extra computational power from a physical process, or (b) an experimenter modelled as a Turing machine performing a test of a known physical (...) theory T. Our earlier work was based upon experiments in Newtonian mechanics. Here we extend the scope of the theory of experimental oracles beyond Newtonian mechanics to electrical theory. First, we specify an experiment that measures resistance using a Wheatstone bridge and start to classify the computational power of this experimental oracle using non-uniform complexity classes. Secondly, we show that modelling an experimenter and experimental procedure algorithmically imposes a limit on our ability to measure resistance by the Wheatstone bridge. The connection between the algorithm and physical test is mediated by a protocol controlling each query, especially the physical time taken by the experimenter. In our studies we find that physical experiments have an exponential time protocol, this we formulate as a general conjecture. Our theory proposes that measurability in Physics is subject to laws which are co-lateral effects of the limits of computability and computational complexity. (shrink)

We have begun a theory of measurement in which an experimenter and his or her experimental procedure are modeled by algorithms that interact with physical equipment through a simple abstract interface. The theory is based upon using models of physical equipment as oracles to Turing machines. This allows us to investigate the computability and computational complexity of measurement processes. We examine eight different experiments that make measurements and, by introducing the idea of an observable indicator, we identify three distinct forms (...) of measurement process and three types of measurement algorithm. We give axiomatic specifications of three forms of interfaces that enable the three types of experiment to be used as oracles to Turing machines, and lemmas that help certify an experiment satisfies the axiomatic specifications. For experiments that satisfy our axiomatic specifications, we give lower bounds on the computational power of Turing machines in polynomial time using nonuniform complexity classes. These lower bounds break the barrier defined by the Church-Turing Thesis. (shrink)

An algebra is effective if its operations are computable under some numbering. When are two numberings of an effective partial algebra equivalent? For example, the computable real numbers form an effective field and two effective numberings of the field of computable reals are equivalent if the limit operator is assumed to be computable in the numberings . To answer the question for effective algebras in general, we give a general method based on an algebraic analysis of approximations by elements of (...) a finitely generated subalgebra. Commonly, the computable elements of a topological partial algebra are derived from such a finitely generated algebra and form a countable effective partial algebra. We apply the general results about partial algebras to the recursive reals, ultrametric algebras constructed by inverse limits, and to metric algebras in general. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. (shrink)

Written as companion texts, the Bendō 弁道 and the Benmei 弁名 present Ogyū Sorai’s most mature and comprehensive expression of his philosophical thought. Sorai modestly spoke of the texts in a letter to a student, Uno Shirō 宇野士朗, calling them “my humble achievements”. In another letter to a student, Yamagata Shūnan 山県周南, Sorai related that after a prolonged bout with ill-health, he feared passing like the morning dew. Therefore, he took up his writing brush and completed the two works. Sorai (...) added that while more than a millennium had passed since Confucius’ death, the Way had only been clarified in recent times. Yet rather than boast of this, Sorai suggested that his hand in the process had been by heaven’s decree. With the two works, he added that even if he passed away soon, his life would not have been wasted. (shrink)

John Tucker; III—Constructivity and Grammar, Proceedings of the Aristotelian Society, Volume 63, Issue 1, 1 June 1963, Pages 45–66, https://doi.org/10.1093/aris.

Shibusawa Eiichi, widely known as the father of Japanese capitalism, was also one of the more outspoken advocates of Confucius’ learning in modern Japan. This paper examines Shibusawa's The Analects and the Abacus in relation to Max Weber's assessment of Confucian cultures and their inability to develop, early on, capitalism. Without making grand claims about Confucianism and capitalism, the paper suggests that Weber's life and thought constitute considerable counterevidence vis‐à‐vis Weber's thesis. The paper also examines Shibusawa's thoughts about China in (...) an effort to offer a historical contextualization of Shibusawa's promotion of Confucius’ thought. (shrink)

John Tucker; II.—Godel and Epimenides, Proceedings of the Aristotelian Society, Volume 59, Issue 1, 1 June 1959, Pages 25–48, https://doi.org/10.1093/aristoteli.

John Tucker; II.—Godel and Epimenides, Proceedings of the Aristotelian Society, Volume 59, Issue 1, 1 June 1959, Pages 25–48, https://doi.org/10.1093/aristoteli.

John Tucker; IX—Rules Automata and Mathematics, Proceedings of the Aristotelian Society, Volume 70, Issue 1, 1 June 1970, Pages 161–180, https://doi.org/10.1093.

John Tucker; II.—Godel and Epimenides, Proceedings of the Aristotelian Society, Volume 59, Issue 1, 1 June 1959, Pages 25–48, https://doi.org/10.1093/aristoteli.

John Tucker; III—Constructivity and Grammar, Proceedings of the Aristotelian Society, Volume 63, Issue 1, 1 June 1963, Pages 45–66, https://doi.org/10.1093/aris.

The imperative that Japanese philosophy faces today, I assert, is the imperative of environmental philosophy. It is an imperative that has decidedly global origins and indisputable global significance. In discussing this imperative, I revive some age-old, perhaps idealistic, and even romantic themes from East Asian Confucian thinking in the hopes that they might become more central motifs of Japanese philosophizing, charting a way forward in the wake of Fukushima, toward a more sustainable future. In the process, I critique admixtures of (...) environmentalism and nationalism, seeking to elevate instead an ecologically sound philosophical perspective that is more globally inclined than narrowly nationalistic. (shrink)

This chapter surveys the philosophical vicissitudes of the ancient Confucian classic, the Mencius, in Japanese history, from the earliest references in the eighth century through contemporary times. It highlights the contested, controversial reception of the Mencius which no doubt had virtually everything to do not with its position on human nature but rather its relatively unequivocal readiness to confront the problem of tyrannic government and deal with it in no uncertain terms, remonstrating with those tyrants willing to listen and then, (...) if need be, punishing those pretending to be legitimate rulers. Accompanying its forthright activism, the Mencius also emphasized the role of the people in mediating heaven’s ultimate authority over those in power. Needless to say, the Mencius’s positions on these matters did not make it a popular text with those presuming to have authority and control at the highest levels, though it did have an enduring appeal to politically-minded people who understood fully the Confucian position that rulers should rule virtuously and compassionately as the father and mother of the people. (shrink)

This paper explores Ogyū Sorai’s 荻生徂徠 thinking on the most sensational and controversial incident of eighteenth-century Japan, and perhaps the most well-known in all Japanese history, the forty-seven rōnin incident of 1701–1703. Viewed in relation to his lifework, Sorai’s views on the incident are significant insofar as they reveal the extent to which his philosophical thinking was occasionally shaped decisively by neither ancient Chinese nor later Confucian texts, Neo- or otherwise, but instead by formative life-experiences he had as a youth (...) living in exile. No doubt, Confucian and Neo-Confucian notions, which Sorai knew in-depth, helped him filter, epistemologically, events, issues, and most importantly what he understood to be righteous and just behaviour in a polity. Yet ironically enough, Sorai’s thinking on the rōnin incident shows that however philosophically erudite, cosmopolitan, and urbane he was as an intellectual, his appraisals of things sometimes harked back to rural experiences he had early on with some of the most primitive and foundational expressions of human agency, civilization, and socio-political ethics in early-eighteenth century Japan. In the process, Sorai’s essay reveals, through its later resonance with some Meiji thought, how his views on those same primitive expressions remained relevant even in modern contexts. (shrink)