The notion of an algebraic semantics of a deductive system was proposed in [3], and a preliminary study was begun. The focus of [3] was the definition and investigation of algebraizable deductive systems, i.e., the deductive systems that possess an equivalent algebraic semantics. The present paper explores the more general property of possessing an algebraic semantics. While a deductive system can have at most one equivalent algebraic semantics, it may have numerous different algebraic semantics. All of these give rise to (...) an algebraic completeness theorem for the deductive system, but their algebraic properties, unlike those of equivalent algebraic semantics, need not reflect the metalogical properties of the deductive system. Many deductive systems that don't have an equivalent algebraic semantics do possess an algebraic semantics; examples of these phenomena are provided. It is shown that all extensions of a deductive system that possesses an algebraic semantics themselves possess an algebraic semantics. Necessary conditions for the existence of an algebraic semantics are given, and an example of a protoalgebraic deductive system that does not have an algebraic semantics is provided. The mono-unary deductive systems possessing an algebraic semantics are characterized. Finally, weak conditions on a deductive system are formulated that guarantee the existence of an algebraic semantics. These conditions are used to show that various classes of non-algebraizable deductive systems of modal logic, relevance logic and linear logic do possess an algebraic semantics. (shrink)

The Platonic MS. Vat. gr. 225 contains tetr. I, VI. 3, 4, II–IV, while its companion volume in the same hand Vat. gr. 226 contains V–VI. 2, VIII. 3, VII, Spp., VIII. 1, 2. Posts states that for tetr. I and VI. 3 A is close to Vind. suppl. gr. 7 and thereafter derives from the Clarkianus . I am here concerned only with the testimony of Δ in. 2 . This manuscript has been largely ignored by commentators and editors. (...) Schanz does not quote it, nor does Bekker . Alline is scornful about it. Neither Burnet nor Croiset quotes it—and indeed Burnet claims that it is merely an interpolated apograph of W. Stallbaum seems to be the only editor who quotes it for Apol. This appears to be an unwarranted neglect since A has, in fact, a good claim to be considered as a primary witness in this dialogue. (shrink)

This paper contains a defense against anti-realism in mathematics in the light both of incompleteness and of the fact that mathematics is a ‘cultural artifact.’. Anti-realism (here) is the view that theorems, say, of aritltmetic cannot be taken at face value to express true propositions about the system of numbers but must be reconstrued to be about somctliiiig else or about nothing at all. A ‘bite-the-bullet’ aspect of the defease is that, adopting new axioms, liitherto independent, is not. a matter (...) of recognizing trutlis wliich had previoasly been unrecognized, but of extending the domain of what is true. (shrink)

Dai Zhen’s philosophy of language took the opportunity of a transition in Chinese philosophy to develop a form of humanist positivism, which was different from both the Song and Ming dynasties’ School of Principles and the early Qing dynasty’s philosophical forms. His philosophy of language had four primary manifestations: It differentiated between “names pointing at entities and real events” and “names describing summum bonum and perfection”; In discussing the metaphysical issue of “the Dao,” it was the first to introduce a (...) syntax analysis of linguistics, clearly differentiating between the different roles of predicate verbs “zhi wei” and “wei zhi” in Classical Chinese; In criticizing Confucian thought during the Song and Ming dynasties, it adopted specific philological skills such as the analysis of phraseology, the meaning of sentences and the thread of words in texts; and It re-interpreted the meaning of Confucian classics by studying characters and language, adopting a positivist and philological manner to seek metaphysical sense in philosophy. In this way, his philosophy was different from the scholars of the School of Principles during the Song and Ming dynasties and from the goal of Western linguistic philosophy in the 20th century, which refuted metaphysics. Accordingly, it helped to develop 18th century Chinese philosophy as it turned towards linguistic philology. (shrink)

The conceptual framework and core courses of the certificate program in Preventive Engineering and Social Development of the Centre for Technology and Social Development at the University of Toronto are briefly described. Preventive approaches for the engi neering, management, and regulation of technology examine how technology fits into, interacts with, and depends on human life, society, and the biosphere in order to apply this understanding in a negative feed back mode to avoid or reduce harmful effects to these contexts. These (...) approaches represent a new paradigm for engineering education and practice enriched through STS. (shrink)

Unlike some other reproductions of classic texts (1) We have not used OCR(Optical Character Recognition), as this leads to bad quality books with introduced typos. (2) In books where there are images such as portraits, maps, sketches etc We have endeavoured to keep the quality of these images, so they represent accurately the original artefact. Although occasionally there may be certain imperfections with these old texts, we feel they deserve to be made available for future generations to enjoy.

Gap junction intercellular communication channels permit the exchange of small regulatory molecules and ions between neighbouring cells and coordinate cellular activity in diverse tissue and organ systems. These channels have short half‐lives and complex assembly and degradation pathways. Much of the recent work elucidating gap junction biogenesis has featured the use of connexins (Cx), the constituent proteins of gap junctions, tagged with reporter proteins such as Green Fluorescent Protein (GFP) and has illuminated the dynamics of channel assembly in live cells (...) by high‐resolution time‐lapse microscopy. With some studies, however, there are potential short‐comings associated with the GFP chimeric protein technologies. A recent report by Gaietta et al., has highlighted the use of recombinant proteins with tetracysteine tags attached to the carboxyl terminus of Cx43, which differentially labels ‘old’ and ‘new’ connexins thus opening up new avenues for studying temporal and spatial localisation of proteins and in situ trafficking events.1 BioEssays 24:876–880, 2002. © 2002 Wiley Periodicals, Inc. (shrink)

"Aristotle was a systematic writer who often cross-referred to the definitions of terms given elsewhere in his work. Book 5 of the Metaphysics is important because it consists of definitions of the main uses of key terms in Aristotle's philosophy, and it is extremely valuable to have a commentary on this important text by Alexander of Aphrodisias, the leading commentator of his school. Alexander provides a detailed commentary on all of the thirty terms analysed in Book 5, weighing alternative interpretations (...) of what Aristotle says one against another, defending Peripatetic views against actual and possible criticisms, and attempting to integrate what is said in Book 5 into the context of the Metaphysics as a whole."--Bloomsbury Publishing. (shrink)

There is a widespread belief, more often implied than explicitly asserted, that Hume considered all necessary propositions to be analytic.Of course Hume did not use the analytic-synthetic distinction explicitly. This only come to the forefront with Kant; and it is Kant who is probably the main source of the above-mentioned belief. Kant ascribed to Hume the view that mathematical propositions are, in his terminology, analytic. If this is correct, then since mathematics was for Hume the paradigm of a body of (...) necessary truths, it is plausible to infer that he considered necessary propositions to be one and all analytic. The absence in Hume's writings of the analytic-synthetic terminology is by no means decisive: though he did not have the terms he may well have possessed the concepts, as evidenced by his use of them. (shrink)

Haeckels theory of recapitulation shall be extended by the following rule: During the ontogenetical recapitulation of the phenotypical effects, the recapitulation of the phylogenetical natural selection factors according to the genotypical potentials is a condition of manifestation. The phylogenetical natural selectionfactor produces the activation of the gen as ontogenetical manifestation-stimulus. Factor of natural selection is the one of the extern or intern environment to which has happened the adaption in the phylogenesis. Concerning the intern environments the phenotypical effect of the (...) preliminary phase of development is not only the phylogenetical factor of natural selection according to the genotypical potential of the following phase of development, but also the ontogenetical stimulus of manifestation for the phenotypical effect of the following phase of development. Phenotypical effects can present themselves as stimulus-dependencial modifications, which are bound to the manifestation-stimulus and cease after its disappearence. They can also present themselves as stimulus-independencial lasting modifications, which become independent from the manifestation-stimulus and remain preserved after its ceasing, because the gen once activated by the stimulus reproduces itself in the state of being activated and is so transmitted during the multiplication of cells from cell to cell and during the multiplication of organisms from generation to generation. This view gives new chances for interpretating causal connections of the phylogenetical evolution and involution as well as new possibilities for an explanation of evolutionary mechanism of maturation and of involutionary mechanism of ageing in the ontogenesis and also the occuring appearences of acceleration and retardation.DieHaeckel'sche Rekapitulationstheorie wird durch die folgende Rekapitulationsregel erweitert: Bei der ontogenetischen Rekapitulation der erscheinungsbildlichen Leistungen ist die Rekapitulation der phylogenetischen Auslesefaktoren der entsprechenden erbildlichen Fähigkeiten Manifestationsbedingung. Der phylogenetische Auslesefaktor bewirkt als ontogenetischer Manifestationsreiz die Genaktivierung. Auslesefaktor ist derjenige Faktor der äusseren oder inneren Umwelt, an den in der Phylogenese die Anpassung erfolgt ist. Im Bereich der inneren Umwelt ist daher die erscheinungsbildliche Leistung der vorhergehenden Entwicklungsstufe sowohl der phylogenetische Auslesefaktor für die erbbildliche Fähigkeit der nachfolgenden Entwicklungsstufe als auch der ontogenetische Manifestationsreiz für die erscheinungsbildliche Leistung der nachfolgenden Entwicklungsstufe. Die erscheinungsbildlichen Leistungen können als reizabhängige Modifikation auftreten, die also vom Manifestationsreiz abhängig bleibt und nach seinem Aufhören auch wieder verschwindet, sie können aber auch als reizunabhängige Dauermodifikation auftreten, die also vom Manifestationsreiz unabhängig wird und nach seinem Aufhören erhalten bleibt, weil das durch den Reiz einmal aktivierte Gen sich im Status des Aktiviertseins bei der Zellvermehrung von Zelle zu Zelle und bei der Vermehrung der Organismen von Generation zu Generation fortpflanzt. Damit ergeben sich neue Möglichkeiten einer Deutung der Kausalzusammenhänge bei der phylogenetischen Evolution und Involution, sowie neue Ansätze einer Erklärung des Evolutionsmechanismus der Reifung und des Involutionsmechanismus des Alterns in der Ontogenese, sowie der dabei auftretenden Erscheinungen der Acceleration und der Retardation. (shrink)

Housman reads assueta euolitans; the former word is a conjecture of his own, the latter a conjecture of Ellis, which I think he would have ignored if the relevant fascicle of the Thesaurus had been available to show that euolitare occurs once in Columella and then not before the sixth century. If assueto is sound, mundi must be changed to mundo or to another noun. Bentley read mundo, and this may well be the right solution: the eagle carries thunderbolts to (...) the sky, “cui scilicet per diuturnas operas assueuerat”. Shackleton Bailey emends to nisu. If emendation were required, I suggest that motu would be palaeographically more satisfactory; the assumed process of corruption is well illustrated by 3.82, motu GL: modum M: mundo LV. (shrink)

A broad evolutionary perspective is essential to fully reverse figure and ground in the rationality debate. Humans' evolved psychological architecture was designed to produce inferences that were adaptive, not normatively logical. This perspective points to several predictable sources of errors in modern laboratory reasoning tasks, including inherent, systematic biases in information-processing systems explained by Error Management Theory.

The six platinum group metals (pgms: ruthenium, rhodium, palladium, osmium, iridium and platinum) posed a number of problems for 19th-century chemists, including Mendeleev, for their Periodic classification. This account discusses the discovery of the pgms, the determination of their atomic weights and their classification.