This work is devoted to the relations between Lambek’s Syntactic Calculus and noncommutative variants of Girard’s Linear Logic; in particular the paper will consider: the geometrical representation of the laws of LC by means of proof-nets; the discovery - due to such a geometrical representation - of some laws of LC not yet considered; the discussion of possible linguistic uses of these new laws.

In lieu of an abstract, here is a brief excerpt of the content:Book Reviews Bibliography on Plato's "'Laws, "" 1920-1970: With Additional Citations through May, 1975. By Trevor J. Saunders. (New York: Arno Press, 1976. Pp. i + 60. $15.00) The Penguin Classics translator of the non-Socratic Laws, as Leo Strauss called them, has here compiled in a most usable way a thorough bibliography of books and articles about the Laws or parts of them. The section "Texts, Translations, and Commentaries" (...) properly excludes translations not made directly from the Greek. In previous centuries this would, also properly, have excluded many a famous or popular translation, such as Thomas Taylor's or Victor Cousin's, worked out from the text of M. Ficino's "first edition" in Latin. Given the state of the Greek text and the practice, inaugurated by Ficino, of improving upon the Greek in the translatioias, some notation about the literalness of the translations cited would have been of additional value. Section B, in thirty pages, is the largest and also deliberately the most selective in striving to limit itself to work concerned exclusively or primarily with the Laws. But it cannot avoid including much material about some aspect of Plato in general rather than about the Laws; this is especially true of the subsection, B1, on comprehensive accounts. Section B2, on the text and its tradition, has overwhelmingly more citations about the indirect tradition than about the texts themselves, an interesting indication of the current state of this question. The next subsections, to B12, divide according to subject matter. BI3 lists studies on the influence of the Laws. The last section, in twenty-four pages, is most valuable. It lists, by Stephanus page number, an abundance of discussions of individual passages from Book I through Book XII wherever these discussions, bibliographically speaking, may have occurred. Students of the Laws will be well served by, and most grateful to, Professor Saunders for this bibliography. I can only second the intent of his parting epigraph that sends us back to the study of the Laws themselves. But I must add that more explicitly detailed work appears to be required both on the difficulties the text itself presents to students of Plato (one thinks of A. Boeckh's analyses of the prose in Books I through III) and on those which arise when the Laws is contrasted--from the point of view of design and intellectuality--with those of Plato's works that are comparable, if not in number of pages, at least in scale of conception and monumentality. V. TEJERA SUNY at Stony Brook Science and Philosophy in Aristotle's Biological Works. By Anthony Preus. (Hildesheim and New York: George Olms, 1975. Pp. ix + 404. DM.88) A reciprocal influence between Aristotle's philosophy and biology--if it could be demonstrated through step-by-step criticism and not merely asserted in generalities about functionalism--might help to explain both, and might also itself be philosophically interesting ; for it should clarify Aristotle's concepts of form, essence, universal, and species-concepts which have been mercilessly jumbled in the traditional interpretations. With the failure of Jaegerian developmental analyses, we can hardly now hope for help from detailed chronology. But a general dating of Aristotle's biological interest to the Assos-Mytilene period, when he was already aged forty, is accepted by most people (though not by Jaeger who [463]... (shrink)

Purpose. The article is aimed to substantiate the view on the phenomenon of laughter as a subject of semiotic analysis, which leads to the following tasks: to reveal the possibilities of semiotics application in the study of laughter nature; to analyze the phenomenon of laughter as a cultural and natural phenomenon, as a sign and as an attribute; to consider the place of laughter in culture, which is understood as a sign system. Theoretical basis. The semiotic approach proceeds from the (...) fact that human lives in the world of signs, all the surrounding reality can be interpreted as a sign system. The basic concept of semiotics is the concept of a sign. The theoretical basis of the article is understanding the culture as a sign-symbolic system. Laughter is considered as a phenomenon ontologically rooted in human culture. At the same time, laughter is on the edge of culture. The research is based on the work of semiotic authors, cultural researchers, and the researchers of laughter. Originality. The originality lies in the application of the semiotic method to the research of laughter phenomenon, consideration of the dialectics of natural and cultural, signedness and non-signedness, manifested in the phenomenon of laughter. Conclusions. Laughter is considered as a psychophysiological phenomenon and as a cultural phenomenon. Laughter acts as an emotional manifestation, a physiological reaction, but socially and culturally mediated. In any case, laughter indicates an emotional or cognitive state of a human. Laughter acts as a process and result of the interpretation of a sign, a reaction to a sign. Laughter is a form and a means of communication. Being a natural phenomenon, in the process of social evolution, laughter acquires signedness, is integrated by culture as a sign system, and, at the same time, maintains a connection with nature. Thus, laughter occupies an ambivalent position between nature and culture. In the phenomenon of laughter, the dual state of human is revealed. In laughter, boundaries are blurred, the unity and opposition of natural and cultural, biological and social, soul and body, thought and feeling, sign and attribute are manifested. (shrink)

We consider a space with Generalized Uncertainty Principle which can be obtained in the frame of the deformed commutation relations. In the space with GUP we have found transformations relating coordinates and times of moving and rest frames of reference in the first order over the parameter of deformation. In the non-relativistic case we find the deformed Galilean transformation which is rotation in Euclidian space–time. This transformation is similar to the Lorentz one but written for Euclidean space–time where the speed (...) of light is replaced by some velocity related to the parameter of deformation. We show that for relativistic particle in the space with GUP the coordinates of the rest and moving frames of reference satisfy the Lorentz transformation with some effective speed of light. (shrink)

In his 1951 Gibbs Memorial Lecture, Kurt Gödel put forth his famous disjunction that either the power of the mind outstrips that of any machine or there are absolutely unsolvable problems. The view that there are no absolutely unsolvable problems is optimism, the view that there are such problems is pessimism. In his 1995—and, revised in 2013—Verificationism Then and Now, Per Martin-Löf presents an illustrative argument for a constructivist form of optimism. In response to that argument, Solomon Feferman points out (...) that Martin-Löf’s reasoning relies upon constructive understandings of key philosophical notions. In the vein of Feferman’s analysis, one might be object to Martin-Löf’s argument for either its reliance upon constructivist considerations, or for its appeal to non-unproblematically mathematical premises. We argue that both of these responses fall short. On one hand, to be critical of Martin-Löf’s reasoning for its constructiveness is to reject what would otherwise be a scientific advance on the basis of the assumption of constructivism’s falsehood or implausibility, which is of course uncharitable at best. On the other hand, to object to the argument for its use of non-unproblematically mathematical premises is to assume that there is some philosophically neutral mathematics, which is implausible. Martin-Löf’s argument relies upon his third law, the claim that from the impossibility of a proof of a proposition we can construct a proof of its negation. We close with a discussion of some ways in which this claim can be criticized from the constructive point of view. Specifically, we contend that Martin-Löf’s third law is incompatible with what has been called “Poincaré’s Principle of Epistemic Conservation”, the thesis that genuine increase in mathematical knowledge requires subject-specific insight. (shrink)