Henry M. Sheffer is well known to logicians for the discovery (or rather, the rediscovery) of the ?Sheffer stroke? of propositional logic. But what else did Sheffer contribute to logic? He published very little, though he is known to have been carrying on a rather mysterious research program in logic; the only substantial result of this research was the unpublished monograph The General Theory of Notational Relativity. The main aim of this paper is to explain, as far as possible (given (...) the scanty evidence), the nature of Sheffer's program, and the reasons for its failure. The paper concludes with a discussion of Sheffer's only true logical descendant, C.H. Langford, and his contributions to model theory. (shrink)

This paper offers a particular intuitionistic negation completion of Urquhart's system C resulting in a super-intuitionistic contractionless propositional logic equivalent to Dummett's LC without contraction.

Etude de l'extension par la negation semi-intuitionniste de la logique positive des propositions appelee logique C, developpee par A. Urquhart afin de definir une semantique relationnelle valable pour la logique des valeurs infinies de Lukasiewicz (Lw). Evitant les axiomes de contraction et de reduction propres a la logique classique de Dummett, l'A. propose une semantique de type Routley-Meyer pour le systeme d'Urquhart (CI) en tant que celle-la ne fournit que des theories consistantes pour la completude de celui-ci.

This study described the relationships between academic class and student moral sensitivity and reasoning and between curriculum design components for ethics education and student moral sensitivity and reasoning. The data were collected from freshman (n = 506) and senior students (n = 440) in eight baccalaureate nursing programs in South Korea by survey; the survey consisted of the Korean Moral Sensitivity Questionnaire and the Korean Defining Issues Test. The results showed that moral sensitivity scores in patient-oriented care and conflict were (...) higher in senior students than in freshman students. Furthermore, more hours of ethics content were associated with higher principled thinking scores of senior students. Nursing education in South Korea may have an impact on developing student moral sensitivity. Planned ethics content in nursing curricula is necessary to improve moral sensitivity and moral reasoning of students. (shrink)

Beginning from Plato, there exists a philosophical tradition, which interprets philosophy as preparation for death. However, for Plato the death of a philosopher does not necessarily imply death in its ordinary meaning, but rather a spiritual way of life maximally free from corporeal affections. This kind of relationship between philosophy and death was intensively discussed in late antique philosophy, Patristics, medieval Byzantine philosophy, and also in medieval Georgian literature. Based on Plato’s and Plotinus’ philosophy, Porphyry presented definitions of three kinds (...) of death in his Sententiae : ‘death’ of a philosopher, natural death, ‘death’ of a soul. The aim of this paper is to provide a philosophical analysis of three concepts of death in the post-Porphyrian tradition, mainly in Byzantine and Georgian texts. The paper is based on the analysis of the above mentioned issues in the texts of Porphyry, Macrobius, Michael Psellos, as well as in the old Georgian versions of the works of Ammonios Hermiae, John of Damascus and John Sinaites. We also take into consideration the views on the relation between philosophy and death in the thought of the philosophers of Humanism and Renaissance, such as Georgios Gemistos Plethon, Marsilio Ficino, Giovanni Pico della Mirandola, and Michel de Montaigne, whether or not and to what extent their views on the relation between philosophy and death are different from the theories of ancient and medieval Platonists. (shrink)

Through this paper, we convey a comparative analysis of how Google Inc. and the Free Software Foundation Europe (FSFE) discursively construct and contest Android, a dominant mobile operating system. Methodologically, we use political discourse theory to engage in the textual analysis; identify and compare key signifiers and nodal points across the exemplary texts from the two actors, and interpret their meaning vis à vis contextual insights about the political economy of Android’s production. Albeit being marketed as ‘the first truly open (...) platform’ for mobiles, through our analysis we find Google’s definition of open source practices strictly conditional. We argue that Google’s usage of compatibility rhetorically as well as techno-legally justifies the conglomerate’s control over the platform. By contrast, the discursive moment by free software activists, through a campaign ‘Free Your Android’ deconstructs the discourse on open source and attempts to politicize the access to code in the mobile domain. This is done by extending from the well-known developer’s four freedoms onto users’ privacy, due to personal character of mobile devices. Such articulation of free software in relation to privacy of user data is a new development and arguably has a potential to contribute to widening support to the movement. (shrink)

A notion of feasible function of finite type based on the typed lambda calculus is introduced which generalizes the familiar type 1 polynomial-time functions. An intuitionistic theory IPVω is presented for reasoning about these functions. Interpretations for IPVω are developed both in the style of Kreisel's modified realizability and Gödel's Dialectica interpretation. Applications include alternative proofs for Buss's results concerning the classical first-order system S12 and its intuitionistic counterpart IS12 as well as proofs of some of Buss's conjectures concerning IS12, (...) and a proof that IS12 cannot prove that extended Frege systems are not polynomially bounded. (shrink)

It is usually believed that science goes with things like theoria, ‘knowing that’, ontology and representing, and that techne, know-how, technology and intervening are only instrumental to science or its beneficial but nonetheless accidental side effect. In this context to be instrumental means also to be eliminable, or at least transparent, something that leaves no trace. Following the historical development of experimentation, from simple observation to modern microscopic experiments. I try to show how that view loses its ground. To produce (...) an artefact, scientific or other, is to be engaged in a complex dynamics, both ontological and epistemological in which at least two component processes, that of bringing forth and that of bringing into, are intertwined. The old dictum: ‘Science discovers, technology invents’, should be replaced by: science discovers because it invents. As a consequence scientific theory becomes an instrument of design. (shrink)

This article presents a simplified proof of the result that bounded depth propositional proofs of the pigeonhole principle are exponentially large. The proof uses the new techniques for proving switching lemmas developed by Razborov and Beame. A similar result is also proved for some examples based on graphs.

The aim of this paper is to analyze the concept of dianoia (discursive mode of thinking) as soul’s activity, and related issues, in the twelfth century work by Ioane Petritsi : his Georgian translation of Proclus’ Elements of Theology and his Commentary on this text, including his prologue to it. The themes related to the discursive mode of cognition are also discussed in the 129th proposition of the Georgian version of the Elements (which is absent in the Greek manuscripts) and (...) in Petritsi’s commentary on it. While analyzing the issues related to dianoia in Petritsi’s work, we focus our attention on the inter‑relationship of ontological, epistemological, linguistic and also existential aspects of this concept as they were interpreted by Petritsi in his Commentary. (shrink)

In the prologue to his Commentary on Proclus’ Elements of theology Ioane Petritsi, Georgian Neoplatonist of the twelfth century, argues that the main subject of Proclus’ Elements is the theory of the supreme One. In Petritsi’s opinion, Proclus’ merit was to elaborate the philosophy of the ‘pure’, absolutely transcendent One which is unperceivable even for the Intellect. On the other hand, the supreme One is, in Petritsi’s interpretation, the cause of everything, including matter, and It has some positive characteristics which (...) cannot be separated from Its hyper-essence. These are, mainly, Its causality and productivity, Its will and providential activity. The aim of this article is to analyse, what the supreme One is in Petritsi’s Commentary and to answer the following question: Do the absolute transcendence of the supreme One and Its positive characteristics contradict each other or are they in a certain way compatible with each other? I argue that for making the transition from the first aspect of the supreme One to another one more coherent, Petritsi made an attempt to introduce in the ontological hierarchy one more one after the supreme One and before the Henads. In my opinion, this ‘second one’, which is almost inseparable from the supreme transcendent One, is Its another aspect, representing Its productive activity. For the same purpose, as I think, Petritsi identified the creative aspect of the One with the Logos/the Son of God and, in certain cases, also with Plato’s Demiurge. (shrink)

(1989). Evolutionary naturalist realism: Can this blend be coherent? 1 . International Studies in the Philosophy of Science: Vol. 3, No. 2, pp. 136-156.

V. A. Lektorsky: Subject, Object, Cognition, Moscow, Progress Publishers 1984, 280 pp.

This paper discusses the general problem of translation functions between logics, given in axiomatic form, and in particular, the problem of determining when two such logics are "synonymous" or "translationally equivalent." We discuss a proposed formal definition of translational equivalence, show why it is reasonable, and also discuss its relation to earlier definitions in the literature. We also give a simple criterion for showing that two modal logics are not translationally equivalent, and apply this to well-known examples. Some philosophical morals (...) are drawn concerning the possibility of having two logical systems that are "empirically distinct" but are both translationally equivalent to a common logic. (shrink)

Ibn al-ʻArabī, 1165-1240; views on freedom; Sufism; Islamic philosophy.

We show that short bounded-depth Frege proofs of matrix identities, such as PQ=I⊃QP=I (over the field of two elements), imply short bounded-depth Frege proofs of the pigeonhole principle. Since the latter principle is known to require exponential-size bounded-depth Frege proofs, it follows that the propositional version of the matrix principle also requires bounded-depth Frege proofs of exponential size.

Michael Kremer defines fixed-point logics of truth based on Saul Kripke’s fixed point semantics for languages expressing their own truth concepts. Kremer axiomatizes the strong Kleene fixed-point logic of truth and the weak Kleene fixed-point logic of truth, but leaves the axiomatizability question open for the supervaluation fixed-point logic of truth and its variants. We show that the principal supervaluation fixed point logic of truth, when thought of as consequence relation, is highly complex: it is not even analytic. We also (...) consider variants, engendered by a stronger notion of ‘fixed point’, and by variant supervaluation schemes. A ‘logic’ is often thought of, not as a consequence relation, but as a set of sentences – the sentences true on each interpretation. We axiomatize the supervaluation fixed-point logics so conceived. (shrink)

Mathematics and philosophy have historically enjoyed a mutually beneficial and productive relationship, as a brief review of the work of mathematician–philosophers such as Descartes, Leibniz, Bolzano, Dedekind, Frege, Brouwer, Hilbert, Gödel, and Weyl easily confirms. In the last century, it was especially mathematical logic and research in the foundations of mathematics which, to a significant extent, have been driven by philosophical motivations and carried out by technically minded philosophers. Mathematical logic continues to play an important role in contemporary philosophy, and (...) mathematically trained philosophers continue to contribute to the literature in logic. For instance, modal logics were first investigated by philosophers and now have important applications in computer science and mathematical linguistics. (shrink)