Categorical proof theory is an approach to understanding the structure of proofs. We illustrate the idea first by analyzing G0̈del's Dialectica interpretation and the Diller-Nahm variant in categorical terms. Then we consider the problematic question of the structure of classical proofs. We show how double negation translations apply in the case of the Dialectica interpretations. Finally we formulate a proposal as to how to give a more faithful analysis of proofs in the sequent calculus.

Mr. F. is a fifty‐year‐old father of two school‐aged daughters. Six years ago, he received a double lung transplant because he was suffering from interstitial lung disease, a fatal illness that causes suffocation by progressive scarring of the lungs. He is now experiencing chronic rejection of the transplant and is being considered to receive another. Without it, he is expected to survive only a year and a half. With it, his prognosis will improve, but the numbers are still not good. (...) Three years after his lung transplant, Mr. F. stopped attending his office visits. For a period of sixteen months he went without the studies and attention essential to posttransplant care. He stopped performing the required daily self‐monitoring of his lung function about eight months after his transplant, but he has maintained a regular exercise regimen. While lost to follow‐up, he continued to take his immunosuppressant medications, but he stopped taking medicine to control his high blood pressure because of its expense. (shrink)

Persian Religion in the Achaemenid Period. Edited by Wouter F. M. Henkelman and Céline Redard. Classica et Orientalia, vol. 16. Wiesbaden: Harrassowitz Verlag, 2017. Pp. 496, illus. €98.

This short note considers the formulation of Full Intuitionistic Linear Logic given by Hyland and de Paiva . Unfortunately the formulation is not closed under the process of cut elimination. This note proposes an alternative formulation based on the notion of patterns.

In their recent article, Kirsch and Hyland questioned the relation between psychological and associated neurophysiological phenomena in the introduction of complementarity into psychology. Mishkin's work on the neurophysiological basis of memory and perception provides an example of the extension of complementarity that I have proposed and that can serve as the basis for empirical testing of this extension. Mishkin's thesis that memory storage occurs at sensory stations in the cortex allows for the resolution of a fundamental problem in cognitive (...) psychology, namely the reciprocal dependence of perception and memory. Also, Mishkin's thesis allows that psychological phenomena do not depend on an objective world for their existence. (shrink)

Writing a thesis or dissertation is a challenging procedure as it is one of the requirements of getting a graduate and postgraduate diploma. Writing an abstract like other parts of a thesis or dissertation has its criterion. For this reason, due to globalism, those abstracts written by non-native English speakers may lack some of the features of the abstract genre and move that must be included. This study examines the moves of M.A. and Ph.D. abstracts written by Turkish students between (...) the 2009 and 2019 academic years on foreign language education at Cyprus International University. The data consisted of 50 abstracts chosen randomly from the ELT department. For the analysis, Hyland’s five-move model has been used. The study results reveal that 40 abstracts did not follow the five moves that Hyland has put forward. Moreover, it can be stated that the absence of some moves in the abstracts may cause restraint for readers to comprehend these studies in terms of communicative purposes. (shrink)

Unlike many other dialogues, Plato’s Charmides has never elicited much sustained scholarly attention, even though it focuses on an important moral excellence, sôphrosunê (temperance, moderation), features two of Plato’s relatives who were members of the oligarchic government of 304–303 BC, and includes two refutations of the Republic’s formula, “doing one’s own things,” as well as a long, complex discussion of “knowledge of knowledge.” The present work is therefore a welcome addition to the small collection of English books on it (Tuckey, (...) Plato’s Charmides; Hyland, The Virtue of Philosophy; Schmid, Plato’s Charmides and the Socratic Ideal of Rationality). Early chapters, comprising nearly half the .. (shrink)

The problem of computational complexity of semantics for some natural language constructions – considered in [M. Mostowski, D. Wojtyniak 2004] – motivates an interest in complexity of Ramsey quantifiers in finite models. In general a sentence with a Ramsey quantifier R of the following form Rx, yH(x, y) is interpreted as ∃A(A is big relatively to the universe ∧A2 ⊆ H). In the paper cited the problem of the complexity of the Hintikka sentence is reduced to the problem of computational (...) complexity of the Ramsey quantifier for which the phrase “A is big relatively to the universe” is interpreted as containing at least one representative of each equivalence class, for some given equvalence relation. In this work we consider quantifiers Rf, for which “A is big relatively to the universe” means “card(A) > f (n), where n is the size of the universe”. Following [Blass, Gurevich 1986] we call R mighty if Rx, yH(x, y) defines N P – complete class of finite models. Similarly we say that Rf is N P –hard if the corresponding class is N P –hard. We prove the following theorems. (shrink)

Explorations in Systems Phenomenology in Relation to Ontology, Hermeneutics and the Meta-dialectics of Design -/- SYNOPSIS A Phenomenological Analysis of Emergent Design is performed based on the foundations of General Schemas Theory. The concept of Sign Engineering is explored in terms of Hermeneutics, Dialectics, and Ontology in order to define Emergent Systems and Metasystems Engineering based on the concept of Meta-dialectics. -/- ABSTRACT Phenomenology, Ontology, Hermeneutics, and Dialectics will dominate our inquiry into the nature of the Emergent Design of the (...) System and its inverse dual, the Meta-system. This is an speculative dissertation that attempts to produce a philosophical, mathematical, and theoretical view of the nature of Systems Engineering Design. Emergent System Design, i.e., the design of yet unheard of and/or hitherto non-existent Systems and Metasystems is the focus. This study is a frontal assault on the hard problem of explaining how Engineering produces new things, rather than a repetition or reordering of concepts that already exist. In this work the philosophies of E. Husserl, A. Gurwitsch, M. Heidegger, J. Derrida, G. Deleuze, A. Badiou, G. Hegel, I. Kant and other Continental Philosophers are brought to bear on different aspects of how new technological systems come into existence through the midwifery of Systems Engineering. Sign Engineering is singled out as the most important aspect of Systems Engineering. We will build on the work of Pieter Wisse and extend his theory of Sign Engineering to define Meta-dialectics in the form of Quadralectics and then Pentalectics. Along the way the various ontological levels of Being are explored in conjunction with the discovery that the Quadralectic is related to the possibility of design primarily at the Third Meta-level of Being, called Hyper Being. Design Process is dependent upon the emergent possibilities that appear in Hyper Being. Hyper Being, termed by Heidegger as Being (Being crossed-out) and termed by Derrida as Differance, also appears as the widest space within the Design Field at the third meta-level of Being and therefore provides the most leverage that is needed to produce emergent effects. Hyper Being is where possibilities appear within our worldview. Possibility is necessary for emergent events to occur. Hyper Being possibilities are extended by Wild Being propensities to allow the embodiment of new things. We discuss how this philosophical background relates to meta-methods such as the Gurevich Abstract State Machine and the Wisse Metapattern methods, as well as real-time architectural design methods as described in the Integral Software Engineering Methodology. One aim of this research is to find the foundation for extending the ISEM methodology to become a general purpose Systems Design Methodology. Our purpose is also to bring these philosophical considerations into the practical realm by examining P. Bourdieu’s ideas on the relationship between theoretical and practical reason and M. de Certeau’s ideas on practice. The relationship between design and implementation is seen in terms of the Set/Mass conceptual opposition. General Schemas Theory is used as a way of critiquing the dependence of Set based mathematics as a basis for Design. The dissertation delineates a new foundation for Systems Engineering as Emergent Engineering based on General Schemas Theory, and provides an advanced theory of Design based on the understanding of the meta-levels of Being, particularly focusing upon the relationship between Hyper Being and Wild Being in the context of Pure and Process Being. (shrink)

When Gödel developed his functional interpretation, also known as the Dialectica interpretation, his aim was to prove consistency of first order arithmetic by reducing it to a quantifier-free theory with finite types. Like other functional interpretations Gödel’s Dialectica interpretation gives rise to category theoretic constructions that serve both as new models for logic and semantics and as tools for analysing and understanding various aspects of the Dialectica interpretation itself. Gödel’s Dialectica interpretation gives rise to the Dialectica categories , in: Contemp. (...) Math., vol. 92, Amer. Math. Soc., Providence, RI, 1989, pp. 47–62] and J.M.E. Hyland in [J.M.E. Hyland, Proof theory in the abstract, Ann. Pure Appl. Logic 114 43–78, Commemorative Symposium Dedicated to Anne S. Troelstra ]). These categories are symmetric monoidal closed and have finite products and weak coproducts, but they are not Cartesian closed in general. We give an analysis of how to obtain weakly Cartesian closed and Cartesian closed Dialectica categories, and we also reflect on what the analysis might tell us about the Dialectica interpretation. (shrink)

We study the lattice of local operators in Hylandʼs Effective Topos. We show that this lattice is a free completion under internal sups indexed by the natural numbers object, generated by what we call basic local operators.We produce many new local operators and we employ a new concept, sight, in order to analyze these.We show that a local operator identified by A.M. Pitts in his thesis, gives a subtopos with classical arithmetic.

My presentation will evidently be the longest since I will be presenting the results of two major surveys done in Moscow, Pskov, and a number of other cities and villages in July-September 1990 and in August-October 1991. The interpretation of the findings of these surveys was done by me together with S.B. Filatov, while the actual investigations were carried out by S.B. Filatov, L.G. Byzov, L.M. Vorontsova, and G.L. Gurevich. The purpose of the surveys was above all to shed (...) some light on the picture of contemporary religiosity and on the connection between religious beliefs and political attitudes. What do the findings of these surveys tell us? (shrink)

ABSTRACT What, if anything, should we do when someone says they don’t believe in anthropogenic climate change? Or that they worry that a COVID-19 vaccine might be dangerous? We argue that in general, we face an epistemic duty to object to such assertions, qua instances of science denial and science sceptical discourse, respectively. Our argument builds on recent discussions in social epistemology, specifically surrounding the idea that we ought to speak up against (epistemically) problematic assertions so as to fulfil an (...) important epistemic obligation – namely, preventing epistemic harms in others. We show that both science denial (SD) and vaccine hesitant (VH) discourses are harmful in a distinctively epistemic sense, and as such generate an especially strong duty to voice our disagreement. As we also argue, this obligation is nonetheless defeasible: depending on the situational features of those involved, voicing an objection to VH discourse may actually end up doing more harm than good. We conclude by tracing what seems like a promising path towards restoring well-placed public trust in scientific testifiers. Doing so is key in order to guarantee equitable access to warranted beliefs about important subject matters, such as the safety of vaccines, to all segments of society. (shrink)

This article will rework the classical question ‘Can a machine think?’ into a more specific problem: ‘Can a machine think anything new?’ It will consider traditional computational tasks such as prediction and decision-making, so as to investigate whether the instrumentality of these operations can be understood in terms of the creation of novel thought. By addressing philosophical and technoscientific attempts to mechanise thought on the one hand, and the philosophical and cultural critique of these attempts on the other, I will (...) argue that computation’s epistemic productions should be assessed vis-à-vis the logico-mathematical specificity of formal axiomatic systems. Such an assessment requires us to conceive automated modes of thought in such a way as to supersede the hope that machines might replicate human cognitive faculties, and to thereby acknowledge a form of onto-epistemological autonomy in automated ‘thinking’ processes. This involves moving beyond the view that machines might merely simulate humans. Machine thought should be seen as dramatically alien to human thought, and to the dimension of lived experience upon which the latter is predicated. Having stepped outside the simulative paradigm, the question ‘Can a machine think anything new?’ can then be reformulated. One should ask whether novel behaviour in computing might come not from the breaking of mechanical rules, but from following them: from doing what computers do already, and not what we might think they should be doing if we wanted them to imitate us. (shrink)

ON DECEMBER 10, 1991 Charles Shonubi, a Nigerian citizen but a resident of the USA, was arrested at John F. Kennedy International Airport for the importation of heroin into the United States.1 Shonubi's modus operandi was ``balloon swallowing.'' That is, heroin was mixed with another substance to form a paste and this paste was sealed in balloons which were then swallowed. The idea was that once the illegal substance was safely inside the USA, the smuggler would pass the balloons and (...) recover the heroin. On the date of his arrest, Shonubi was found to have swallowed 103 balloons containing a total of 427.4 grams of heroin. There was little doubt about Shonubi's guilt. In fact, there was considerable evidence that he had made at least seven prior heroin-smuggling trips to the USA (although he was not tried for these). In October 1992 Shonubi was convicted in a United States District Court for possessing and importing heroin. Although the conviction was only for crimes associated with Shonubi's arrest date of December 10, 1991, the sentencing judge, Jack B. Weinstein, also made a ®nding that Shonubi had indeed made seven prior drug-smuggling trips to the USA. The interesting part of this case was in the sentencing. According to the federal sentencing guidelines, the sentence in cases such as this should depend on the total quantity of heroin involved. This instruction was interpreted rather broadly.. (shrink)