We investigate some logics with Henkin quantifiers. For a given logic L, we consider questions of the form: what is the degree of the set of L–tautologies in a poor vocabulary (monadic or empty)? We prove that the set of tautologies of the logic with all Henkin quantifiers in empty vocabulary L*∅ is of degree 0’. We show that the same holds also for some weaker logics like L ∅(Hω) and L ∅(Eω). We show that each logic of the form (...) L ∅ (k)(Q), with the number of variables restricted to k, is decidable. Nevertheless – following the argument of M. Mostowski from [Mos89] – for each reasonable set theory no concrete algorithm can provably decide L (k) (Q), for some (Q). We improve also some results related to undecidability and expressibility for logics L(H4) and L(F2) of Krynicki and M. Mostowski from [KM92]. (shrink)

We examine second order intuitionistic propositional logic, IPC². Let $F_\exists $ be the set of formulas with no universal quantification. We prove Glivenko's theorem for formulas in $F_\exists $ that is, for φ € $F_\exists $ φ is a classical tautology if and only if ¬¬φ is a tautology of IPC². We show that for each sentence φ € $F_\exists $ (without free variables), φ is a classical tautology if and only if φ is an intuitionistic tautology. As a corollary (...) we obtain a semantic argument that the quantifier V is not definable in IPC² from ⊥, V, ^, →. (shrink)

We prove that for each β, γ < ε0 there existsα < ε0 such that whenever A ⊆ ω is α ‐large and G: A → β is such that (∀a ∈ A)(psn(G (a)) ≤ a), then there exists a γ ‐large C ⊆ A on which G is nondecreasing. Moreover, we give upper bounds for α for small ordinals β ≤ ω (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim).

We investigate theories of initial segments of the standard models for arithmetics. It is easy to see that if the ordering relation is definable in the standard model then the decidability results can be transferred from the infinite model into the finite models. On the contrary we show that the Σ₂—theory of multiplication is undecidable in finite models. We show that this result is optimal by proving that the Σ₁—theory of multiplication and order is decidable in finite models as well (...) as in the standard model. We show also that the exponentiation function is definable in finite models by a formula of arithmetic with multiplication and that one can define in finite models the arithmetic of addition and multiplication with the concatenation operation. We consider also the spectrum problem. We show that the spectrum of arithmetic with multiplication and arithmetic with exponentiation is strictly contained in the spectrum of arithmetic with addition and multiplication. (shrink)

It is known that various complexity-theoretical problems can be translated into some special spectra problems. Thus, questions about complexity classes are translated into questions about the expressive power of some languages. In this paper we investigate the spectra of some logics with Henkin quantifiers in the empty vocabulary.

It is known that various complexity-theoretical problems can be translated into some special spectra problems (see e.g. Fagin [Fa74] or Blass and Gurevich, [Bl-Gu86]). So questions about complexity classes are translated into questions about the expressive power of some languages. In this paper we investigate the spectra of some logics with Henkin quanti fiers in the empty vocabulary. This problem has been investigated fi rstly by Krynicki and Mostowski in [Kr-Mo 92] and [Kr- Mo 95]. All presented results can be (...) also treated as results about the expressive power of certain languages in fi nite models. (shrink)

How (Not) to Be Secular is what Jamie Smith calls "your hitchhiker's guide to the present" -- it is both a reading guide to Charles Taylor's monumental work A Secular Age and philosophical guidance on how we might learn to live in our times. Taylor's landmark book A Secular Age (2007) provides a monumental, incisive analysis of what it means to live in the post-Christian present -- a pluralist world of competing beliefs and growing unbelief. Jamie Smith's book is a (...) compact field guide to Taylor's insightful study of the secular, making that very significant but daunting work accessible to a wide array of readers. Even more, though, Smith's How (Not) to Be Secular is a practical philosophical guidebook, a kind of how-to manual on how to live in our secular age. It ultimately offers us an adventure in self-understanding and maps out a way to get our bearings in today's secular culture, no matter who "we" are -- whether believers or skeptics, devout or doubting, self-assured or puzzled and confused. This is a book for any thinking person to chew on. (shrink)

Building on our diverse research traditions in the study of reasoning, language and communication, the Polish School of Argumentation integrates various disciplines and institutions across Poland in which scholars are dedicated to understanding the phenomenon of the force of argument. Our primary goal is to craft a methodological programme and establish organisational infrastructure: this is the first key step in facilitating and fostering our research movement, which joins people with a common research focus, complementary skills and an enthusiasm to work (...) together. This statement—the Manifesto—lays the foundations for the research programme of the Polish School of Argumentation. (shrink)

Practical deliberation often involves conditional judgements about what will (likely) happen if certain alternatives are pursued. It is widely assumed that the conditionals useful in deliberation are counterfactual or subjunctive conditionals. Against this, I argue that the conditionals of deliberation are indicatives. Key to the argument is an account of the relation between 'straightforward' future-directed conditionals like ' If the house is not painted, it will soon look quite shabby' and * "w e r e ' ' e d F (...) D C s like ' If the house were not to be painted, it would soon look quite shabby': an account on which both of these types of FDCs are grouped with the indicatives for semantic treatment and on which, while conditionals of both types are properly used in means/ends deliberations, those of the ' were'ed-up variety are especially well suited for that purpose. (shrink)

The provability problem in intuitionistic propositional second-order logic with existential quantifier and implication (∃,→) is proved to be undecidable in presence of free type variables (constants). This contrasts with the result that inutitionistic propositional second-order logic with existential quantifier, conjunction and negation is decidable.

'Pataphysics: The Poetics of an Imaginary Science is a survey that attempts to describe a hypothetic philosophy--the avant-garde pseudo-science imagined by Alfred Jarry. 'Pataphysics is a supplement to metaphysics, accenting it, then replacing it, in order to create a philosophic alternative, whose discipline can study cases, not of conception, but of exception: variance , alliance , and deviance . 'Pataphysics synthesizes the romantic schism between a literal, scientized discourse and a figural, poeticized discourse, and my thesis suggests that this revision (...) of the signifier "science" by 'pataphysics is symptomatic of a postmodern transition in science from a paradigm of absolutism to a paralogy of relativism. Structured as a descriptive explication, which emphasizes a theoretical perspective, this survey is divided into five chapters: the first chapter recounts the history of the conflict between science and poetry ; the second chapter examines the avant-garde pseudo-science of 'pataphysics itself ; and finally, the last three chapters discuss the influence of 'pataphysics upon the poetics of its subsequent successors . While my thesis focuses upon theories of textual poetics rather than poetry itself , my thesis does nevertheless strive to be as conceptually encyclopedic as 'pataphysics itself: instead of normalizing 'pataphysics within one theoretical perspective, this survey alludes intermittently to 'pataphysical enterprises that constitute exceptions to such a genealogy of Jarryites. What is at stake is the status of poetry in a world of science. How might poetry reclaim its own viable truth? How might science benefit from its own poetic irony? For the postmodern condition, such questions have already opened up a novel space for speculative imagination; hence, this survey presents itself as a kind of primer for a future of possible research. (shrink)

In this short but meaty book, Peter Unger questions the objective answers that have been given to central problems in philosophy. As Unger hypothesizes, many of these problems are unanswerable, including the problems of knowledge and scepticism, the problems of free will, and problems of causation and explanation. In each case, he argues, we arrive at one answer only relative to an assumption about the meaning of key terms, terms like "know" and like "cause," even while we arrive at an (...) opposite answer relative to quite different assumptions, but equally arbitrary assumptions, about what the key terms mean. (shrink)

This article explores the enduring mysteries of consciousness and the afterlife, two enigmatic topics that have fascinated humanity for ages. Despite extensive scientific efforts, the existence of an afterlife remains unproven, and understanding consciousness remains a significant challenge. The research introduces innovative hypotheses through simple thought experiments with empirical evidence and robust theoretical foundations. It delves into the complexities of consciousness, its relationship with the brain, and the need for interdisciplinary approaches encompassing physics, psychology, and philosophy. Boldly contemplating the probability (...) of a continuous consciousness after death, the study argues that existing evidence strongly supports this idea. Beyond theoretical implications, it envisions practical outcomes, suggesting that insights into these mysteries could enhance human well-being and contribute to a more harmonious world. In summary, this article embarks on a quest to shed light on age-old questions about consciousness and the afterlife. Through fresh methodologies, it aims to provide new perspectives that could reshape our understanding of existence and inspire intellectuals to positive individual and societal advancements. -/- . (shrink)

Neoplatonic allegorical interpretation expounds how literary texts present philosophical ideas in an enigmatic and coded form, offering an alternative path to the divine truths. The Neoplatonist Porphyry’s _On the Cave of the Nymphs_ is one of the most significant allegorical interpretation handed down to us from Antiquity. This monograph, exclusively dedicated to the analysis of _On the Cave of Nymphs_, demonstrates that Porphyry interprets Homer’s verse from Odyssey 13.102-112 to convey his philosophical thoughts, particularly on the material world, relationship between (...) soul and body and the salvation of the soul through the doctrines of Plato and Plotinus. The Homeric cave of the nymphs with two gates is a station where the souls descend into genesis and ascend to the intelligible realm. Porphyry associates Odysseus’ long wanderings with the journey of the soul and its salvation from the irrational to rational through escape from all toils of the material world. (shrink)

are ambiguous. In the mouth of someone who cannot remember whether it was Michael, or rather someone else, who was top scorer, can express the epistemic possibility that Michael led the league in scoring. But from someone who knows that Michael did not even play last season, but is wondering what would have happened if he had, means something quite different. Now where it has this quite different meaning, may still turn out to be the expression of some epistemic possibility. (...) Perhaps where does not express the epistemic possibility of ‘Michael led the league in scoring’, it expresses the epistemic possibility of ‘Michael would have led the league in scoring’. Analysis of this ‘would have’ statement, together with an exploration of the suspicion that the ‘might have’ statement is ambiguous between these two epistemic possibilities, will have to await another occasion. The important point for present purposes is that is ambiguous between an expression of the epistemic possibility of ‘Michael led the league in scoring’ and some quite different reading. (shrink)

What are the criteria for reasonable clinical judgements? The reasonableness of macro-level decision-making has been much discussed, but little attention has been paid to the reasonableness of applying guidelines generated at a macro-level to individual cases. This paper considers a framework for reasonable clinical decision-making that will capture cases where relevant guidelines cannot reasonably be followed. There are three main sections. (1) Individual claims on healthcare from the point of view of concerns about equity are analysed. (2) The demands of (...) responsibility and equity on professional clinical performance are discussed, and how the combination of these demands emerges into seven requirements that constitute the framework is explored. Since this framework is developed to assist in reasonable clinical decision-making, practical implications of all these requirements are also suggested. (3) Challenges concerning the framework are discussed. First, a crucial presumption that the framework relies upon is considered—namely, clinicians’ willingness to justify their decisions as requested. Then how public deliberation may influence clinical decision-making is discussed. Next is a consideration of how clinicians’ need to have confidence in their own judgements in order to perform in a manner worthy of trust would be compatible with adherence to the framework supported by public deliberation. It is concluded that fair distribution in the interplay between macro- and micro-level considerations can be secured by legitimising procedures on each level, by ensuring well-organised and continuing public debate and by basing individual clinical judgements upon well-justified and principled normative bases. (shrink)

It is only when mixing two or more pure substances along a reversible path that the entropy of the mixing can be made physically manifest. It is not, in this case, a mere mathematical artifact. This mixing requires a process of successive stages. In any finite number of stages, the external manifestation of the entropy change, as a definite and measurable quantity of heat, isa fully continuous function of the relevant variables. It is only at an infinite and unattainable limit (...) thata non-uniform convergence occurs. And this occurs when considered in terms of the number of stages together with a distinguishability parameter appropriate to the particular device which is used to achieve reversibility. These considerations, which are of technological interest to chemical engineers, resolve a paradox derived in chemical theory called Gibbs'' Paradox. (shrink)

University human research ethics application procedures can be complicated and daunting, especially for international students unfamiliar with the process and the language. We conducted focus groups and interviews with four research higher degree and 21 Master’s coursework international students at an Australian university to gain their views on the human ethics application process. We found the most important influences on their experience were: the time it took to do an application; support from supervisors, peers and others; their own language skills; (...) and their lack of familiarity with research ethics procedures. To improve the experience of international students undertaking research involving human research ethics applications, we recommend universities provide guidance on institutional ethics review processes, concepts and terminology, with translations in a range of languages, together with guidance on how to conduct research ethically within and outside the students’ own countries. We also recommend curricula be developed to further students’ understanding of the importance of ethical research practice, and that these curricula be embedded in undergraduate and postgraduate degree programs and reflected in course learning outcomes. (shrink)

What is interest and how has it been conceptualized and studied? -- What explains the power of interest? : Why are students who have an interest for content more likely to continue to reengage and develop more conceptual sophistication? -- What is known about assessing existing interest? How do new interests develop? How can the phase of a person's interest be identified and measured? -- What is the relation between the development of interest and other motivational variables? -- Is it (...) a paradox that interest declines as subject matter gets more developed? What is "interest driven learning"? Does it matter if interests are taken up in rather than out of school? How different is an interest in one versus another subject matter, or domain? -- What we can now say about interest, its generation and development? What are the implications of knowing that interest can be developed? What could further research help us to understand? (shrink)

The widespread potential for somatic fusion among different conspecific multicellular individuals suggests that such fusion is adaptive. However, because recognition of non‐kin (allorecognition) usually leads to a rejection response, successful somatic fusion is limited to close kin. This is consistent with kin‐selection theory, which predicts that the potential cost of fusion and the potential for somatic parasitism decrease with increasing relatedness. Paradoxically, however, Crozier1 found that, in the short term, positive‐frequency‐dependent selection eliminates the required genetic polymorphism at allorecognition loci. The (...) ‘Crozier paradox’ may be solved if allorecognition is based on extrinsically balanced polymorphisms, for example at immune loci. Alternatively, the assumption of most models that self fusion is mutually beneficial is wrong. If fusion is on average harmful, selection will promote unconditional rejection. However, we propose that fusion within individuals is beneficial, selecting for the ability to fuse, but fusion between individuals on average costly, selecting for non‐self recognition (rather than non‐kin recognition). We discuss experimental data on fungi that are consistent with this hypothesis. BioEssays 30:1193–1203, 2008. © 2008 Wiley Periodicals, Inc. (shrink)

I examine two challenges that collaborative research raises for science. First, collaborative research threatens the motivation of scientists. As a result, I argue, collaborative research may have adverse effects on what sorts of things scientists can effectively investigate. Second, collaborative research makes it more difficult to hold scientists accountable. I argue that the authors of multi-authored articles are aptly described as plural subjects, corporate bodies that are more than the sum of the individuals involved. Though journal editors do not currently (...) conceive of the authors of multi-authored articles this way, this conception provides us with the conceptual resources to make sense of how collaborating scientists behave.Keywords: Collaborative research; Authorship; Multi-authored articles; Responsibility; Reward system; Plural subject. (shrink)

In welchem Verhaltnis steht die Seelenlehre zur Kosmologie in Platons Phaidon?

that Buddhism is best understood as a philosophy of practice-or a.