We study finite ℓ‐colourable structures with an underlying pregeometry. The probability measure that is used corresponds to a process of generating such structures by which colours are first randomly assigned to all 1‐dimensional subspaces and then relationships are assigned in such a way that the colouring conditions are satisfied but apart from this in a random way. We can then ask what the probability is that the resulting structure, where we now forget the specific colouring of the generating process, has (...) a given property. With this measure we get the following results: (1) A zero‐one law. (2) The set of sentences with asymptotic probability 1 has an explicit axiomatisation which is presented. (3) There is a formula (not directly speaking about colours) such that, with asymptotic probability 1, the relation “there is an ℓ‐colouring which assigns the same colour to x and y” is defined by. (4) With asymptotic probability 1, an ℓ‐colourable structure has a unique ℓ‐colouring (up to permutation of the colours). (shrink)

Let V be a finite relational vocabulary in which no symbol has arity greater than 2. Let be countable V‐structure which is homogeneous, simple and 1‐based. The first main result says that if is, in addition, primitive, then it is strongly interpretable in a random structure. The second main result, which generalizes the first, implies (without the assumption on primitivity) that if is “coordinatized” by a set with SU‐rank 1 and there is no definable (without parameters) nontrivial equivalence relation on (...) M with only finite classes, then is strongly interpretable in a random structure. (shrink)

A probability distribution can be given to the set of isomorphism classes of models with universe {1, ..., n} of a sentence in first-order logic. We study the entropy of this distribution and derive a result from the 0–1 law for first-order sentences.

We study a class of 0-categorical simple structures such that every M in has uncomplicated forking behavior and such that definable relations in M which do not cause forking are independent in a sense that is made precise; we call structures in independent. The SU-rank of such M may be n for any natural number n>0. The most well-known unstable member of is the random graph, which has SU-rank one. The main result is that for every strongly independent structure M (...) in , if a sentence φ is true in M then φ is true in a finite substructure of M. The same conclusion holds for every structure in with SU-rank one; so in this case the word ‘strongly’ can be removed. A probability theoretic argument is involved and it requires sufficient independence between relations which do not cause forking. A stable structure M belongs to if and only if it is 0-categorical, 0-stable and every definable strictly minimal subset of is indiscernible. (shrink)

A condition, in two variants, is given such that if a property P satisfies this condition, then every logic which is at least as strong as first-order logic and can express P fails to have the compactness property. The result is used to prove that for a number of natural properties P speaking about automorphism groups or connectivity, every logic which is at least as strong as first-order logic and can express P fails to have the compactness property. The basic (...) idea underlying the results and examples presented here is that it is possible to construct a countable first-order theory T such that every model of T has a very rich automorphism group, but every finite subset T′ of T has a model which is rigid. (shrink)

We work with a finite relational vocabulary with at least one relation symbol with arity at least 2. Fix any integer m > 1. For almost all finite structures such that at least m elements are moved by some automorphisms, the automorphism group is i\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${^{i}}$$\end{document} for some i≤/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${i \leq /2}$$\end{document}; and if some relation symbol has arity at least 3, then the automorphism (...) group is almost always Z2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{Z}_{2}}$$\end{document}. (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)

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)

'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)