Results for 'Paul Howard Frampton'
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- Possible solution of dark matter, the solution of dark energy and Gell-Mann as great theoretician.PaulHowardFrampton -2010 - In Harald Fritzsch & K. K. Phua,Proceedings of the Conference in Honour of Murray Gell-Mann's 80th Birthday. World Scientific.
- The beautiful union of science, philosophy, and religion.PaulHoward Ellson -2006 - Tipperary, Ireland: AASB Media.Humankind : a limited company? -- From volume to point: 1. Philosophy, 2. Religion -- Science : specialised but not special -- Cosmic hierarchies -- Consciousness -- Cognition -- In theory -- Back to Genesis -- The beautiful union.
- Charles Darwin: A CompanionR. B. Freeman.PaulHoward Barrett -1980 -Isis 71 (2):353-353.
- Pre-string theory.PaulFrampton -2016 - In Lars Brink, L. N. Chang, M. Y. Han, K. K. Phua & Yoichiro Nambu,Memorial volume for Y. Nambu. Hackensack, NJ: World Scientific Publishing Co. Pte..Export citation
Bookmark - Models of $${{\textsf{ZFA}}}$$ in which every linearly ordered set can be well ordered.PaulHoward &Eleftherios Tachtsis -2023 -Archive for Mathematical Logic 62 (7):1131-1157.We provide a general criterion for Fraenkel–Mostowski models of $${\textsf{ZFA}}$$ (i.e. Zermelo–Fraenkel set theory weakened to permit the existence of atoms) which implies “every linearly ordered set can be well ordered” ( $${\textsf{LW}}$$ ), and look at six models for $${\textsf{ZFA}}$$ which satisfy this criterion (and thus $${\textsf{LW}}$$ is true in these models) and “every Dedekind finite set is finite” ( $${\textsf{DF}}={\textsf{F}}$$ ) is true, and also consider various forms of choice for well-ordered families of well orderable sets in these (...) models. In Model 1, the axiom of multiple choice for countably infinite families of countably infinite sets ( $${\textsf{MC}}_{\aleph _{0}}^{\aleph _{0}}$$ ) is false. It was the open question of whether or not such a model exists (fromHoward and Tachtsis “On metrizability and compactness of certain products without the Axiom of Choice”) that provided the motivation for this paper. In Model 2, which is constructed by first choosing an uncountable regular cardinal in the ground model, a strong form of Dependent choice is true, while the axiom of choice for well-ordered families of finite sets ( $${\textsf{AC}}^{{\textsf{WO}}}_{{\textsf{fin}}}$$ ) is false. Also in this model the axiom of multiple choice for well-ordered families of well orderable sets fails. Model 3 is similar to Model 2 except for the status of $${\textsf{AC}}^{{\textsf{WO}}}_{{\textsf{fin}}}$$ which is unknown. Models 4 and 5 are variations of Model 3. In Model 4 $${\textsf{AC}}_{\textrm{fin}}^{{\textsf{WO}}}$$ is true. The construction of Model 5 begins by choosing a regular successor cardinal in the ground model. Model 6 is the only one in which $$2{\mathfrak {m}} = {\mathfrak {m}}$$ for every infinite cardinal number $${\mathfrak {m}}$$. We show that the union of a well-ordered family of well orderable sets is well orderable in Model 6 and that the axiom of multiple countable choice is false. (shrink)No categories
- Facial Emblems of ‘Right’ and ‘Wrong’: Topographical Analysis and Derivation of a Recognition Test.Howard M. Rosenfeld,Marilyn Shea &Paul Greenbaum -1979 -Semiotica 26 (1-2).
- Contingent partial reinforcement and the anticipation of correct alternatives.Howard Brand,James M. Sakoda &Paul J. Woods -1957 -Journal of Experimental Psychology 53 (6):417.
- The Objects of Perceptual Experience.Paul Snowdon &Howard Robinson -1990 -Aristotelian Society Supplementary Volume 64 (1):121-166.
- Phase evolution in nanocrystalline silicon films: Hydrogen dilution and the cone kinetics model.Paul Stradins,Charles W. Teplin &Howard M. Branz -2009 -Philosophical Magazine 89 (28-30):2461-2468.No categories
- Conceptualising and Understanding Artistic Creativity in the Dementias: Interdisciplinary Approaches to Research and Practise.Paul M. Camic,Sebastian J. Crutch,Charlie Murphy,Nicholas C. Firth,Emma Harding,Charles R. Harrison,SusannahHoward,Sarah Strohmaier,Janneke Van Leewen,Julian West,Gill Windle,Selina Wray &Hannah Zeilig -2018 -Frontiers in Psychology 9.
- Portrait of Canterbury CathedralPortrait of Salisbury CathedralColonial Williamsburg-Its Buildings and Gardens.Paul Zucker,G. H. Cook,A. Lawrence Kocher &Howard Dearstyne -1950 -Journal of Aesthetics and Art Criticism 8 (4):269.
- On a variant of Rado’s selection lemma and its equivalence with the Boolean prime ideal theorem.PaulHoward &Eleftherios Tachtsis -2014 -Archive for Mathematical Logic 53 (7-8):825-833.We establish that, in ZF, the statementRLT: Given a setIand a non-empty setF\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{F}}$$\end{document}of non-empty elementary closed subsets of 2Isatisfying the fip, ifF\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{F}}$$\end{document}has a choice function, then⋂F≠∅\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\bigcap\mathcal{F} \ne \emptyset}$$\end{document},which was introduced in Morillon :739–749, 2012), is equivalent to the Boolean Prime Ideal Theorem. The result provides, on one hand, an affirmative answer to Morillon’s corresponding (...) question in Morillon and, on the other hand, a negative answer—in the setting of ZFA —to the question in Morillon of whether RLT is equivalent to Rado’s selection lemma. (shrink)
- Paracompactness of Metric Spaces and the Axiom of Multiple Choice.PaulHoward,K. Keremedis &J. E. Rubin -2000 -Mathematical Logic Quarterly 46 (2):219-232.The axiom of multiple choice implies that metric spaces are paracompact but the reverse implication cannot be proved in set theory without the axiom of choice.
- Von Rimscha's Transitivity Conditions.PaulHoward,Jean E. Rubin &Adrienne Stanley -2000 -Mathematical Logic Quarterly 46 (4):549-554.In Zermelo-Fraenkel set theory with the axiom of choice every set has the same cardinal number as some ordinal. Von Rimscha has weakened this condition to “Every set has the same cardinal number as some transitive set”. In set theory without the axiom of choice, we study the deductive strength of this and similar statements introduced by von Rimscha.
- Repertoire d'art et d'archeologieLeon Trotsky on Literature and ArtArte precolombino de Mexico y de la America CentralThe Homeric Imagination.Howard Clarke,Paul N. Siegel,Salvador Toscano &Paolo Vivante -1971 -Journal of Aesthetics and Art Criticism 30 (1):142.
- U.S. Responses To Japanese Wartime Inhuman Experimentation After World War Ii: National Security and Wartime Exigency.Howard Brody,Sarah E. Leonard,Jing-bao Nie &Paul Weindling -2014 -Cambridge Quarterly of Healthcare Ethics 23 (2):220-230.In 1945–46, representatives of the U.S. government made similar discoveries in both Germany and Japan, unearthing evidence of unethical experiments on human beings that could be viewed as war crimes. The outcomes in the two defeated nations, however, were strikingly different. In Germany, the United States, influenced by the Canadian physician John Thompson, played a key role in bringing Nazi physicians to trial and publicizing their misdeeds. In Japan, the United States played an equally key role in concealing information about (...) the biological warfare experiments and in securing immunity from prosecution for the perpetrators. The greater force of appeals to national security and wartime exigency help to explain these different outcomes. (shrink)
- (1 other version)A Proof of a Theorem of Tennenbaum.Paul E.Howard -1972 -Mathematical Logic Quarterly 18 (7):111-112.
- Separablilty of metric measure spaces and choice axioms.PaulHoward -2024 -Archive for Mathematical Logic 63 (7):987-1003.In set theory without the Axiom of Choice we prove that the assertion “For every metric space (_X_, _d_) with a Borel measure \(\mu \) such that the measure of every open ball is positive and finite, (_X_, _d_) is separable.’ is implied by the axiom of choice for countable collections of sets and implies the axiom of choice for countable collections of finite sets. We also show that neither implication is reversible in Zermelo–Fraenkel set theory weakend to permit the (...) existence of atoms and that the second implication is not reversible in Zermelo–Fraenkel set theory. This gives an answer to a question of Dybowski and Górka (Arch Math Logic 62:735–749, 2023. https://doi.org/10.1007/s00153-023-00868-4 ). (shrink)No categories
- Divine Hiddenness: New Essays.DanielHoward-Snyder &Paul Moser -2001 - New York, NY: Cambridge University Press.For many people the existence of God is by no means a sufficiently clear feature of reality. This problem, the fact of divine hiddenness, has been a source of existential concern and has sometimes been taken as a rationale for support of atheism or agnosticism. In this collection of essays, a distinguished group of philosophers of religion explore the question of divine hiddenness in considerable detail. The issue is approached from several perspectives including Jewish, Christian, atheist and agnostic. There is (...) coverage of the historical treatment of divine hiddenness as found in the work of Maimonides, St. John of the Cross, Jonathan Edwards, Kierkegaard, and various Biblical writers. A substantial introduction clarifies the main problems of and leading solutions to divine hiddenness. Primarily directed at philosophers of religion, theologians, and scholars of religious studies, this collection could also serve as a textbook for upper-level courses in philosophy of religion. (shrink)
- The influence of disability on suicidal behaviour.Howard Meltzer,Traolach Brugha,Michael S. Dennis,Angela Hassiotis,Rachel Jenkins,Sally McManus,Deeraj Rai &Paul Bebbington -2012 -Alter - European Journal of Disability Research / Revue Européenne de Recherche Sur le Handicap 6 (1):1-12.No categories
- Letter to the Editor.Howard Mann,Benjamin Djulbegovic &Paul Gold -2003 -Journal of Law, Medicine and Ethics 31 (1):5-6.
- Introduction.Howard Sankey &Paul Hoyningen-Huene -2001 - In Paul Hoyningen-Huene & Howard Sankey,Incommensurability and Related Matters. Kluwer Academic Publishers.
- Bases, spanning sets, and the axiom of choice.PaulHoward -2007 -Mathematical Logic Quarterly 53 (3):247-254.Two theorems are proved: First that the statement“there exists a field F such that for every vector space over F, every generating set contains a basis”implies the axiom of choice. This generalizes theorems of Halpern, Blass, and Keremedis. Secondly, we prove that the assertion that every vector space over ℤ2 has a basis implies that every well-ordered collection of two-element sets has a choice function.
- Short-Term Fasting Selectively Influences Impulsivity in Healthy Individuals.MaxineHoward,Jonathan P. Roiser,Sam J. Gilbert,Paul W. Burgess,Peter Dayan &Lucy Serpell -2020 -Frontiers in Psychology 11.Previous research has shown that short-term fasting in healthy individuals is associated with changes in risky decision-making. The current experiment was designed to examine the influence of short-term fasting in healthy individuals on four types of impulsivity: reflection impulsivity, risky decision-making, delay aversion, and action inhibition. Participants were tested twice, once when fasted for 20 hours, and once when satiated. Participants demonstrated impaired action inhibition when fasted; committing significantly more errors of commission during a food-related Affective Shifting Task. Participants also (...) displayed decreased reflection impulsivity when fasted, opening significantly more boxes during the Information Sampling Task (IST). There were no significant differences in performance between fasted and satiated sessions for risky decision-making or delay aversion. These findings may have implications for understanding eating disorders such as Bulimia Nervosa (BN). Although BN has been characterised as a disorder of poor impulse control, inconsistent findings when comparing individuals with BN and healthy individuals on behavioural measures of impulsivity question this characterisation. Since individuals with BN undergo periods of short-term fasting, the inconsistent findings could be due to differences in the levels of satiation of participants. The current results indicate that fasting can affect performance on the IST, a measure of impulsivity previously studied in BN, whilst performance on other impulsivity measures were unaffected. However, the results from the IST were contrary to the original hypothesis and should be replicated before specific conclusions can be made. (shrink)
- The axiom of choice for countable collections of countable sets does not imply the countable union theorem.Paul E.Howard -1992 -Notre Dame Journal of Formal Logic 33 (2):236-243.
- Limitations on the Fraenkel-Mostowski method of independence proofs.Paul E.Howard -1973 -Journal of Symbolic Logic 38 (3):416-422.The Fraenkel-Mostowski method has been widely used to prove independence results among weak versions of the axiom of choice. In this paper it is shown that certain statements cannot be proved by this method. More specifically it is shown that in all Fraenkel-Mostowski models the following hold: 1. The axiom of choice for sets of finite sets implies the axiom of choice for sets of well-orderable sets. 2. The Boolean prime ideal theorem implies a weakened form of Sikorski's theorem.
- Introduction: The Hiddenness of God.DanielHoward-Snyder &Paul K. Moser -2001 - In Daniel Howard-Snyder & Paul Moser,Divine Hiddenness: New Essays. New York, NY: Cambridge University Press.
- Anticipation of reward as a function of partial reinforcement.Howard Brand,Paul J. Woods &James M. Sakoda -1956 -Journal of Experimental Psychology 52 (1):18.
- BURGGRAEVE, Roger, The Ethical Meaning of Money in the Thought of Emmanuel Levinas. p. 85 DEKKERS, Wim, What Do We Call 'Death'? Some Re-flections on the End of Life in Western Culture. p. 188. [REVIEW]Howard H. Harriott,Samuel Ijsseling,Koen Raes,Bert Roebben,Erik Schokkaert,André van de Putte,Jef van Gerwen,Toon van Houdt,Paul van Tongeren &Johan Verstraeten -1995 -Ethical Perspectives 2 (3):220.
- A Multiperspective Approach to Neuroeducational Research.Paul A.Howard-Jones -2011 -Educational Philosophy and Theory 43 (1):24-30.There is increasing interest in research that combines neuroscientific and educational perspectives on learning, but significant philosophical issues divide these perspectives. This article examines the value of such neuroeducational research and how concepts from different perspectives may be interrelated through a ‘level of actions’ model. This model, which encourages a multiperspective approach, may be helpful in avoiding some of the worst transgressions of sense-making in constructing concepts that span neuroscience and education. Application of the model is explored in the context (...) of teaching strategies intended to foster creativity, and its affordances and limitations are discussed. (shrink)
- The History of SurrealismAn Introduction to Surrealism.Paul C. Ray,Maurice Nadeau,RichardHoward &J. H. Matthews -1966 -Journal of Aesthetics and Art Criticism 24 (3):446.
- Philosophical challenges for researchers at the interface between neuroscience and education.PaulHoward-Jones -2008 -Journal of Philosophy of Education 42 (3-4):361-380.This article examines how discussions around the new interdisciplinary research area combining neuroscience and education have brought into sharp relief differences in the philosophies of learning in these two areas. It considers the difficulties faced by those working at the interface between these two areas and, in particular, it focuses on the challenge of avoiding 'non-sense' when attempting to include the brain in educational argument. The paper relates common transgressions in sense-making with dualist and monist notions of the mind-brain relationship. (...) It then extends a brain-mind-behaviour model from cognitive neuroscience to include a greater emphasis on social interaction and construction. This creates a tool for examining the potentially complex interrelationships between the different learning philosophies in this emerging new field. (shrink)
- The principles and practices of educational neuroscience: Comment on Bowers (2016).Paul A.Howard-Jones,Sashank Varma,Daniel Ansari,Brian Butterworth,Bert De Smedt,Usha Goswami,Diana Laurillard &Michael S. C. Thomas -2016 -Psychological Review 123 (5):620-627.No categories
- The strength of the $\Delta$-system lemma.PaulHoward &Jeffrey Solski -1992 -Notre Dame Journal of Formal Logic 34 (1):100-106.
- No decreasing sequence of cardinals.PaulHoward &Eleftherios Tachtsis -2016 -Archive for Mathematical Logic 55 (3-4):415-429.In set theory without the Axiom of Choice, we investigate the set-theoretic strength of the principle NDS which states that there is no function f on the set ω of natural numbers such that for everyn ∈ ω, f ≺ f, where for sets x and y, x ≺ y means that there is a one-to-one map g : x → y, but no one-to-one map h : y → x. It is a long standing open problem whether NDS implies (...) AC. In this paper, among other results, we show that NDS is a strong axiom by establishing that ACLO ↛ NDS in ZFA set theory. The latter result provides a strongly negative answer to the question of whether “every Dedekind-finite set is finite” implies NDS addressed in G. H. Moore “Zermelo’s Axiom of Choice. Its Origins, Development, and Influence” and in P.Howard–J. E. Rubin “Consequences of the Axiom of Choice”. We also prove that ACWO ↛ NDS in ZF and that “for all infinite cardinals m, m + m = m” ↛ NDS in ZFA. (shrink)
- Making Practice Publishable: What Practice Academics Need to Do to Get Their Work Published, and What that Tells Us about the Theory-practice Gap.Helen Wolfenden,Howard Sercombe &Paul Tucker -2019 -Social Epistemology 33 (6):555-573.ABSTRACTFor centuries, universities have supported the pursuit of knowledge through the academic disciplines while also preparing students for the professions. These two purposes are frequently in...
- The axiom of choice for well-ordered families and for families of well- orderable sets.PaulHoward &Jean E. Rubin -1995 -Journal of Symbolic Logic 60 (4):1115-1117.We show that it is not possible to construct a Fraenkel-Mostowski model in which the axiom of choice for well-ordered families of sets and the axiom of choice for sets are both true, but the axiom of choice is false.
- Compactness in Countable Tychonoff Products and Choice.PaulHoward,K. Keremedis &J. E. Rubin -2000 -Mathematical Logic Quarterly 46 (1):3-16.We study the relationship between the countable axiom of choice and the Tychonoff product theorem for countable families of topological spaces.
- Divisibility of dedekind finite sets.David Blair,Andreas Blass &PaulHoward -2005 -Journal of Mathematical Logic 5 (1):49-85.A Dedekind-finite set is said to be divisible by a natural number n if it can be partitioned into pieces of size n. We study several aspects of this notion, as well as the stronger notion of being partitionable into n pieces of equal size. Among our results are that the divisors of a Dedekind-finite set can consistently be any set of natural numbers, that a Dedekind-finite power of 2 cannot be divisible by 3, and that a Dedekind-finite set can (...) be congruent modulo 3, to all of 0, 1, and 2 simultaneously. (shrink)
- The need for interdisciplinary dialogue in developing ethical approaches to neuroeducational research.Paul A.Howard-Jones &Kate D. Fenton -2011 -Neuroethics 5 (2):119-134.This paper argues that many ethical issues in neuroeducational research cannot be appropriately addressed using the principles and guidance available in one of these areas alone, or by applying these in simple combination. Instead, interdisciplinary and public dialogue will be required to develop appropriate normative principles. In developing this argument, it examines neuroscientific and educational perspectives within three broad categories of ethical issue arising at the interface of cognitive neuroscience and education: issues regarding the carrying out of interdisciplinary research, the (...) scrutiny and communication of findings and concepts, and the application of research and associated issues of policy likely to arise in the future. To help highlight the need for interdisciplinary and public discussion, we also report the opinions of a group of educators (comprising trainee teachers, teachers and head teachers) on the neuroeducational ethics of cognitive enhancing drugs, infant screening, genetic profiling and animal research. (shrink)
- Maximal $p$-subgroups and the axiom of choice.Paul E.Howard &Mary Yorke -1987 -Notre Dame Journal of Formal Logic 28 (2):276-283.
- Darwin on Man: A Psychological Study of Scientific Creativity; Together with Darwin's Early and Unpublished Notebooks.Howard E. Gruber &Paul H. Barrett -1976 -Journal of the History of Biology 9 (2):323-324.
- Disjoint Unions of Topological Spaces and Choice.PaulHoward,Kyriakos Keremedis,Herman Rubin &Jean E. Rubin -1998 -Mathematical Logic Quarterly 44 (4):493-508.We find properties of topological spaces which are not shared by disjoint unions in the absence of some form of the Axiom of Choice.
- Independence results for class forms of the axiom of choice.Paul E.Howard,Arthur L. Rubin &Jean E. Rubin -1978 -Journal of Symbolic Logic 43 (4):673-684.Let NBG be von Neumann-Bernays-Gödel set theory without the axiom of choice and let NBGA be the modification which allows atoms. In this paper we consider some of the well-known class or global forms of the wellordering theorem, the axiom of choice, and maximal principles which are known to be equivalent in NBG and show they are not equivalent in NBGA.
- The finiteness of compact Boolean algebras.PaulHoward -2011 -Mathematical Logic Quarterly 57 (1):14-18.We show that it consistent with Zermelo-Fraenkel set theory that there is an infinite, compact Boolean algebra.
- (1 other version)Rado's selection lemma does not imply the Boolean prime ideal theorem.Paul E.Howard -1984 -Mathematical Logic Quarterly 30 (9‐11):129-132.
- Subgroups of a free group and the axiom of choice.Paul E.Howard -1985 -Journal of Symbolic Logic 50 (2):458-467.
- On infinite‐dimensional Banach spaces and weak forms of the axiom of choice.PaulHoward &Eleftherios Tachtsis -2017 -Mathematical Logic Quarterly 63 (6):509-535.We study theorems from Functional Analysis with regard to their relationship with various weak choice principles and prove several results about them: “Every infinite‐dimensional Banach space has a well‐orderable Hamel basis” is equivalent to ; “ can be well‐ordered” implies “no infinite‐dimensional Banach space has a Hamel basis of cardinality ”, thus the latter statement is true in every Fraenkel‐Mostowski model of ; “No infinite‐dimensional Banach space has a Hamel basis of cardinality ” is not provable in ; “No infinite‐dimensional (...) Banach space has a well‐orderable Hamel basis of cardinality ” is provable in ; (the Axiom of Choice for denumerable families of non‐empty finite sets) is equivalent to “no infinite‐dimensional Banach space has a Hamel basis which can be written as a denumerable union of finite sets”; Mazur's Lemma (“If X is an infinite‐dimensional Banach space, Y is a finite‐dimensional vector subspace of X, and, then there is a unit vector such that for all and all scalars α”) is provable in ; “A real normed vector space X is finite‐dimensional if and only if its closed unit ball is compact” is provable in ; (Principle of Dependent Choices) + “ can be well‐ordered” does not imply the Hahn‐Banach Theorem () in ; and “no infinite‐dimensional Banach space has a Hamel basis of cardinality ” are independent from each other in ; “No infinite‐dimensional Banach space can be written as a denumerable union of finite‐dimensional subspaces” lies in strength between (the Axiom of Countable Choice) and ; implies “No infinite‐dimensional Banach space can be written as a denumerable union of closed proper subspaces” which in turn implies ; “Every infinite‐dimensional Banach space has a denumerable linearly independent subset” is a theorem of, but not a theorem of ; and “Every infinite‐dimensional Banach space has a linearly independent subset of cardinality ” implies “every Dedekind‐finite set is finite”. (shrink)No categories
- Definitions of compact.Paul E.Howard -1990 -Journal of Symbolic Logic 55 (2):645-655.
- The Boolean Prime Ideal Theorem Plus Countable Choice Do Not Imply Dependent Choice.PaulHoward &Jean E. Rubin -1996 -Mathematical Logic Quarterly 42 (1):410-420.Two Fraenkel-Mostowski models are constructed in which the Boolean Prime Ideal Theorem is true. In both models, AC for countable sets is true, but AC for sets of cardinality 2math image and the 2m = m principle are both false. The Principle of Dependent Choices is true in the first model, but false in the second.
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David Bourget (Western Ontario)
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Area Editors:
David Bourget
Gwen Bradford
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David Chalmers
James Chase
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