We reimplement the creature forcing construction used by Fischer et al. :1045–1103, 2017. https://doi.org/10.1007/S00153-017-0553-8. arXiv:1402.0367 [math.LO]) to separate Cichoń’s diagram into five cardinals as a countable support product. Using the fact that it is of countable support, we augment our construction by adding uncountably many additional cardinal characteristics, sometimes referred to as localisation cardinals.

We study regularity properties related to Cohen, random, Laver, Miller and Sacks forcing, for sets of real numbers on the Δ31\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{\Delta}^1_3}$$\end{document} level of the projective hieararchy. For Δ21\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{\Delta}^1_2}$$\end{document} and Σ21\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{\Sigma}^1_2}$$\end{document} sets, the relationships between these properties follows the pattern of the well-known Cichoń diagram for cardinal characteristics of the continuum. It is known (...) that assuming suitable large cardinals, the same relationships lift to higher projective levels, but the questions become more challenging without such assumptions. Consequently, all our results are proved on the basis of ZFC alone or ZFC with an inaccessible cardinal. We also prove partial results concerning Σ31\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{\Sigma}^1_3}$$\end{document} and Δ41\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{\Delta}^1_4}$$\end{document} sets. (shrink)

Using matrix iterations of ccc posets, we prove the consistency with ZFC of some cases where the cardinals on the right hand side of Cichon’s diagram take two or three arbitrary values (two regular values, the third one with uncountable cofinality). Also, mixing this with the techniques in J Symb Log 56(3):795–810, 1991, we can prove that it is consistent with ZFC to assign, at the same time, several arbitrary regular values on the left hand side of Cichon’s (...) class='Hi'>diagram. (shrink)

We prove that in many situations it is consistent with ZFC that part of the invariants involved in Cichon's diagram are equal to κ while the others are equal to λ, where $\kappa < \lambda$ are both arbitrary regular uncountable cardinals. We extend some of these results to the case when λ is singular. We also show that $\mathrm{cf}(\kappa_U(\mathscr{L})) < \kappa_A(\mathscr{M})$ is consistent with ZFC.

We prove that in many situations it is consistent with ZFC that part of the invariants involved in Cichon's diagram are equal to $\kappa$ while the others are equal to $\lambda$, where $\kappa < \lambda$ are both arbitrary regular uncountable cardinals. We extend some of these results to the case when $\lambda$ is singular. We also show that $\mathrm{cf}) < \kappa_A$ is consistent with ZFC.

Some cardinal invariants from Cichon's diagram can be characterized using the notion of cut-and-choose games on cardinals. In this paper we give another way to characterize those cardinals in terms of infinite games. We also show that some properties for forcing, such as the Sacks Property, the Laver Property and ω ω -boundingness, are characterized by cut-and-choose games on complete Boolean algebras.

We present several models which satisfy CH and some ♦-like principles while others fail, answering a question of Moore, Hrušák and Džamonja.

We use a creature construction to show that consistently $$\begin{aligned} \mathfrak d=\aleph _1= {{\mathrm{cov}}}< {{\mathrm{non}}}< {{\mathrm{non}}}< {{\mathrm{cof}}} < 2^{\aleph _0}. \end{aligned}$$The same method shows the consistency of $$\begin{aligned} \mathfrak d=\aleph _1= {{\mathrm{cov}}}< {{\mathrm{non}}}< {{\mathrm{non}}}< {{\mathrm{cof}}} < 2^{\aleph _0}. \end{aligned}$$.

We discuss in the paper the following problem: Given a function in a given Baire class, into "how many" (in terms of cardinal numbers) functions of lower classes can it be decomposed? The decomposition is understood here in the sense of the set-theoretical union.

We conclude the discussion of additivity, Baire number, uniformity, and covering for measure and category by constructing the remaining 5 models. Thus we complete the analysis of Cichon's diagram.

We make a more systematic study of the van Douwen diagram for cardinal coefficients related to combinatorial properties of partitions of natural numbers.

We investigate the behavior of cardinal characteristics of the reals under extensions that do not add new [Formula: see text]-sequences (for some regular [Formula: see text]). As an application, we show that consistently the following cardinal characteristics can be different: The (“independent”) characteristics in Cichoń’s diagram, plus [Formula: see text]. (So we get thirteen different values, including [Formula: see text] and continuum). We also give constructions to alternatively separate other MA-numbers (instead of [Formula: see text]), namely: MA for (...) [Formula: see text]-Knaster from MA for [Formula: see text]-Knaster; and MA for the union of all [Formula: see text]-Knaster forcings from MA for precaliber. (shrink)

The aim of the present study is to explore pre-service elementary teachers’ evaluations of the evidence and models and their positions on a socio-scientific topic, namely genetically modified organisms, after evaluating them through Model Evidence Link diagrams. The findings of this study show that the participants mostly constructed accurate evidence-model links. However, they mostly generated inaccurate relationships between the model and the evidence when the evidence had nothing to do with the model. The results also show that the participants mostly (...) evaluated the model-evidence relationships at the descriptive and relational levels. The participants were able to construct accurate links; however, they could not critically evaluate the model-evidence links. Finally, although the participants read supportive, opposing and irrelevant evidence about the benefits of GMOs, and discussed them with their group mates, most of them still thought that GMOs are not beneficial to society. Furthermore, none of them stated the belief that GMOs are beneficial to society. (shrink)

The Medical Research Council Laboratory of Molecular Biology (formerly the Medical Research Council Unit for the Study of Molecular Structure of Biological Systems) in Cambridge (England) played a key role in the postwar history of molecular biology. The paper, focussing on the early history of the institution, aims to show that the creation of the laboratory and the making of molecular biology were part of a new scientific culture set in place after World War II. In five interlinked parts it (...) deals with the institutional creation of the MRC unit dedicated to the crystallographic analysis of biological molecules; the attraction of postwar biophysics, the heading under which the work of the unit initially fell; the people who joined the laboratory and their appropriation of new technologies, in particular the electronic computer for protein crystal structure determination; the cultural appeal of postwar crystallography, as exemplified in the use of crystal structure diagrams for a wide series of consumer goods at the Festival of Britain in 1951 and the display of molecular models at the Brussels World's Fair in 1958, a key site for the presentation of science and its role in the postwar world. (shrink)

Continuing [6], [8] and [16], we study the consequences of the weak Freese-Nation property of (?(ω),⊆). Under this assumption, we prove that most of the known cardinal invariants including all of those appearing in Cichoń's diagram take the same value as in the corresponding Cohen model. Using this principle we could also strengthen two results of W. Just about cardinal sequences of superatomic Boolean algebras in a Cohen model. These results show that the weak Freese-Nation property of (?(ω),⊆) captures (...) many of the features of Cohen models and hence may be considered as a principle axiomatizing a good portion of the combinatorics available in Cohen models. (shrink)

Some sufficient conditions on a Symmetric Monoidal Closed category K are obtained such that a diagram in a free SMC category generated by the set A of atoms commutes if and only if all its interpretations in K are commutative. In particular, the category of vector spaces on any field satisfies these conditions . Instead of diagrams, pairs of derivations in Intuitionistic Multiplicative Linear logic can be considered . Two derivations of the same sequent are equivalent if and only (...) if all their interpretations in K are equal. In fact, the assignment of values to atoms is defined constructively for each pair of derivations. Taking into account a mistake in R. Voreadou's proof of the “abstract coherence theorem” found by the author, it was necessary to modify her description of the class of non-commutative diagrams in SMC categories; our proof of S. Mac Lane conjecture also proves the correctness of the modified description. (shrink)

I desire to invite the attention of students of Plato and of Greek mathematics to a solution of a passage which has long been a field of controversy for critics. For brevity's sake I shall take for granted an acquaintance with the two solutions which at present dispute the field, and further adopt certain positions which previous enquirers have established beyond reasonable doubt.

Twenty years after cultivating a new orientation for aesthetics via the concept of non-photography, François Laruelle returns, having further developed his notion of a non-standard aesthetics. Published for the first time in a bilingual edition, _Photo-Fiction, a Non-Standard Aesthetics_ expounds on Laruelle’s current explorations into a photographic thinking as an alternative to the worn-out notions of aesthetics based on an assumed domination of philosophy over art. He proposes a new philosophical photo-fictional apparatus, or philo-fiction, that strives for a discursive mimesis (...) of the photographic apparatus and the flash of the Real entailed in its process of image making. “A bit like if an artisan, to use a Socratic example, instead of making a camera based off of diagrams found in manuals, on the contrary had as his or her project the designing of a completely new apparatus of philo-fiction, thus capable of producing not simply photos, but photo-fictions.” One must enter into a space for seeing the vectorial and the imaginary number. Laruelle’s philo-fictions become not art installations, but “theoretical installations” calling for the consideration of the possibility of a non-standard aesthetics being of an equal or superior power to art and philosophy, an aesthetics in-the-last-instance that is itself an inventive and creative act of the most contemporary kind. (shrink)

I argue the relationship between déjà vu and autobiographical memory is not continuous, but more akin to a path diagram. The starting points might be overlapping, but eventually the paths diverge dependent on whether there is memory content to be retrieved. I am worried that considering déjà vu as part of autobiographical memory solves more problems than it creates.

This first volume of the Logic of the Future edition collects Peirce's writings on the historical development, theory and application of his graphical method and diagrammatic reasoning. Its 28 selections of texts and extensive general and volume int.

Epistemology mirrors reality but notperfectly, and in the process molds reality butnot exactly as intended or anticipated. Horizontal interconnections also exist betweenand among epistemology, ideology, theory andpraxiology. However, these relations areneither deductive nor deterministic in naturebut are merely resonant, and then unclear,ambiguous and confounded. In this paper, thepoint is made that we need a grand reflectionon both our paradigms of reality and ourpredicaments of life as lived, to deal with thediscontent of humanity at this moment of thehistory of our civilization, (...) and to engage inpraxis ``to act on our world and to reconstructit'' to make it moral, just and more humane. Toundertake such a grand reflection, we need apractical philosophy of knowledge – that is, apractical epistemology – to bridge across themultiple epistemological approaches nowcrowding our discussions. An epistemictriangle formed by systems thinking,constructivist thinking, and dialecticalthinking is offered to serve as the startingpoint of crystallization for building a commonground for epistemologies. It is shown how suchan epistemological diagram could be first usedto develop a minimum ideological consensus andthen to bring orderliness to the chaos ofcontemporary themes of our civilization andissues of education and culture within andacross nations. Finally, an agenda foreducational leadership for educational practiceis offered to fit the needs of the globalcommunity of nations as we enter thetwenty-first century. (shrink)

When testing logical formulae for validity by applying Venn's diagrams we are using a kind of picture writing i. e. a writing in which certain facts are represented by drawings rather than sentences. This diagrammatic decision procedure may however be translated into ordinary language. Translating for instance the respective procedure of testing the mood Darii we obtain the following reasoning.

Wood informs the reader that Buber rejected "isms," hard and fast rules and principles, and systems, but he goes on to systematize Buber's thought nonetheless. The result is often enlightening. I and Thou, which Wood considers the central work of the philosopher's thought, is finely broken down and analyzed in its component parts. In this manner it is less formidable to the uninitiated, and the reader who is puzzled by a particular passage can find in Wood's book an authoritative, well-researched (...) explanation. There are also excellent biographical data woven in with glimpses of Buber's voluminous works and the influences on them, and a complete bibliography that is as definitive as any published to date. But Buber's thought does not lend itself to systematization. One cannot substitute Ontology for Metaphysics and then proceed to dissect a philosophy which declares itself to be beyond metaphysics, and which points to the existential meeting of a person here and now with another person and/or with God. Wood provides a diagram showing the structure of I and Thou which may be useful for locating selections in the book as they relate to a certain code, but at the same time it illustrates what Buber describes as objectification, an I-it relationship with a person or his work, which is far from the I-Thou relationship.--S. J. B. (shrink)

It is shown that a notion of natural place is possible within modern physics. For Aristotle, the elements—the primary components of the world—follow to their natural places in the absence of forces. On the other hand, in general relativity, the so-called Carter–Penrose diagrams offer a notion of end for objects along the geodesics. Then, the notion of natural place in Aristotelian physics has an analog in the notion of conformal infinities in general relativity.

We establish the hierarchy among twelve equivalence relations on the class of relational structures: the equality, the isomorphism, the equimorphism, the full relation, four similarities of structures induced by similarities of their self-embedding monoids and intersections of these equivalence relations. In particular, fixing a language L and a cardinal κ, we consider the interplay between the restrictions of these similarities to the class ModL of all L-structures of size κ. It turns out that, concerning the number of different similarities and (...) the shape of the corresponding Hasse diagram, the class of all structures naturally splits into three parts: finite structures, infinite structures of unary languages, and infinite structures of non-unary languages. (shrink)

Modern Studies in Philosophy, we are informed on the page facing the title-page, "is a series of anthologies presenting contemporary interpretations and evaluations of the works of major philosophers." The volumes are "intended to be contributions to contemporary debates as well as to the history of philosophy; they not only trace the origins of many problems important to modern philosophy, but also introduce major philosophers as interlocutors in current discussions." In the first of the two volumes on Plato three of (...) the articles chosen by Gregory Vlastos have not appeared elsewhere: Julius Moravcsik, Learning as Recollection; G. E. L. Owen, Plato on Not-Being; David Higgins, Sentence Meaning, Negation, and Plato's Problem of Non-Being. The other studies in Volume One are reprints: R. Robinson and J. D. Denniston, Plato; H. F. Cherniss, The Philosophical Economy of the Theory of Ideas; A. Wedberg, The Theory of Ideas; R. C. Cross and A. D. Woozley, Knowledge, Belief and the Forms; R. Robinson, Hypothesis in the Republic; G. Vlastos, Reasons and Causes in the Phaedo; R. E. Allen, Participation and Predication in Plato's Middle Dialogues; Colin Strang, Plato and the Third Man; J. L. Ackrill, Symplokë eidön; J. L. Ackrill, Plato and the Copula: Sophist 251-259. In Volume Two Terry Penner, "Thought and Desire in Plato" has not been published before. The others have: Paul Shorey, Plato's Ethics; David Sachs, A Fallacy in Plato's Republic; Raphael Demos, A Fallacy in Plato's Republic?; J. D. Mabbott, Is Plato's Republic Utilitarian?; G. Vlastos, Justice and Happiness in the Republic; F. M. Cornford, The Doctrine of Eros in Plato's Symposium; R. A. Markus, The Doctrine of Eros in Plato's Symposium; Glenn R. Morrow, Plato and the Rule of Law; Wayne A. R. Leys, Was Plato Non-Political?; F. E. Sparshott, Plato as Anti-Political Thinker; Renford Bambrough, Plato's Political Analogies; E. R. Dodds, Plato and the Irrational Soul; W. K. C. Guthrie, Plato's Views on the Nature of the Soul; Harold Cherniss, The Sources of Evil According to Plato; W. J. Verdenius, Plato's Doctrines of Artistic Imitation. Obviously, the above listed articles will be welcome to those debating issues in Plato and to historians of twentieth-century philosophy. There are two difficulties, however. The print is too small in the body of the text and is nearly microscopic in the footnotes and diagrams. Reading thus becomes almost painful. Margins to the left, right, top and bottom of the pages are practically nonexistent. On occasion footnote material is misplaced--for example, the comment on Strang's article as originally published elsewhere should be on p. 184, not on p. 187, of Volume One. But a greater problem is the fact that almost all the articles on metaphysics and epistemology are by linguistic analysts. Vlastos in his introductory remarks admits as much: "Volume One is heavily weighted on the 'analytical' side." He reports the statement of an un-named advocate of conceptual analysis "that these [analytic] methods now enable us to understand Plato better than he was ever understood by anyone in history--better than by any of his own contemporaries, even better than by himself!" He disclaims such euphoria but insists "there is an element of truth in it after all" insofar as analytic tools can alert a student to ambiguity and its consequences in some of Plato's sentences. Hence, "if we come across such sentences in Plato, it would be plainly true to say that we can understand them better than he did and even to add that we can, therefore, understand him better, since we can see both what he meant to say and the logical liabilities of his incautious sentences." All this is true enough, but a warning still is in order. Linguistic analysts tend to read only some of Plato's dialogues and, even within them, to concentrate on some passages only. This is understandable in view of their interests and the capacity of the analytic technique. But that selectivity might lead them to believe that the Plato thus revealed is the complete and authentic Plato, which it is not. Hence, in reading and teaching Plato one must complement language- and concept-analysis with other approaches. Vlastos himself is aware of this necessity : [[sic]] "Once we have made full allowance for what modern semantics and logic can do to make Plato more intelligible and alive for us today, we should be quick to concede that borrowings from this quarter must be used with economy and discretion, and that continuing reliance on older linguistic and historical disciplines is as essential now as it has ever been in the past if the object of our inquiries is Plato himself, instead of some mock-up more pleasing to current taste." One could only wish that Vlastos had fostered that reliance on other disciplines by including articles of that sort among those he actually chose.--L. S. (shrink)

This book is a detailed examination of Thomistic objectivist aesthetics in the context of a criticism of contemporary subjective theories. The thesis of the book is developed logically with many, and often detailed, references to the history of aesthetics. There are numerous useful footnotes and a large bibliography and index. In the context of his realist position, Kovach seeks "... the ultimate principles or causes of the beauty of things" which he argues entail the "... extramental, objective reality of beauty." (...) His thesis rests on empirical fact; "... while seeing and/or hearing certain objects, some people experience delight" and the beauty "in" the things causes this delight. After discussing problems of causality, Kovach defends the argument that beauty is similar to other physical qualities which the realist believes are in necessary cause-and-effect relationships. This involves him in a criticism of subjectivism and relativism. He does this by means of a thorough description and treatment of thirty-six reasons for aesthetic disagreement. I would agree that relationism is a form of objectivism but not, as he claims, "ill-disguised." Aesthetic perception may be a way of perceiving things that have the required components to elicit this response. Such a relation might be described phenomenologically. Beauty for Kovach is explained cosmologically; we reach an understanding of absolutely universal beauty by determining the essence of material beauty through progressively complex instances. His defense is interesting. For example, he diagrams the most plausible divisions of beauty from the history of aesthetics and argues that all things in creation participate in beauty by a clever examination of theories of ugliness.—P.S. (shrink)

Computable model theory, also called effective or recursive model theory, studies algorithmic properties of mathematical structures, their relations, and isomorphisms. These properties can be described syntactically or semantically. One of the major tasks of computable model theory is to obtain, whenever possible, computability-theoretic versions of various classical model-theoretic notions and results. For example, in the 1950's, Fröhlich and Shepherdson realized that the concept of a computable function can make van der Waerden's intuitive notion of an explicit field precise. This led (...) to the notion of a computable structure. In 1960, Rabin proved that every computable field has a computable algebraic closure. However, not every classical result “effectivizes”. Unlike Vaught's theorem that no complete theory has exactly two nonisomorphic countable models, Millar's and Kudaibergenov's result establishes that there is a complete decidable theory that has exactly two nonisomorphic countable models with computable elementary diagrams. In the 1970's, Metakides and Nerode [58], [59] and Remmel [71], [72], [73] used more advanced methods of computability theory to investigate algorithmic properties of fields, vector spaces, and other mathematical structures. (shrink)

Modern Studies in Philosophy, we are informed on the page facing the title-page, "is a series of anthologies presenting contemporary interpretations and evaluations of the works of major philosophers." The volumes are "intended to be contributions to contemporary debates as well as to the history of philosophy; they not only trace the origins of many problems important to modern philosophy, but also introduce major philosophers as interlocutors in current discussions." In the first of the two volumes on Plato three of (...) the articles chosen by Gregory Vlastos have not appeared elsewhere: Julius Moravcsik, Learning as Recollection; G. E. L. Owen, Plato on Not-Being; David Higgins, Sentence Meaning, Negation, and Plato's Problem of Non-Being. The other studies in Volume One are reprints: R. Robinson and J. D. Denniston, Plato; H. F. Cherniss, The Philosophical Economy of the Theory of Ideas; A. Wedberg, The Theory of Ideas; R. C. Cross and A. D. Woozley, Knowledge, Belief and the Forms; R. Robinson, Hypothesis in the Republic; G. Vlastos, Reasons and Causes in the Phaedo; R. E. Allen, Participation and Predication in Plato's Middle Dialogues; Colin Strang, Plato and the Third Man; J. L. Ackrill, Symplokë eidön; J. L. Ackrill, Plato and the Copula: Sophist 251-259. In Volume Two Terry Penner, "Thought and Desire in Plato" has not been published before. The others have: Paul Shorey, Plato's Ethics; David Sachs, A Fallacy in Plato's Republic; Raphael Demos, A Fallacy in Plato's Republic?; J. D. Mabbott, Is Plato's Republic Utilitarian?; G. Vlastos, Justice and Happiness in the Republic; F. M. Cornford, The Doctrine of Eros in Plato's Symposium; R. A. Markus, The Doctrine of Eros in Plato's Symposium; Glenn R. Morrow, Plato and the Rule of Law; Wayne A. R. Leys, Was Plato Non-Political?; F. E. Sparshott, Plato as Anti-Political Thinker; Renford Bambrough, Plato's Political Analogies; E. R. Dodds, Plato and the Irrational Soul; W. K. C. Guthrie, Plato's Views on the Nature of the Soul; Harold Cherniss, The Sources of Evil According to Plato; W. J. Verdenius, Plato's Doctrines of Artistic Imitation. Obviously, the above listed articles will be welcome to those debating issues in Plato and to historians of twentieth-century philosophy. There are two difficulties, however. The print is too small in the body of the text and is nearly microscopic in the footnotes and diagrams. Reading thus becomes almost painful. Margins to the left, right, top and bottom of the pages are practically nonexistent. On occasion footnote material is misplaced--for example, the comment on Strang's article as originally published elsewhere should be on p. 184, not on p. 187, of Volume One. But a greater problem is the fact that almost all the articles on metaphysics and epistemology are by linguistic analysts. Vlastos in his introductory remarks admits as much: "Volume One is heavily weighted on the 'analytical' side." He reports the statement of an un-named advocate of conceptual analysis "that these [analytic] methods now enable us to understand Plato better than he was ever understood by anyone in history--better than by any of his own contemporaries, even better than by himself!" He disclaims such euphoria but insists "there is an element of truth in it after all" insofar as analytic tools can alert a student to ambiguity and its consequences in some of Plato's sentences. Hence, "if we come across such sentences in Plato, it would be plainly true to say that we can understand them better than he did and even to add that we can, therefore, understand him better, since we can see both what he meant to say and the logical liabilities of his incautious sentences." All this is true enough, but a warning still is in order. Linguistic analysts tend to read only some of Plato's dialogues and, even within them, to concentrate on some passages only. This is understandable in view of their interests and the capacity of the analytic technique. But that selectivity might lead them to believe that the Plato thus revealed is the complete and authentic Plato, which it is not. Hence, in reading and teaching Plato one must complement language- and concept-analysis with other approaches. Vlastos himself is aware of this necessity : [[sic]] "Once we have made full allowance for what modern semantics and logic can do to make Plato more intelligible and alive for us today, we should be quick to concede that borrowings from this quarter must be used with economy and discretion, and that continuing reliance on older linguistic and historical disciplines is as essential now as it has ever been in the past if the object of our inquiries is Plato himself, instead of some mock-up more pleasing to current taste." One could only wish that Vlastos had fostered that reliance on other disciplines by including articles of that sort among those he actually chose.--L. S. (shrink)

This introduction to quantum mechanics requires little previous knowledge of physics. The book consists of three separate projects completed with varying degrees of success. The first chapters discuss classical physics with special attention to the concepts of matter and light. The middle chapters are devoted to quantum physics itself and how it developed from, and accounted for, problematic phenomena of earlier physics. Detailed, although not heavily mathematical, attention is given to the key experiments of quantum physics. These chapters go on (...) to discuss the so-called elementary particles, conservation laws, "strangeness," spin, various field theories, and other topics of current research. The final chapters are devoted to the philosophical implications of quantum mechanics. This section, focused mainly on causality and free will, is superficial and disappointing--of more interest to ethics and theology than to the philosophy of science. The philosophical remarks which were made parenthetically in the first two sections of the book were more provocative and might well have been expanded in this section. If this last section were eliminated, the first section abbreviated, and the book released in paperback, the book would be a better buy as informative introduction to quantum mechanics. There are many diagrams, tables, illustrations, and photographs, as well as a glossary of technical terms and a critical bibliography.--S. O. H. (shrink)

This is an extremely simplified yet remarkably thorough introduction to how computers work. It is for the "computer widow" and the interested layman. I think it would well serve as a minimal grounding for the philosopher forced by his colleagues and others into discussions of artificial intelligence. The language is condescendingly simple with each new technical term introduced with appropriate fanfare and placed in italics. The exposition is accompanied by many diagrams and examples. The book covers the binary operation of (...) the computer and the role of symbols: how they are interpreted, how they get in to the computer, how they get out, how they are stored, and the logical categories by which they are processed. It discusses the control process by which the sequential order of computer operations is determined and the role of the programmer. The latter chapters of the book discuss a number of issues relating to the socio-economic implications of the widespread use of computers. Crowley takes great pains to point out the limitations of computers both with respect to current applicability and to future developments. He defends the computer as a potentially humanizing force in spite of its dehumanizing aspects. The book contains a short critical bibliography.--S. O. H. (shrink)

Establishing interdisciplinary academic departments has been a common response to the challenge of addressing complex problems. However, the assumptions that guide the formation of such departments are rarely questioned. Additionally, the designers and managers of interdisciplinary academic departments in any field of endeavour struggle to set an organisational climate appropriate to the diversity of their members. This article presents a preliminary analysis of collaborative dynamics within two interdisciplinary university departments in Australia focused on sustainability. Social network diagrams and metrics of (...) coauthorship and cosupervision are analysed qualitatively. A "vicarious interdisciplinarity" was identified among key academics working narrowly in order to earn the resources that allow them to support others working interdisciplinarily. Those supported in this way appear to benefit from the esteem and nonredundant collaborative connections their mentors provide via this strategy, but they experience uncertainty about their own career opportunities in similar settings. This article thus unearths a conundrum of succession for interdisciplinary academic environments, and suggests that simple colocation of diverse academic stars is an inadequate strategy to achieve effective intradepartmental collaboration. (shrink)

In considering this problem a distinction should first be made between its scientific and it philosophical aspects. The scientific problem is that of defining in exact understandable terms those conditions and factors which make possible the synthesis of the living organism from the simpler elements of the non-living environment, and also its maintenance in the adult state as a fully developed and autonomous organic individual. The problem as thus stated is one to be approached by methods of observation and experiment, (...) leading to verifiable results which are then expressed in systematic and intelligible form. The final statements or representations thus reached, the accepted scientific generalizations, inevitably take on a theoretical form, and as such are necessarily partial and abstract. Many of them, in fact, are to be regarded primarily as simplifications or models devised in the interest of clear representation or understanding. Their relation to concrete reality may range from attempts at exact portraiture to formulæ or diagrams having little more than heuristic significance. Any realistic philosophy of nature must always remember how incomplete and provisional are the theoretical conceptions of any natural science. (shrink)

A diagram that places two planets in orbit around the sun was inserted into the textual space of a Timaeus manuscript of the late 11th century as well as three more in the 12th century. The diagram derives from a Carolingian tradition of study of Martianus Capella’s astronomy and shows his continued authority into the twelfth century. By way of Capella and through similarly-inspired commentaries on Macrobius’ Commentary on the Dream of Scipio, the idea of circumsolar motion for (...) Mercury and Venus became a well-known and authoritative theme for William of Conches and other scholars in the eleventh and twelfth centuries wo interpreted Plato in terms of current scientific knowledge. (shrink)

Predation and escaping from predation through hiding are two fundamental phenomena in ecology. The most common approach to reducing the chance of predation is to use a refuge. Here, we consider a three species fishery model system with prey refuge induced by a Holling type-II functional response. These three species of fish populations are named prey, middle predator, and top predator. Harvesting is employed in most fishery models to achieve both ecological and commercial benefits. Research proves that non-linear harvesting (Michaelis–Menten (...) type) returns more realistic outcomes. So, we have combined the Michaelis–Menten type of harvesting efforts for all populations. Uniform boundedness conditions for the solutions of the model are discussed. The existence conditions for possible equilibrium points with stability are presented. We explain the dynamical behavior at each equilibrium point through bifurcation analysis. The persistent criteria of the system are examined. Bionomic equilibrium and optimal harvesting control using Pontryagin’s maximum principle are calculated. For validation of the model in the real world, we have implemented this in the freshwater ecosystem of Lake Victoria. Extraction of native fish species and ecological balances are the foremost solicitude of Lake Victoria. We may resolve this concern partially by implementing prey refuge, since it may sustain the ecology of Lake Victoria, and therefore also its economical importance. Lake Victoria is acclaimed worldwide for the trade of fishing. Also, it provides the largest employment in east-central Africa and is beneficial to fishing equipment manufacturers. So, the bionomic equilibrium and harvesting control have significant applications in the fisheries. All the analytical studies are verified by numerical simulations. We have plotted phase portraits, bifurcation diagrams, Lyapunov exponents to explore the dynamics of the proposed model. (shrink)