Seven Generations since the Fall of Akkad. Edited by Harvey Weiss. Studia Chaburensia, vol. 3. Wiesbaden: Harrassowitz Verlag, 2012. Pp. viii + 299, illus. €64.

From Alexander to Jesus. By Ory Amitay. Hellenistic Culture and Society, vol. 52. Berkeley and Los Angeles: University of California Press, 2010. Pp. xii + 246. $49.95.

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Otot ha-Shamayim: Samuel Ibn Tibbon’s Hebrew Version of Aristotle’s “Meteorology.” by AristotleSteven HarveyAristotle. Otot ha-Shamayim: Samuel Ibn Tibbon’s Hebrew Version of Aristotle’s “Meteorology.” Translated and edited by Resianne Fontaine. Leiden: E.J. Brill, 1995. Pp. lxxx + 268. Cloth, $108.50.This modest, seemingly unimportant, volume is in fact a surprisingly fascinating text that should be of interest to all historians of philosophy. Under the rather boring guise of an edition (...) and English translation of a medieval Hebrew translation of an early ninth-century Arabic translation of Aristotle’s Meteorology, this book is destined to be ignored by most historians of philosophy and even by those who have a special interest in Aristotle. This is a shame, and it is the goal of this brief review to alert the reader to the book’s value.The Hebrew translation of the Meteorology is, to be more precise, a creative translation of an inadequate Arabic version of the text, corrected, interpreted, and expanded on the basis of the commentaries of Alexander of Aphrodisias and Averroes, by a philosopher struggling to understand what was for him a seminal text of Aristotle’s. The philosopher-translator was Samuel Ibn Tibbon, best known for his faithful translation into Hebrew of Maimonides’s Guide of the Perplexed. What is immediately significant about the translation of the Meteorology, which was completed in 1210, is that it was the first text of Aristotle’s to be translated into Hebrew and, as far as is known, the first Hebrew translation of any philosophic or scientific work of a non-Jew. For the philosophically inclined Jew who did not know Arabic and who had struggled through Maimonides’s Guide without the benefit of translations, paraphrases, or even commentaries on Aristotle’s Physics and other prerequisite writings on natural science, the translation must have been an eagerly awaited and much welcome work. But why, of all things, the historian of philosophy will ask, the Meteorology? And however much appreciated the translation may have been in 1210, what possible use could an English translation of this patchwork Hebrew translation of a garbled and abridged Arabic translation of perhaps a Syriac translation of the Greek original or compendium of the Meteorology have for us today when we have a fine Greek edition of the text and modern translations from that edition?There were good reasons not to translate the Meteorology first. In contrast to most of Aristotle’s writings on natural science which existed in impressively reliable Arabic translations, the Meteorology existed in a poor and incomplete one. Ibn Tibbon comments in his Introduction to the translation that “errors and omissions” in the Arabic translation are evident from the context, from a comparison with Alexander’s commentary and the lemmata found therein, and from a comparison with other Aristotelian works that existed in trustworthy translations. The text could not simply be translated, [End Page 130] but needed to be reconstructed on the basis of a careful study of the commentaries of Alexander of Aphrodisias, Averroes, and the other commentaries that were available. Yet, even if the text had existed in a reliable translation, the tradition of text-study required that the sciences be studied in a proper order and this meant—as is clear from the opening words of the Meteorology—beginning the study of natural sciences with the Physics and turning to the Meteorology only after completing On the Heavens and On Generation and Corruption. Ibn Tibbon acknowledged this, and, in fact, interjected in his own name (27, 29) that “all the statements the philosopher has [made] thus far, are introductory remarks taken from earlier discussions in other books.... Someone who has not previously acquired knowledge and learning from his books that precede this one, will understand very little of this introduction.” Unfortunately for Ibn Tibbon’s reader, it would be forty years before any of those books or epitomes of them would be translated into Hebrew. Resianne Fontaine, in her wide-ranging and informative Introduction (xi–xii), brings support for A. Ravitzky’s suggestion that Ibn Tibbon’s decision to translate the Meteorology was motivated by his personal interest in the text... (shrink)

Introduction A Brief Conceptual Framework for Biology PART ONE: UNDERSTANDING NATURE 1. The Antecedents of Scientific Thought Animism, Totemism, and Shamanism The Paleolithic View Mesopotamia Egypt 2. Aristotle and the Greek View of Nature The Science of Animal Biology The Parts of Animals The Classification of Animals The Aristotelian System Basic Questions 3. Those Rational Greeks? Theophrastus and the Science of Botany The Roman Pliny Hippocrates, the Father of Medicine Erasistratus Galen of Pergamum The Greek Miracle 4. The Judeo-Christian Worldview (...) The Bishop of Hippo Scholastic Thought Islamic Science Books on Beasts Antecedents of a Revolution 5. The Revival of Science Andreas Vesalius and the Study of Structure William Harvey and the Study of Function Sir Francis Bacon’s Great Instauration Induction, Hypothesis, Deduction The Very Small--Animalcules Robert Hooke and the Discovery of Cells 6. Figur’d Stones and Plastick Virtue Marine Life on Mountain Tops? Figured Stones of Unknown Creatures Baron Cuvier Quarries of the Paris Basin Catastrophism and Uniformitarianism William Smith and the Geological Column Understanding Nature in 1850 PART TWO: THE GROWTH OF EVOLUTIONARY THOUGHT 7. The Paradigm of Evolution First Questions The Paradigm of Natural Theology First Answers 8. Testing Darwins Hypotheses Have Life Forms Changed over Time? Do Species Evolve into Different Species over Time? Has There Been Time Enough for Evolution? Is Natural Selection the Mechanism of Change? The Genetic Basis of Natural Selection Accounting for the Diversity of Life 9. In the Light of Evolution Comparative Anatomy Embryonic Development Classification Microstructure Molecular Processes 10. Life over Time The Origin of Life The Rise of Multicelled Organisms What Is a Phylum? Burgess Shale Metazoans Early Evolution of the Vertebrates The Age of Dinosaurs Birds, Mammals, and Flowering Plants The Rancho La Brea Tar Pits Human Evolution The Role of Extinction in Evolution PART THREE: CLASSICAL GENETICS 11. Pangenesis What Is the Question? Hippocrates and Aristotle The Darwinian Answer Assembling the Data Formulating the Hypothesis by Induction Galton’s Rabbits 12. The Cell Theory The Discovery of Cells: Robert Hooke Schwann and Cells in Animals Gametes as Cells Omnis cellula e cellula? The Technology of Cell Research 13. The Hypothesis of Chromosomal Continuity The Ephemeral Nucleus Schneider, Flemming, and Cell Division The Chromosomes and inheritance Gamete Formation Fertilization 14. Mendel and the Birth of Genetics Model for Monohybrid Crosses Model for Dihybrid Crosses Mendel’s Laws Initial Opposition to Mendelism 15. Genetics + Cytology: 1900-1910 Sutton’s Model The Cytological Basis of Mendel’s Laws Boveri and Abnormal Chromosome Sets Variations in Mendelian Ratios The Discovery of Sex Chromosomes 16. The Genetics of the Fruit Fly Morgan’s First Hypothesis Morgan’s Second Hypothesis The Fly Room Linkage and Crossing-Over The Cytological Proof of Crossing-Over Mapping the Chromosomes The Final Proof The Determinants of Sex The Conceptual Foundations of Classical Genetics 17. The Structure and Function of Genes One Gene, One Enzyme The Substance of Inheritance The Watson-Crick Model of DNA Genes and the Synthesis of Proteins The Genetic Code PART FOUR: THE ENIGMA OF DEVELOPMENT 18. First Principles The Peripatetic Stagirite The Death and Rebirth of Scientific Thought Harvey and Malpighi A Two-Millennial Summing Up Preformation versus Epigenesis 19. The Century of Discovery Von Baer’s Discovery of the Mammalian Ovum Darwin’s Contribution to Embryology Haeckel and Recapitulation 20. Descriptive Embryology Germ Layers The External Development of the Amphibian Embryo The Internal Development of the Amphibian Embryo 21. The Dawn of Analytical Embryology His, Roux, and Mosaic Development Driesch and Regulative Development Novelty in Development Cell Lineage Nucleus or Cytoplasm? Fin de Siècle 22. Interactions during Development Amphibian Organizers Secondary Organizers The Reacting Tissue The Chemical Nature of the Organizer Putting It All Together Conclusion Further Reading References Illustration Credits Index. (shrink)

ABSTRACTIn 1651, Alexander Ross published an attack on Thomas Browne's Pseudodoxia Epidemica, Bacon's Natural History and William Harvey's De generatione. Ross's work, Arcana Microcosmi, defended Aristotelian natural philosophy against the ‘new philosophy’ that figures like Bacon, Harvey and Browne represented. Though Ross's attacks on these authors make up no more than half of the treatise’s contents, the book’s paratextual materials emphasise scientific debate. While Ross's authorial approach advocates reading exclusively ancient authorities for the sake of glossing and (...) transmitting their knowledge to a wider public, in order to argue against the new philosophy Ross must engage with its textual production. Furthermore, his works advertise their focus on Bacon, Harvey and Browne, which would have attracted a readership drawn to new scientific approaches to knowledge formation. Ross's polemic represents an effort to model his devotion to ancient authority while also generating a reading public that would resist the new approach to reading that the new philosophy proposed. (shrink)

We introduce a reducibility preordering between classes of countable structures, each class containing only structures of a given similarity type (which is allowed to vary from class to class). Though we sometimes work in a slightly larger context, we are principally concerned with the case where each class is an invariant Borel class (i.e. the class of all models, with underlying set $= \omega$, of an $L_{\omega_1\omega}$ sentence; from this point of view, the reducibility can be thought of as a (...) (rather weak) sort of $L_{\omega_1\omega}$-interpretability notion). We prove a number of general results about this notion, but our main thrust is to situate various mathematically natural classes with respect to the preordering, most notably classes of algebraic structures such as groups and fields. (shrink)

As a master narrative for understanding the emergence of the modern world, the concept of a seventeenth-century scientific revolution has been central to the history of science. It is generally believed that this key analytical framework was created in Europe and became widely used for the first time during the Cold War through the writings of Herbert Butterfield and Alexander Koyré. This view, however, is mistaken. The scientific revolution is largely a product of debates about social reconstruction in the (...) United States in the aftermath of World War I. Promoted in a pioneering book by the Austrian immigrant Martha Ornstein, highlighted in a provocative bestseller by the historian James Harvey Robinson, the scientific revolution was taught in thousands of interwar high schools and colleges. Based on John Dewey’s advocacy of “the scientific method” and on evolutionary psychology and anthropology, the concept underpinned campaigns for women’s rights, racial equality, secular humanism, and global peace. These progressive political ambitions were abandoned after World War II, when the scientific revolution became fundamental not only to forging the history of science as a discipline but also to redefining what it meant to be “modern” during an era of decolonization and the consolidation of global capitalism. (shrink)

Mathematicians do not claim to know a proposition unless they think they possess a proof of it. For all their confidence in the truth of a proposition with weighty non-deductive support, they maintain that, strictly speaking, the proposition remains unknown until such time as someone has proved it. This article challenges this conception of knowledge, which is quasi-universal within mathematics. We present four arguments to the effect that non-deductive evidence can yield knowledge of a mathematical proposition. We also show that (...) some of what mathematicians take to be deductive knowledge is in fact non-deductive. 1 Introduction2 Why It Might Matter3 Two Further Examples and Preliminaries4 An Exclusive Epistemic Virtue of Proof?5 Analyses of Knowledge6 The Inductive Basis of Deduction7 Physical to Mathematical Linkages8 Conclusion. (shrink)

This volume brings together for the first time thirteen recent interviews with the brightest names in contemporary philosophy, including W.V.O. Quine, Richard Rorty, Stanley Cavell, Hilary Putnam and John Rawls. The pieces are culled from the Harvard Review of Philosophy, which has operated at the core of Harvard's Philosophy Department since 1991. Covering wide range of topics from the philosophy of law to logic to metaphysics to literature, the interviews provide a fascinating introduction to some of the most influential thinkers (...) of the day. The book also includes a foreword by Thomas Scanlon. Interviews with Henry Alison, Stanley Cavell, Alan Dershowitz, Cora Diamond, Umberto Eco, Harvey C. Mansfield, Jr., Alexander Nehemas, Hilary Putnam, W.V. Quine, John Rawls, Richard Rorty, Michael Sandel, Cornel West. (shrink)

We introduce insertion domains that support the placement of new, higher, vertices into finite trees. We prove that every nonincreasing insertion domain has an element with simple structural properties in the style of classical Ramsey theory. This result is proved using standard large cardinal axioms that go well beyond the usual axioms for mathematics. We also establish that this result cannot be proved without these large cardinal axioms. We also introduce insertion rules that specify the placement of new, higher, vertices (...) into finite trees. We prove that every insertion rule greedily generates a tree with these same structural properties; and every decreasing insertion rule generates (or admits) a tree with these same structural properties. It is also necessary and sufficient to use the same large cardinals (in the precise sense of Corollary D.25). The results suggest new areas of research in discrete mathematics called "Ramsey tree theory" and "greedy Ramsey theory" which demonstrably require more than the usual axioms for mathematics. (shrink)

We define a class of functions, the descent recursive functions, relative to an arbitrary elementary recursive system of ordinal notations. By means of these functions, we provide a general technique for measuring the proof-theoretic strength of a variety of systems of first-order arithmetic. We characterize the provable well-orderings and provably recursive functions of these systems, and derive various conservation and equiconsistency results.

Two countable well orderings are weakly comparable if there is an order preserving injection of one into the other. We say the well orderings are strongly comparable if the injection is an isomorphism between one ordering and an initial segment of the other. In [5], Friedman announced that the statement “any two countable well orderings are strongly comparable” is equivalent to ATR 0 . Simpson provides a detailed proof of this result in Chapter 5 of [13]. More recently, Friedman has (...) proved that the statement “any two countable well orderings are weakly comparable” is equivalent to ATR 0 . The main goal of this paper is to give a detailed exposition of this result. (shrink)

Based on the relevant logic R, the system R# was proposed as a relevant Peano arithmetic. R# has many nice properties: the most conspicuous theorems of classical Peano arithmetic PA are readily provable therein; it is readily and effectively shown to be nontrivial; it incorporates both intuitionist and classical proof methods. But it is shown here that R# is properly weaker than PA, in the sense that there is a strictly positive theorem QRF of PA which is unprovable in R#. (...) The reason is interesting: if PA is slightly weakened to a subtheory P+, it admits the complex ring C as a model; thus QRF is chosen to be a theorem of PA but false in C. Inasmuch as all strictly positive theorems of R# are already theorems of P+, this nonconservativity result shows that QRF is also a nontheorem of R#. As a consequence, Ackermann's rule γ is inadmissible in R#. Accordingly, an extension of R# which retains its good features is desired. The system R##, got by adding an omega-rule, is such an extension. Central question: is there an effectively axiomatizable system intermediate between R# and R##, which does formalize arithmetic on relevant principles, but also admits γ in a natural way? (shrink)

Contemporary philosophy’s three main naturalisms are methodological, ontological and epistemological. Methodological naturalism states that the only authoritative standards are those of science. Ontological and epistemological naturalism respectively state that all entities and all valid methods of inquiry are in some sense natural. In philosophy of mathematics of the past few decades methodological naturalism has received the lion’s share of the attention, so we concentrate on this. Ontological and epistemological naturalism in the philosophy of mathematics are discussed more briefly in section (...) 6. (shrink)

Naturalism in the philosophy of mathematics is the view that philosophy cannot legitimately gainsay mathematics. I distinguish between reinterpretation and reconstruction naturalism: the former states that philosophy cannot legitimately sanction a reinterpretation of mathematics (i.e. an interpretation different from the standard one); the latter that philosophy cannot legitimately change standard mathematics (as opposed to its interpretation). I begin by showing that neither form of naturalism is self-refuting. I then focus on reinterpretation naturalism, which comes in two forms, and examine the (...) only available argument for it. I argue that this argument, the so-called Failure Argument, itself fails. My overall conclusion is that although there is no self-refutation argument against reinterpretation naturalism, there are as yet no good reasons to accept it. Naturalism in mathematics The consistency of mathematical naturalism The failure argument Objections to the failure argument Philosophy as the default. (shrink)

George Boolos has argued that the iterative conception of set justifies most, but not all, the ZFC axioms, and that a second conception of set, the Frege-von Neumann conception (FN), justifies the remaining axioms. This article challenges Boolos's claim that FN does better than the iterative conception at justifying the axioms in question.

The notion of interpretation is absolutely fundamental to mathematical logic and the foundations of mathematics. It is also crucial for the foundations and philosophy of science - although here some crucial conditions generally need to be imposed; e.g., “the interpretation leaves the mathematical concepts unchanged”.

"A learned work of rhetoric... compiled and made in the English tongue, of [one] who in judgment is profound, in wisdom and eloquence most famous." Thus in 1563 rhetorician Richard Rainolde praised _The Art of Rhetoric_, the work that brought into English the procedures of Ciceronian rhetoric-invention, disposition, style, memory, and delivery—the core of the academic curriculum in Renaissance England. Written in vigorous, native English, the _Art_ went through eight editions between 1553 and 1585. At least part of its appeal (...) was practicality. On the final page of his copy on Quintilian, Gabriel Harvey noted that _The Art of Rhetoric _is the "Daily bread of our common pleaders and discoursers." But its appeal was also academic. In 1619, nearly forty years after the _Art_ had lapsed from print, John Milton's teacher Alexander Gill invoked Wilson as he ridiculed the affectations of pretentiously learned language. Seen in its historical context, Wilson's _The Art of Rhetoric _reveals a great deal about the formal education of such authors as Shakespeare, Spenser, Jonson, and Milton. Since it bears directly on what is basic to imaginative literature—the art of language—the _Art_ encapsulates a literary context relevant to all those studying the English Renaissance, whether their approach is historicist, structuralist, deconstructionist, or new historicist. In addition, it will be of interest to students of rhetoric, education, and intellectual history in general. There have been four editions of the _Art_ in the twentieth century: two facsimiles and two original-spelling texts, none of which is in print. Peter Medine's edition modernizes the spelling and punctuation of the text of the second edition, which Wilson revised and expanded in 1560, and furnishes a fully critical apparatus, including introduction, textual notes, commentary, and glossary. As such, this edition makes available a central work of the English Renaissance in an accessible format. (shrink)

Paternity certainty and matrilineal family ties have been used to explain the asymmetric caregiving of grandparents and aunts and uncles. The proximate mechanisms underlying biased kin investment, however, remain unclear. A central question of the study presented here was whether the parent-kin relationship is an important link in the caregiving. In a two-generational questionnaire study, we asked subjects to estimate the intensity of their relationships to parents, grandparents, aunts, and uncles (emotional closeness, investment received in childhood). In addition, the subjects’ (...) parents rated their emotional closeness to their parents and siblings. We found that the parent-kin relationship was closely linked to the relatives’ child care and could partly explain asymmetric caregiving. Maternal aunts played a special role as caregivers. Especially the mother’s younger or last-born sister cared intensively for nieces and nephews, regardless of her closeness to the subjects’ mother. (shrink)

PrécisThe administration of Pre-Mortem Interventions (PMIs) to preserve the opportunity to donate, to assess the eligibility to donate, or to optimize the outcomes of donation and transplantation are controversial as they offer no direct medical benefit and include at least the possibility of harm to the still-living patient. In this article, we describe the legal analysis surrounding consent to PMIs, drawing on existing legal commentary and identifying key legal problems. We provide an overview of the approaches in several jurisdictions that (...) have chosen to explicitly address PMIs within codified law. We then provide, as an example, a detailed exploration of how PMIs are likely to be addressed in one jurisdiction where general medical consent law applies because there is no specific legislation addressing PMIs — the province of Ontario in Canada. (shrink)

John Divers and Joseph Melia have argued that Lewis's modal realism is extensionally inadequate. This paper explains why their argument does not succeed.

The subtraction argument aims to show that there is an empty world, in the sense of a possible world with no concrete objects. The argument has been endorsed by several philosophers. I show that there are currently two versions of the argument around, and that only one of them is valid. I then sketch the main problem for the valid version of the argument.

First-order formalisations are often preferred to propositional ones because they are thought to underwrite the validity of more arguments. We compare and contrast the ability of some well-known logics—these two in particular—to formally capture valid and invalid arguments. We show that there is a precise and important sense in which first-order logic does not improve on propositional logic in this respect. We also prove some generalisations and related results of philosophical interest. The rest of the article investigates the results’ philosophical (...) significance. A first moral is that the correct way to state the oft-cited superiority of first-order logic vis-`a-vis propositional logic is more nuanced than often thought. The second moral concerns semantic theory; the third logic’s use as a tool for discovery. A fourth and final moral is that second-order logic’s transcendence of first-order logic is greater than first-order logic’s transcendence of propositional logic. (shrink)

We study the formalization within sybsystems of second-order arithmetic of theorems concerning periodic points in dynamical systems on the real line. We show that Sharkovsky's theorem is provable in WKL0. We show that, with an additional assumption, Sharkovsky's theorem is provable in RCA0. We show that the existence for all n of n-fold iterates of continuous mappings of the closed unit interval into itself is equivalent to the disjunction of Σ02 induction and weak König's lemma.

The paper raises some difficulties for the typical motivations behind set reductionism, the view that sets are reducible to entities identified independently of set theory.

The use of x[y,z,w] rather than the more usual y Πx has many advantages for this work. One of them is that we have found a convenient way to eliminate any need for axiom schemes. All axioms considered are single sentences with clear meaning. (In one case only, the axiom is a conjunction of a manageable finite number of sentences).

From the mid-nineteenth century to the Gilded Age, Catharine Beecher and other American social reformers combined natural theology and evangelism to instruct their audiences how to lead healthy, virtuous, and happy lives. Worried about the consequences of urbanization, industrialization, unstable sexual and gender roles, and immigration, these “Christian physiologists” provided prescriptive scientific advice for hygiene and personal conduct based on the traditional norms of white, middle-class, Protestant domesticity. According to Beecher and her counterparts, the biosocial reproduction of ideal American households (...) promised to reverse the degeneration of men and women across the country and to ensure the long-term vitality of their children. Using evidence from Beecher, Harriet Beecher Stowe, Charlotte Perkins Gilman, and other nineteenth-century writers, I investigate the methods and aims of Christian physiology along with its relationships to natural theology, Darwinian feminism, and other reform movements. I also analyze how Beecher and her successors employed concepts including the machine, the tissue, the cell, and the germ to justify their conclusions about the optimal structure and functions of American society. Overall, I demonstrate how these actors leveraged the body and the family as mechanisms to produce healthy parents, children, and communities for an ailing nation. (shrink)

Russell’s way out of his paradox via the impre-dicative theory of types has roughly the same logical power as Zermelo set theory - which supplanted it as a far more flexible and workable axiomatic foundation for mathematics. We discuss some new formalisms that are conceptually close to Russell, yet simpler, and have the same logical power as higher set theory - as represented by the far more powerful Zermelo-Frankel set theory and beyond. END.

PREFACE. We present a variety of basic theories involving fundamental concepts of naive thinking, of the sort that were common in "natural philosophy" before the dawn of physical science. The most extreme forms of infinity ever formulated are embodied in the branch of mathematics known as abstract set theory, which forms the accepted foundation for all of mathematics. Each of these theories embodies the most extreme forms of infinity ever formulated, in the following sense. ZFC, and even extensions of ZFC (...) with the so called large cardinal axioms, are mutually interpretable with these theories. This is an extended abstract. Proofs of the claims will appear elsewhere. (shrink)

This is the initial publication on Concept Calculus, which establishes mutual interpretability between formal systems based on informal commonsense concepts and formal systems for mathematics through abstract set theory. Here we work with axioms for "better than" and "much better than", and the Zermelo and Zermelo Frankel axioms for set theory.

Let k ≥ 2 and f:Nk Æ [1,k] and n ≥ 1 be such that there is no x1 < ... < xk+1 £ n such that f(x1,...,xk) = f(x1,...,xk+1). Then we want to find g:Nk+1 Æ [1,3] such that there is no x1 < ... < xk+2 £ n such that g(x1,...,xk+1) = g(x2,...,xk+2). This reducees adjacent Ramsey in k dimensions with k colors to adjacent Ramsey in k+1 dimensions with 3 colors.

The subtle, almost ineffable, and ineffable cardinals were introduced in an unpublished 1971 manuscript of R. Jensen and K. Kunen. The concepts were extended to that of k-subtle, k-almost ineffable, and k-ineffable cardinals in 1975 by J. Baumgartner. In this paper we give a self contained treatment of the basic facts about this level of the large cardinal hierarchy, which were established by J. Baumgartner. In particular, we give a proof that the k-subtle, k-almost ineffable, and k-ineffable cardinals define three (...) properly intertwined hierarchies with the same limit, lying strictly above “total indescribability” and strictly below “arrowing ω”. The innovation here is presented in Section 2, where we take a distinctly minimalist approach. Here the subtle cardinal hierarchy is characterized by very elementary properties that do not mention closed unbounded or stationary sets. This development culminates in a characterization of the hierarchy by means of a striking universal second-order property of linear orderings. (shrink)

My paper addresses a number of questions raised in the Statesman by the Eleatic Visitor’s identification of certain ontological conditions for the existence of art of due measure, and therefore of all the technai. My view is that evidence relevant to these questions can be found in the Philebus, and specifically, in an ontological doctrine presented at 23c–27c. What emerges from an examination of the Statesman and Philebus is a highly developed conception of technê, one that affords a place for (...) such ordinary human activities within the broader framework of Plato’s philosophy. (shrink)

In my paper , I noted that Fitch's argument, which purports to show that if all truths are knowable then all truths are known, can be blocked by typing knowledge. If there is not one knowledge predicate, ‘ K’, but infinitely many, ‘ K 1’, ‘ K 2’, … , then the type rules prevent application of the predicate ‘ K i’ to sentences containing ‘ K i’ such as ‘ p ∧¬ K i⌜ p⌝’. This provides a motivated response (...) to Fitch's argument so long as knowledge typing is itself motivated. It was the burden of my paper to explore the case that knowledge typing is as motivated as truth typing by drawing on the parallels between epistemic paradoxes generated by sentences of the kind ‘this sentence is unknown’ and semantic paradoxes generated by sentences such as ‘this sentence is untrue’. Given that typing truth is one of the acknowledged options for solving semantic paradoxes, if the parity argument succeeds it follows that epistemic typing is as well-motivated as truth typing and that the typing response to Fitch's argument is correspondingly strong.Halbach presents an apparent problem for this argument. Let ‘ N’ and ‘ P’, respectively, denote the necessity and possibility predicates, ‘ K 1’ the knowledge predicate of first type, and let ‘γ’ be a K-free sentence such that γ ↔¬ P⌜ K 1⌜γ⌝⌝; we know such a ‘γ’ exists by a standard diagonalization argument. If we assume that γ is knowable at the next knowledge type, that is, at type 1, and that the possibility typing does not interfere with the knowledge typing, a contradiction quickly ensues. Formally: γ ↔¬ P⌜ …. (shrink)

Here we take the view that LPC(=) is applicable to structures whose domain is too large to be a set. This is not just a matter of class theory versus set theory, although it can be interpreted as such, and this interpretation is discussed briefly at the end.

Six years ago, the Singer lab published a landmark paper which described how individual mRNA particles cross the nuclear pore complex in mammalian tissue culture cells. This involved the simultaneous imaging of mRNAs, each labeled by a large number of tethered fluorescent proteins and fluorescently tagged nuclear pore components. Now two groups have applied this technique to the budding yeast Saccharomyces cerevisiae. Their results indicate that in the course of nuclear export, mRNAs likely engage complexes that are present on either (...) side of the pore and that these interactions are modulated by proteins present in the messenger ribonucleoprotein (mRNP) complex. These findings lend support to the notion that just before and/or after the completion of nuclear export, mRNPs undergo one or more maturation steps that prepare the packaged mRNAs for translation. These results represent new and exciting insights into the mechanism of mRNA nuclear export. (shrink)