In this paper we introduce a system S5U, formed by adding to the modal system S5 a new connective U, Up being read “probably”. A few theorems are derived in S5U, and the system is provided with a decision procedure. Several decidable extensions of S5U are discussed, and probability logic is related to plurality quantification.

This paper is the third of a multi-part examination of the Babylonian mathematical lunar theories known as Systems A and B. Part I (Britton, AHES 61:83–145, 2007) addressed the development of the empirical elements needed to separate the effects of lunar and solar anomaly on the intervals between syzygies, accomplished in the construction of the System A lunar theory early in the fourth century B.C. Part II (Britton, AHES 63:357–431, 2009) examines the accomplishment of this separation by the construction of (...) a successful theory depicting the variations due to lunar anomaly in System A and its subsequent adaptation in System B. The present paper examines the introduction of the uniform zodiac, necessary for any theory depicting variations depending on the position of syzygy. It addresses three questions: (1) In light of all available evidence, what is the magnitude of the constant term in the expression Δλ* = C − 1.3828°Y, describing the difference between the Babylonian sidereal longitudes and modern tropical longitudes? (2) What considerations governed the placement of the Babylonian sidereal zodiac relative to the fixed stars? (3) When was the uniform zodiac introduced? To the first question it finds C = 3.20° ± 0.1°, scarcely different from Huber’s (Centaurus 5:192–208, 1958) estimate of 3.08°, essentially confirming Huber’s result obtained from much less data. For the second it shows that accommodating the three asterisms comprising Taurus limited the placement of the zodiac to within 3°, while the prominence of half sign multiples among the measured intervals between prominent Normal Stars led irresistibly to the choice adopted. Finally, it finds that the zodiac was introduced between −408 and −397 and probably within a very few years of −400. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:John P. Anton C. P. CAVAFY'S ARS POETICA ' It is generally recognized that Constantine P. Cavafy (1863-1933) was not born a poet but became one only through persistence and labor, reaching his "first step" sometime after the midpoint of his life. In his effort to assess the quality of his earlier poetic production and sharpen his sensitivity in facing self-criticism, he decided to put in writing his (...) personal thoughts on his work sometime in 1903. The text was written in English in a personal shorthand Cavafy had devised for his own use. It was found among the papers he left to A. Sengopoulos and published for the first time in 1963 by M. Peridis, who also supplied the suitable title Ars Poetica. It falls outside the scope of this essay to discuss the antecedents of this document. Taken as a whole, the text has all the clarity and directness required of a testament designed to serve as a personal guide and handbook. The problems it discusses are limited to the needs of the poet. In this regard, the Ars Poetica has neither the range of topics nor the theoretical scope of, for instance, Aristotle's Poetics. It is quite certain that the ideas that preoccupy Cavafy in the Ars Poetica had been on his mind for a period of years. However, the Ars Poetica is his first prose piece where he gives a systematic treatment to technical and critical issues directly related to the assessment of his work and his role as a poet. In order to project here a clear image of Cavafy's struggle to reach his technical maturity which came after 1910, we need first to discuss the persistent problems he faced during this crucial decade, then to examine the attitudes and values he embodied in certain representative early poems, and finally to relate them to the guiding principles he formulated in his self-addressed poetics of 1903. A number of interrelated problems confronted Cavafy in his late twenties and throughout his thirties. They emerged one by one, to 85 86Philosophy and Literature make more pressing the demand for a consistent solution and a complete recasting of his outlook. Coming to terms with them was extremely difficult. Aside from the emotional and sexual pressures he had to face alone, there was the absence of suitable ideas and conceptual tools to provide him with even the rudiments of an intellectual framework. Whatever he borrowed from Europe and England, or resurrected from his own Hellenic heritage, proved either beyond assimilation or insufficiently digested. The lingering issues fell roughly into four areas. (i) Despite his determination to devote his life to the writing of poetry, the quality of his work was discouraging. He knew this and as a result he often expressed uncertainty about his ability to proceed. Time and again he appeared suffering from a feeling of inadequacy, but nevertheless he sought to engage a reflective mood from which to draw encouragement and hope. (ii) On the theoretical side, he identified with the long tradition which assigned a coveted cultural role to the savant-poet as discloser of truth and spokesman for humanity; this despite the prevailing climate of opinion in his immediate environment which recognized no such high position in his case. Cavafy knew that his standing with the Greek community of Alexandria had gradually dwindled with the loss of family wealth and his lowly employment, and also that his expectations to be respected in his role as a poet and leader in communal affairs were futile. This denial of personal recognition in a society dominated by commerce and finance contributed to his mood of depression. The feeling of being an outcast, despite his associations with the upper social circles of Alexandria, became a constant irritant to his sense of pride. (iii) The course of culture, the destiny of human institutions and the workings of history, became puzzles as he tried to view them through the opaque glass of disillusionment. These were the grand themes actively discussed in the writings of leading European intellectuals, but to the young poet they had a different personal urgency. His vital concern in this connection was not understanding science... (shrink)

John Norton says that philosophers have been led astray for thousands of years by their attempt to treat induction formally. He is correct that such an attempt has caused no end of trouble, but he is wrong about the history. There is a rich tradition of non-formal induction. In fact, material theories of induction prevailed all through antiquity and from the Renaissance to the mid-1800s. Recovering these past systems would not only fill lacunae in Norton’s own theory but would (...) highlight areas where Norton has not freed himself from the straightjacket of formal induction as much as he might think. This essay begins that recovery. (shrink)

The complexity of the set of truths of arithmetic is determined for various theories of truth deriving from Kripke and from Gupta and Herzberger.

A new axiomatization of set theory, to be called Bernays-Boolos set theory, is introduced. Its background logic is the plural logic of Boolos, and its only positive set-theoretic existence axiom is a reflection principle of Bernays. It is a very simple system of axioms sufficient to obtain the usual axioms of ZFC, plus some large cardinals, and to reduce every question of plural logic to a question of set theory.

One hundred years ago, in his lecture Science as a Vocation, Max Weber prefigured a transition from science as a calling to science as bureaucratically organized work. He argued that a calling for science is critical for sustaining scientific work. Using Weber’s arguments for science as a vocation as a lens, in this paper, we discuss whether a calling for science may become difficult to maintain in increasingly bureaucratized scientific work—and also whether such a calling is necessary for the advance (...) of science. We present empirical evidence for this bureaucratization of scientific work and further develop Weber’s discussion of science by contrasting it with the views of other theorists of science and innovation. Finally, we discuss the implications of these theories, develop a set of policy recommendations, and outline a research agenda designed to develop science policies and a sociology of science that match this shift from vocation to bureaucracy in scientific work. (shrink)

Used as the basis of the program at the Equinox Holistic Alternative School in Toronto, The Holistic Curriculum advocates for an integrative approach to teaching and learning with a focus on developing a deep connection between mind and body.

This paper is the second of a multi-part examination of the creation of the Babylonian mathematical lunar theories known as Systems A and B. Part I (Britton 2007) addressed the development of the empirical elements needed to separate the effects of lunar and solar anomaly on the intervals between syzygies. This was accomplished in the construction of the System A lunar theory by an unknown author, almost certainly in the city of Babylon and probably early in the 4th century B.C. (...) The present paper focuses mainly on System A and the likely process of its construction. The first three sections are largely descriptive – first of the basic concepts which underlie the theory; then of the component schemes comprising the theory; and finally of two distinctive texts which suggest how the theory was constructed. The crux of the paper is Sect. 4, which describes how the theory seems likely to have been constructed. Here the crucial insight in separating the effects of lunar and solar anomaly appears to have been recognizing that – of all the measurable intervals bounded by eclipses – only 235 months exhibits a variation due solely to lunar anomaly, and that by means of an elegant mathematical model the amplitudes of 223 and 12 months could be deduced from its amplitude. The rest of the section describes the likely details of the derivation of the Φ ~ Λ scheme, and the extension of the methodology to the other components of the theory. It concludes with a demonstration that Φ and its dependent schemes were anchored through the Φ ~ W scheme to the syzygy on –403 Aug 18 (GN 7391) which concluded the shortest 6-month interval in the first 24 saros cycles since –746 (and in fact in the 900 years separating Nabonassar and Ptolemy). The next three sections address a number of largely technical details and amplifications of the theory, beginning with the schemes describing the variation of lunar velocity (column F) in Sect. 5. Section 6 addresses issues concerning the interpretation of Φ and the so-call Saros Text (BM 36705), while Sect. 7 discusses System B’s corresponding treatment of the effects of lunar anomaly, illustrating both its derivative nature and mathematically less rigorous structure. Section 8 examines the accuracy of the two theories, showing that the System A theory was both remarkably accurate and superior to System B. The final section offers some brief remarks on the power and elegance of the mathematical treatment of the problem by the author of System A. (shrink)

(2013). Informed Consent, Big Data, and the Oxymoron of Research That Is Not Research. The American Journal of Bioethics: Vol. 13, No. 4, pp. 40-42. doi: 10.1080/15265161.2013.768864.

This paper traces the diverse contexts of radiation protection from liberation in post-1945 South Korea to its professionalization by the early 1970s, using the emerging field of health physics as the focus. The Korean nuclear center, AERI, started two affiliates, RRIA and RRIM in the early 1960s. In particular, RRIM emphasized the use of radiation within cancer research, especially the use of cobalt in treating patients. In this context, health physics initially took the form of “radiation medicine.”With the two institutes (...) returning to AERI’s fold in 1973, health physics took another turn: the second major subfield, following “radiation medicine,” invoked a broader conception of “radiation protection,” which now referred to a cluster of related interests, including the environment and the effects of industrialization.Rather than a simple transfer of American and international models after 1953, Korean health physics reflects its origins in a post-colonial research setting, one more diverse than its “official” institutional context at AERI. (shrink)

Overstated generalizability is common in research. It may coexist with inflation of the magnitude and statistical support for effects and dismissal of internal validity problems. Generalizability may be secured before attempting replication of proposed discoveries or replication may precede efforts to generalize. These opposite approaches may decrease or increase, respectively, the use of inferential statistics with advantages and disadvantages.

The question, "Which modal logic is the right one for logical necessity?," divides into two questions, one about model-theoretic validity, the other about proof-theoretic demonstrability. The arguments of Halldén and others that the right validity argument is S5, and the right demonstrability logic includes S4, are reviewed, and certain common objections are argued to be fallacious. A new argument, based on work of Supecki and Bryll, is presented for the claim that the right demonstrability logic must be contained in S5, (...) and a more speculative argument for the claim that it does not include S4.2 is also presented. (shrink)

Cognitive Science, Volume 46, Issue 5, May 2022.

Scientific authorship has become a contested terrain in contemporary science. Based on a survey of authors across fields, we measure the likelihood of specialist authors : people who only made specialized contributions, such as data, materials, or funding; and “nonauthor collaborators” : those who did significant work on the project but do not appear as authors, across different research contexts, including field, size of the project team, commercial orientation, impact of publication, and organization of the collaboration. We find that guest (...) and ghost authors are common, with about one-third of publications having at least one specialist author and over half having at least one nonauthor collaborator. We see significant cross-field variations in both overall rates and types of specialist authors and nonauthor collaborators. We find there are generally fewer specialist authors among highly cited papers and more graduate student nonauthor collaborators in single location projects. The results suggest authorship practices vary across fields, and by project characteristics, complicating the use of authorship lists as a basis for evaluation. We discuss implications of these findings for interpreting author lists in the context of science policy. (shrink)

The great logician Gottlob Frege attempted to provide a purely logical foundation for mathematics. His system collapsed when Bertrand Russell discovered a contradiction in it. Thereafter, mathematicians and logicians, beginning with Russell himself, turned in other directions to look for a framework for modern abstract mathematics. Over the past couple of decades, however, logicians and philosophers have discovered that much more is salvageable from the rubble of Frege's system than had previously been assumed. A variety of repaired systems have been (...) proposed, each a consistent theory permitting the development of a significant portion of mathematics. This book surveys the assortment of methods put forth for fixing Frege's system, in an attempt to determine just how much of mathematics can be reconstructed in each. John Burgess considers every proposed fix, each with its distinctive philosophical advantages and drawbacks. These systems range from those barely able to reconstruct the rudiments of arithmetic to those that go well beyond the generally accepted axioms of set theory into the speculative realm of large cardinals. For the most part, Burgess finds that attempts to fix Frege do less than advertised to revive his system. This book will be the benchmark against which future analyses of the revival of Frege will be measured. (shrink)

We show it is consistent with ZFC that the Hanf number of Ellentuck's Souslin logic should be exactly $\beth_{\omega_2}$.

Critics of organ donation after circulatory death (DCD) argue that, even if donors are past the point of autoresuscitation, they have not satisfied the “irreversibility” requirement in the circulatory and respiratory criteria for determining death, since their circulation and respiration could be artificially restored. Thus, removing their vital organs violates the “dead-donor” rule. I defend DCD donation against this criticism. I argue that practical medical-ethical considerations, including respect for do-not-resuscitate orders, support interpreting “irreversibility” to mean permanent cessation of circulation and (...) respiration. Assuming a consciousness-related formulation of human death, I then argue that the loss of circulation and respiration is significant, because it leads to the permanent loss of consciousness and thus to the death of the human person. The DNR request by an organ donor should thus be interpreted to mean “do not restore to consciousness.” Finally, I respond to an objection that if “irreversibility” has a medical-ethical meaning, it would entail the absurd possibility that one of two individuals in the same physical state could be alive and the other dead—an implication that some think is inconsistent with understanding death as an objective biological state of the organism. I argue that advances in medical technology have created phenomena that challenge the assumption that human death can be understood in strictly biological terms. I argue that ethical and ontological considerations about our nature bear on the definition and determination of death and thus on the permissibility of DCD. (shrink)

Al-Maʾmūn, the Inquisition, and the Quest for Caliphal Authority. By John Abdallah Nawas. Resources in Arabic and Islamic Studies, vol. 4. Atlanta: Lockwood Press, 2015. Pp. xvi + 340. $45.

Søren Kierkegaard and Walter Lippmann wrote in very different times and places but both characterized the public as a “phantom.” Importantly, each did so within the context of a broader analysis that linked the press with specific notions about the public and democracy. This paper highlights the specific characteristics of the press that each thinker believed were responsible for the construction of the phantom public and its effects. While taking seriously the differences between Kierkegaard and Lippmann, in both their respective (...) sociopolitical contexts and their formulations of the public and the press, this paper applies their critiques to a vastly different media terrain than either thinker could have envisioned. (shrink)

Perhaps if the future existed, concretely and individually, as something that could be discerned by a better brain, the past would not be so seductive: its demands would he balanced by those of the future. Persons might then straddle the middle stretch of the seesaw when considering this or that object. It might be fun. But the future has no such reality (as the pictured past and the perceived present possess); the future is but a figure of speech, a specter (...) of thought. (shrink)

Dummett's case against platonism rests on arguments concerning the acquisition and manifestation of knowledge of meaning. Dummett's arguments are here criticized from a viewpoint less Davidsonian than Chomskian. Dummett's case against formalism is obscure because in its prescriptive considerations are not clearly separated from descriptive. Dummett's implicit value judgments are here made explicit and questioned. ?Combat Revisionism!? Chairman Mao.