Ancient Indian Logic and Analogy

B.K.Matilal, and earlier J.F.Staal, have suggested a reading of the `Nyaya five limb schema' (also sometimes referred to as the Indian Schema or Hindu Syllogism) from Gotama's Nyaya-Sutra in terms of a binary occurrence relation. In this paper we provide a rational justification of a version of this reading as Analogical Reasoning within the framework of Polyadic Pure Inductive Logic

Second Order Inductive Logic and Wilmers' Principle

We extend the framework of Inductive Logic to Second Order languages and introduce Wilmers' Principle, a rational principle for probability functions on Second Order languages. We derive a representation theorem for functions satisfying this principle and investigate its relationship to the first order principles of Regularity and Super Regularity

The Counterpart Principle of Analogical Support by Structural Similarity

We propose and investigate an Analogy Principle in the context of Unary Inductive Logic based on a notion of support by structural similarity which is often employed to motivate scientific conjectures

Superspace formulation of general massive gauge theories and geometric interpretation of mass-dependent BRST symmetries

A superspace formulation is proposed for the osp(1,2)-covariant Lagrangian quantization of general massive gauge theories. The superalgebra os0(1,2) is considered as subalgebra of sl(1,2); the latter may be considered as the algebra of generators of the conformal group in a superspace with two anticommuting coordinates. The mass-dependent (anti)BRST symmetries of proper solutions of the quantum master equations in the osp(1,2)-covariant formalism are realized in that superspace as invariance under translations combined with mass-dependent special conformal transformations. The Sp(2) symmetry - in particular the ghost number conservation - and the "new ghost number" conservation are realized as invariance under symplectic rotations and dilatations, respectively. The transformations of the gauge fields - and of the full set of necessarily required (anti)ghost and auxiliary fields - under the superalgebra sl(1,2) are determined both for irreducible and first-stage reducible theories with closed gauge algebra.Comment: 35 pages, AMSTEX, precision of reference

Every countable model of set theory embeds into its own constructible universe

The main theorem of this article is that every countable model of set theory M, including every well-founded model, is isomorphic to a submodel of its own constructible universe. In other words, there is an embedding $j:M\to L^M$ that is elementary for quantifier-free assertions. The proof uses universal digraph combinatorics, including an acyclic version of the countable random digraph, which I call the countable random Q-graded digraph, and higher analogues arising as uncountable Fraisse limits, leading to the hypnagogic digraph, a set-homogeneous, class-universal, surreal-numbers-graded acyclic class digraph, closely connected with the surreal numbers. The proof shows that $L^M$ contains a submodel that is a universal acyclic digraph of rank $Ord^M$. The method of proof also establishes that the countable models of set theory are linearly pre-ordered by embeddability: for any two countable models of set theory, one of them is isomorphic to a submodel of the other. Indeed, they are pre-well-ordered by embedability in order-type exactly $\omega_1+1$. Specifically, the countable well-founded models are ordered by embeddability in accordance with the heights of their ordinals; every shorter model embeds into every taller model; every model of set theory $M$ is universal for all countable well-founded binary relations of rank at most $Ord^M$; and every ill-founded model of set theory is universal for all countable acyclic binary relations. Finally, strengthening a classical theorem of Ressayre, the same proof method shows that if $M$ is any nonstandard model of PA, then every countable model of set theory---in particular, every model of ZFC---is isomorphic to a submodel of the hereditarily finite sets $HF^M$ of $M$. Indeed, $HF^M$ is universal for all countable acyclic binary relations.Comment: 25 pages, 2 figures. Questions and commentary can be made at http://jdh.hamkins.org/every-model-embeds-into-own-constructible-universe. (v2 adds a reference and makes minor corrections) (v3 includes further changes, and removes the previous theorem 15, which was incorrect.

Globalisation and health security: a case study of distant individual risk perceptions of the 2014 Ebola outbreak

The wider awareness and recognition of human security threats has developed over the last several decades. Spurred on by globalization, greater human mobility, global media, economic interconnectedness and technological advancements, the securitization of non-military security threats have deepened and widened security discourses. The percieved risk posed by truly global threats have resulted in new international regimes and cooperation, national governments have reevaluated their national security strategies, and grassroots movements have revealed and mobileized individuals around the world to action. Global health security threats, and in particular, pandemic diseases, are one just one of many threats currently facing the global community that has the potential to envoke fear and feelings of insecurity and panic, particularly when securitized through twenty four hour news networks and social media. The purpose of this study is to explore the securitization process of a health security threat, the 2014 Ebola outbreak, and risk perceptions of individuals living in a global city geographically distant from the outbreak. This study reports the findings from interviews with eleven individuals based in the United Arab Emirates to explore their individual risk perceptions of the outbreak of the Ebola virus, and to understand how information about the outbreak was obtained, processed and consequently construed by these individuals. The findings suggested that with the increasing securitization of diseases, individual risk perceptions of the 2014 Ebola outbreak were a reflection of a variety of discourses concerning the security issue at the national and global levels. Therefore, in light of the increasing emergence and re-emergence of pandemic diseases and transborder global threats, it is important to consider individual perceptions of the threats and the influence of government, media (traditional and social media), and individual experiences in a global and interconnected world

Elliptical instability of a rapidly rotating, strongly stratified fluid

The elliptical instability of a rotating stratified fluid is examined in the regime of small Rossby number and order-one Burger number corresponding to rapid rotation and strong stratification. The Floquet problem describing the linear growth of disturbances to an unbounded, uniform-vorticity elliptical flow is solved using exponential asymptotics. The results demonstrate that the flow is unstable for arbitrarily strong rotation and stratification; in particular, both cyclonic and anticyclonic flows are unstable. The instability is weak, however, with growth rates that are exponentially small in the Rossby number. The analytic expression obtained for the growth rate elucidates its dependence on the Burger number and on the eccentricity of the elliptical flow. It explains in particular the weakness of the instability of cyclonic flows, with growth rates that are only a small fraction of those obtained for the corresponding anticyclonic flows. The asymptotic results are confirmed by numerical solutions of Floquet problem.Comment: 17 page

A microwave systems approach to measuring root zone soil moisture

Computer microwave satellite simulation models were developed and the program was used to test the ability of a coarse resolution passive microwave sensor to measure soil moisture over large areas, and to evaluate the effect of heterogeneous ground covers with the resolution cell on the accuracy of the soil moisture estimate. The use of realistic scenes containing only 10% to 15% bare soil and significant vegetation made it possible to observe a 60% K decrease in brightness temperature from a 5% soil moisture to a 35% soil moisture at a 21 cm microwave wavelength, providing a 1.5 K to 2 K per percent soil moisture sensitivity to soil moisture. It was shown that resolution does not affect the basic ability to measure soil moisture with a microwave radiometer system. Experimental microwave and ground field data were acquired for developing and testing a root zone soil moisture prediction algorithm. The experimental measurements demonstrated that the depth of penetration at a 21 cm microwave wavelength is not greater than 5 cm

Results of soil moisture flights during April 1974

The results presented here are derived from measurements made during the April 5 and 6, 1974 flights of the NASA P-3A aircraft over the Phoenix, Arizona agricultural test site. The purpose of the mission was to study the use of microwave techniques for the remote sensing of soil moisture. These results include infrared (10-to 12 micrometers) 2.8-cm and 21-cm brightness temperatures for approximately 90 bare fields. These brightness temperatures are compared with surface measurements of the soil moisture made at the time of the overflights. These data indicate that the combination of the sum and difference of the vertically and the horizontally polarized brightness temperatures yield information on both the soil moisture and surface roughness conditions