scholarly journals A Note on Identity and Higher Order Quantification

2009 ◽  
Vol 7 ◽  
Author(s):  
Rafal Urbaniak
Keyword(s):  
Higher Order ◽  
Second Order ◽  
Identity Relation ◽  
First Order ◽  
Order Language ◽  
Order Set

It is a commonplace remark that the identity relation, even though not expressible in a first-order language without identity with classical set-theoretic semantics, can be defined in a language without identity, as soon as we admit second-order, set-theoretically interpreted quantifiers binding predicate variables that range over all subsets of the domain. However, there are fairly simple and intuitive higher-order languages with set-theoretic semantics (where the variables range over all subsets of the domain) in which the identity relation is not definable. The point is that the definability of identity in higher-order languages not only depends on what variables range over, but also is sensitive to how predication is construed. This paper is a follow-up to (Urbaniak 2006), where it has been proven that no actual axiomatization of Leśniewski’s Ontology determines the standard semantics for the epsilon connective.

Categoricity and the sets

2018 ◽  
Author(s):  
Tim Button ◽  
Sean Walsh
Keyword(s):  
Set Theory ◽  
Second Order ◽  
Order Logic ◽  
First Order ◽  
The Status ◽  
Second Order Logic ◽  
Philosophy Of Set Theory ◽  
Order Set

In this chapter, the focus shifts from numbers to sets. Again, no first-order set theory can hope to get anywhere near categoricity, but Zermelo famously proved the quasi-categoricity of second-order set theory. As in the previous chapter, we must ask who is entitled to invoke full second-order logic. That question is as subtle as before, and raises the same problem for moderate modelists. However, the quasi-categorical nature of Zermelo's Theorem gives rise to some specific questions concerning the aims of axiomatic set theories. Given the status of Zermelo's Theorem in the philosophy of set theory, we include a stand-alone proof of this theorem. We also prove a similar quasi-categoricity for Scott-Potter set theory, a theory which axiomatises the idea of an arbitrary stage of the iterative hierarchy.

scholarly journals Higher-Order Illative Combinatory Logic

2013 ◽  
Vol 78 (3) ◽  
pp. 837-872 ◽  
Author(s):  
Łukasz Czajka
Keyword(s):  
Strong Consistency ◽  
Predicate Logic ◽  
Higher Order ◽  
Second Order ◽  
Model Construction ◽  
Partial Answer ◽  
Combinatory Logic ◽  
First Order ◽  
Propositional Quantifiers

AbstractWe show a model construction for a system of higher-order illative combinatory logic thus establishing its strong consistency. We also use a variant of this construction to provide a complete embedding of first-order intuitionistic predicate logic with second-order propositional quantifiers into the system of Barendregt, Bunder and Dekkers, which gives a partial answer to a question posed by these authors.

Higher-Order Multilevel Solvers for the EHL Line and Point Contact Problem

1994 ◽  
Vol 116 (4) ◽  
pp. 741-750 ◽  
Author(s):  
C. H. Venner
Keyword(s):  
Contact Problem ◽  
Computing Time ◽  
Point Contact ◽  
Higher Order ◽  
Second Order ◽  
Point Of View ◽  
First Order ◽  
Fundamental Point ◽  
Numerical Solver ◽  
Circular Contact

This paper addresses the development of efficient numerical solvers for EHL problems from a rather fundamental point of view. A work-accuracy exchange criterion is derived, that can be interpreted as setting a limit to the price paid in terms of computing time for a solution of a given accuracy. The criterion can serve as a guideline when reviewing or selecting a numerical solver and a discretization. Earlier developed multilevel solvers for the EHL line and circular contact problem are tested against this criterion. This test shows that, to satisfy the criterion a second-order accurate solver is needed for the point contact problem whereas the solver developed earlier used a first-order discretization. This situation arises more often in numerical analysis, i.e., a higher order discretization is desired when a lower order solver already exists. It is explained how in such a case the multigrid methodology provides an easy and straightforward way to obtain the desired higher order of approximation. This higher order is obtained at almost negligible extra work and without loss of stability. The approach was tested out by raising an existing first order multilevel solver for the EHL line contact problem to second order. Subsequently, it was used to obtain a second-order solver for the EHL circular contact problem. Results for both the line and circular contact problem are presented.

From First-Order Coherence to Higher-Order Coherence of Synchrotron Radiation

1998 ◽  
Vol 5 (3) ◽  
pp. 305-308 ◽  
Author(s):  
Tsuneaki Miyahara
Keyword(s):  
Synchrotron Radiation ◽  
Free Electron ◽  
Higher Order ◽  
Second Order ◽  
Free Electron Lasers ◽  
First Order ◽  
Noise Characteristics ◽  
The Difference

The difference between first-order and second-order coherence of synchrotron radiation is discussed in relation to how they can be measured and how they affect the noise characteristics of future free-electron lasers.

KK Compatibilism

2021 ◽  
pp. 40-54
Author(s):  
Mona Simion
Keyword(s):  
Higher Order ◽  
Second Order ◽  
High Stakes ◽  
Proper Action ◽  
First Order ◽  
Knowing That

According to KK Compatibilism, the unassertability in the high-stakes contextualist cases can be explained in terms of the subjects lack of higher-order knowledge: although, strictly speaking, all that is needed for proper action—assertion included—is first-order knowledge, when the stakes are high, we tend to find people who act without knowing that they meet the condition for proper action blameworthy for so doing. This chapter argues that (1) the view misidentifies the epistemic deficit that is explanatorily salient in contextualist cases, in that the absence of second-order knowledge is not a difference maker, and (2) on closer look, the account requires normative finessing for extensional adequacy.

Second-Order Backward Blocking and Unovershadowing in Human Causal Learning

2002 ◽  
Vol 49 (1) ◽  
pp. 27-33 ◽  
Author(s):  
Jan De Houwer ◽  
Tom Beckers
Keyword(s):  
Higher Order ◽  
Second Order ◽  
Causal Learning ◽  
First Order ◽  
Human Causal Learning ◽  
Before And After ◽  
Causal Status

Abstract. De Houwer and Beckers (in press , Experiment 1) recently demonstrated that ratings about the relation between a target cue T2 and an outcome are higher when training involves CT1+ and T1T2+ followed by C+ trials than when training involves CT1+ and T1T2+ followed by C- trials. We replicated this study but now explicitly asked participants to rate the causal status of the cues both before and after the C+ or C- trials. Results showed that causal ratings for T2 were significantly higher after C+ trials than before C+ trials and that T2 received significantly lower ratings after C- trials than before C- trials. The results thus provide the first evidence for higher-order unovershadowing and higher-order backward blocking. In addition, the ratings for T1 revealed that first-order backward blocking (i.e., decrease in ratings for T1 as the result of C+ trials) was stronger than first-order unovershadowing (i.e., increase in ratings for T1 as the result of C- trials).

scholarly journals Conservative Transport Schemes for Spherical Geodesic Grids: High-Order Reconstructions for Forward-in-Time Schemes

2010 ◽  
Vol 138 (12) ◽  
pp. 4497-4508 ◽  
Author(s):  
William C. Skamarock ◽  
Maximo Menchaca
Keyword(s):  
Volume Transport ◽  
Higher Order ◽  
Second Order ◽  
Time Step ◽  
First Order ◽  
Order Reconstruction ◽  
Flow Test ◽  
Mesh Density ◽  
Original Scheme ◽  
Dependent Flow

Abstract The finite-volume transport scheme of Miura, for icosahedral–hexagonal meshes on the sphere, is extended by using higher-order reconstructions of the transported scalar within the formulation. The use of second- and fourth-order reconstructions, in contrast to the first-order reconstruction used in the original scheme, results in significantly more accurate solutions at a given mesh density, and better phase and amplitude error characteristics in standard transport tests. The schemes using the higher-order reconstructions also exhibit much less dependence of the solution error on the time step compared to the original formulation. The original scheme of Miura was only tested using a nondeformational time-independent flow. The deformational time-dependent flow test used to examine 2D planar transport in Blossey and Durran is adapted to the sphere, and the schemes are subjected to this test. The results largely confirm those generated using the simpler tests. The results also indicate that the scheme using the second-order reconstruction is most efficient and its use is recommended over the scheme using the first-order reconstruction. The second-order reconstruction uses the same computational stencil as the first-order reconstruction and thus does not create any additional parallelization issues.

scholarly journals Moving breathers and breather-to-soliton conversions for the Hirota equation

2015 ◽  
Vol 471 (2180) ◽  
pp. 20150130 ◽  
Author(s):  
A. Chowdury ◽  
A. Ankiewicz ◽  
N. Akhmediev
Keyword(s):  
Schrodinger Equation ◽  
Higher Order ◽  
Nonlinear Schrodinger Equation ◽  
Second Order ◽  
Periodic Oscillations ◽  
Hirota Equation ◽  
First Order ◽  
Special Values ◽  
Analytic Expression ◽  
Free Parameters

We find that the Hirota equation admits breather-to-soliton conversion at special values of the solution eigenvalues. This occurs for the first-order, as well as higher orders, of breather solutions. An analytic expression for the condition of the transformation is given and several examples of transformations are presented. The values of these special eigenvalues depend on two free parameters that are present in the Hirota equation. We also find that higher order breathers generally have complicated quasi-periodic oscillations along the direction of propagation. Various breather solutions are considered, including the particular case of second-order breathers of the nonlinear Schrödinger equation.

scholarly journals In situremoval of carbon contamination from a chromium-coated mirror: ideal optics to suppress higher-order harmonics in the carbonK-edge region

2015 ◽  
Vol 22 (6) ◽  
pp. 1359-1363 ◽  
Author(s):  
Akio Toyoshima ◽  
Takashi Kikuchi ◽  
Hirokazu Tanaka ◽  
Kazuhiko Mase ◽  
Kenta Amemiya
Keyword(s):  
Synchrotron Radiation ◽  
Vacuum Ultraviolet ◽  
Higher Order ◽  
Second Order ◽  
Edge Region ◽  
Carbon Contamination ◽  
X Ray ◽  
Photon Factory ◽  
First Order ◽  
Edge Absorption

Carbon-free chromium-coated optics are ideal in the carbonK-edge region (280–330 eV) because the reflectivity of first-order light is larger than that of gold-coated optics while the second-order harmonics (560–660 eV) are significantly suppressed by chromiumL-edge and oxygenK-edge absorption. Here, chromium-, gold- and nickel-coated mirrors have been adopted in the vacuum ultraviolet and soft X-ray branch beamline BL-13B at the Photon Factory in Tsukuba, Japan. Carbon contamination on the chromium-coated mirror was almost completely removed by exposure to oxygen at a pressure of 8 × 10−2 Pa for 1 h under irradiation of non-monochromated synchrotron radiation. The pressure in the chamber recovered to the order of 10−7 Pa within a few hours. The reflectivity of the chromium-coated mirror of the second-order harmonics in the carbonK-edge region (560–660 eV) was found to be a factor of 0.1–0.48 smaller than that of the gold-coated mirror.

scholarly journals הכל הבל in Ecclesiastes 1:2 and 12:8 – Descriptive metaphysics of properties as comparative-philosophical supplement

2021 ◽  
Vol 77 (1) ◽  
Author(s):  
Jaco Gericke
Keyword(s):  
Second Order ◽  
Property Theory ◽  
First Order ◽  
Conceptual Clarification ◽  
Order Language ◽  
The World ◽  
Original Contribution ◽  
The Way

In this article, a supplementary yet original contribution is made to the ongoing attempts at refining ways of comparative-philosophical conceptual clarification of Qohelet’s claim that הבל הכל in 1:2 (and 12:8). Adopting and adapting the latest analytic metaphysical concerns and categories for descriptive purposes only, a distinction is made between הבל as property of הכל and the properties of הבל in relation to הכל. Involving both correlation and contrast, the second-order language framework is hereby extended to a level of advanced nuance and specificity for restating the meaning of the book’s first-order language on its own terms, even if not in them.Contribution: By considering logical, ontological, mereological and typological aspects of property theory in dialogue with appearances of הכל and of הבל in Ecclesiastes 1:2 and 12:8 and in-between, a new way is presented in the quest to explain why things in the world of the text are the way they are, or why they are at all.

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