scholarly journals Is Epistemology Autonomous?

2018 ◽  
pp. 67-87
Author(s):  
Daniel Greco
Keyword(s):  
First Order ◽  
Autonomy Of Ethics ◽  
The Right ◽  
Judgment Internalism

It’s commonly held that the best metaethical account of our normative thought and language won’t place any significant constraints on our first-order normative theorizing; once we have the right metaethics, we can go on having the same first-order normative debates, and accepting the same first-order normative views. This thesis of the “autonomy of ethics” is particularly popular among writers in the expressivist tradition. This chapter argues, however, that broadly expressivist metanormative commitments have significant consequences in first-order normative epistemological debates. It begins with the example of judgment internalism—a thesis endorsed by expressivists, but many non-expressivists as well. While judgment internalism is generally seen as irrelevant to first-order ethical debates, it is argued here that it has significant consequences for some putatively “first-order” debates in epistemology. It is then argued that accepting more thoroughly expressivist metaepistemological commitments has more far-reaching epistemological consequences, focusing on the internalism/externalism debate.

scholarly journals Global Schauder Estimates for the $$\mathbf {p}$$-Laplace System

2021 ◽  
Author(s):  
D. Breit ◽  
A. Cianchi ◽  
L. Diening ◽  
S. Schwarzacher
Keyword(s):  
Global Regularity ◽  
Regularity Theory ◽  
Divergence Form ◽  
Dirichlet Problems ◽  
Schauder Estimates ◽  
First Order ◽  
Right Hand ◽  
Regularity Results ◽  
The Right ◽  
Linear Setting

AbstractAn optimal first-order global regularity theory, in spaces of functions defined in terms of oscillations, is established for solutions to Dirichlet problems for the p-Laplace equation and system, with the right-hand side in divergence form. The exact mutual dependence among the regularity of the solution, of the datum on the right-hand side, and of the boundary of the domain in these spaces is exhibited. A comprehensive formulation of our results is given in terms of Campanato seminorms. New regularity results in customary function spaces, such as Hölder, $$\text {BMO}$$ BMO and $${{\,\mathrm{VMO}\,}}$$ VMO spaces, follow as a consequence. Importantly, the conclusions are new even in the linear case when $$p=2$$ p = 2 , and hence the differential operator is the plain Laplacian. Yet in this classical linear setting, our contribution completes and augments the celebrated Schauder theory in Hölder spaces. A distinctive trait of our results is their sharpness, which is demonstrated by a family of apropos examples.

DIFFERENTIAL EQUATIONS IN A HYPERCOMPLEX SYSTEM

2020 ◽  
Vol 69 (1) ◽  
pp. 7-11
Author(s):  
A.K. Abirov ◽  
◽  
N.K. Shazhdekeeva ◽  
T.N. Akhmurzina ◽  
◽  
...  
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Inhomogeneous System ◽  
Homogeneous Solutions ◽  
First Order ◽  
Zero Divisors ◽  
Hypercomplex System ◽  
Independent Variable ◽  
The Right

The article considers the problem of solving an inhomogeneous first-order differential equation with a variable with a constant coefficient in a hypercomplex system. The structure of the solution in different cases of the right-hand side of the differential equation is determined. The structure of solving the equation in the case of the appearance of zero divisors is shown. It turns out that when the component of a hypercomplex function is a polynomial of an independent variable, the differential equation turns into an inhomogeneous system of real variables from n equations and its solution is determined by certain methods of the theory of differential equations. Thus, obtaining analytically homogeneous solutions of inhomogeneous differential equations in a hypercomplex system leads to an increase in the efficiency of modeling processes in various fields of science and technology.

An axiomatization of the logic with the rough quantifier

1991 ◽  
Vol 56 (2) ◽  
pp. 608-617 ◽  
Author(s):  
Michał Krynicki ◽  
Hans-Peter Tuschik
Keyword(s):  
Equivalence Relation ◽  
Equivalence Relations ◽  
Order Structure ◽  
Partition Model ◽  
Weak Model ◽  
First Order ◽  
Basic Properties ◽  
Generalized Quantifier ◽  
Order Language ◽  
The Right

We consider the language L(Q), where L is a countable first-order language and Q is an additional generalized quantifier. A weak model for L(Q) is a pair 〈, q〉 where is a first-order structure for L and q is a family of subsets of its universe. In case that q is the set of classes of some equivalence relation the weak model 〈, q〉 is called a partition model. The interpretation of Q in partition models was studied by Szczerba [3], who was inspired by Pawlak's paper [2]. The corresponding set of tautologies in L(Q) is called rough logic. In the following we will give a set of axioms of rough logic and prove its completeness. Rough logic is designed for creating partition models.The partition models are the weak models arising from equivalence relations. For the basic properties of the logic of weak models the reader is referred to Keisler's paper [1]. In a weak model 〈, q〉 the formulas of L(Q) are interpreted as usual with the additional clause for the quantifier Q: 〈, q〉 ⊨ Qx φ(x) iff there is some X ∊ q such that 〈, q〉 ⊨ φ(a) for all a ∊ X.In case X satisfies the right side of the above equivalence we say that X is contained in φ(x) or, equivalently, φ(x) contains X.

TYPE-DEFINABILITY, COMPACT LIE GROUPS, AND o-MINIMALITY

2004 ◽  
Vol 04 (02) ◽  
pp. 147-162 ◽  
Author(s):  
ANAND PILLAY
Keyword(s):  
Compact Lie Group ◽  
Compact Lie Groups ◽  
First Order ◽  
Special Cases ◽  
Definable Groups ◽  
Small Index ◽  
Logic Topology ◽  
The Right ◽  
Study Type ◽  
Order Structures

We study type-definable subgroups of small index in definable groups, and the structure on the quotient, in first order structures. We raise some conjectures in the case where the ambient structure is o-minimal. The gist is that in this o-minimal case, any definable group G should have a smallest type-definable subgroup of bounded index, and that the quotient, when equipped with the logic topology, should be a compact Lie group of the "right" dimension. I give positive answers to the conjectures in the special cases when G is 1-dimensional, and when G is definably simple.

scholarly journals Hysteresis Modelling of Mechanical Systems at Nonstationary Vibrations

2018 ◽  
Vol 2018 ◽  
pp. 1-15
Author(s):  
A. N. Danilin ◽  
A. D. Shalashilin
Keyword(s):  
Differential Equation ◽  
Phenomenological Models ◽  
Low Frequency ◽  
Hysteresis Cycle ◽  
Nonstationary Vibrations ◽  
Kinematic Parameters ◽  
First Order ◽  
Starting Point ◽  
The Right ◽  
Best Fit

This paper considers and reviews a number of known phenomenological models, used to describe hysteretic effects of various natures. Such models consider hysteresis system as a “black box” with experimentally known input and output, related via formal mathematical dependence to parameters obtained from the best fit to experimental data. In particular, we focus on the broadly used Bouc-Wen and similar phenomenological models. The current paper shows the conditions which the Bouc-Wen model must meet. An alternative mathematical model is suggested where the force and kinematic parameters are related by a first-order differential equation. In contrast to the Bouc-Wen model, the right hand side is a polynomial with two variables representing hysteresis trajectories in the process diagram. This approach ensures correct asymptotic approximation of the solution to the enclosing hysteresis cycle curves. The coefficients in the right side are also determined experimentally from the hysteresis cycle data during stable oscillations. The proposed approach allows us to describe hysteretic trajectory with an arbitrary starting point within the enclosed cycle using only one differential equation. The model is applied to the description of forced vibrations of a low-frequency pendulum damper.

scholarly journals STRING QUANTIZATION IN CURVED SPACETIMES: NULL STRING APPROACH

1995 ◽  
Vol 10 (32) ◽  
pp. 2479-2484 ◽  
Author(s):  
H.J. DE VEGA ◽  
I. GIANNAKIS ◽  
A. NICOLAIDIS
Keyword(s):  
Equations Of Motion ◽  
Critical Dimension ◽  
String Tension ◽  
Conformal Anomaly ◽  
De Sitter ◽  
Gravitational Fields ◽  
First Order ◽  
Sitter Spacetime ◽  
The Right ◽  
Null String

We study quantum strings in strong gravitational fields. The relevant small parameter is [Formula: see text] where Rc is the curvature of the spacetime and T0 is the string tension. Within our systematic expansion we obtain to zeroth-order the null string (string with zero tension), while the first-order correction incorporates the string dynamics. We apply our formalism to quantum null strings in de Sitter spacetime. After a reparametrization of the worldsheet coordinates, the equations of motion are simplified. The quantum algebra generated by the constraints is considered, ordering the momentum operators to the right of the coordinate operators. No critical dimension appears. It is anticipated, however, that the conformal anomaly will appear when the first-order corrections proportional to T0, are introduced.

scholarly journals Vulnerability of Religious Minority in Indonesia due to the Implementation of the Blasphemy Law

2021 ◽  
Vol 9 (11) ◽  
pp. 261-298
Author(s):  
Muktiono Muktiono ◽  
Moh. Bakri ◽  
Masruchin Ruba’i ◽  
Muchamad Ali Safa’at
Keyword(s):  
Minority Group ◽  
Religious Conflict ◽  
Violent Conflict ◽  
Access To Justice ◽  
Religious Minority ◽  
Legal Reason ◽  
First Order ◽  
Social Facts ◽  
Service Conception ◽  
The Right

The establishment and application of blasphemy law in Indonesia is generally under the justification of maintaining public order, preventing violent-conflict, and protecting the enjoyment of the right to freedom of religion. However, when the blasphemy law should be applied to adjudicate an internal religious conflict among the sects then the debate arises on whose interpretation and how it will be referred by the State authorities as demarcation or exclusionary standard to distinguish between the deviant religion and legally valid ones. Issues on the fragility of fair and impartial trial as protection to the existence of religious minority group therefore becomes very central due to the implementation and application of blasphemy law will be always influenced by power relation among the involved parties. This paper is intended to explore Tajul Muluk case that has been exhaustively ruled by all level of Indonesian courts in order to reveal complex roles of judiciary in applying service-conception of blasphemy law into first-order reason of person’s faith. Source-based legal reason of the court which merely refers to the historical or social facts as texted in the blasphemy law with prejudice to human rights’ moral test has been paradoxically widen penumbra of legal rule to uncertainty that undermines access to justice for religious minority group especially when addressing social conflict.

scholarly journals Generalisation of Induction Formulae based on Proving by Symbolic Execution

10.29007/72nn ◽  
2018 ◽  
Author(s):  
Angela Wallenburg
Keyword(s):  
Symbolic Execution ◽  
Theorem Prover ◽  
Constraint Solving ◽  
Powerful Method ◽  
First Order ◽  
Total Correctness ◽  
The Right

Induction is a powerful method that can be used to prove the total correctness of program loops. Unfortunately the induction proving process in an interactive theorem prover is often very cumbersome. In particular it can be difficult to find the right induction formula. We describe a method for generalising induction formulae by analysing a symbolic proof attempt in a semi-interactive first-order theorem prover. Based on the proof attempt we introduce universally quantified variables, meta-variables and sets of constraints on these. The constraints describe the conditions for a successful proof. By the help of examples, we outline some classes of problems and their associated constraint solutions, and possible ways to automate the constraint solving.

scholarly journals Pharmacokinetics and Toxicity Evaluation of a PLGA and Chitosan-Based Micro-Implant for Sustained Release of Methotrexate in Rabbit Vitreous

Pharmaceutics ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1227
Author(s):  
Soumyarwit Manna ◽  
Anna M. Donnell ◽  
Rafaela Q. Caixeta Faraj ◽  
Blanca I. Riemann ◽  
Christopher D. Riemann ◽  
...  
Keyword(s):  
Current Treatment ◽  
Invasive Procedures ◽  
Toxicity Evaluation ◽  
Therapeutic Concentration ◽  
First Order ◽  
First Order Kinetics ◽  
Histopathologic Evaluation ◽  
Potential Alternative ◽  
The Right ◽  
Micro Implants

The present research investigates the pharmacokinetics and toxicity of a chitosan (CS) and poly(lactic-co-glycolic) acid (PLGA)-based methotrexate (MTX) intravitreal micro-implant in normal rabbit eyes. PLGA and CS-based micro-implants containing 400 µg of MTX were surgically inserted in the vitreous of twenty-four New Zealand rabbits using minimally invasive procedures. The PLGA-coated CS-MTX micro-implant and the placebo micro-implant were inserted in the right eye and in the left eye, respectively, of each rabbit. The intravitreal MTX concentration was evaluated on Days 1, 3, 7, 14, 28 and 56. A therapeutic concentration of MTX (0.1–1.0 µM) in the rabbit vitreous was observed for 56 days. The release of MTX in the therapeutic release phase followed first-order kinetics. Histopathologic evaluation on Days 14, 28 and 56 of the enucleated eyes demonstrated no signs of toxicity or any anatomical irregularity in the vitreoretinal domain. Additionally, the micro-implants were stationary at the position of their implantation throughout the duration of the study. The PLGA-coated CS-MTX micro-implant can serve as a potential alternative to the current treatment modality of intravitreal MTX injections based on its performance, thereby avoiding associated complications and the treatment burden of multiple injections.

Introduction and Overview

2017 ◽  
Author(s):  
Neil Tennant
Keyword(s):  
Scientific Method ◽  
Proof Theory ◽  
Valid Argument ◽  
First Order ◽  
Proof Systems ◽  
Formal Systems ◽  
Deductive Logic ◽  
Order Language ◽  
Foundational Work ◽  
The Right

This is a foundational work, written not just for philosophers of logic, but for logicians and foundationalists generally. Like Frege we seek to deal with the formal first-order language of mathematics. We revisit Gentzen’s proof theory in order to build relevance into proofs, while leaving intact all the logical power one is entitled to expect of a deductive logic for mathematics and for scientific method generally. Proof systems are constituted by particular choices of rules of inference. We raise the issue of the reflexive stability of any argument for a particular choice of logic as the ‘right’ logic. We examine the question of pluralism v. absolutism in choice of logic, and suggest that the informal notion of valid argument is stable and robust enough for us to be able to ‘get it right’ with our formal systems of proof for both constructive and non-constructive reasoning.

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