scholarly journals On Valdivia strong version of Nikodym boundedness property

2017 ◽  
Vol 446 (1) ◽  
pp. 1-17 ◽  
Author(s):  
J. Ka̧kol ◽  
M. López-Pellicer
Keyword(s):  
Strong Version ◽  
Boundedness Property

scholarly journals On the existence of various bounded harmonic functions with given periods, II

1975 ◽  
Vol 56 ◽  
pp. 1-5
Author(s):  
Masaru Hara
Keyword(s):  
Riemann Surface ◽  
Harmonic Function ◽  
Harmonic Functions ◽  
Dirichlet Integral ◽  
Period Function ◽  
Boundedness Property ◽  
One Dimensional ◽  
Bounded Harmonic Functions

Given a harmonic function u on a Riemann surface R, we define a period functionfor every one-dimensional cycle γ of the Riemann surface R. Γx(R) denote the totality of period functions Γu such that harmonic functions u satisfy a boundedness property X. As for X, we let B stand for boundedness, and D for the finiteness of the Dirichlet integral.

Virtue as Loving the Good

1992 ◽  
Vol 9 (2) ◽  
pp. 149-168 ◽  
Author(s):  
Thomas Hurka
Keyword(s):  
Strong Version ◽  
Right Action ◽  
Henry Sidgwick ◽  
Intrinsic Good

In a chapter of The Methods of Ethics entitled “Ultimate Good”, Henry Sidgwick defends hedonism, the theory that pleasure and only pleasure is intrinsically good, that is, good in itself and apart from its consequences. First, however, he argues against the theory that virtue is intrinsically good. Sidgwick considers both a strong version of this theory — that virtue is the only intrinsic good — and a weaker version — that it is one intrinsic good among others. He tries to show that neither version is or can be true.Against the strong version of the theory, Sidgwick argues as follows. Virtue is a disposition to act rightly, and right action is identified by the good it promotes. (He believes the second, consequentialist premise has been justified by his lengthy critique of nonconsequentialist moralities in Book III of The Methods of Ethics.) But this means that treating virtue as the only intrinsic good involves a “logical circle”: virtue is a disposition to promote what is good, where what is good is itself just a disposition to promote what is good. Virtue turns out to be a disposition to promote virtue.As Hastings Rashdall notes in a commentary on Sidgwick, one can accept many of this argument's premises yet reject its conclusion. One can agree that right action is identified by its consequences but still hold that virtue is the only intrinsic good. One can do this if one denies that the relevant consequences are good. This is the Stoic view: certain states are “preferred”, and thus supply the criterion of right action, but are not themselves intrinsically good.

scholarly journals A geometric approach to Quillen’s conjecture

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Antonio Díaz Ramos ◽  
Nadia Mazza
Keyword(s):  
Finite Group ◽  
Prime Divisor ◽  
Geometric Approach ◽  
Classical Groups ◽  
Strong Version ◽  
Finite Classical Groups ◽  
A Finite Group

Abstract We introduce admissible collections for a finite group 𝐺 and use them to prove that most of the finite classical groups in non-defining characteristic satisfy the Quillen dimension at 𝑝 property, a strong version of Quillen’s conjecture, at a given odd prime divisor 𝑝 of | G | \lvert G\rvert . Compared to the methods in [M. Aschbacher and S. D. Smith, On Quillen’s conjecture for the 𝑝-groups complex, Ann. of Math. (2) 137 (1993), 3, 473–529], our techniques are simpler.

scholarly journals Is preregistration worthwhile?

2019 ◽  
Author(s):  
Aba Szollosi ◽  
David Kellen ◽  
Danielle Navarro ◽  
Rich Shiffrin ◽  
Iris van Rooij ◽  
...  
Keyword(s):  
Statistical Models ◽  
Statistical Tests ◽  
Error Rates ◽  
Statistical Techniques ◽  
Weak Version ◽  
Strong Version ◽  
Statistical Problems

Proponents of preregistration argue that, among other benefits, it improves the diagnosticity of statistical tests [1]. In the strong version of this argument, preregistration does this by solving statistical problems, such as family-wise error rates. In the weak version, it nudges people to think more deeply about their theories, methods, and analyses. We argue against both: the diagnosticity of statistical tests depend entirely on how well statistical models map onto underlying theories, and so improving statistical techniques does little to improve theories when the mapping is weak. There is also little reason to expect that preregistration will spontaneously help researchers to develop better theories (and, hence, better methods and analyses).

scholarly journals On the Contrary: Inferential Analysis and Ontological Assumptions of the A Contrario Argument

2008 ◽  
Vol 28 (1) ◽  
pp. 31 ◽  
Author(s):  
Damiano Canale ◽  
Giovanni Tuzet
Keyword(s):  
Strong Version ◽  
Judicial Decisions ◽  
Robert Brandom ◽  
Inferential Analysis ◽  
The Law ◽  
Normative Sentence

We remark that the A Contrario Argument is an ambiguous technique of justification of judicial decisions. We distinguish two uses and versions of it, strong and weak, taking as example the normative sentence “Underprivileged citizens are permitted to apply for State benefit”. According to the strong version, only underprivileged citizens are permitted to apply for State benefit, so stateless persons are not. According to the weak, the law does not regulate the position of underprivileged stateless persons in this respect. We propose an inferential analysis of the two uses along the lines of the scorekeeping practice as described by Robert Brandom, and try to point out what are the ontological assumptions of the two. We conclude that the strong version is justified if and only if there is a relevant incompatibility between the regulated subject and the present case.

scholarly journals Considerations for Goldbach's Strong Conjecture

2021 ◽  
Author(s):  
Carleilton Severino Silva
Keyword(s):  
Number Theory ◽  
Prime Numbers ◽  
Weak Version ◽  
Strong Version ◽  
Leonhard Euler

Since 1742, the year in which the Prussian Christian Goldbach wrote a letter to Leonhard Euler with his Conjecture in the weak version, mathematicians have been working on the problem. The tools in number theory become the most sophisticated thanks to the resolution solutions. Euler himself said he was unable to prove it. The weak guess in the modern version states the following: any odd number greater than 5 can be written as the sum of 3 primes. In response to Goldbach's letter, Euler reminded him of a conversation in which he proposed what is now known as Goldbach's strong conjecture: any even number greater than 2 can be written as a sum of 2 prime numbers. The most interesting result came in 2013, with proof of weak version by the Peruvian Mathematician Harald Helfgott, however the strong version remained without a definitive proof. The weak version can be demonstrated without major difficulties and will not be described in this article, as it becomes a corollary of the strong version. Despite the enormous intellectual baggage that great mathematicians have had over the centuries, the Conjecture in question has not been validated or refuted until today.

scholarly journals Skeptical Theism and the Threshold Problem

1970 ◽  
Vol 18 (1) ◽  
pp. 73-92
Author(s):  
Yishai A. Cohen
Keyword(s):  
Weak Version ◽  
Strong Version ◽  
Skeptical Theism ◽  
Cognitive Faculties ◽  
Threshold Problem

In this paper I articulate and defend a new anti-theodicy challenge to Skeptical Theism. More specifically, I defend the Threshold Problem according to which there is a threshold to the kinds of evils that are in principle justifiable for God to permit, and certain instances of evil are beyond that threshold. I further argue that Skeptical Theism does not have the resources to adequately rebut the Threshold Problem. I argue for this claim by drawing a distinction between a weak and strong version of Skeptical Theism, such that the strong version must be defended in order to rebut the Threshold Problem. However, the skeptical theist’s appeal to our limited cognitive faculties only supports the weak version.

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