scholarly journals How to Prove Hume’s Law

2021 ◽  
Author(s):  
Gillian Russell
Keyword(s):  
Logical Consequence ◽  
General Theorem

AbstractThis paper proves a precisification of Hume’s Law—the thesis that one cannot get an ought from an is—as an instance of a more general theorem which establishes several other philosophically interesting, though less controversial, barriers to logical consequence.

Glarner Waldwirtschaft im letzten Viertel des 20. Jahrhunderts | Glarner Forest Management in the last quarter of the 20th Century

2002 ◽  
Vol 153 (7) ◽  
pp. 249-250
Author(s):  
Fritz Marti
Keyword(s):  
Forest Management ◽  
20Th Century ◽  
Logical Consequence ◽  
Mountain Forest ◽  
Wood Production ◽  
Looking Back

Looking back on the last quarter of the 20th century, we see that the most striking changes in forest management have come about following large and frequent catastrophes. Management– concerned solely with wood production in former times – is oriented more towards retaining stability of the stands nowadays. In addition, the aspect of tending and improving the environment continues to gain ground. The growing gap between expenditure and profit is particularly acute in Glarner mountain forest areas. The extension of promotional silvicultural measures, which widely determines today's management, is to be seen as a logical consequence.

Essentialism and Logical Consequence

2018 ◽  
Author(s):  
Rosanna Keefe ◽  
Jessica Leech
Keyword(s):  
Logical Consequence ◽  
Prima Facie ◽  
Logical Pluralism ◽  
Logical Necessity ◽  
Popular View

According to an increasingly popular view, the source of logical necessity is to be found in the essences of logical entities. One might be tempted to extend the view further in using it to tackle fundamental questions surrounding logical consequence. This chapter enquires: how does a view according to which the facts about logical consequence are determined by the essences of logical entities look in detail? Are there any more or less obvious problems arising for such a view? The chapter uncovers a prima facie result in favour of logical pluralism. However, it then goes on to raise some concerns for this result. It argues that, considered generally, it is difficult to see how essence could do all of the requisite work alone. The chapter also shows how considering things from the perspective of disputes between particular rival logics makes an interesting and important difference to the picture of things presented by the essentialist account.

scholarly journals Hodge decomposition of string topology

2021 ◽  
Vol 9 ◽  
Author(s):  
Yuri Berest ◽  
Ajay C. Ramadoss ◽  
Yining Zhang
Keyword(s):  
Lie Algebras ◽  
General Theorem ◽  
Hodge Decomposition ◽  
String Topology ◽  
Free Loop Space ◽  
Oriented Manifold ◽  
Universal Enveloping Algebras ◽  
Finite Dimensional ◽  
Equivariant Homology ◽  
Simply Connected

Abstract Let X be a simply connected closed oriented manifold of rationally elliptic homotopy type. We prove that the string topology bracket on the $S^1$ -equivariant homology $ {\overline {\text {H}}}_\ast ^{S^1}({\mathcal {L}} X,{\mathbb {Q}}) $ of the free loop space of X preserves the Hodge decomposition of $ {\overline {\text {H}}}_\ast ^{S^1}({\mathcal {L}} X,{\mathbb {Q}}) $ , making it a bigraded Lie algebra. We deduce this result from a general theorem on derived Poisson structures on the universal enveloping algebras of homologically nilpotent finite-dimensional DG Lie algebras. Our theorem settles a conjecture of [7].

scholarly journals Undecidability in quantum thermalization

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Naoto Shiraishi ◽  
Keiji Matsumoto
Keyword(s):  
Turing Machine ◽  
Thermal Equilibrium ◽  
General Theorem ◽  
Nearest Neighbour ◽  
Many Body ◽  
Initial State ◽  
One Dimensional ◽  
Universal Turing Machine ◽  
Many Body Systems ◽  
Neighbour Interaction

AbstractThe investigation of thermalization in isolated quantum many-body systems has a long history, dating back to the time of developing statistical mechanics. Most quantum many-body systems in nature are considered to thermalize, while some never achieve thermal equilibrium. The central problem is to clarify whether a given system thermalizes, which has been addressed previously, but not resolved. Here, we show that this problem is undecidable. The resulting undecidability even applies when the system is restricted to one-dimensional shift-invariant systems with nearest-neighbour interaction, and the initial state is a fixed product state. We construct a family of Hamiltonians encoding dynamics of a reversible universal Turing machine, where the fate of a relaxation process changes considerably depending on whether the Turing machine halts. Our result indicates that there is no general theorem, algorithm, or systematic procedure determining the presence or absence of thermalization in any given Hamiltonian.

The Generating Functions of Certain Special Determinants

1904 ◽  
Vol 24 ◽  
pp. 387-392 ◽  
Author(s):  
Thomas Muir
Keyword(s):  
Generating Functions ◽  
General Theorem ◽  
Image Position

(1) From a general theorem, known since 1855, and perhaps earlier, regarding the reciprocal of the seriesit follows thatwhere β0 = 1 and

scholarly journals Sets of Semi-Commutative Matrices

1933 ◽  
Vol 3 (3) ◽  
pp. 179-188
Author(s):  
J. Williamson
Keyword(s):  
General Theorem ◽  
Unit Matrix ◽  
Maximum Value ◽  
Image Position

In a paper entitled “Sets of anticommuting matrices” Eddington proved that if El, E2, …., Eqform a set of q four-rowed square matrices satisfying the relations,,where E is the unit matrix, then the maximum value of q is five. Later Newman showed that this result is a particular case of the general theorem that ifE1, E2, …., Eqform a set of q t-rowed square matrices satisfying (1), where t = 2Pτ and τ is odd, then the maximum value of q is 2p + 1.

scholarly journals Regular and residual Eisenstein series and the automorphic cohomology of Sp(2,2)

2009 ◽  
Vol 146 (1) ◽  
pp. 21-57 ◽  
Author(s):  
Harald Grobner
Keyword(s):  
Algebraic Group ◽  
Eisenstein Series ◽  
Symplectic Group ◽  
Automorphic Forms ◽  
General Theorem ◽  
Simple Algebraic Group ◽  
Ramanujan Conjecture ◽  
Eisenstein Cohomology ◽  
Derivatives Of

AbstractLetGbe the simple algebraic group Sp(2,2), to be defined over ℚ. It is a non-quasi-split, ℚ-rank-two inner form of the split symplectic group Sp8of rank four. The cohomology of the space of automorphic forms onGhas a natural subspace, which is spanned by classes represented by residues and derivatives of cuspidal Eisenstein series. It is called Eisenstein cohomology. In this paper we give a detailed description of the Eisenstein cohomologyHqEis(G,E) ofGin the case of regular coefficientsE. It is spanned only by holomorphic Eisenstein series. For non-regular coefficientsEwe really have to detect the poles of our Eisenstein series. SinceGis not quasi-split, we are out of the scope of the so-called ‘Langlands–Shahidi method’ (cf. F. Shahidi,On certainL-functions, Amer. J. Math.103(1981), 297–355; F. Shahidi,On the Ramanujan conjecture and finiteness of poles for certainL-functions, Ann. of Math. (2)127(1988), 547–584). We apply recent results of Grbac in order to find the double poles of Eisenstein series attached to the minimal parabolicP0ofG. Having collected this information, we determine the square-integrable Eisenstein cohomology supported byP0with respect to arbitrary coefficients and prove a vanishing result. This will exemplify a general theorem we prove in this paper on the distribution of maximally residual Eisenstein cohomology classes.

scholarly journals DEGREE SUPERVALUATIONAL LOGIC

2010 ◽  
Vol 4 (1) ◽  
pp. 130-149 ◽  
Author(s):  
J. ROBERT G. WILLIAMS
Keyword(s):  
Logical Consequence ◽  
Positive Side ◽  
Semantic Treatment ◽  
Bare Bones

Supervaluationism is often described as the most popular semantic treatment of indeterminacy. There’s little consensus, however, about how to fill out the bare-bones idea to include a characterization of logical consequence. The paper explores one methodology for choosing between the logics: pick a logic that norms belief as classical consequence is standardly thought to do. The main focus of the paper considers a variant of standard supervaluational, on which we can characterize degrees of determinacy. It applies the methodology above to focus on degree logic. This is developed first in a basic, single-premise case; and then extended to the multipremise case, and to allow degrees of consequence. The metatheoretic properties of degree logic are set out. On the positive side, the logic is supraclassical—all classical valid sequents are degree logic valid. Strikingly, metarules such as cut and conjunction introduction fail.

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