scholarly journals Negating as turning upside down

2018 ◽  
Vol 54 (1) ◽  
pp. 115-129 ◽  
Author(s):  
Bartłomiej Skowron ◽  
Wiesław Kubiś
Keyword(s):  
Category Theory ◽  
Contravariant Functor ◽  
States Of Affairs ◽  
Truth Values ◽  
Paper Making ◽  
The Third ◽  
Entire Structure ◽  
Ontological Problem

Abstract In order to understand negation as such, at least since Aristotle’s time, there have been many ways of conceptually modelling it. In particular, negation has been studied as inconsistency, contradictoriness, falsity, cancellation, an inversion of arrangements of truth values, etc. In this paper, making substantial use of category theory, we present three more conceptual and abstract models of negation. All of them capture negation as turning upside down the entire structure under consideration. The first proposal turns upside down the structure almost literally; it is the well known construction of opposite category. The second one treats negation as a contravariant functor and the third one captures negation as adjointness. Traditionally, negation was investigated in the context of language as negation of sentences or parts of sentences, e.g. names. On the contrary we propose to negate structures globally. As a consequence of our approach we provide a solution to the ontological problem of the existence of negative states of affairs.

Logicism Reconsidered

2009 ◽  
Author(s):  
Agustín Rayo
Keyword(s):  
Fourth Section ◽  
Truth Values ◽  
The Third

This article is divided into four sections. The first two identify different logicist theses, and show that their truth-values can be established given minimal assumptions. The third section sets forth a notion of “content-recarving” as a possible constraint on logicist theses. The fourth section—which is largely independent from the rest of the article—is a discussion of “neologicism.”

Puzzles: Noisy Prisoners, Manhattan Locations, and More

1987 ◽  
Vol 1 (1) ◽  
pp. 185-191 ◽  
Author(s):  
Barry Nalebuff
Keyword(s):  
Category Theory ◽  
Prisoner's Dilemma ◽  
Location Problem ◽  
Prisoner’S Dilemma ◽  
Optimal Location ◽  
The Third ◽  
Economic Interpretation ◽  
Mathematical Problems

Each “Puzzles” will begin with a few speed problems. These puzzles have answers provided in the same issue. Puzzles 1 and 2 will give you a chance to get up to speed. Then, we continue with longer puzzles taken from two very broadly defined categories: strategy puzzles and theory puzzles. Strategy puzzles will give the readers an opportunity to compete against each other in problems of coordination and competition. The third puzzle, a noisy prisoner's dilemma tournament, falls dead center in this category. Theory puzzles are meant to offer mathematical problems that have an economic interpretation. The fourth puzzle, an optimal location problem, is in this category.

scholarly journals Double Solids, Categories and Non-Rationality

2013 ◽  
Vol 57 (1) ◽  
pp. 145-173 ◽  
Author(s):  
Atanas Iliev ◽  
Ludmil Katzarkov ◽  
Victor Przyjalkowski
Keyword(s):  
Category Theory ◽  
Mirror Symmetry ◽  
Homology Group ◽  
Hochschild Homology ◽  
Singular Points ◽  
Double Covering ◽  
Homological Mirror Symmetry ◽  
New Approach ◽  
The Third

AbstractThis paper suggests a new approach to questions of rationality of 3-folds based on category theory. Following work by Ballard et al., we enhance constructions of Kuznetsov by introducing Noether–Lefschetz spectra: an interplay between Orlov spectra and Hochschild homology. The main goal of this paper is to suggest a series of interesting examples where the above techniques might apply. We start by constructing a sextic double solid X with 35 nodes and torsion in H3(X, ℤ). This is a novelty: after the classical example of Artin and Mumford, this is the second example of a Fano 3-fold with a torsion in the third integer homology group. In particular, X is non-rational. We consider other examples as well: V10 with 10 singular points, and the double covering of a quadric ramified in an octic with 20 nodal singular points. After analysing the geometry of their Landau–Ginzburg models, we suggest a general non-rationality picture based on homological mirror symmetry and category theory.

scholarly journals ProCS15: A DFT-based chemical shift predictor for backbone and Cβ atoms in proteins

2015 ◽  
Author(s):  
Anders S Larsen ◽  
Lars A Bratholm ◽  
Anders S Christensen ◽  
Maher Jan Channir ◽  
Jan H. Jensen
Keyword(s):  
Hydrogen Bonding ◽  
Chemical Shift ◽  
Chemical Shifts ◽  
Structural Models ◽  
Protein G ◽  
Chemical Shielding ◽  
The Third ◽  
Entire Structure ◽  
Igg Binding ◽  
Structural Ensembles

We present ProCS15: A program that computes the isotropic chemical shielding values of backbone and C β atoms given a protein structure in less than a second. ProCS15 is based on around 2.35 million OPBE/6-31G(d,p)//PM6 calculations on tripeptides and small structural models of hydrogen-bonding. The ProCS15-predicted chemical shielding values are compared to experimentally measured chemical shifts for Ubiquitin and the third IgG-binding domain of Protein G through linear regression and yield RMSD values of up to 2.2, 0.7, and 4.8 ppm for carbon, hydrogen, and nitrogen atoms. These RMSD values are very similar to corresponding RMSD values computed using OPBE/6-31G(d,p) for the entire structure for each proteins. These maximum RMSD values can be reduced by using NMR-derived structural ensembles of Ubiquitin. For example, for the largest ensemble the largest RMSD values are 1.7, 0.5, and 3.5 ppm for carbon, hydrogen, and nitrogen. The corresponding RMSD values predicted by several empirical chemical shift predictors range between 0.7 - 1.1, 0.2 - 0.4, and 1.8 - 2.8 ppm for carbon, hydrogen, and nitrogen atoms, respectively.

The Ontological Problem

2018 ◽  
Author(s):  
Christopher McCrudden
Keyword(s):  
Human Rights ◽  
Human Dignity ◽  
Legal Interpretation ◽  
Human Rights Law ◽  
Specific Element ◽  
The Third ◽  
The Relationship ◽  
Ontological Problem

This chapter deals with the third of three problems that dominate religious litigation, the ontological problem, which arises in two particular respects in the relationship between human rights law and religion. The first respect is in the need to give content to the ‘human’ in ‘human rights’, and we see religions and legal interpretation giving diverse, and sometimes conflicting, answers to this question. One of the contested sites of this conflict is over how we are to understand the idea of ‘human dignity’, which is seen by several religions and by the human rights system as a foundational concept for the understanding of human rights. The second respect in which the ontological problem arises has to do with a specific element in what it means to be human, namely the place of religion in that understanding. Is religion central to our view of what it means to be human, and are protections for religion central, therefore, to the human rights enterprise? Or should we, rather, view religion as marginal, or even contrary to our conception of what it means to be fully human, and query whether religion should be part of human rights protections at all?

Structural Realism and Category Mistakes

2018 ◽  
Author(s):  
Elaine Landry
Keyword(s):  
Category Theory ◽  
Physical Theory ◽  
Structural Realism ◽  
Conceptual Tool ◽  
The Third ◽  
Meta Level ◽  
Formal Framework ◽  
Fundamental Physical ◽  
Use Category ◽  
Category Mistakes

Structural realists have made use of category theory in three ways. The first is as a meta-level formal framework for a structural realist account of the structure of scientific theories, either syntactic or semantic. The second is an appeal to the category-theoretic structure of some successful, successive or fundamental, physical theory to argue that this is the structure we should be physically committed to, either epistemically or ontically. The third is to use category theory as a conceptual tool to argue that it makes conceptual sense to talk of relations without relata and structures without objects. After a brief overview of structural realism, I consider how each appeal to the use of category theory stands up against the aims of the structural realist.

Ethics and Description

Philosophy ◽  
1968 ◽  
Vol 43 (166) ◽  
pp. 360-370
Author(s):  
R. W. Newell
Keyword(s):  
The Other ◽  
States Of Affairs ◽  
Truth Values ◽  
The Past ◽  
Uncritical Acceptance ◽  
The Common ◽  
Physical Objects ◽  
Common Observation

To some extent, perhaps under Moore's chastening influence, eccentric philosophical denials of the existence of physical objects, other people's minds, the past, and so on, have gone out of fashion. All the same there is at least one very common philosophical conclusion which, though not as extravagant as these, is no less paradoxical. This is the dogma that ethical statements could not describe anything at all, and the collateral claim that they could not be true or false. This is, I suggest, as paradoxical as traditional denials of the existence of chairs and tables, since the denial that ethical statements could be descriptive, like the denial that chairs and tables could exist, is opposed by the common observation that ethical statements do describe, just as the other is opposed by the common observation that chairs and tables do exist. I hope to make two things perfectly clear. First of all, that ethical statements do describe states of affairs; and secondly, that the reason ultimately given for saying that they could not describe anything, namely that they differ in verification from statements of fact, is only partly true, and its uncritical acceptance has led to the canonisation of the belief that ethical statements are non-descriptive and have no truth-values.

scholarly journals Truth in Mathematics

2018 ◽  
Author(s):  
Øystein Linnebo
Keyword(s):  
Mathematical Truth ◽  
Mathematical Objects ◽  
Truth Values ◽  
Objective Truth ◽  
The Third ◽  
Philosophical Account ◽  
Classical Conception ◽  
Concept Of Truth

This chapter discusses four questions concerning the nature and role of the concept of truth in mathematics. First, the question as to whether the concept of truth is needed in a philosophical account of mathematics is answered affirmatively: a formalist approach to the language of mathematics is inadequate. Next, following Frege, a classical conception of mathematical truth is defended, involving the existence of mathematical objects. The third question concerns the relation between the existence of mathematical objects and the objectivity of mathematical truth. A traditional platonist seeks to explain the latter in terms of the former, while Frege reverses this order of explanation. Finally, the question regarding the extent to which mathematical statements have objective truth-values is discussed.

scholarly journals How does God know that 2 + 2 = 4?

2019 ◽  
pp. 1-16
Author(s):  
ANDREW BRENNER
Keyword(s):  
General Model ◽  
States Of Affairs ◽  
Truth Values ◽  
The Subject ◽  
Free Actions ◽  
In Virtue Of

AbstractSometimes theists wonder how God's beliefs track particular portions of reality, e.g. contingent states of affairs, or facts regarding future free actions. In this article I sketch a general model for how God's beliefs track reality. God's beliefs track reality in much the same way that propositions track reality, namely via grounding. Just as the truth values of true propositions are generally or always grounded in their truthmakers, so too God's true beliefs are grounded in the subject matters of those beliefs (i.e. God believes that p in virtue of the fact that p). This is not idle speculation, since my proposal allows the theist to account for God's true beliefs regarding causally inert portions of reality.

scholarly journals Arbitrary grounding

2021 ◽  
Author(s):  
Jonas Werner
Keyword(s):  
Metaphysical Explanation ◽  
States Of Affairs ◽  
Fourth Section ◽  
The Third

AbstractThe aim of this paper is to introduce, elucidate and defend the usefulness of a variant of grounding, or metaphysical explanation, that has the feature that the grounds explain of some states of affairs that one of them obtains without explaining which one obtains. I will dub this variant arbitrary grounding. After informally elucidating the basic idea in the first section, I will provide three metaphysical hypotheses that are best formulated in terms of arbitrary grounding in the second section. The third section will be concerned with the relation between arbitrary grounding and non-arbitrary grounding. The fourth section will compare arbitrary grounding to two extant proposals in the literature.

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