Is the law displacing morality? And should it? ‘Law is a bottomless pit and I have no inclination to fathom its depths.’.

We systematically study the interrelations between all possible variations of \(\Delta ^0_1\) variants of the law of excluded middle and related principles in the context of intuitionistic arithmetic and analysis.

We introduce a new framework for asymptotic probabilities of sentences, in which we have a σ-additive measure on the sample space of all sequences A = {A n } of finite models, where the universe of A n is {1,2... n}, and use this framework to strengthen 0-1 laws for logics.

We introduce a new framework for asymptotic probabilities of sentences, in which we have a σ-additive measure on the sample space of all sequencesA= {} of finite models, where the universe ofis {1,2, …, n}. and use this framework to strengthen 0-1 laws for logics.

We discuss resource-bounded measures on the class of recursive structures and prove that with respect to such measures a random recursive structure is almost surely isomorphic to the unique countable model of the extension axioms.

We propose an original use of techniques from random graph theory to find a Monadic ∑ 1 1 sentence without an asymptotic probability. Our result implies that the 0-1 law fails for the logics ∑ 1 1 and ∑ 1 1 . Therefore we complete the classification of first-order prefix classes with or without equality, according to the existence of the 0-1 law for the corresponding ∑ 1 1 fragment. In addition, our counterexample can be viewed as a single explanation (...) of the failure of the 0-1 law of all the fragments of existential second-order logic for which the failure is already known. (shrink)

Fix an integer $r \ge 3$. We consider metric spaces on n points such that the distance between any two points lies in $\left\{ {1, \ldots,r} \right\}$. Our main result describes their approximate structure for large n. As a consequence, we show that the number of these metric spaces is $\left\lceil {{{r + 1} \over 2}} \right\rceil ^{\left + o\left}.$Related results in the continuous setting have recently been proved by Kozma, Meyerovitch, Peled, and Samotij [34]. When r is even, our (...) structural characterization is more precise and implies that almost all such metric spaces have all distances at least $r/2$. As an easy consequence, when r is even, we improve the error term above from $o\left$ to $o\left$, and also show a labeled first-order 0-1 law in the language ${\cal L}_r $, consisting of r binary relations, one for each element of $[r]$. In particular, we show the almost sure theory T is the theory of the Fraïssé limit of the class of all finite simple complete edge-colored graphs with edge colors in $\left\{ {r/2, \ldots,r} \right\}$.Our work can be viewed as an extension of a long line of research in extremal combinatorics to the colored setting, as well as an addition to the collection of known structures that admit logical 0-1 laws. (shrink)

Thinking Tools is a regular feature that introduces tips and pointers on thinking clearly and rigorously. Here we get to grips with two everyday reasoning errors.

The law giveth and the law taketh away. The question ‘Who is law for’ has of late received increased attention in mainstream jurisprudence.1 Whether at a general, conceptual level o...

We systematically study the interrelations between all possible variations of Δ10\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta ^0_1$$\end{document} variants of the law of excluded middle and related principles in the context of intuitionistic arithmetic and analysis.

A Hegelian Liberal Theory of the Penal Law Content Type Journal Article Category Book Review Pages 219-224 DOI 10.1007/s11572-011-9119-8 Authors Alfonso Donoso, Pontificia Universidad Cat’olica de Chile, ICP, Santiago, Chile Journal Criminal Law and Philosophy Online ISSN 1871-9805 Print ISSN 1871-9791 Journal Volume Volume 5 Journal Issue Volume 5, Number 2.

Practical philosophy of law is a theory about concrete existence of law which holds that due to the asymmetry between existing law and social facts and case facts, the existing law needs to be developed in a reflective manner through application and this is the inevitable process of mutation from law 1.0 to law 2.0. Practical philosophy of law is founded on the generative thinking of practical philosophy, and distinct from other philosophies of law hereof.

Many people are uncomfortable with the idea that pleasure from certain sources is genuinely beneficial. These sources can be sorted into two classes: ones that involve others’ pain; and ones that involve what seems to be damage rather than benefit to the person involved. Here’s an example of the latter: a woman who claims that she enjoys her work performing in hard-core pornographic films. Some find it hard to take such a claim at face value – they instinctively assume that (...) the woman is insincere or self-deceived.1 The reason seems a strongly paternalistic one: because the activity is assumed to be bad, it’s thought that only someone who was in some way damaged could genuinely like it. A statement from Brian Hill, the director of a documentary about such women, illustrates this: ‘I felt certain that she couldn’t enjoy what she does, that there must be some reason why she’s undergoing this kind of experience. But there was nothing: no messed-up childhood, no sense of pain or humiliation.’ Forced to conclude that the woman in question really does enjoy her work, Hill changes his view to imply that the pleasure gained cannot be truly beneficial: ‘When I hear a young woman talking about doing videos of fisting and asphyxiation, I have to wonder what it’s doing to her – even if she says that she’s having fun.’. (shrink)

Recently, several authors have utilized the notion of dependence to respond to the traditional argument for the incompatibility of freedom and divine foreknowledge. However, proponents of this response have not always been so clear in specifying where the incompatibility argument goes wrong, which has led to some unfounded objections to the response. We remedy this dialectical confusion by clarifying both the dependence response itself and its interaction with the standard incompatibility argument. Once these clarifications are made, it becomes clear both (...) (1.) that the dependence response does not beg the question against the proponent of the incompatibility argument and (2.) that the dependence response advances the dialectic whether it is developed as a version of Ockhamism or as a version of multiple-pasts compatibilism. (shrink)

ABSTRACTBuilding on Google's efforts to scan millions of books, this article introduces methodology using a database of annual word frequencies of the 40,000 most frequently occurring words in the American literature between 1800 and 2009. The current paper uses this methodology to replicate and identify terror management processes in historical context. Variation in frequencies of word usage of constructs relevant to terror management theory are investigated over a time period of 209 years. Study 1 corroborated previous TMT findings and demonstrated (...) that word use of constructs related to death and of constructs related to patriotism and romantic relationships significantly co-vary over time. Study 2 showed that the use of the word “death” most strongly co-varies over time with the use of medical constructs, but also co-varies with the use of constructs related to violence, relationships, religion, positive sentiment, and negative sentiment. Study 3 foun... (shrink)