We extend Morley's Theorem to show that if a theory is κ-p-categorical for some uncountable cardinal κ, it is uncountably categorical. We then discuss ω-p-categoricity and provide examples to show that similar extensions for the Baldwin-Lachlan and Lachlan Theorems are not possible.
Many years after the publication of “A Logical Calculus of the Ideas Immanent in Nervous Activity,” Warren McCulloch gave Walter Pitts credit for contributing his knowledge of modular mathematics to their joint project. In 1941 I presented my notions on the flow of information through ranks of neurons to Rashevsky’s seminar in the Committee on Mathematical Biology of the University of Chicago and met Walter Pitts, who then was about seventeen years old. He was working on a mathematical theory of (...) learning and I was much impressed. He was interested in problems of circularity, how to handle regenerative nervous activity in closed loops....For two years Walter and I worked on these problems whose solution depended upon modular mathematics of which I knew nothing, but Walter did.. In this paper, we will fill in some of the details regarding Pitts’s interest in problems of circularity, regenerative activity in closed loops of neurons, and modular mathematics, and the way in which they relate to “A Logical Calculus.”. (shrink)
Spatial asymmetries are an intriguing feature of directed attention. Recent observations indicate an influence of temperament upon the direction of these asymmetries. It is unknown whether this influence generalises to visual orienting behaviour. The aim of the current study was therefore to explore the relationship between temperament and measures of spatial orienting as a function of target hemifield. An exogenous cueing task was administered to 92 healthy participants. Temperament was assessed using Carver and White's (1994) Behavioural Inhibition System and Behavioural (...) Activation System (BIS/BAS) scales. Individuals with high sensitivity to punishment and low sensitivity to reward showed a leftward asymmetry of directed attention when there was no informative spatial cue provided. This asymmetry was not present when targets were preceded by spatial cues that were either valid or invalid. The findings support the notion that individual variations in temperament influence spatial asymmetries in visual orienting, but only when lateral targets are preceded by a non-directional (neutral) cue. The results are discussed in terms of hemispheric asymmetries and dopamine activity. (shrink)
We extend Shelah's first many model result to show that an unstable theory has 2$^\kappa$ many non-permutation group isomorphic models of size $\kappa$, where $\kappa$ is an uncountable regular cardinal.
An examination of the contemporary Italian movement associated with M. P. Sciacca, and the serious application of dialectical and phenomenological methods to unveil the structure of "intentionality" or "spirit." An appraisal of Sciacca together with a sample critique of Dante follows a competent summary of the prevailing positions.--D. B. B.
If libertarianism is true, then there is a sense in which agents have it within their power to bring it about that some world is actual. Against recent arguments for the incompatibility of divine foreknowledge and human freedom, I offer an account of power over the past which takes this implication of libertarianism into consideration. I argue that the resulting account is available to Ockhamists and that it is immune to recent criticisms of the notion of counterfactual power over the (...) past. But I contend that it is not an option for Molinists and that this fact leaves that position vulnerable to incompatibilist arguments. (shrink)
In response to Mark D. White's Kantian critique of my article "A Modest Proposal: Accounting for the Virtuousness of Modesty," I argue that invoking Kant's notions of dignity and respect in order to provide an egalitarian account of modesty brings with it conceptual commitments that are not always easy to reconcile with the moral phenomenology of that virtue. In light of this I question White's claim that a Kantian account of modesty offers a better explanation than the existential phenomenological (...) approach that I endorse. (shrink)
This volume makes an excellent and very important contribution to English-language scholarship on the life, thought, and influence of the Majorcan lay theologian and philosopher, Ramon Llull, the Doctor Illuminatus, from his own day through the Renaissance period into the European exploration of the New World. Llull was a brilliant but idiosyncratic thinker, whose interests and writings touched upon, it seems, every major theological and philosophical theme of his day as well as many topics that only would gain greater interest (...) in later centuries. The editors, Amy M. Austin and Mark D. Johnston, in their preface to the volume note right away the main obstacles contemporary (especially... (shrink)
It is customary to remark, in writings on retributivism, that the meaning of the term is so diffuse and variably applied that there is no one concept or justificatory principle picked out by the term. Cottingham identified 9 different ideas captured by the term retributivism, and a similar paper could today no doubt identify as many again. This edited volume of essays on retributivism does justice to that customary remark, by bringing together a range of writings on retributivism many of (...) which present quite different ways of construing the core of retributivist thinking, the virtues of it, and its role in criminal justice.The book is organised around three themes: the first part entitled ‘Conceptualizing Retributivism’, the second ‘Philosophical Perspectives on Retributivism’, and the third ‘Retributivism and Policy’. In the following I provide an overview of the chapters, before making some general remarks on the emerging themes of the edited collec .. (shrink)