The computational complexity of finding a shortest path in a two-dimensional domain is studied in the Turing machine-based computational model and in the discrete complexity theory. This problem is studied with respect to two formulations of polynomial-time computable two-dimensional domains: domains with polynomialtime computable boundaries, and polynomial-time recognizable domains with polynomial-time computable distance functions. It is proved that the shortest path problem has the polynomial-space upper bound for domains of both type and type ; and it has a polynomial-space lower (...) bound for the domains of type , and has a #P lower bound for the domains of type. (shrink)

The computational complexity of finding a shortest path in a two-dimensional domain is studied in the Turing machine-based computational model and in the discrete complexity theory. This problem is studied with respect to two formulations of polynomial-time computable two-dimensional domains: domains with polynomialtime computable boundaries, and polynomial-time recognizable domains with polynomial-time computable distance functions. It is proved that the shortest path problem has the polynomial-space upper bound for domains of both type and type ; and it has a polynomial-space lower (...) bound for the domains of type, and has a #P lower bound for the domains of type. (shrink)

In “Imagination and Judgment” W.P. Ker argues, contrary to the “ordinary teaching” of the moralists of his day, that we have good reason to consider imagination as “the highest form of practical wisdom or prudence” (475). Modes of imaginative thought that direct human passion towards morally valuable ends are best understood as a form of reason or an intellectual virtue, as opposed to a dangerous distraction from reality and threat to good judgment. Ker’s piece remains of interest partly because it (...) anticipates some of the most important contributions to moral theory made by philosophers, most notably Iris Murdoch and Martha Nussbaum, who have developed conceptions of ‘moral imagination’ in more recent decades. More significantly, reflecting on Ker’s catalogue of the positive and direct roles played by imagination in moral reasoning reveals that there is further work to be done in clarifying the concept of imagination in relation to practical reason. (shrink)

Originally published in 1977, this volume analyzes aspects of elementary schooling in the nineteenth century and the ways in which it prepared working-class children for life in industrial Britain. The book examines: The procedures and practices of different types of schools. The ideologies guiding elementary education The social implications of curriculum content and pupils’ and parents’ attitudes to the education provided by the church and state.

Neuroscience of art might give us traction with aesthetic issues. However it can be seen to have trouble modeling the artistically salient semantic properties of artworks. So if meaning really matters, and it does, even in aesthetic contexts, the prospects for this nascent field are dim. The issue boils down to a question of whether or not we can get a grip on the kinds of constraints present and available to guide interpretive behavior in our engagement with works of fine (...) art. I argue that biased competition models of selective attention can be used to solve this problem, generalize to the affective content of our responses to artworks, and so show that research in cognitive neuroscience is germane to the types of problems of interest within the philosophy of art. (shrink)

Heidegger affirmed traditional technology, but was opposed to science-based modern technology, in which everything (including man) is considered to be a mere “resource”. This opposition was expressed in the form of deep questioning and a suspicion of superficial evaluation, because the true nature of things was often concealed, though disclosed at times. Ways in which engineers should question technology are proposed, highlighting some of the hazards and injustices associated with technology and also its subtle sociological and psychological influences. The demands (...) of engineering ethics and the use of metaphor in design are other ways in which a narrowly rationalistic technological outlook can be confronted. (shrink)

There are a growing number of publications arguing that if we had more wonder in social life, then its quality would be significantly improved, and that we therefore need an “ethics” or a “politics” of wonder. The aim of this paper is to show that that message is unfortunate, and this is for two reasons. First, wonder does not generally have the positive political and moral effects that are attributed to it, so to assume that it does may lead one (...) to adopt unrealistic social policies. Second, wonder does potentially have a number of negative moral and politicaleffects, so social policies that put a premium on wonder may bring adverse consequences. In this way, the paper makes a general case against wonder as a positive force in morality and politics. (shrink)

This paper describes how some aspects of Martin Heidegger’s philosophy resonate strongly with an engineering outlook. He argued that practice was more “primordial” than theory, though preserving an important role for theoretical understanding as well, thus speaking to the gap between engineering education (highly theoretical) and engineering practice (mostly empirical). He also underlined the reality of “average” practices into which we are socialized, though affirming the potential for original work and action too, thus providing the grounds for self-actualization whether within (...) the routine or in transcending it. His notion of “thrownness” emphasizes the importance of context, with which engineers are constantly engaged. While all this relates to the idea of our “being”, Heidegger also dealt with the influence of time on our practices. Future death could be seen as spurring innovation, cultural history as a source for critiquing current practice and the present “situation” as the immediate context for corrective action. His major book is appropriately called “Being and Time”.1. (shrink)

Each Girard quantale (i.e., commutative quantale with a selected dualizing element) provides a support for a semantics for linear propositional formulas (but not for linear derivations). Several constructions of Girard quantales are known. We give two more constructions, one using an arbitrary partially ordered monoid and one using a partially ordered group (both commutative). In both cases the semantics can be controlled be a relation between pairs of elements of the support and formulas. This gives us a neat way of (...) handling duality. (shrink)