Puzzling the 120-cell

We introduce Quintessence: a family of burr puzzles based on the geometry and combinatorics of the 120-cell. We discuss the regular polytopes, their symmetries, the dodecahedron as an important special case, the three-sphere, and the quaternions. We then construct the 120-cell, giving an illustrated survey of its geometry and combinatorics. This done, we describe the pieces out of which Quintessence is made. The design of our puzzle pieces uses a drawing technique of Leonardo da Vinci; the paper ends with a catalogue of new puzzles.Comment: 25 pages, many figures. Exposition and figures improved throughout. This is the long version of the shorter published versio

The System Paradigm

The introduction explains the sense in which the concept of a paradigm, whose originator, T.S. Kuhn, was inspired by the history of the national sciences, is applied to the context of the social sciences. Here the new paradigm does not necessarily replace the old; several paradigms may function effectively side by side. The milestones in the development of the system paradigm have been the works of Marx, Mises, Hayek, Polányi, Schumpeter and Eucken. Although these make a heterogeneous list in terms of their philosophies and political positions, they share a 'system approach'. They deal not just with individual details of the economy but with the system as a whole, and not just with the economy but with the political, ideological and social dimensions, paying special heed to the interactions between each sphere. The great task for the system paradigm is to study the post-socialist transition. For this, it is indispensable; its explanatory power cannot be replaced by any other paradigm. On the other hand, those applying the system paradigm (like the exponents of other paradigms) are often gravely mistaken. The predictive force of the system paradigm is limited, which urges modesty upon those who employ it.http://deepblue.lib.umich.edu/bitstream/2027.42/39662/3/wp278.pd

-A rope breaks. A bell chimes. A man dies.- The kwispel: a neglected international narrative riddle genre.

Retoric

Special Divine Action and Natural Science

A number of modern theologians have concluded that the rise of natural science makes it necessary to give up the idea that God acts in particular ways to affect the course of events in the world. I reply to this claim, taking up the challenge to explain what might be meant by a ”special’ act of God. There are several ways to conceive of such acts, including the possibility that God might determine what is left determinable in the structures of nature, e.g., at the quantum level. I address objections to this view, and consider metaphysical puzzles that it presents

Bayesianism, Infinite Decisions, and Binding

We pose and resolve several vexing decision theoretic puzzles. Some are variants of existing puzzles, such as ‘Trumped’ (Arntzenius and McCarthy 1997), ‘Rouble trouble’ (Arntzenius and Barrett 1999), ‘The airtight Dutch book’ (McGee 1999), and ‘The two envelopes puzzle’ (Broome 1995). Others are new. A unified resolution of the puzzles shows that Dutch book arguments have no force in infinite cases. It thereby provides evidence that reasonable utility functions may be unbounded and that reasonable credence functions need not be countably additive. The resolution also shows that when infinitely many decisions are involved, the difference between making the decisions simultaneously and making them sequentially can be the difference between riches and ruin. Finally, the resolution reveals a new way in which the ability to make binding commitments can save perfectly rational agents from sure losses

Creativity Skills Applied to Earth Science Education: Examples from K-12 Teachers in a Graduate Creativity Class

NOTE: This is a large file, 10.7 mb in size! This article briefly explores different aspects of creativity, and then examines K-12 teachers' reactions to exercises applied to earth science concepts in a graduate creativity class. Different types of puzzle activities centering on geoscience content include a quiz game based on Odyssey of the Mind spontaneous problems, and other exercises related to embedded words, transformed cliches, remotely associated word sets, and wordsmithing. Teachers used visualization for an imaginary interview with a geoscientist, along with personal analogy of an earth science feature. As a culminating activity, teachers fashioned a geoscience curriculum material with a given set of items. Ideas for applying the activities to geoscience classes at various grade levels are included. Educational levels: Graduate or professional, Graduate or professional

An argument for the use of Aristotelian method in bioethics

The main claim of this paper is that the method outlined and used in Aristotle's Ethics is an appropriate and credible one to use in bioethics. Here “appropriate” means that the method is capable of establishing claims and developing concepts in bioethics and “credible” that the method has some plausibility, it is not open to obvious and immediate objection. It begins by suggesting why this claim matters and then gives a brief outline of Aristotle's method. The main argument is made in three stages. First, it is argued that Aristotelian method is credible because it compares favourably with alternatives. In this section it is shown that Aristotelian method is not vulnerable to criticisms that are made both of methods that give a primary place to moral theory (such as utilitarianism) and those that eschew moral theory (such as casuistry and social science approaches). As such, it compares favourably with these other approaches that are vulnerable to at least some of these criticisms. Second, the appropriateness of Aristotelian method is indicated through outlining how it would deal with a particular case. Finally, it is argued that the success of Aristotle's philosophy is suggestive of both the credibility and appropriateness of his method.</p