Where the Sum of Our Expectation Fails Us: The Exchange Paradox

In the exchange paradox, two players receive envelopes containing different amounts of money. The assignment of the amounts ensures each player has the same probability of receiving each possible amount. Nonetheless, for each specific amount a player may find in his envelope, there is a positive expectation of gain if the player swaps envelopes with the other player, in apparent contradiction with the symmetry of the game. I consider a variant form of the paradox that avoids problems with improper probabilities and I argue that in it these expectations give no grounds for a decision to swap since that decision must be based on a summation of all the expectations. But this sum yields a non-convergent series that has no meaningful value. The conflicting recommendations – that it is to one or the other player's advantage to swap – arise from different ways of grouping terms in the sum that yield an illusion of convergence. I describe a generalized exchange paradox, explore some of its properties and display another example.     

PEIRCE'S PRAGMATIC THEOLOGY AND STOIC RELIGIOUS ETHICS1

Charles S. Peirce believed that his pragmatic philosophy could reconcile religion and science and that this reconciliation involves a religious ethics creating a real community with the cosmos and God. After some rival pragmatic approaches to God and religious belief inconsistent with Peirce's philosophy are set aside, his metaphysical plan for a reconciliation of religion and science is outlined. A panentheistic God makes the best match with his desired conclusions from the Neglected Argument for the reality of God, and this God is also capable of fulfilling the pragmatic role demanded by Peirce's ethical expectations for the intelligent functioning of religion. The discussion proceeds to an elaboration of the aesthetic, metaphysical, and ethical elements of Peirce's philosophical system, which indicate why Peirce's religious ethics is best categorized as akin to Stoicism, with some Christian elements. For Peirce, religious ethics proceeds from the (potentially universal) agapic community's cooperation with God's loving creativity of the universe.     

The Life Attitudes Schedule Short Form: An Abbreviated Measure of Life-Enhancing and Life-Threatening Behaviors in Adolescents

An abbreviated version of the Life Attitudes Schedule (LAS) was developed, consisting of 24 items, each representing one cell of the original LAS theoretical matrix (4 content categories × 2 behavior types × 2 valence). Items were retained on the basis of high correlations with LAS total score and low correlations with gender. Psychometric properties of the LAS Short Form were robust and the Short Form total score correlated .93 with the original LAS total score. As with the original LAS, boys reported more injury-related behaviors than girls. Future research and clinical directions are suggested.