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.     

Philosophy of Education in a Poor Historical Moment: A Personal Account

Under the post-metaphysical sky “old” humanistic-oriented education is possible solely at the cost of its transformation into its negative, into a power that is determined to diminish human potentials for self-exaltation. Nothing less than total metamorphosis is needed to rescue the core of humanistic genesis: the quest for edifying Life and resistance to the call for “home-returning” into the total harmony that is promised to us within nothingness.