P, but I lack sufficient evidence for p

P but I Shall Believe That Not

There is a well-known opposition, about the ethics of belief, between the "Victorian" position heralded by Clifford's famous maxim:"It is wrong, always, everywhere, and for everyone, to believe anything on insufficient evidence", and the so-called "pragmatist" view put forward by William James in his essay "The Will to Believe", according to which believing may be under the control of the will,...

On Bayes Tests for p ~ i Versus p > i :

Few if any obtain a measure of success in their chosen profession without the beneficent influence of others. The first author is no exception. His interest in optimal stopping problems was ignited as a student in 1965 when Professor Robbins was visiting the University of Minnesota. Perhaps a fitting way of expressing appreciation would be to use this occasion to introduce the second author, Xi...

B. I. P. P. in Septic Wounds

P I   C C  P  M

Hilbert’s original aim, to show the consistency of the use of such ideal elements by finitistic means, which would suffice to eliminate these ideal elements from proofs of purely universal (‘real’) theorems (‘Hilbert’s program’), turned out to be impossible for theories containing a sufficient amount of number theory by K. Gödel’s 2nd incompleteness theorem. Nevetheless, various partial realiza...

P-Sets and (i)-P-Sets for Real Function Space

We study p-sets and (i)-p-sets for a real function space A and compare them with p-sets for its complexification. We also discuss the relation of p-sets and (i)-p-sets with weak peak sets and weak (i)-peak sets which generalize our result of [7]. Using some of the results, we generalize a result of Izzo [2] (proved for a complex function algebra) for a real function space A. Mathematics Subject...