# A Critical Evaluation of Comparative Probability

Vincenzo Fano

## Introduction

In recent times a partially *logical* perspective on probability has come back into fashion.^{1} The deepest modern formulation of the concept of probability is certainly that of John Maynard Keynes's *A Treatise on Probability* (Keynes, 1973 [1921], hereafter *TP).* Elsewhere (Fano, 1999) I have shown that Carnap's logical approach (1950), which attempts to avoid Keynes's reference to the concept of intuition, is obliged to move towards a weakening of his logistic perspective, from both a formal and an epistemological point of view, which results in a more complex position, closer to that of the Keynes's *TP* (Carnap, 1968). Here I would like to retrieve a Keynesian perspective on two aspects: first, proceeding from the datum that most probabilistic evaluations are comparative, not quantitative;^{2} second, naturalizing the procedures of ascription of initial probabilities, reaching back beyond Keynes to von Kries (1886), as has been recently presented by Heidelberger (2001).^{3}