Ayache presents a view of markets and mathematics that attempts to conform to the philosophies of Alain Badiou and Quentin Meillassoux. However, this attempt is unsuccessful because Ayache adopts a view of probability rooted in nineteenth-century conceptions that cannot accommodate the radical uncertainty of the markets. This is unfortunate as it is reasonable to believe that the ideas of Badiou and Meillassoux, when synthesised with contemporary ideas of probability, could offer interesting insights. Roffe presents a better argued synthesis of Deleuze and markets, however he makes similar assumptions about contemporary probability that undermine his conclusions.

Timothy Johnson's working hypothesis in his review of my latest book, The Medium of Contingency, is that I (as well as the ‘quants’ involved in the derivative pricing industry) do not understand the foundations of abstract probability theory. In this response, I show that this is not the case. On the contrary, rules and protocols which are common in the derivative pricing industry, the result of which can be an extension of abstract probability theory as it now stands, seem to elude Johnson. To address these failings, I provide theoretical reflections on probability theory and its formalisms.

In his review of my recent book, Abstract Market Theory, Johnson mistakes my investigation into the conditions and limits of probabilistic reasoning as a rejection of its sense and utility. The same misunderstanding also appears in a review by Munger published recently. In both cases this leads to a skewed and reductive understanding of my reconception of the relationship between price and value. In this response, I present an outline of the philosophical goals of Abstract Market Theory. My intent is not just to show that these reviews are incorrect in their presentation of my argument, but to also indicate why a philosophical perspective remains indispensable for our understanding of the market.