Martin Munoz

In this paper we analyze object-talk, some of its uses and misuses, more closely. Our main claim is that object-talk should be understood in the context of faith instead of that of rational argumentation. Hence, object-talk is compared with God-talk and the way of understanding the so-called 'abstract entities' from logic and mathematics turns out to be essentially linked with how the contact with the Divine is conceived. Moreover, we discuss the particular case of the independence phenomenon and some of the proposals that have been made in order to deal with it. The conclusion is that, even if we succeed in granting such status to object-talk, different accounts of its nature may arise. We finally present our view as one of these alternatives.

The purpose of the present dialogue is threefold: (a) Refining our previous interpretation of Wittgenstein's philosophy of mathematics through the 'Phenomenology' chapter of the 'Big Typescript'; (b) Examining the role of phenomenological and historical analysis in the contemporary debate surrounding the axioms of set theory; (c) Providing a brief interpretation of Kant's Architectonic as a general framework for such debate. The conclusion of the article, which add certain theological connotations to the topic being discussed, has to be explored in future research.

Putnam and Finkelstein can be read as providing an answer to Kripke's skeptical argument by appealing to the way mathematics is commonly pursued. Nowadays, the debate surrounding pluralism has questioned the postulation of a unique way of developing mathematical activity. In this paper, we wish to reformulate Kripke's argument as a challenge for the conjunction of 'ifthenism' and a reasonable form of pluralism and, at the same time, propose a reading of some passages of the 'Philosophical Investigations' as a solution. Our conclusion is that, in order for pluralism to be preserved, we need to clarify both the fact that we make definite 'decisions' and the philosophical value that they, as we argue, bear. To investigate the nature of this value is one of the further tasks that we want to cover in this article.