**December 5** FRI — 14.30-16.30

Aula Seminari — Cortile Ghiacciaia, II floor (Via Festa del Perdono 7, Milano)

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**A reason for a mathematical reason?**

**The problem of mathematical explanation ****in science and in mathematics**

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*Abstract*: The philosophical problem of mathematical explanation steps from a very simple observation that we face when we are asked to account for (some bits of) scientific practice: there are cases in which the function of mathematics in science (*i.e.* the natural and social sciences, which we distinguish from mathematics), and in mathematics itself, is not simply to show *that* an empirical phenomenon (or a mathematical fact) occurs (or it’s true, in the case of mathematics), but it extends to that of shed light on *why* the empirical phenomenon (or the mathematical fact) occurs (or it’s true, in the case of mathematics). In other words, in these situations the mathematics we use seems to provide an answer to the question "Why does the empirical phenomenon F occur?" (or, in the case of pure mathematics, “Why is that particular mathematical fact M true?”). The problem amounts then to capture an adequate notion of mathematical explanation, *i.e.* a notion capable to account for those situations (in science and in mathematics itself) in which mathematics seems to have explanatory power.

In this talk I shall provide an introduction to the problem of mathematical explanation. I shall offer some examples of mathematical explanation and show how the recent interest in this topic can be traced back to Aristotle. Moreover, by focusing on two topics that are often discussed in relation to mathematical explanation (the new indispensability argument for mathematical realism and the applicability of mathematics in science), I shall show how the ongoing debate on mathematical explanation has important ramifications in different areas of philosophy of science and philosophy of mathematics.

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**November 28** FRI — 14.30-16.30

Aula Seminari — Cortile Ghiacciaia, II floor (Via Festa del Perdono 7, Milano)

**McTaggart and the Nature of Ontological Regress. A Case Study.**

* Abstract: *This talk has two objectives. First, I shall present and analyse an entirely novel reconstruction of McTaggart’s infamous regress argument, which was designed to show that the passage of time leads into an infinite vicious regress. Second, I want to use the reconstructed McTaggartian regress as a case study to elucidate more about the nature of regresses. Looking at the regress in its novel form reveals some surprising new insights. The McTaggartian regress, I argue, is ontological and whether or not it is vicious depends on the structural features we allow reality to have.

More specifically, I argue that McTaggart’s argument is a variation of the general problem of change. McTaggart’s conception of temporal passage as qualitative change in terms of pastness, presentness and futurity implies that the change constituting passage must be merely relational. The regress, an infinite chain of ontologically dependent relational changes, ensues from applying the only available solution to the problem of change.

Ontological regresses come in two broad kinds. Infinitist regresses, non well-founded chains of dependency where each thing asymmetrically depends for its existence on the next, and coherentist regresses, where the dependency structures are circular or symmetrical. The McTaggartian regress, I shall show, is of the latter sort. Although the traditional consensus is that infinitist and coherentist structures are both vicious, this orthodox opinion has recently been challenged by several authors. There is a danger that discussions about these matters are perceived as simply trading on different intuitions, with no progress to be made. This might be particularly salient in the case of metaphysical coherentism. I hope to advance matters by using the McTaggartian regress as a case study, thereby bringing fresh arguments to an important debate that has been neglected for too long. Although most coherentist regresses are probably vicious, McTaggart’s regress, or my interpretation of it, may well be benign. One surprising conclusion to draw from this is that there may not be an answer for or against coherentist regresses that applies across the board. Instead, a more apt methodology requires an individual treatment of ontological regresses on a case by case basis.

**November 21** FRI — 14.30-16.30

Aula Seminari — Cortile Ghiacciaia, II floor (Via Festa del Perdono 7, Milano)

**IS QUALITATIVE INDUCTION A KIND OF INDUCTION?**

*Abstract. *In one of his papers Peirce distinguishes three kinds of induction: *Crude Induction*, *Quantitative Induction*, and *Qualitative Induction*. The third is not based on the experience of a mass (as the first), nor on the experience of a definite collection of instances (as the second), but on a “stream of experience” of different parts whose evidential value must be critically scrutinized. To illustrate the dynamics of Qualitative Induction, Peirce uses the example of an *investigator *who starts from a hypothesis and tries to construct a thesis out of it, considering the evidential weight of the hypothesis, elaborating some conditional predictions from it and testing them. The presentation will discuss the idea of Qualitative Induction compared with other classifications of our inductive processes, and will ask whether it is a genuine kind of induction, or a (disguised) form of abduction, or something else.

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**September 12** FRI — 12.30-14.30

Sala Riunioni — Direzione del Dipartimento (Via Festa del Perdono 7, Milano)

**Generics**

*Abstract*: I propose a new theory of bare plural generics in terms of plural logic. This new theory preserves most virtues and avoids most vices of the two standard type of accounts already out there.