Existential predictions are very rare in science. For this reason, when scientists can predict the existence of a new entity—a new planet, or a new particle, for example—we feel that something very exciting is going on! But what is going on is not only exciting—it is also very interesting from a philosophical point of view. These predictions raise various philosophically interesting puzzles, which relate to the epistemological, metaphysical, and methodological roles that mathematics can play in scientific representation. In this post, I want to present two main kinds of existential prediction in science and to sketch some philosophical problems related to them. However, I will not address these problems in this context. The interested reader may refer to Ginammi (2016) for a more detailed analysis and for a solution to these problems.^{1}

# Category Archives: Applicability of mathematics

# Avoiding Reification. A new article on the Studies in History and Philosophy of Modern Physics!

I am pleased to announce that my new article ** Avoiding Reification **will be published on the volume 53 of the

*Studies in History and Philosophy of Modern Physics*(February 2016)!

The article is already accessible online at this address. By clicking on this link until February 23, 2016, you will be taken to the final version of my paper on ScienceDirect ** for free**! No sign up or registration!

In this article I have discussed and critically examined a very interesting case of existential prediction in particle physics: the prediction of the particle (a particle of the class of the spin- baryons). Existential predictions in science are always very thrilling, as you may imagine; but this prediction is even more interesting than usual *because of the peculiar role that mathematics seems to play*. Such a peculiar role raises a serious philosophical problem, since apparently we cannot justify it on the basis of standard methodological criteria. In this paper I discuss this problem and I offer a solution to it by offering a new logical reconstruction of the prediction of the particle, based on the representative and heuristic effectiveness that mathematics may exhibit under certain conditions.

Here is the abstract of the paper, just to give you an idea of the content:

According to Steiner (1998), in contemporary physics new important discoveries are often obtained by means of strategies which rely on

purely formalmathematical considerations. In such discoveries, mathematics seems to have a peculiar and controversial role, which apparently cannot be accounted for by means of standard methodological criteria. M. Gell-Mann and Y. Ne׳eman׳s prediction of the particle is usually considered a typical example of application of this kind of strategy. According to Bangu (2008), this prediction is apparently based on the employment of a highly controversial principle—what he calls the “reification principle”. Bangu himself takes this principle to be methodologically unjustifiable, but still indispensable to make the prediction logically sound. In the present paper I will offer a new reconstruction of the reasoning that led to this prediction. By means of this reconstruction, I will show that we do not need to postulate any “reificatory” role of mathematics in contemporary physics and I will contextually clarify the representative and heuristic role of mathematics in science.

Good read and happy new year to everybody!

# From Logic to Practice. Italian Studies in the Philosophy of Mathematics

I’m happy to announce that the new book *From Logic to Practice* is now available on Amazon.com! My contribution, *Structure and Applicability*, can be found in Part III, chapter 11 of the book.

*This book — *it is written in the back cover* — brings together young researchers from a variety of fields within mathematics, philosophy and logic. It discusses questions that arise in their work, as well as themes and reactions that appear to be similar in different contexts. The book shows that a fairly intensive activity in the philosophy of mathematics is underway, due on the one hand to the disillusionment with respect to traditional answers, on the other to exciting new features of present day mathematics. The book explains how the problem of applicability once again plays a central role in the development of mathematics. It examines how new languages different from the logical ones (mostly figural), are recognized as valid and experimented with and how unifying concepts (structure, category, set) are in competition for those who look at this form of unification. It further shows that traditional philosophies, such as constructivism, while still lively, are no longer only philosophies, but guidelines for research. Finally, the book demonstrates that the search for and validation of new axioms is analyzed with a blend of mathematical historical, philosophical, psychological considerations.*

Let me express my gratitude to Gabriele Lolli, Marco Panza and Giorgio Venturi, whose initiative and perseverance made this work possible.

# Conference: The Analysis of Theoretical Terms

Next week I will be in Munich for a conference on theoretical terms at the Munich Center for Mathematical Philosophy (MCMP). I will talk about the role of mathematics in a very interesting case of existential prediction in physics: the discovery of the omega minus particle. Here is the website of the conference.

# The coconut puzzle

Some time ago, I chanced upon the following puzzle:

Five men find themselves shipwrecked on an island, with nothing edible in sight but coconuts, plenty of these, and a monkey. They agree to split the coconuts into five equal integer lots, any remainder going to the monkey.

Man 1 suddenly feels hungry in the middle of the night, and decides to take his share of coconuts at that very moment. He finds the remainder to be one after division by five, so he gives this remaining coconut to the monkey and takes his fifth of the rest, lumping the coconuts that remain back together. A while later, also Man 2 wakes up hungry, and does exactly the same thing: takes a fifth of the coconuts, gives the monkey the remainder, which is again one, and leaves the rest behind. So do men 3, 4, and 5. In the morning they all get up, and no one mentions anything about his coconut-affair on the previous night. So they share out the remaining lot in five equal parts finding, once again, a remainder of one left for the monkey. Find the initial number of coconuts.^{1}

I won’t give you the answer, so you can enjoy finding it by yourself. The solution is not trivial, for you have to solve a Diophantine equation, but in the end it is not too much complicated. Obviously, there is an infinite number of possible solutions, but the problem implicitly asks for the smallest one.

The puzzle, * per se*, is not very intriguing, but what makes it interesting is a story that usually goes with it. Continue reading