BOOK REVIEW On the connections between reality and logic Majda Trobok, Nenad Mis ˇc ˇevic ´ and Berislav Z ˇ arnic ´ (eds): Between logic and reality: modeling inference, action and understanding. Dordrecht: Springer, 2012, x+278pp, €139,95 HB Costas Dimitracopoulos Published online: 6 February 2013 Ó Springer Science+Business Media Dordrecht 2013 The volume is a collection of papers concerning connections between reality and logic, where the latter term is thought to refer to logical structures that are used to describe reality. Most of the papers included in the volume owe their present form to international conferences and/or scientific projects that were realized in Croatia in the last decade, with the active involvement of academics from all around the world. The book is composed of fifteen chapters, the first of which, authored by the editors of the volume, is an introduction to the other fourteen chapters, which are grouped into four parts. The first part contains chapters 2–5, which deal with foundational questions on logico-mathematical structures. In chapter 2, Stewart Shapiro studies the question how much mathematics should a philosopher of mathematics know to be able to do research in his discipline. After discussing shortly the main twentieth century schools in the philosophy of mathematics, that is, logicism, formalism and intuitionism, he considers this question in relation to work done in the area in the last two decades or so. Dale Jacquette, in the next chapter, deals with the problem of explaining the relation between pure and applied mathematics. After criticizing the solutions to this problem offered by all main streams in the philosophy of mathematics, he proposes a novel approach, which he calls ‘‘Aristotelian inherence metaphysics,’’ and argues that it provides satisfactory answers to the main questions confronting a philosophy of applied mathematics. The fourth chapter, authored by Milos ˇ Arsenijevic ´, concerns the philosophical impact of the Lo ¨wenheim-Skolem theorem, one of the landmark results on properties of models of first-order theories. The author gives a short presentation of the historical background, the generaliza- tions and consequences of the theorem and then explains why this result follows from both the limitations of first-order logic and the language independence of the C. Dimitracopoulos (&) Department of Philosophy and History of Science, University of Athens, University Campus, 15771 Athens, Greece e-mail: cdimitr@phs.uoa.gr 123 Metascience (2013) 22:443–445 DOI 10.1007/s11016-013-9772-8