Between Philosophy and Science. Edited by Michael Heller, Bartosz Brożek, and Łukasz Kurek. Kraków: Copernicus Center Press, 2013. 255 pp. Hardcover 39,90 Euro.

Church's Thesis: Logic, Mind and Nature. Edited by Adam Olszewski, Bartosz Brożek, and Piotr Urbańczyk. Kraków: Copernicus Center Press, 2014. 431 pp. Hardcover 49,90 Euro.

Logic in Theology. Edited by Bartosz Brożek, Adam Olszewski, and Mateusz Hohol. Kraków: Copernicus Center Press, 2013. 308 pp. Hardcover 39,90 Euro.

Philosophy of Chance: A Cosmic Fugue with a Prelude and a Coda. By Michael Heller. Kraków: Copernicus Center Press, 2013. 237 pp. 39,90 Euro.

Rule‐Following: From Imitation to the Normative Mind. By Bartosz Brożek. Kraków: Copernicus Center Press, 2013. 234 pp. Hardcover 39,90 Euro.

The Causal Universe. Edited by George F. R. Ellis, Michael Heller, and Tadeus Pabjan. Kraków: Copernicus Center Press, 2013. 328 pp. Hardcover 39,90 Euro.

The Emotional Brain Revisited. Edited by Jacek Dębiec, Michael Heller, Bartosz Brożek, and Joseph LeDoux. Kraków: Copernicus Center Press, 2014. 371 pp. Hardcover 49,90 Euro.

The Many Faces of Normativity. Edited by Jerzy Stelmach, Bartosz Brożek, and Mateusz Hohol. Kraków: Copernicus Center Press, 2013. 362 pp. Hardcover 39,90 Euro.

In this review, I present eight books recently produced by the Copernicus Center in Kraków. These eight are not their full production, as the website of their publishing venture, , testifies. The Copernicus Center is an interdisciplinary collaboration of philosophers, theologians, scientists, and lawyers. Of these, Michael Heller, cosmologist and mathematician, philosopher and priest, winner of the Templeton Prize in 2008, is the most well‐known among readers of Zygon, I assume. This extraordinarily fertile group represents a very coherent program that has deep roots in the intellectual culture of Kraków, as described in a very readable contribution by Bartosz Brożek and Michael Heller in this issue of Zygon: Journal of Religion and Science.

A characteristic title in their program is Between Philosophy and Science. The authors analyze in depth philosophical issues informed by science, and scientific developments that are also philosophical in kind. In this volume, Robert Audi clarifies scientific and methodological naturalism, and with such a naturalism the possibility of ontological pluralism. Roman Murawski, Krzysztof Wójtowic, and Bartosz Brożek each consider issues related to the nature of mathematics and logic. Michael Heller and Wojciech P. Grygiel reflect on quantum gravity and ontology at the Planck scale, and Helge Kragh and Bogdan Dembiński consider philosophy of science in historical and Platonic perspective. Wojciech Załuski and Łukasz Kurek focus on the human, with evolutionary anthropology and neurophilosophy, while Teresa Obolevitch discusses knowledge and faith in the Russian academic milieu. A great collection of original articles.

Michael Heller's Philosophy of Chance discusses in brief the history of probability theory, from Antiquity via Pascal, Fermat, and Jacob Bernouilli to probability theory as it was incorporated in physics in the twentieth century. In the final part, he applies insights from this tour to contemporary controversies, especially the anti‐evolutionary “Intelligent Design” movement. Heller argues that chance should not be associated with the collapse of rationality; “chance” is a notion that can be analyzed in precise terms. Thus, one need not view these two options, a world designed by God or one that came about by mere chance, as opposites.

The Causal Universe reflects on cosmology, causality, and complexity. There is a substantial introduction by Michael Heller, who reflects on the migration of concepts from philosophy to science and vice versa; “causality” is an example. Mathematical cosmologist George Ellis offers an extensive contribution on the question why the laws of nature are as they are, followed by a second paper on top‐down causation as key to the emergence of complexity. Jean‐Philippe Uzan follows up with discussions of the emergence of complexity in cosmic history, while Derek Raine offers various challenges to the concept “top‐down causality”; it might be sufficient to describe the multiplicity of coexisting causes (or of causes and the context as a landscape) as “adaptive evolution.” The second part of the book speaks of causality and the structure of the Universe (Marek Kuś, Julian Barbour, Andrzej M. Sołtan, Andrzej Sitarz, Michael Heller, and Mariusz P. Dąbrowski). The third part reflects on “ultimate causality,” with contributions by Bogdan Dembiński, William R. Stoeger SJ, Thomas Tracy, and the author of this review.

The second characteristic title for the program, Logic in Theology, is representative also of the earlier Kraków Circle (e.g., Józef Bóchenski), continuing into the present, an interest in rationality in theology, its conceptual world, and its intellectual articulation and justification. This volume has contributions by Jan Woleński, Jerzy Dadaczyński, Antonio Rotolo and Erica Calardo, Kazimierz Trzęsicki, Bartosz Brożek and Adam Olszewski, Damian Waşek, Marek Porwolik, Marie DužžKim Solin, Pavel Materna, Jan D. Szczzurek, Mieszko Talasiewicz, and Wojciech P. Grygiel.

More focused qua topic and more voluminous qua treatment is the volume Church's Thesis: Logic, Mind and Nature. Alonso Church's Thesis, from 1936, is about calculable functions; only those that are recursive are computable. The same year, Alan Turing came up with a similar idea, formulated in terms of a procedure for an abstract machine. The first decades of the twentieth century were a most interesting period in the philosophy and foundations of mathematics, with the optimism of the Hilbert program, undermined by the work of Kurt Gödel, the constructivist or intuitionist approach developed by L. E. J. Brouwer and by Hermann Weil, the conceptualization of provability and algorithms by Alan Turing, Alonso Church, and John von Neumann, and much else. Church belonged to that same class of philosophically sensitive mathematicians. This volume has substantial articles on philosophical aspects, logical aspects, the relation with ideas about abilities of the mind, and on a physicalist version of the thesis. Given the conceptual significance as well as the widespread use of algorithms in contemporary technology, this meta‐mathematical study is highly relevant, though the contributions are written more for specialists than for those without substantial expertise in logic and mathematics.

Bartosz Brożek's Rule‐Following: From Imitation to the Normative Mind also touches upon algorithms, or rather rules, in mathematics, linguistics, and morality. Such rules can be descriptive and prescriptive. For the analysis in this book, the point of departure is Ludwig Wittgenstein, while neuroscientific insights about imitation, language, language, morality, and mathematics are discussed in subsequent chapters. The author comes to a revised version of the “three worlds” distinguished by Karl Popper: the world of physical states, the world of mental states, and the conceptual world of ideas. Specific to Brożek's view is that world 3 is based not only on mental processes (world 2), but also rooted in social interactions that propagate patterns (world 1). He thus seeks to steer a course that avoids a peculiar Platonic view of mathematics as disconnected from reality, while at the same time making the “objective” strength of mathematics conceivable. And thus, he suggests a response to the philosophical question why mathematics is so effective in understanding the physical world.

In The Many Faces of Normativity somewhat similar issues are discussed by various authors. Robert Audi analyzes the extent to which normativity can be naturalized. Jan Woleński reflects on similarities between normative and epistemic discourse. Jaap Hage discusses rules, and the way they differ from facts. Anna Brożek and Jerzy Stelmach both discuss “the naturalistic fallacy” and its limitations. After these papers on foundational and conceptual issues, the second section turns to contemporary debates on claims about the normativity of language (Bartosz Brożek and Aeddan Shaw), the normativity of mathematics (Mateusz Hohol) and legal philosophy (Marcin Gorazda), while Marta Soniewicka argues that value‐based views of normativity by Max Scheler and Nicolai Hartmann are preferred over Immanuel Kant's view of normativity rooted in obligation. The third section considers normativity in the context of the sciences, especially psychology, neuroscience and evolutionary theory, with contributions by Edward Nęcka, Marcin Siwek, Rafal Jaeschke, Dominika Dudek and Natalia Czyżowska, Bartlomiej Kucharzyk, and Woljciech Załuski.

The Emotional Brain Revisited considers the emotions. Too often considered as the antithesis of rationality, emotions are relevant for consciousness and introspection, and hence for rationality as well. In the first group of contributions, the neurosciences are central. Joseph LeDoux, author of the book The Emotional Brain (), discusses recent research. Regina Sullivan and Margo Landfers speak of animal studies and infant attachment. Justin Kim and colleagues concentrate on the amygdala, a particular brain structure associated with anxiety. Jacek Dębiec offers a brain based view of emotions, while Bram Heerebout and Hans Phaf consider computational models. In the second group, psychology takes the center, with contributions by Nico Frijda and James Russell. The third group of papers takes up the philosophical issues, with essays by Łukasz Kurek, Mateusz Hohol and Piotr Urbańczyk on social cognition, Wojciech Załuski on rationality, Bartosz Brożek on morality, and Dominika Dudek on concepts of mental illness.

Seeing these eight volumes side by side, I am impressed by the work done by these Polish colleagues and their international guests. A minor desire would have been for more volumes to have indexes, at least by personal names. The books are well designed, aesthetically pleasing. More important, the Kraków group around Michael Heller has an interesting agenda of understanding human rationality and the rationality of the world, in relation to science, mathematics, and morality. A religious concern remains in the background, but does not distract or dominate: the human intellectual quest is by itself enough. Though all this work is interesting, my own favorite from these books is Bartosz Brożek's Rule‐Following, as it seeks to understand the “objectivity” of mathematics and morality in harmony with their human character. Worth rereading.