Hans Halvorson

In this text, I explore the intertwined relationship between philosophy of science and theology, and the challenges they both encounter in the academic realm. While theology is struggling to maintain its relevance, philosophy of science has gained recognition and offers valuable insights to theologians. I argue that theologians can benefit from engaging with the content and methods of specific sciences, and philosophers of science can help affirm the methodological legitimacy of theology. However, it is important to note that science itself is facing its own set of problems. There is a decline in interest and job satisfaction among scientists, a growing gap between science and the humanities, a crisis of conceptual understanding, and a perceived lack of meaning and purpose. In this context, I propose that theology and philosophy can play a crucial role in addressing these issues. In particular, theology can offer a supportive environment for discussing meaning, values, and the ultimate questions of human existence. Philosophy, on the other hand, can help bridge the gap between science and the humanities, fostering interdisciplinary dialogue and a more holistic understanding of our world.

Max Jammer claimed that, "There can be no doubt that the Danish precursor of modern existentialism and neo-orthodox theology, Soren Kierkegaard, through his influence on Bohr, affected also the course of modern physics to some extent." Despite Jammer's failure to supply sufficient evidence for this claim, I argue that it is not completely off base. In particular, I argue that Kierkegaard and Bohr belong to a common philosophical tradition, and I begin to investigate some of the themes that characterize this tradition.

Kierkegaard's Either-Or is a book about the choice between aesthetic, ethical, and religious approaches to life. I show that Either-Or also contains a proposal for philosophy of science, and in particular, about the ideal epistemic state for human beings. Whereas the Cartesian-Hegelian tradition conceived of the ideal state as one of detached deliberation -- i.e. "seeing the world as it is in itself" -- Kierkegaard envisions the ideal state as the achievement of equilibrium between the "spectator" and "actor" aspects of the human being. Kierkegaard's proposal thus sets the stage for Niels Bohr's "epistemological lesson of quantum mechanics".

I argue against the claim -- advocated by Albert Einstein, Bernard Williams, and Ted Sider, among others -- that a description is objective only if it says how the world is in itself. Instead, I argue for the claim -- inspired by comments of Niels Bohr -- that a family of descriptions is objective only if they co-vary with their respective descriptive contexts. Moreover, I claim that "there is a shared objective reality" simply means that it is possible to satisfy this kind of covariance requirement.

How Logic Works is an introductory logic textbook that is different by design. Rather than teaching elementary symbolic logic as an abstract or rote mathematical exercise divorced from ordinary thinking, Hans Halvorson presents it as the skill of clear and rigorous reasoning, which is essential in all fields and walks of life, from the sciences to the humanities—anywhere that making good arguments, and spotting bad ones, is critical to success. Instead of teaching how to apply algorithms using “truth trees,” as in the vast majority of logic textbooks, How Logic Works builds on and reinforces the innate human skills of making and evaluating arguments. It does this by introducing the methods of natural deduction, an approach that teaches students not only how to carry out a proof and solve a problem but also what the principles of valid reasoning are and how they can be applied to any subject. The book also allows students to transition smoothly to more advanced topics in logic by teaching them general techniques that apply to more complicated scenarios, such as how to formulate theories about specific subject matter. How Logic Works shows that formal logic—far from being only for mathematicians or a diversion from the really deep questions of philosophy and human life—is the best account we have of what it means to be rational. By teaching logic in a way that makes students aware of how they already use it, the book will help them to become even better thinkers. A concise, readable, and user-friendly introduction to elementary symbolic logic that primarily uses natural deduction rather than algorithmic “truth trees” Draws on more than two decades’ experience teaching introductory logic to undergraduates Provides a stepping stone to more advanced topics

No scientific theory has caused more puzzlement and confusion than quantum theory. Physics is supposed to help us to understand the world, but quantum theory makes it seem a very strange place. This book is about how mathematical innovation can help us gain deeper insight into the structure of the physical world. Chapters by top researchers in the mathematical foundations of physics explore new ideas, especially novel mathematical concepts, at the cutting edge of future physics. These creative developments in mathematics may catalyze the advances that enable us to understand our current physical theories, especially quantum theory. The authors bring diverse perspectives, unified only by the attempt to introduce fresh concepts that will open up new vistas in our understanding of future physics.

Here is a fresh look at how science contributes to the bigger picture of human flourishing, through a collage of science and philosophy, richly illustrated by the authors' own experience and personal reflection. They survey the territory of fundamental physics, machine learning, philosophy of human identity, evolutionary biology, miracles, arguments from design, naturalism, the history of ideas, and more. The natural world can be appreciated not only for itself, but also as an eloquent gesture, a narrative and a pointer beyond itself. Our human journey is not to a theorem or a treatise, but to a meeting which encompasses all our capacities. In this meeting, science is the way to find out about the structure of the physical world of which we are a part, not a means to reduce ourselves and our fellow human beings to mere objects of scrutiny, and still less to attempt the utterly futile exercise of trying to do that to God. We have intellectual permission to be open to the notion that God can be trusted and known. The material world encourages an open-hearted reaching out to something more, with a freedom to seek and to be received by what lies beyond the scope of purely impersonal descriptions and attitudes.

Quine often argued for a simple, untyped system of logic rather than the typed systems that were championed by Russell and Carnap, among others. He claimed that nothing important would be lost by eliminating sorts, and the result would be additional simplicity and elegance. In support of this claim, Quine conjectured that every many-sorted theory is equivalent to a single-sorted theory. We make this conjecture precise, and prove that it is true, at least according to one reasonable notion of theoretical equivalence. Our clarification of Quine’s conjecture, however, exposes the shortcomings of his argument against many-sorted logic

This volume gathers together ground-breaking work on the foundations and philosophy of quantum physics, by one of the most brilliant and productive researchers in the field. Rob Clifton died tragically in 2002 at the age of 38; two of his colleagues, themselves leading philosophers of physics, present fourteen of his finest papers here, all of which combine exciting philosophical discussion with rigorous mathematical results. Quantum Entanglements offers inspiration and substantial reward to anyone working on the foundations of quantum theory, with backgrounds in philosophy, physics, or mathematics.

Major figures of twentieth-century philosophy were enthralled by the revolution in formal logic, and many of their arguments are based on novel mathematical discoveries. Hilary Putnam claimed that the Löwenheim-Skølem theorem refutes the existence of an objective, observer-independent world; Bas van Fraassen claimed that arguments against empiricism in philosophy of science are ineffective against a semantic approach to scientific theories; W. V. O. Quine claimed that the distinction between analytic and synthetic truths is trivialized by the fact that any theory can be reduced to one in which all truths are analytic. This book dissects these and other arguments through in-depth investigation of the mathematical facts undergirding them. It presents a systematic, mathematically rigorous account of the key notions arising from such debates, including theory, equivalence, translation, reduction, and model. The result is a far-reaching reconceptualization of the role of formal methods in answering philosophical questions.

The Univalent Foundations of mathematics take the point of view that all of mathematics can be encoded in terms of spatial notions like "point" and "path". We will argue that this new point of view has important implications for philosophy, and especially for those parts of analytic philosophy that take set theory and first-order logic as their benchmark of rigor. To do so, we will explore the connection between foundations and philosophy, outline what is distinctive about the logic of the Univalent Foundations, and then describe new philosophical theses one can express in terms of this new logic.