Publications by Type: Book Chapters

Lotem Elber-Dorozko and Oron Shagrir. 2018. “Computation and Levels in the Cognitive and Neural Sciences.” In Routledge Handbook of the Computational Mind, edited by Matteo Colombo and Mark Sprevak, Pp. 205-222. Routledege.
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Jack Copeland, Oron Shagrir, and Mark Sprevak. 2018. “Zuse's Thesis, Gandy's Thesis, and Penrose's Thesis.” In Computational Perspectives on Physics, Physical Perspectives on Computation, edited by Michael Cuffaro and Sam Fletcher, Pp. 39-59. Cambridge University Press. Abstract

Computer pioneer Konrad Zuse (1910-1995) built the world's first working programcontrolled general-purpose digital computer in Berlin in 1941. After the Second World War he supplied Europe with cheap relay-based computers, and later transistorized computers. Mathematical logician Robin Gandy (1919-1995) proved a number of major results in recursion theory and set theory. He was Alan Turing's only PhD student. Mathematician Roger Penrose (1931- ) is famous for his work with Stephen Hawking. What we call Zuse's thesis, Gandy's thesis, and Penrose's thesis are three fundamental theses concerning computation and physics. Zuse hypothesized that the physical universe is a computer. Gandy offered a profound analysis supporting the thesis that every discrete deterministic physical assembly is computable (assuming that there is an upper bound on the speed of propagation of effects and signals, and a lower bound on the dimensions of an assembly's components). Penrose argued that the physical universe is in part uncomputable. We explore these three theses. Zuse's thesis we believe to be false: the universe might have consisted of nothing but a giant computer, but in fact does not. Gandy viewed his claim as a relatively apriori one, provable on the basis of a set-theoretic argument that makes only very general physical assumptions about decomposability into parts and the nature of causation. We maintain that Gandy's argument does not work, and that Gandy's thesis is best viewed, like Penrose's, as an open empirical hypothesis.

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Oron Shagrir and William Bechtel. 2017. “Marr's Computational-Level Theories and Delineating Phenomena.” In Integrating Psychology and Neuroscience: Prospects and Problems, edited by David Kaplan, Pp. 190-214. Oxford University Press. Abstract

A key component of scientific inquiry, especially inquiry devoted to developing mechanistic explanations, is delineating the phenomenon to be explained. The task of delineating phenomena, however, has not been sufficiently analyzed, even by the new mechanistic philosophers of science. We contend that Marr’s characterization of what he called the computational level (CL) provides a valuable resource for understanding what is involved in delineating phenomena. Unfortunately, the distinctive feature of Marr’s computational level, his dual emphasis on both what is computed and why it is computed, has not been appreciated in philosophical discussions of Marr. Accordingly we offer a distinctive account of CL. This then allows us to develop two important points about delineating phenomena. First, the accounts of phenomena that figure in explanatory practice are typically not qualitative but precise, formal or mathematical, representations. Second, delineating phenomena requires consideration of the demands the environment places on the mechanism—identifying, as Marr put it, the basis of the computed function in the world. As valuable as Marr’s account of CL is in characterizing phenomena, we contend that ultimately he did not go far enough. Determining the relevant demands of the environment on the mechanism often requires detailed empirical investigation. Moreover, often phenomena are reconstituted in the course of inquiry on the mechanism itself.

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Jack Copeland, Mark Sprevak, and Oron Shagrir. 2017. “Is the Universe Computational?.” In The Turing Guide, edited by Jonathan Bowen, Jack Copeland, Mark Sprevak, and Robin Wilson, Pp. 445-462. Oxford University Press. Abstract


The theory that the whole universe is a computer is a bold and striking one. It is a theory of everything: the entire universe is to be understood, fundamentally, in terms of the universal computing machine that Alan Turing introduced in 1936. We distinguish between two versions of this grand-scale theory and explain what the universe would have to be like for one or both versions to be true. Spoiler: the question is in fact wide open – at the present stage of science, nobody knows whether it's true or false that the whole universe is a computer. But the issues are as fascinating as they are important, so it's certainly worthwhile discussing them. 


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Oron Shagrir. 2016. “Advertisement for the Philosophy of the Computational Sciences.” In The Oxford Handbook of Philosophy of Science, edited by Paul Humphreys, Pp. 15-42. Oxford University Press. Abstract

This chapter deals with those fields that study computing systems. Among these computational sciences are computer science, computational cognitive science, computational neuroscience, and artificial intelligence. In the first part of the chapter, it is shown that there are varieties of computation, such as human computation, algorithmic machine computation, and physical computation. There are even varieties of versions of the Church-Turing thesis. The conclusion is that different computational sciences are often about different kinds of computation. The second part of the chapter discusses three specific philosophical issues. One is whether computers are natural kinds. Another issue is the nature of computational theories and explanations. The last section of the chapter relates remarkable results in computational complexity theory to problems of verification and confirmation.

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Oron Shagrir. 2014. “Putnam and Computational Functionalism.” In Key Thinkers in Philosophy of Mind, edited by Andrew Bailey, Pp. 147-168. Continuum Press.
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Jack Copeland, Carl Posy, and Oron Shagrir. 2013. “The Revolutions of the 1930s.” In Computability: Turing, Gödel, Church, and Beyond, Pp. vii-x. MIT Press.
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Oron Shagrir and Vera Hoffmann-Kolss. 2013. “Supervenience.” In Encyclopedia of Philosophy and the Social Sciences, edited by Byron Kaldis, 18: Pp. 970-975. SAGE Publications.
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Oron Shagrir and Jack Copeland. 2013. “Turing versus Gödel on Computability and the Mind.” In Computability: Turing, Gödel, Church, and Beyond, Pp. 1-33. MIT Press.
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Oron Shagrir. 2011. “Towards a Modeling View of Computing.” In Information and Computation: Essays on Scientific and Philosophical Understanding of Foundations of Information and Computation, edited by Gordana Dodig-Crnkovic and Mark Burgin, Pp. 381-391. World Scientific Publishing.
Oron Shagrir. 2010. “Davidson's Notion of Supervenience.” In Hues of Philosophy – Essays in Memory of Ruth Manor, edited by Anat Biletzki, Pp. 43-58. London: College Publications.
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Oron Shagrir. 2008. “Davidson on Supervenience.” In Reduction and Elimination in Philosophy and the Sciences (Papers of the 31st International Wittgenstein Symposium), edited by Alexander Hieke and Hannes Leitgeb, Pp. 318-320. Austrian Ludwig Wittgenstein Society. Abstract

Donald Davidson introduces supervenience to the philosophy of mind in his "Mental Events". Curiously, however, there has been little effort to explicate what Davidson means by supervenience. My aim here is to explicate the passages where Davidson discusses supervenience, and to point out that his notion of supervenience is very different from the one assumed in contemporary philosophy of mind.

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Oron Shagrir. 2006. “Gödel on Turing on Computability.” In Church's Thesis after 70 years, edited by Adam Olszewski, Jan Wolenski, and Robert Janusz, Pp. 393-419. Ontos-Verlag.
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Oron Shagrir. 2005. “Accelerating Turing Machines.” In Time and History (Papers of the 28th International Wittgenstein Symposium), edited by Friedrich Stadler and Michael Stöltzner, Pp. 276-278. Austrian Ludwig Wittgenstein Society. Abstract

An accelerating Turing machine, as the name suggests, is a Turing machine that performs its tasks in an accelerated fashion. For example, it completes the first operation in one moment, the second in 1/2 of a moment, the third in 1/4 of a moment, and so on. As such, it can perform supertasks, namely, complete infinitely many computation steps in a finite span of time. Jack Copeland has recently argued that, by performing supertasks, accelerating Turing machines can compute functions, such as the halting function, that no standard, "non-accelerating", Turing machine can handle. However, my claim is, to the contrary, that accelerating Turing machines have the same computational power as the non-accelerating machines, and that none solves the halting problem.

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Oron Shagrir. 2005. “The Rise and Fall of Computational Functionalism.” In Contemporary Philosophy in Focus: Hilary Putnam, edited by Yemima Ben Menahem, Pp. 220-250. Cambridge University Press.
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