Topics in Recent and Contemporary Philosophy:
Computation and Mind

PHI 513, Fall 2005. Professor: Adam Elga (follow link for contact information, office hour). Class meets 2:30-5:20 Mondays, in Marx Hall 201. Not open to undergraduates.

What is it for a hunk of physical stuff to instantiate a particular computer architecture? Which computing architectures, if any, do human brains instantiate? Does externalism from the philosophy of mind infect the analysis of computation? Does running a particular sort of computer program suffice for having conscious experience? Do our physical laws permit the computation of non-Turing-computable functions? Can the intuitive notion of computability be analyzed? Do results in metamathematics show that human insight cannot be implemented mechanically? Does understanding the human mind as a computer help address the problem of logical omniscience and Kripke's skeptical rule-following paradox?

Note: an excellent complement to this seminar would be PHI 312 Intermediate Logic, which is also offered Fall 2005. To be comfortable in PHI 513, one should either have some background in logic or computer science or attend PHI 312 concurrently. (In the latter case, no previous technical background is required.)

Guests discussion-leaders will include Agustín Rayo, Paul Benacerraf, Colin Klein, and Andy Egan.

Term papers will be due at 4pm on Tuesday January 17.


To access the readings (all available electronically, as linked below), you will need a userid (the userid is "guest") and a password (announced in class). If you would like to preview some of the readings, please email

Session outline

Note: in many cases, only a subsection of the linked reading is required. In those cases, the required page range is listed to the right of the reading.

Introduction, Turing machines

Mon Sep 19

Boolos, Burgess, Jeffrey. Computability and Logic. Chapter 3. 23-27

Boolos, Burgess, Jeffrey. Computability and Logic. Chapter 4. 35-40

Turing. On computable numbers with an application to the entscheidungsproblem In collection edited by M. Davis. 117-118, 135-138.

Is everything a Turing machine?

Mon Sep 26

Searle. Is the brain a digital computer?

Chalmers. The Conscious Mind. Chapter 9: Strong artificial intelligence 315-320

Brown. Implementation and indeterminacy.

Optional: Copeland. What is computation?

The Church-Turing thesis

Mon Oct 03

Homework on arithmetization

Copeland and Sylvan. Beyond the universal Turing machine.

Rescorla. Church's Thesis and the Conceptual Analysis of Computability. (Manuscript. Please ask permission of author before citing in published work.)

Optional: Stanford Encyc. Entry: Church-Turing Thesis.

Optional: Shapiro. Acceptable Notation.

Optional: Copeland. Narrow versus wide mechanism.

Optional: Gandy Church's Thesis and principles for mechanisms.


Mon Oct 10

Kripke. Wittgenstein on rules and private language. Chapter 2: The Wittgenstinian paradox. 7-39

Chomsky. Knowledge of language. Chapter 4: Questions about rules. 223-243

Optional: Lewis. Radical interpretation.

Rule-following and functionalism / Physical models of super-Turing computation

Mon Oct 17

Lewis. Radical interpretation.

Pitowsky The physical Church thesis and physical computational complexity.

Optional: Moore. Unpredictability and undecidability in dynamical systems.

Optional: Davies. Building infinite machines.

Optional: Earman and Norton. Forever is a day: supertasks in Pitowsky and Malament-Hogarth spacetimes.

Second incompleteness theorem prep

Mon Oct 24

Boolos. Godel's second incompletness theorem explained in words of one syllable.

Penrose. Shadows of the mind, chapters 2 and 3

Chalmers. Review of "Shadows of the Mind"

Godel, Lucas and mechanism

Mon Nov 07

Guest: Paul Benacerraf, Princeton University

Godel (readings/with introduction by Boolos). Some basic theorems on the foundations of mathematics and their implications. 292-295,304-311

Lucas. Minds, machines, and Godel.

Benacerraf. God, the devil, and Godel.. Sections I-III (pp. 9-23)

Boolos. Review of "Minds, machines and Godel" and "God, the devil, and Godel".

Computation and Externalism

Mon Nov 14

We will finish up the Moore construction, and then discuss the Peacocke article below.

Peacocke. Content, Computation, and Externalism

Mathematical commitment / probabilistic mathematical knowledge

Mon Nov 21

Guest: Agustín Rayo, MIT

Optional: Section 1 of: Rayo. Commitment in mathematics. Manuscript. Please ask permission of author before citing in published work.)

Functionalism, computationalism

Mon Nov 28

Guest: Colin Klein, Princeton University

Maudlin. Computation and consciousness.

Klein. Functions as dispositions

Logical omnsicience

Mon Dec 05

Guest: Andy Egan, University of Michigan

Chihara. Some problems for Bayesian confirmation theory..

Stalnaker. The problem of logical omniscience I.

Optional: Stalnaker. The problem of logical omniscience II.

Fragmentation overflow / computational limitations and rationality

Mon Dec 12

You needn't read anything in advance for this meeting.

Other readings


Chalmers. Review of "Shadows of the Mind"

Turing. Systems of logic based on ordinals

Earman. Primer on Determinism. Chapters 6, 9.

Boolos, Burgess, Jeffrey. Computability and Logic. Chapter 17.

Boolos, Burgess, Jeffrey. Computability and Logic. Chapter 18.

Siegelmann and Sontag. Analog computation via neural networks.

Copeland. Turing's O-machines, Searle, Penrose, and the brain.

Fallis. The epistemic status of probabilistic proofs.

Earman. Primer on Determinism. Chapter 8: Determinism, randomness, and chaos

Bennett. Logical reversibility of computation

Fallis. The reliability of randomized algorithms.

Goodman. Fact, fiction and forecast. Chapter 3: The new riddle of induction.

Shoemaker. On projecting the unprojectible.