**NEW TITLE: ****A Dozen Philosophical No-Go Theorems**

**Prerequisites**

Graduate Standing and Consent of Graduate Advisor or instructor required.

**Course Description**

A Dozen Philosophical No-Go Theorems

Philosophical progress is often driven (and sometimes frustrated), by *no-go* or *impossibility* theorems showing that some pre-theoretically desirable situation cannot be obtained. The grandparent of all no-go theorems is perhaps the Liar paradox, or its formal realization in Tarski’s Undefinability Theorem, showing that a truth predicate with certain features can’t be obtained. In this seminar we will consider twelve philosophically important no-go theorems. One of the goals is simply to become familiar with the various theorems (some of which have been greatly underappreciated in the philosophical literature) and to think about both what escape routes might be available and what alternative paths might be explored if the no-go barrier survives testing. Another goal is to consider some common structural elements, themes, and philosophical sources that may underlie many of the no-go theorems collectively. (The genetic stamp of the Liar ancestor can be seen in several cases.) Finally, we’ll engage in some metaphilosophical reflection on the question of whether the very idea of a no-go theorem is philosophically applicable and philosophically profitable.

The planned list of no-go theorems is (with a very brief statement of each):

(1) Tarski’s undefinability theorem (a language cannot contain its own truth predicate)

(2) Godel’s first and second incompleteness theorem (a sufficiently rich theory must be incomplete and cannot prove its own completeness)

(3) Arrow’s theorem (a fair voting system inevitably creates a dictatorship)

(4) Lewis triviality theorem (a language assigning probabilities to conditionals must assign only probabilities of 0 and 1)

(5) Kaplan-Prior theorem (propositions cannot be modelled using possible worlds)

(6) Bell’s theorem (quantum behavior cannot be explained using hidden variables)

(7) Gardenfors’ triviality theorem (conditionals make belief change impossible)

(8) Arrhenius’ theorem (any population-level axiology is sadistic)

(9) Probabilistic gap theorem (no probability function assigning probabilities to all propositions)

(10) Gibbard-Satterthwaite theorem (dictatorship is the only non-manipulable social choice procedure)

(11) Third-order reflection theorem (certain natural reflection principles make set theory inconsistent when extended to a natural point)

(12) Williamson’s luminosity theorem (there can’t be a logical guarantee of introspective knowledge)

**Grading Policy**

Grade based on final seminar paper and class participation.

**Texts**

Various readings made available in the class.