If You Can't Change What You Believe, You Don't Believe It

I develop and defend the view that subjects are necessarily psychologically able to revise their beliefs in response to relevant counter-evidence. Specifically, subjects can revise their beliefs in response to relevant counter-evidence, given their current psychological mechanisms and skills. If a subject lacks this ability, then the mental state in question is not a belief, though it may be some other kind of cognitive attitude, such as a supposi-tion, an entertained thought, or a pretense. The result is a moderately revisionary view of belief: while most mental states we thought were beliefs are beliefs, some mental states which we thought were beliefs are not beliefs. The argument for this view draws on two key claims: First, subjects are rationally obligated to revise their beliefs in response to relevant counter-evidence. Second, if some subject is rationally obligated to revise one of her mental states, then that subject can revise that mental state, given her current psychological mechanisms and skills. Along the way to defending these claims, I argue that rational obligations can govern activities which reflect on one’s rational character, whether or not those activities are under one’s voluntary control. I also show how the relevant version of epistemic ‘ought’ implies ‘can’ survives an objection which plagues other variants of the principle

Proper Analytic Free Maps

This paper concerns analytic free maps. These maps are free analogs of classical analytic functions in several complex variables, and are defined in terms of non-commuting variables amongst which there are no relations - they are free variables. Analytic free maps include vector-valued polynomials in free (non-commuting) variables and form a canonical class of mappings from one non-commutative domain D in say g variables to another non-commutative domain D' in g' variables. As a natural extension of the usual notion, an analytic free map is proper if it maps the boundary of D into the boundary of D'. Assuming that both domains contain 0, we show that if f:D->D' is a proper analytic free map, and f(0)=0, then f is one-to-one. Moreover, if also g=g', then f is invertible and f^(-1) is also an analytic free map. These conclusions on the map f are the strongest possible without additional assumptions on the domains D and D'.Comment: 17 pages, final version. To appear in the Journal of Functional Analysi

Visually Perceiving the Intentions of Others

I argue that we sometimes visually perceive the intentions of others. Just as we can see something as blue or as moving to the left, so too can we see someone as intending to evade detection or as aiming to traverse a physical obstacle. I consider the typical subject presented with the Heider and Simmel movie, a widely studied ‘animacy’ stimulus, and I argue that this subject mentally attributes proximal intentions to some of the objects in the movie. I further argue that these attributions are unrevisable in a certain sense and that this result can be used to as part of an argument that these attributions are not post-perceptual thoughts. Finally, I suggest that if these attributions are visual experiences, and more particularly visual illusions, their unrevisability can be satisfyingly explained, by appealing to the mechanisms which underlie visual illusions more generally

Recent Issues in High-Level Perception

Recently, several theorists have proposed that we can perceive a range of high-level features, including natural kind features (e.g., being a lemur), artifactual features (e.g., being a mandolin), and the emotional features of others (e.g., being surprised). I clarify the claim that we perceive high-level features and suggest one overlooked reason this claim matters: it would dramatically expand the range of actions perception-based theories of action might explain. I then describe the influential phenomenal contrast method of arguing for high-level perception and discuss some of the objections that have been raised against this strategy. Finally, I describe two emerging defenses of high-level perception, one of which appeals to a certain class of perceptual deficits and one of which appeals to adaptation effects. I sketch a challenge for the latter approach

Semidefinite programming in matrix unknowns which are dimension free

One of the main applications of semidefinite programming lies in linear systems and control theory. Many problems in this subject, certainly the textbook classics, have matrices as variables, and the formulas naturally contain non-commutative polynomials in matrices. These polynomials depend only on the system layout and do not change with the size of the matrices involved, hence such problems are called "dimension-free". Analyzing dimension-free problems has led to the development recently of a non-commutative (nc) real algebraic geometry (RAG) which, when combined with convexity, produces dimension-free Semidefinite Programming. This article surveys what is known about convexity in the non-commutative setting and nc SDP and includes a brief survey of nc RAG. Typically, the qualitative properties of the non-commutative case are much cleaner than those of their scalar counterparts - variables in R^g. Indeed we describe how relaxation of scalar variables by matrix variables in several natural situations results in a beautiful structure.Comment: 25 pages; surve

Non-commutative polynomials with convex level slices

Let a and x denote tuples of (jointly) freely noncommuting variables. A square matrix valued polynomial p in these variables is naturally evaluated at a tuple (A,X) of symmetric matrices with the result p(A,X) a square matrix. The polynomial p is symmetric if it takes symmetric values. Under natural irreducibility assumptions and other mild hypothesis, the article gives an algebraic certificate for symmetric polynomials p with the property that for sufficiently many tuples A, the set of those tuples X such that p(A,X) is positive definite is convex. In particular, p has degree at most two in x. The case of noncommutative quasi-convex polynomials is of particular interest. The problem analysed here occurs in linear system engineering problems. There the A tuple corresponds to the parameters describing a system one wishes to control while the X tuple corresponds to the parameters one seeks in designing the controller. In this setting convexity is typically desired for numerical reasons and to guarantee that local optima are in fact global. Further motivation comes from the theories of matrix convexity and operator systems