Absolutely No Free Lunches!

This paper is concerned with learners who aim to learn patterns in infinite binary sequences: shown longer and longer initial segments of a binary sequence, they either attempt to predict whether the next bit will be a 0 or will be a 1 or they issue forecast probabilities for these events. Several variants of this problem are considered. In each case, a no-free-lunch result of the following form is established: the problem of learning is a formidably difficult one, in that no matter what method is pursued, failure is incomparably more common that success; and difficult choices must be faced in choosing a method of learning, since no approach dominates all others in its range of success. In the simplest case, the comparison of the set of situations in which a method fails and the set of situations in which it succeeds is a matter of cardinality (countable vs. uncountable); in other cases, it is a topological matter (meagre vs. co-meagre) or a hybrid computational-topological matter (effectively meagre vs. effectively co-meagre)

Transcendental Idealism among the Jersey Metaphysicians

A discussion van Fraassen's book Scientific Representation: Paradoxes of Perspective that focuses on his account of time as a logical space and on his attitudes towards metaphysics

Sober as a Judge

In Ockham's Razors: A User's Guide, argues that parsimony considerations are epistemically relevant on the grounds that certain methods of model selection, such as the Akaike Information Criterion, exhibit good asymptotic behaviour and take the number of adjustable parameters in a model into account. I raise some worries about this form of argument

Symmetry and Equivalence

This paper is concerned with the relation between two notions: that of two solutions or models of a theory being related by a symmetry of the theory and that of solutions or models being physically equivalent (in the sense of being equally well- or ill-suited to represent any given situation, relative to any reasonable interpretation). A number of authors have recently discussed this relation, some taking an optimistic view, on which there is a suitable concept of the symmetry of a theory relative to which these two notions coincide, others taking a pessimistic view, on which there is no such concept. The present paper arrives at a cautiously pessimistic conclusion

Objectivity and Bias

The twin goals of this essay are: to investigate a family of cases in which the goal of guaranteed convergence to the truth is beyond our reach; and to argue that each of three strands prominent in contemporary epistemological thought has undesirable consequences when confronted with the existence of such problems. Approaches that follow Reichenbach in taking guaranteed convergence to the truth to be the characteristic virtue of good methods face a vicious closure problem. Approaches on which there is a unique rational doxastic response to any given body of evidence can avoid incoherence only by rendering epistemology a curiously limited enterprise. Bayesian approaches rule out humility about one’s prospects of success in certain situations in which failure is typical

Curve-Fitting for Bayesians?

Bayesians often assume, suppose, or conjecture that for any reasonable explication of the notion of simplicity a prior can be designed that will enforce a preference for hypotheses simpler in just that sense. But it is shown here that there are simplicity-driven approaches to curve-fitting problems that cannot be captured within the orthodox Bayesian framework

Sober as a Judge

In Ockham's Razors: A User's Guide, argues that parsimony considerations are epistemically relevant on the grounds that certain methods of model selection, such as the Akaike Information Criterion, exhibit good asymptotic behaviour and take the number of adjustable parameters in a model into account. I raise some worries about this form of argument

Down to Earth Underdetermination

There are many parts of science in which a certain sort of underdetermination of theory by evidence is known to be common. It is argued that reflection on this fact should serve to shift the burden of proof from scientific anti-realists to scientific realists at a crucial point in the debate between them

Transcendental Idealism among the Jersey Metaphysicians

A discussion van Fraassen's book Scientific Representation: Paradoxes of Perspective that focuses on his account of time as a logical space and on his attitudes towards metaphysics

Curve-Fitting for Bayesians?

Bayesians often assume, suppose, or conjecture that for any reasonable explication of the notion of simplicity a prior can be designed that will enforce a preference for hypotheses simpler in just that sense. But it is shown here that there are simplicity-driven approaches to curve-fitting problems that cannot be captured within the orthodox Bayesian framework