Alistair Isaac

Taking mistakes seriously: equivalence notions for game scenarios with off equilibrium play

This paper investigates strategies for responding rationally to opponents who make mistakes. We identify two distinct interpretations of mistakes in the game theory literature: trembling hand and risk averse mistakes. We introduce the concept of an EFG Scenario, a game plus strategy profile, in order to probe the properties of these different types of mistake. An analysis of equivalence preserving transformations over EFG Scenarios reveals that risk averse mistakes are a form of rational play, while trembling hand mistakes are equivalent to moves by nature.

Logic and Complexity in Cognitive Science

This chapter surveys the use of logic and computational complexity theory in cognitive science. We emphasize in particular the role played by logic in bridging the gaps between Marr’s three levels: representation theorems for non-monotonic logics resolve algorithmic/implementation debates, while complexity theory probes the relationship between computational task analysis and algorithms. We argue that the computational perspective allows feedback from empirical results to guide the development of increasingly subtle computational models. We defend this perspective via a survey of the role of logic in several classic problems in cognitive science (the Wason selection task, the frame problem, the connectionism/symbolic systems debate) before looking in more detail at case studies involving quantifier processing and social cognition. In these examples, models developed by Johan van Benthem have been supplemented with complexity analysis to drive successful programs of empirical research.

Objective Similarity and Mental Representation

The claim that similarity plays a role in representation has been philosophically discredited. Psychologists, however, routinely analyse the success of mental representations for guiding behaviour in terms of a similarity between representation and the world. I provide a foundation for this practice by developing a philosophically responsible account of the relationship between similarity and representation in natural systems. I analyse similarity in terms of the existence of a suitable homomorphism between two structures. The key insight is that by restricting attention to only those homomorphisms induced by causal processes, we can solve two philosophical problems with a single assumption. First, causal structure provides an adequate source for the bias required to ensure the similarity relation is non-trivial; second, it provides an adequate source for the directionality required to move from similarity to representation. I defend this account against objections by Goodman and van Fraassen and demonstrate that it is indeed the account of similaritys role in representation assumed by psychological practice.

Mindreading deception in dialog

This paper considers the problem of detecting deceptive agents in a conversational context. We argue that distinguishing between types of deception is required to generate successful action. This consideration motivates a novel taxonomy of deceptive and ignorant mental states, emphasizing the importance of an ulterior motive when classifying deceptive agents. After illustrating this taxonomy with a sequence of examples, we introduce a Framework for Identifying Deceptive Entities (FIDE) and demonstrate that FIDE has the representational power to distinguish between the members of our taxonomy. We conclude with some conjectures about how FIDE could be used for inference.

Modeling without representation

How can mathematical models which represent the causal structure of the world incompletely or incorrectly have any scientific value? I argue that this apparent puzzle is an artifact of a realist emphasis on representation in the philosophy of modeling. I offer an alternative, pragmatic methodology of modeling, inspired by classic papers by modelers themselves. The crux of the view is that models developed for purposes other than explanation may be justified without reference to their representational properties.

Synchronizing Diachronic Uncertainty

Diachronic uncertainty, uncertainty about where an agent falls in time, poses interesting conceptual difficulties. Although the agent is uncertain about where she falls in time, this uncertainty can only obtain at a particular moment in time. We resolve this conceptual tension by providing a transformation from models with diachronic uncertainty relations into “equivalent” models with only synchronic uncertainty relations. The former are interpreted as capturing the causal structure of a situation, while the latter are interpreted as capturing its epistemic structure. The models are equivalent in the sense that agents pass through the same information sets in the same order, In this paper, we investigate how such a transformation may be used to define an appropriate notion of equivalence, which we call epistemic equivalence. Although our project is motivated by problems which have arisen in a variety of disciplines, especially philosophy and game theory, our formal development takes place within the general and flexible framework provided by epistemic temporal logic.

Quantifying the subjective: Psychophysics and the geometry of color

Early psychophysical methods as codified by Fechner motivate the development of quantitative theories of subjective experience. The basic insight is that just noticeable differences between experiences can serve as units for measuring a sensory domain. However, the methods described by Fechner tacitly assume that the experiences being investigated can be linearly ordered. This assumption is not true for all sensory domains; for example, there is no trivial linear order over all possible color sensations. This paper discusses key developments in the history of psychophysical methods for measuring color experience. In particular, a clear distinction between topological and metrical structure allowed Helmholtz to use opponent colors as a standard for measuring the gross structure of color space. Once this gross structure had been determined, lines through color space could be defined and Fechner-style methods employed for determining local structure. Extensions of these methods due to Wright, MacAdam, and others provide detailed evidence for the degree of agreement in the qualities of color experience across individuals. This allows a precise statement of the evidential support for the claim that your experience of color and mine are the same.

Prospects for Naturalizing Color

Paul Churchland has recently offered a novel argument for the “objective reality” of color. The strategy he employs to make this argument is an instance of a more general research program for interpreting perceptual content, “domain‐portrayal semantics.” In the first half of the article, I point out some features of color vision that complicate Churchlands conclusion, in particular, the context‐sensitive and inferential nature of color perception. In the second half, I examine and defend the general research program, concluding it is naturalistic in a minimal sense and should be of interest to naturalists and nonnaturalists alike.