# Logic and Decision Theory

**Professor Mark Colyvan**

Department of Philosophy

phone: +61 2 9036 6175

fax: +61 2 9351 3918

Room N285

A14 - Quadrangle

The University of Sydney

NSW 2006 Australia

Homepage

### About Decision Theory

Decision theory is the formal theory of how individuals and groups make decisions. The decision theory research group in the Sydney Centre for the Foundations of Science work on both the philosophical issues in the abstract theory itself but also on the applications of this theory in various real-world scenarios. The latter include legal decisions, conservation biology and environmental management.

### Logic and Decision Theory Research Cluster

The Decision theory research cluster in the SCFS investigates the philosophical and mathematical foundations of the theory of rational choice. This work includes decisions made by individuals and by groups, and thus includes work in decision theory, game theory, social choice theory and consensus theory.

### Research projects

**Mathematical Explanation** (Australian Research Council Funded)

Project Leader: Mark Colyvan

The best mathematical proofs tell us why some mathematical fact holds, not simply that it holds. But to understand how one piece of mathematics explains another piece of mathematics is poorly understood. Mathematics may also be involved in explaining facts outside mathematics. Examples include empirical phenomenon such as the existence of certain weather patters, the shape of the cells in bee hives, and the impossibility of certain population cycles in ecology. This project will advance a new theory of mathematical explanation, for both internal mathematical purposes and for extra-mathematical explanations. Applications to conservation biology and conservation management will be developed.**Mathematical Notation: A Philosophical Account** (Australian Research Council Funded)

Project Leader: Mark Colyvan

This project will provide a philosophical account of mathematical notation and thus make sense of the idea of mathematics as the language of science. The project will show how mathematical notation can lead to new mathematical discoveries and enable explanations. It will also investigate the role of mathematical notation in facilitating connections across different branches of science. The project will thus make significant contributions to our philosophical understanding of both pure and applied mathematics. It will shed light on the variety of roles mathematical notation plays in our scientific and mathematical theorising.**Group Decision Methods** (Department of Agriculture, Fisheries, and Forestry Funded)

Project Leader: Mark Colyvan

The objectives of this project are to: review formal ‘consensus’ methods in the existing literature; consider the properties of these methods from a more pragmatic standpoint than is usually considered; and determine where the methods fit into the larger decision-making framework, using a pertinent problem in plant pest management as a case study. The idea is to develop guidelines for choosing a formal model that offers a repeatable, transparent, reliable and understandable basis for resolving group disagreement over various issues in a larger decision problem in biosecurity settings. **Formal Approaches to Social Epistemology** (Dutch Science Foundation Funded)

Project Leader: Mark Colyvan

Social Epistemology is a new research field that systematically explores social aspects of the acquisition and justification of knowledge. The work on this project focusses on consensus models and questions regarding the aggregation of judgments and on preference change.The project has repercussions for social decision-making, especially for environmental management. **Ethics and Formal Theories of Decision** (Australian Research Council Funded)

Project Leader: Mark Colyvan

This project aims to reconcile ethics with formal decision theory. This will be achieved by developing a theory of formal constraints on the utility functions employed in decision theory. The resulting formal framework will have significant applications in many ethically-charged decision environments, such as legal decision making and conservation management. The project will enable decision makers in these areas to accommodate ethical concerns into the formal process of decision. It will also allow ethical decisions in situations where there is uncertainty about either the relevant outcomes or the situation itself.**Vagueness in Language and Objects: A Logical Approach** (University of Sydney Funded)

Project Leader: Nick Smith

In philosophy, a word or object is said to be vague if it is not clearly or sharply defined. Upon inspection, most words and objects turn out to be vague to some extent. Yet we lack logical and mathematical tools that are fully adequate for handling vagueness. This is both a profound theoretical problem (we do not understand our world) and a pressing practical one (we cannot adequately represent and reason about vague objects using computers). The overall goal of this project is to contribute theoretical tools for handling vagueness, based in new developments in logic.**A Computational Solution to the Problem of Reference** (Australian Research Council Funded)

Project Leader: Nick Smith

The fact that words refer to external objects is central to the power and utility of language. It allows us to represent the world as being thus or so, by combining words in particular ways on paper or in speech. Yet there is no theory that adequately explains how it is possible for words to reach beyond themselves in this way and refer to objects in the world. This project will attack the problem of reference by extending and developing tools from algorithmic complexity theory and then applying these tools to the problem of reference.