Bayesian Networks in Philosophy of Science and Epistemology

University Of Colorado At Boulder, Boulder CO

Investigators

Abstract

SES 00-80580 - Luc J. Bovens (University of Colorado at Boulder) "Bayesian Networks in Philosophy of Science and Epistemology" There is a long philosophical tradition of addressing questions in philosophy of science and epistemology by means of the tools of Bayesian probability theory. In the late 1970s, an axiomatic approach to conditional independence was developed within a Bayesian framework. This approach in conjunction with developments in graph theory are the two pillars of the theory of Bayesian Networks, which is a theory of probabilistic reasoning in artificial intelligence. The theory has been very successful over the last two decades and has found a wide array of applications ranging from medical diagnosis to safety systems for hazardous industries. Aside from some excellent work in the theory of causation, philosophers have been sadly absent in reaping the fruits from these new developments in artificial intelligence. This is unfortunate, since there are some long-standing questions in philosophy of science and epistemology in which the route to progress has been blocked by a type of complexity that is precisely the type of complexity that Bayesian Networks are designed to deal with: questions in which there are multiple variables in play and the conditional independences between these variables can be clearly identified. Integrating Bayesian Networks into philosophical research leads to theoretical advances on long-standing questions in philosophy and has a potential for practical applications. In philosophy of science, there is the question of how we can confirm a hypothesis with unreliable instruments. What is the impact of repeating the experiment many times over? Of repeating the experiment with different instruments? Of developing a theoretical underpinning that boosts the reliability of the instrument? Of calibrating the instrument? These are the sort of questions that can be fruitfully modeled by means of Bayesian Networks. The results have surprising repercussions on standard theses in philosophy of science (e.g. the variety of evidence thesis and the Duhem-Quine thesis) and yield some novel theoretical insights. As to practical applications, our methodology will be applied to a case study on the discovery of the top quark: what makes this case interesting is that the theory at hand and the methods that are used to analyze the data that confirm the theory are probabilistically dependent. In epistemology, foundational questions have not been addressed sufficiently within a probabilistic framework. There is the sceptical challenge dating back to Descartes' Meditations that we cannot trust our senses and that our empirical knowledge has no justification. The coherentist answer is that even though the processes by means of which we gather information about the world may be less than fully reliable, the very fact that the scientific story fits together, i.e. has an internal coherence, provides justification that the story is true. But how are we to understand the claim that our information gathering processes are less than fully reliable? How are we to understand the claim that a story is internally coherent? There are many open questions about these central notions in coherentism. Within the framework of Bayesian Networks, multiple notions of less-than-full reliability can be modeled and a probabilistic measure of coherence, which has been a long-time dream of coherentists, can be developed. With a clear understanding of these central notions in hand, the coherentist answer to the Cartesian sceptic can be assessed. This theoretical work on reliability and coherence has practical applications in the theory of belief change. How does a cognitive system (a person or an expert system) update its beliefs when it receives new information as its input? Under what conditions does it add this new item of information to its previous beliefs? Under what conditions does it discard some of its previous beliefs? On the standard approach, new information is added to the belief set until an inconsistency appears. It is more realistic to let belief change be determined by two factors, viz. how reliable are our information sources and how well does the new information cohere with what we already believe. These factors can be directly modeled by Bayesian Networks. Such modeling yields novel theoretical insights about belief change and carries a promise of applications to information management in expert systems.