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The Nature of Degrees of Belief

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Belief vs knowledge – how uncertainty affects our decision-making

A philosopher at the University of Leeds in Britain is carving out a more realistic picture of what our degrees of belief are and how they impact our decision-making. His EU-funded project calls into question what we thought we knew about doubt.


Do you ever say you are ‘doubtful’, ‘quite certain’ or ‘confident’ about something happening? Philosophers refer to those mental states as ‘degrees of belief’ and usually represent them with the language of probability. But what are these mental states really like and what is the best way to represent them mathematically? Australian philosopher Dr Edward Elliott argues it is time to develop a more realistic picture of our degrees of belief and how they relate to decision-making. During EU-project Degrees of Belief, with support from the Marie Curie programme, Dr Elliott made progress towards more sophisticated models of degrees of belief in order to better represent uncertainty. Supervised by Professor Robert Williams, he worked as a fellow at the University of Leeds. “This is a big project, and many people in many disciplines have been engaged in it for a long time,” said Dr Elliott. “It is a long way from completion, I think. But I like to think we have made some small steps in the right direction.” “When we represent a person’s degrees of belief using a probability function, we represent them, for example, as being 100 percent confident in any and all logical truths. This is problematic if what we are aiming for is a realistic representation. Most people aren’t 100 percent confident in every logical truth.” Dr Elliott shared some of his conclusions in the paper ‘Impossible Worlds and Partial Belief’ in the journal Synthese, which argues there is a major problem with one popular way of trying to formally represent non-probabilistic degrees of belief. He wrote four other papers on realistically representing degrees of belief, which are now being revised for publication. Capturing uncertainty He also organised a workshop at Leeds, asking the question, ‘What are degrees of belief?’ which attracted philosophers from the UK, the rest of Europe and the United States. Dr Elliott’s thinking has ramifications for other disciplines, like physics and mathematics, where people are interested in examining the rules by which we deal with evidence. “One of Dr Elliott’s papers shows that a way you might try to make models ‘more realistic’ means saying that people have as many attitudes to questions that they can’t express in language, as they do to questions they can express,” said Prof. Williams. “If he’s right, then my own approach to modelling logical uncertainty is wrong. So I will need to either rebuild that model, or try to pinpoint how I can avoid the arguments Dr Elliot gives!” He now wants to be more precise about the exact theoretical role of degrees of belief and their relationship to other mental states like desires, preferences and emotions. “Too much of the work we philosophers do is at a highly abstract level, glossing over details to make very general points and arguments,” he said. “This kind of thing is valuable, but it shouldn’t be the sole focus – we need to get firmer on the details as well.”


Degrees of Belief, decision-making, probability function, philosophy, non-probabilistic degrees of belief

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