Bayesianism views belief as a matter of degree and uses a probabilistic approach to explain changes in belief. Let’s look at how it differs from traditional epistemology.
Many traditional epistemologists believe that for any given proposition, we can only have one of three belief attitudes. For example, we can believe the proposition “It will snow tomorrow” to be true, false, or neither true nor false. Bayesians, on the other hand, see belief as a matter of degree. For example, each cognitive agent can have a degree of belief ranging from the strongest to the weakest belief that “It will snow tomorrow” is true. By including degrees of belief in the attitude of belief, Bayesians, unlike many traditional epistemologists, enrich the attitude of belief.
According to Bayes, degrees of belief take on values between 0 and 1, where 0 means not believing at all and 1 means believing completely. By representing belief as a continuum of values, Bayesians allow for more fine-grained epistemological analysis. This fits well with our everyday experience. For example, when we look at the weather forecast and see the information “there is a 70% chance of rain tomorrow”, we don’t believe it with certainty or not at all, but with some degree of confidence.
We often learn anew whether an arbitrary proposition is true or false. To put this in Bayesian terms, we often learn anew whether a proposition is true or false, and we have a new strongest belief about whether it is true or false. Bayesianism provides a sophisticated account of how beliefs should change in this case. According to this, when a cognitive agent learns that an arbitrary proposition A is true or false at a given point in time, the change in the agent’s prior belief about another arbitrary proposition B is governed by the principle of conditioning. This principle states that if a perceiver learns that A is true only, then the perceiver’s degree of belief that B is true must change from the initial degree of belief to the degree of belief that B is true under the condition that A is true.
For example, suppose that Ick weakly believes that “It will rain tomorrow” is true, and strongly believes that “It will rain tomorrow” is true under the condition that “It is raining today” is true. According to the Conditioning Principle, it is reasonable for Gu to believe that “it rains tomorrow” is true more strongly than before when she only newly learns that “it rains today” is in fact true. The conditioning principle also applies when there is more than one newly learned proposition at the same time. However, this principle is about the degree of belief, not the behavior.
Some of the propositions are related to the newly learned proposition, whether true or false, as in the example above, while others are not. According to the Conditioning Principle, learning that a proposition is true or false should not change the degree of belief in propositions that are not related to that proposition. For example, as shown above, if Guy learns that “It’s raining today” is true, his belief in the unrelated proposition “Aliens exist in other galaxies” should not change. In this way, a Bayesian believes that our degrees of belief should remain the same unless there is a compelling reason to change them.
To justify this common-sense idea, a Bayesian might appeal to the practical efficiency gained by maintaining the existing degree of belief. Switching schools for no particular reason is an unnecessary use of our energy in some way. A Bayesian would see changing one’s beliefs for no particular reason as a similarly unnecessary use of energy. From this perspective, it is rational to maintain our existing degree of belief unless we have a specific reason to do so, if we are seeking utilitarian efficiency.
In conclusion, Bayesianism allows for a richer and more sophisticated analysis by considering degrees of belief, unlike traditional epistemologies that view belief as binary. This is useful for explaining how beliefs should change when we encounter new information, and it also makes sense from a practical efficiency perspective. As such, Bayesian approaches have an important place in modern epistemology.
