Principles of Inference
Scientific evidence is evidence that does not concede the dependence of the evidence on principles of inference. This allows the relevancy of observations to a hypothesis to be determined by examining the assumptions made.
A person’s assumptions or beliefs about the relationship between observations and a hypothesis will affect whether that person takes the observations as evidence. These assumptions or beliefs will also affect how a person utilizes the observations as evidence. For example, the Earth's apparent lack of motion may be taken as evidence for a geocentric cosmology. However, after sufficient evidence is presented for heliocentric cosmology and the apparent lack of motion is explained, the initial observation is strongly discounted as evidence.
When rational observers have different background beliefs, they may draw different conclusions from the same scientific evidence. For example, Priestley, working with phlogiston theory, explained his observations about the decomposition of mercuric oxide using phlogiston. In contrast, Lavoisier, developing the theory of elements, explained the same observations with reference to oxygen. Note that a causal relationship between the observations and hypothesis does not exist to cause the observation to be taken as evidence, but rather the causal relationship is provided by the person seeking to establish observations as evidence.
A more formal method to characterize the effect of background beliefs is Bayesian inference. In Bayesian inference, beliefs are expressed as percentages indicating one's confidence in them. One starts from an initial probability (a prior), and then updates that probability using Bayes' theorem after observing evidence. As a result, two independent observers of the same event will rationally arrive at different conclusions if their priors (previous observations that are also relevant to the conclusion) differ. However, if they are allowed to communicate with each other, they will end in agreement (per Aumann's agreement theorem).
The importance of background beliefs in the determination of what observations are evidence can be illustrated using as provided by deductive reasoning, such as syllogisms. If either of the propositions is not accepted as true, the conclusion will not be accepted either.
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