Empirical Hypothesis

References

http://plato.stanford.edu/entries/learning-formal/supplement.html
- An empirical hypothesis is a claim whose truth supervenes on a data stream. That is, a complete infinite sequence of observations settles whether or not an empirical hypothesis is true. For example, the hypothesis that “all observed emeralds are green” is true on the data stream featuring only green emeralds, and false on any data stream featuring a nongreen emerald. In general, we assume that a correctness relation on C has been specified, where C(ε,H) holds just in case hypothesis H is correct an data stream ε. What hypotheses are taken as correct on which data streams is a matter of the particular application. Given a correctness relation, we can define the empirical content of a hypothesis H as the set of data streams on which H is correct. Thus the empirical content of hypothesis H is given by {ε: C(ε, H)}. For formal purposes, it is often easiest to dispense with the correctness relation and simply to identify hypotheses with their empirical content. With that understanding, in what follows hypotheses will often be viewed as sets of data streams. For ease of exposition, I do not always distinguish between a hypothesis viewed as a set of data streams and an expression denoting that hypothesis, such as “all emeralds are green”.