  In celebration of the work of Richard Threlkeld Cox, we explore inductive
logic and its role in science touching on both experimental design and analysis
of experimental results. In this exploration we demonstrate that the duality
between the logic of assertions and the logic of questions has important
consequences. We discuss the conjecture that the relevance or bearing, b, of a
question on an issue can be expressed in terms of the probabilities, p, of the
assertions that answer the question via the entropy.
  In its application to the scientific method, the logic of questions,
inductive inquiry, can be applied to design an experiment that most effectively
addresses a scientific issue. This is performed by maximizing the relevance of
the experimental question to the scientific issue to be resolved. It is shown
that these results are related to the mutual information between the experiment
and the scientific issue, and that experimental design is akin to designing a
communication channel that most efficiently communicates information relevant
to the scientific issue to the experimenter. Application of the logic of
assertions, inductive inference (Bayesian inference) completes the experimental
process by allowing the researcher to make inferences based on the information
obtained from the experiment.
