Theory vs. Theory

What does it mean to invoke “evolutionary theory”? Is “neo-Darwinism” (or “Darwinism”) a theory, a school of thought, or something else? What gives a theory structure and meaning (e.g., axioms, themes, formulae)? What is the relationship between mathematical formalisms and other statements of “theory” (e.g., what does it mean for a lecturer to show a key equation of quantitative evolutionary genetics and assert “this is neo-Darwinism” 1)? Who decides how a theory is defined, or redefined (e.g., is Ohta’s “nearly neutral” theory an alternative to, or a variant of, Kimura’s Neutral Theory of Molecular Evolution)?

For various purposes, I would like to begin developing a framework for productively discussing “theory” and “theories”.  Here I begin by addressing an ambiguity in the use of the word “theory”, partly because this particular ambiguity is important, and partly as an exercise in addressing semantics. 2