Ronald Parr: > If you are simply choosing between models in a world without time, then > there is no point in talking about induction Me: >[Counterexamples: timeless mathematical conjectures; the sciences of >paleontology, archaeology, etc., where we make inferences about the *past* >from evidence in the *present*.] Ronald Parr: > The topic of discussion here is scientific induction. Mathematical > induction, which is formally grounded, is a separate topic. The proof technique that is called "mathematical induction" is not what I was talking about. The making of mathematical conjectures is most certainly *not* formally grounded. It is a highly intuitive process based on a mathematician's experience solving mathematical problems and his/her knowledge of known theorems. Somehow, some mathematicians can look at a problem and guess the answer years, decades, or even centuries before anybody can prove that it is the right answer. This is an example of induction in precisely the sense we have been talking about -- something you can't *prove* with certainty, but have good reason for believing in based on some evidence. >Inferences made about the past are not what is typically referred to as >scientific induction and they do not have the same difficulty since we >typically view the past as static. You can just as easily view the future as static but unknown. Mathematically, there is no difference between making inferences about the past and making inferences about the future. Your distinction is an artificial one.
