LOGIC Modern symbolic logic no longer uses the actual symbol system of its founder Frege, which was difficult to print The illustration shows the pattern, in his notation, for deriving results such as ‘‘If this ostrich is a bird and cannot fly, it follows that some birds cannot fly’’ depend essentially on sampling Any account, therefore, of non-deductive inference must be related to the mathematical theory of probability (EWP 177) Scientists frame hypotheses, make predictions on the bases of these hypotheses, and then make observations with a view to confirming or refuting their hypotheses These three stages of inquiry are called by Peirce abduction, deduction, and induction In the abductive phase the inquirer selects a theory for consideration In the deductive phase he formulates a method to test it In the inductive phase he evaluates the results of the test How does a scientist decide which hypotheses are worth inductive testing? Indefinitely many different theories might explain the phenomena he wishes to investigate If he is not to waste his time, his energy, and his research funding, the scientist needs some guidance about which theories to explore This guidance is given by the rules of the logic of abduction The theory must, if true, be genuinely explanatory; it must be empirically testable; it should be simple and natural and cohere with existing knowledge, though not necessarily with our subjective opinions about antecedent likelihood (P 7.220–1) Rules of abduction, however, not by themselves explain the success of scientists in their choice of hypotheses We have to believe that in their investigation of nature they are assisted by nature herself Science presupposes that we have a capacity for ‘guessing’ right We shall better to abandon the whole attempt to learn the truth unless we can trust to the human mind’s having such a power of guessing right that before very many 108