Desiderata of Theories • Accuracy of Prediction • Adequacy of Explanation • Adherence to Conceptual ‘Facts’ • Fecundity • Elegance / Simplicity
Ptolemy’s System Let’s see how it stacks up
Desiderata of Theories • Accuracy of Prediction • Does fairly well here • http://jove.geol.niu.edu/faculty/stoddard/JAVA/ptolemy.html • http://zebu.uoregon.edu/~soper/Orbits/ptolemy.html • Adequacy of Explanation • This one is more complex (but handles retrograde and variable brightness) • Adherence to Conceptual ‘Facts’
Desiderata of Theories • What about the ‘minor’ desiderata? • Fecundity • How does it do on this score? • Simplicity / Elegance
But is the Cosmos REALLY like this? • Does the model reflect the way the world really is? • Can we know this? • Should we care?
Realism and Instrumentalism Realism about Theories Instrumentalism about Theories What is this? Theories and models are just tools for making accurate predictions for whatever phenomena we care about It is not necessary for theories or models to be literally true in order to be able to account for the various data • What is this? • Theories and models are literal reflections of the way the world really is • Without being literally true, theories and models would have no ‘explanatory power’
Realism and Instrumentalism(about Math) Mathematical Realism Mathematical Instrumentalism What’s this about? Mathematical analyses are simply handy ways to get some practical stuff done Nothing about the nature of the world follows from the success (or failure) of any given mathematical model • What’s this about? • Mathematical analysis reveals the way things must be • Accurate prediction is possible because physical systems just are mathematical
Plato Athenian – circa 427 (or 428) to 348 (or so) BCE