Transcript Desiderata of Theories - University of Colorado Boulder

Desiderata of Theories
• Accuracy of Prediction
• Adequacy of Explanation
• Adherence to Conceptual ‘Facts’
– Fecundity
– Elegance / Simplicity
What is ‘Elegance’, Anyway?
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
• 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’
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
Realism and Instrumentalism
(about Math)
Mathematical Realism
• What’s this about?
– Mathematical analysis reveals
the way things must be
– Accurate prediction is
possible because physical
systems just are
mathematical
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
Plato
Athenian – circa 427 (or 428) to 348 (or so) BCE