Archive for July 6th, 2012

July 6th, 2012

The Problem with Inductive Arguments

by Max Andrews

All induction problems may be phrased in a way that depicts a sequence of predictions.  Inductive problems will contain a previous indicator or explanans for the explanandum.  For instance, Carl Hempel’s example of Jones’ infection:

Where j is Jones, p is the probability, Sj is Jones’ infection, Pj is he being treated with penicillin, and Rj is his recovery.  If the probability of observing R at any time given the past observations of S&P1S&P2S&Pn (the probability of the set meeting R is m) where R was close to 1 then a predictive explanans (the S&Pn ) can be made for future instances of m using an inductive-statistical explanation.  For if the probability m(S&Pn | S&P1S&P2 …) is a computable function, the range of data is finite then a posterior predication M can be made from mM can be legitimately referred to as a universal predictor in cases of m. This is where Hempel rejects the requirement of maximal specificity (RMS), contra Rudolph Carnap, in which the RMS is a maxim for inductive logic that states that this is a necessary condition for rationality of any given knowledge situation K.  Let K represent the set of data known in m.  According to Hempel we cannot have all the material for K