Saturday, 1 December 2012

Induction, deduction and prediction

An induction is an inference from observed or examined things to unknown things. Okasha (2002) gives the following example:

Premise 1: The first five eggs in the box were rotten.
Premise 2: All the eggs have the same best-before date stamped on them.
Conclusion: Therefore, the sixth egg will be rotten too.

While perfectly sensible, this induction does not come with a guarantee to be correct. This is easier to see when formulated as:

Premise 1: The first five marbles were red.
Premise 2: All marbles are from the same urn.
Conclusion: Therefore, the sixth marble from that urn will also be red.

Everybody with some basic training in statistics knows that this conclusion does not follow necessarily even though the premises are correct. Deductions differ in this respect because their conclusion will necessarily follow, if the premises are all correct. The conclusion is entailed by the premises.

P1: All humans are immortal.
P2: Socrates is human.
C: Therefore, Socrates is immortal.

If the presmises were true (which they are not), then the conclusion would necessarily follow. Deductions start from a general claim (a law) and an instance to which the law should apply.

Scientific predictions can either be derived from general (law-like) theories or from observations and examinations (evidence). Hence some predictions will necessarily follow, if the premises are true, and some will not.

An example for the latter is a phylogenetic prediction detailed by David Morrison at The Genealogical World of Phylogenetic Networks. It has the structure:

P1: The first five parasites in taxon A have a canid definitive host.
P2: The sixths parasite also belongs to taxon A.
C: Therefore, the sixths parasite will have a canid definitive host too.  

This is clearly an induction starting from observations. And even if the premises were true, there is no guarantee for the sixths parasite to have a canid definitive host. It might, for some evolutionary contingency, have switched hosts.

Much of the obsession of researchers with predictive power seems to be due to a mixture of physics envy and misunderstanding what hypothetico-deductive means.

A hypothesis is an inference to the best explanation, which is the inverse of an induction. Some C has been observed and the premises that would make this observation a sensible conclusion are then hypothesised (conjectured). Thereafter new predictions are derived from the hypothesis. Thus the hypothesis replaces the premises and new predictions derived from it are being tested. Often, however, the hypothesis does not replace the law-like premise in a deduction but the observations in an induction.

Therefore, hypothetico-deductive often really means hypothetico-inductive and does not entail the prediction in the cogent way that a deduction does. 
  • Samir Okasha (2002) Philosophy of science. A very short introduction. Oxford University Press.