## April 21, 2006

### Inductive and deductive reasoning

I have often been unsure about the difference between inductive reasoning and deductive reasoning. The difference was explained to me by my math prof. and I will try and record it here.

DEDUCTIVE REASONING follows from rules of logic. It is an "If a then b" type of reasoning. Conclusions are not drawn from experiment or measurement. For example, you could not prove that global warming existed using deductive reasoning. But to prove that 2 odd numbers when added produce an even number it is ideal. The formalization of deductive reasoning goes back to the Greeks. They were disdainful of physical measurements. They started with a few basis assumptions about lines and points on a plane. These were called axioms and were considered to be "self evident." (They were, however, not comfortable with one axiom the parallel postulate and with good reason). Using the axioms one can deduce one proposition from another proposition.

INDUCTIVE REASONING is based on empirical data. Most proofs outside mathematics invoke empirical data. The law of gravity is not a theorem. It is a probabilistic statement based on the fact that historically it has always been the case. It is a physical law.

Inductive reasoning is not the same as mathematical induction.

Posted by sdelaney at 12:31 AM | Comments (0) | TrackBack