: Induction is not logically compelling
: Science is based on induction
: therefore science is not logical.Induction is not totally compelling, but it has worked to date.
This does not mean that it is always going to work; but the same can be applied to any posited axiom you care to mention.
Will you therefore take the path of Russell's lunatic?
If you accept that the world exists, as you do, then the inductive method is the one with the fewest unproveables; it is entirely self-consistent.
This might not satisify the logical purist seeking the Platonic Form he or she calls 'logic'; but a moderately logical model is logically more sound than a totally alogical one.
Define 'compelling'; define 'logic'
If you want to be totally consistent, try defining them without reference to any physical observation point.
You can't. Logic is based on science; it's an abstraction of observed science.
So *of course* science isn't perfect in logical terms; in the same way that a real-world circle is never perfectly round; the concept of 'roundness' is an abstraction of a concept from physical observation.
Science is the act of making models that describe the observed world; the logic is the mechanism on which the model is based.
When a model is shown to be faulty, it is revised or discarded; this process occurs in what Kuhn calls a 'crisis in science'; the competing models are weighed in the balance and the lesser is found wanting.
(Of course, as Kuhn and Lakatos pointed out, this isn't always the case in the sociological human world, but...)
The best scientific model is the one that most simply explains all scientific observations.
(Examine Popper's answer to the Quine-Duhem thesis.)
Induction comes before logic; not after it. So your three lines should read;
1. There appears to be a 'real world'. This is inductive.
2. Distillation of what appear to be common 'rules' leads to a system of 'logic'
3. A scientific theory is a self-consistent one that agrees with all evidence provided by points 1 and 2.
Gideon.
(I'll reply more on the Popper post when I've the time; I'm at work.)
