I read this when studying page 3 of statistics book "In All Likelihood" by Yudi Pawitan:
In deductive problems the truth quality of the new theorem is the same as the quality of the 'data' (axioms, definitions and previous theorems) used in establishing it. In contrast, the degree of certainty in an inductive conclusion is typically stronger than the degree in the data constituent, and the truth quality of the conclusion improves as we use more and more data.
I don't see how this makes sense. The "truth quality", or the "degree of certainty", for deductive problems is 100%, since, beginning with some set of axioms and then proceeding with logic, we can be certain of whether some proposition true or false. On the other hand, the nature of inductive problems, such as those encountered in statistics, is such that the degree of certainty is <100% for nontrivial problems. Why is the author making this argument? Is it valid? Is my argument incorrect? Thank you.