Answer to Question #114916 in Geometry for Aviwe

Question

Can deductive and inductive reasoning be applied simultaneously or they need to be applied separately?

Answer 1

It is better to apply separately, because these are two different lines of reasoning. Deductive reasoning proceeds from a priori ideas and postulates and tries to extract from them with the help of logical rules to which our thinking obeys consequences; these consequences can then be compared with facts. The mathematical language provides deduction with the exact tool it needs to complete, as accurately as possible, the transition from premises to conclusions.

Inductive reasoning is much more difficult to define and analyze. Relying on analogy and intuition, appealing to the insightful mind rather than the geometric mind, so to speak, it seeks to guess what is not yet known, so as to establish new principles that can serve as the basis for new deductions