Remember how irrational numbers petrified the bejesus out of the Pythagoreans? Or the interminable time it took mankind to introduce a zero into arithmetic? Recall the centuries of debate that occurred over whether negative numbers are valid or not?
Reductionism has its limitations. Is a human being -- one who bristles at injustice, weeps at Pachelbel's Canon, loves her children, is awestruck by beauty, and craves chocolate -- simply the product of Pavlov's conditioned reflexes to stimuli?
A logical deduction can tell you nothing that is not already embedded in its premises. All a logical deduction does is enable you to determine whether or not some conclusion is consistent with some set of premises.