I want to dredge below these two terms; I'm not asking about the definition or concept, which I perceive thanks to http://www.socialresearchmethods.net/kb/dedind.php and my math studies.
How do these two words consist with their respective meanings in logic?
deduce = ...from de- "down" (see de-) + ducere "to lead" (see duke (n.))...
induce: ...from in- "into, in, on, upon" (see in- (2)) + ducere "to lead" (see duke (n.))...
What is being 'lead'? Does the 'down' start at the theory? Why not start 'down' from the observation?
Similarly, why lead INTO the theory? Why not lead INTO the observation?
Couldn't I reverse the direction of the approaches and thus upend these words?