[stripes1776]

By geometric, I mean it was expressed in geometric terms, as was Ptolemy’s, or any scientist for still another hundred years after Galileo until modern annaliyical tools were developed. But don’t despise induction: this is really the approach that St. Thomas did when he was trying to “prove” the existence of God

You have misinterpreted. I didn't say anything about despising inductive reasoning, only that inductive reasoning is not a proof except under very limited conditions, namely complete enumeration. There are never proofs in science.

You used the word "proof". It's not a proof.

[RobbyS]

Galileo did not think of science in the terms you describe. He was concerned to know truth. As a matter of fact, the tentativeness you ascribe to scientific statements is psychologically unsatisfying, implying a skepticism that no scientist feels, at least about his subject matter. A historian —I cannot remember whom—pointed out that the scientific revolution saved us from a growing skepticism caused by the wars that discredited Christianity in the minds of the elite. IAC, we get a good look at the situation in Pascal’s Pensees. So many of his friends were skeptics. Unable to find certainty in Christianity, the following generations founded it in science. Descartes thought of his insights as revelations of sorts, and the Enlightenment was described by Lewis Mumford as a sort of revival of the religion of Apollo, with Newton as Prophet.