I wouldn't be too fussy about a distinction between natural philosopher and scientist. Newton believed he was doing natural philosophy. Galileo, Descartes and Leibniz too. This was because natural philosophy meant wondering how nature (as opposed to theology or morality) worked.
Adding to what Lanatin said:
The error, I believe, in the ancient thinkers was fivefold:
1. Trust of authority
2. Trust in analogy (or assuming things which are logically possible to be erroneous)
3. Trust in the simplest inference possible
4. Lack of data
5. Lack of decent means of gathering data
Galileo's Aristotelian opponent had 4 out of 5 deficiencies:
1. He trusted Aristotle, because he was the philosopher
2. Aristotle in turn drew an analogy between the behaviour of things in water and in air
3. Rather than invoke gravitational acceleration, it seemed simpler to them to believe in objects having intrinsic properties (how, in hindsight I can't imagine)
4. They didn't know much about the objects, since they had not experimented with them in different settings
Galileo showed 1 to be baseless arguing, 2 to be logically incoherent, 3 to be exasperated fiction, 4 to be a problem which he then remedied with 5.
So, far from logic being the bad guy in the hands of bad science, it is actually the good guy in the service of good science, refuting the incoherent hypotheses and helping to prove the correct ones.
Galileo reasoned that two weights held together would fall at the same rate as one weight.
Then he did experiments to test the idea — and, not surprisingly to us, it was true.
This was the start of modern empirical science, and our collective understanding of the universe hasn’t been the same since.
“Empirical” refers to ideas that are capable of being verified or disproved by observation or experiment. Empirical evidence is not simply one type of evidence, but rather it is the only evidence that we can rely on, because it is reproducible.
Empirical evidence is the basis for physical science.
Logic alone is not sufficient.