I am forewarned that this is a highly controversial subject. Your kindness in answering is greatly appreciated.
There are some who think the history of philosophy is such that it split with science but were once the same thing. Philosophy became associated with the rationalists, and science with empericism. I might hold a different view, and tend to think that we can look at philosophy in at least the Platonist tradition and the Aristotelean tradition on the other hand. I would take the rationalists to be associated with the former (Descartes, Kant?), and empericists like Hume with the other. I'd say that the latter is science, and that insofar as reason and logic are a part of science, philosophy in general is a science.
Do you agree with this characterization? Do you think philosophy and science are distinct?
Some people like to say that science is limited by what can be proven. Philosophy concerns that which cannot be proven. This distinction implies that much of string theory should be properly understood as philosophy as the scientific method (the ability to prove and disprove theory) is not applicable to string theory and some other areas of particle physics.
Seen this way, science and philosophy can tackle the same subjects and the distinction is one of whether or not experiments are practicable regarding the subject. (The Higgs Boson, in this view, only recently went from being a subject of scientific philosophy to being a proper part of science, thanks to the Hadron Collider.)
You suggest that the application of reason and logic are the only necessary characteristics of a study to define it as scientific. To me, this seems like an Aristolelian view of science, which is what you are going for, right? That is workable.
I'd offer a counter-argument though to this definition of science. Personally, I can't ascribe the same kind of empirical value to logic and reason as I can to scientific study that includes rigorous testing and experimentation.
There is still great value to logical and rational consideration of ideas that cannot be tested. Some of those ideas might be "scientific" in nature, but the untested contemplation of these ideas does not necessarily constitute science.
Generally, I would say that the study of philosophy belongs properly to the humanities. You make a good suggestion that we might separate types of philosophy into, effectively, non-scientific and scientific branches. That seems fine, but scientific philosophy, to me, is not identical with science.
I think that our modern conception of both philosophy and science is very different than it was in the past. At one point, early in our history, we basically had neither. Then each developed.
That was interesting. I'm not sure I grasped all of that. But yes, I'd say in one sense we can separate philosophy into empericism and rationalism. But my point about rationalism being like science or a science is not that it's the only criteria for science, but simply that insofar as reason and logic are a part of science, that it is a type of science. There are others. I'm not sure I got the part about Aristotle, but I don't think he was a rationalist (which I thought was what you were suggesting). He did come up with the rules of logic, still used in mathematics (a type of science). But he was certainly an empiricist in many ways in the way he tried to make sense of matter and even everyday species he found in the rivers.