First, I think that rationalism is about understanding. It is a belief that some universal truths (set vs. the truths about individual events and things) can be in principle understood – that is, rationalism is the view that one can not just know the universal truths which obtain in the world, but also that one can understand the reasons why those universal truths obtain. I say in principle, because it easily might be that our reason is limited in that way, that we can’t understand everything (which is what I believe anyway).
It is a belief of rationalist then that there are explanatory reasons for some universal truths (I say “some” as rationalist can be rationalist about some specific thing, without being rationalist about every universal truth), and that we can become aware of that explanation. It is this which I think is important difference with empiricist – the empiricist as far as I can see denies one of the following a)that there are universal truths or b)that there are explanatory reasons for those universal truths or c)that we can become aware of those explanatory reasons. It is because of this, I think of empiricism basically as more pragmatic, or ultimately pessimistic stance, and I don’t believe there will be definite arguments of why one should prefer rationalist or empiricist stance. It might go even into personal character traits!
However I personally think that every philosopher has a little rationalist inside, because as far as I can tell they are all interested in understanding. And not just philosophers, scientists too. They are trying to understand the world – to figure out the reasons for these or those phenomena being as they are, or behaving as they do. (They are not very happy with “shut up and calculate”) And without assuming both a), b) and c) from previous paragraph, I can’t see how one can claim that there is a possibility to be understanding the world, or understanding some specific phenomenon.
But to some other thoughts…
First, I think that rationalism is compatible with empirical research. That is – there is nothing wrong with path to understanding being through empirical research. I think even that given the fallibility and general limits of our reason, that empirical research and empirical confirmation are to be preferred and required by rationalists too. The requirement for empirical confirmation, being able to give predictions which can be confirmed empirically, doesn’t mean that the prediction have to be based on empirical research. The common sense requirement for good predictions, and need of empirical confirmation, is separate issue from how we did cam to those predictions. Given the sense of rationalism that I pointed to, rationalist expects that it is possible to understand the phenomenon, and based on this understanding to give good predictions (even they can be fallible). One can on this issue, easily compare a method which may be used by mathematicians to discover if the theorem is good or not. One can just take few specific cases/numbers, and check if the theorem is really OK. If there are some specific numbers for which what the theorem states doesn’t hold, there is something wrong with the theorem. And with the thinking behind its proof. Of course, this is not perfect analogy, but it might show how I think that different venues of research are compatible with the idea that we can understand things.
Other thing is relating rationalism with experience in general. Given that understanding will probably require awareness of things, it is normal for rationalist to accept that experience, or becoming aware to be necessary requirement for the ability for a priori thought. Even in cases like Kantian rationalism, even the forms of perception and pure concepts of understanding are innate, we don’t become aware of them in any other way but through experience. This will be even more so for other kind of rationalists (like me) which think that we become aware of things in the world through experience, in which there appears identity between our idea of those things and the things themselves. So to say, what we become aware, and what we have in mind are the things themselves (the notions). It is clear that this presupposes the great role of experience, as something through which we become aware of things – about which later we can think.
Third thing about rationalism is that when put vs. the holistic models like Quinean one it seems very simplified. But, it should be clear, from how I described rationalism, that there is nothing which goes against holistic view on knowledge, and really also on metaphysics. Even, seems most natural given this view on rationalism, to say that the ideal goal of understanding is to understand everything, and that full understanding can be reached only by understanding everything. And that what we in fact gain is just partial understanding. However for a rationalist like me, even partial understanding is possible only if the world is in principle understandable (of course, it doesn’t follow that we do in fact have abilities to do so. Personally, I doubt that).
Fourth thing which is usually brought against rationalism is the non-euclidean nature of space time. It is pointed that based on a priori thinking Kant has came to wrong conclusion – to the assumptions that the phenomena in space time are best described through euclidean model. But, one can point that a)in the years that followed Kant, Hegel has argued against this taking of space and time as separate entities, or as forms, and b)that the Einsteinian conclusions regarding space and time are in big part based on a priori thinking. (thought experiments, math, logic, and so on). And, if that is not enough, one can point to the non-euclidean geometries being developed within the math, which is a discipline where we know how things are settled – not through research of the world, but through rational arguments. How else could the abstract questions of math be settled? We can’t really find numbers or abstract spaces in the given abstract form in the reality. To those that deny the importance of this form of thought, one should just point to the number of theorems that math has already came to, which didn’t have any use at the time, only to find use later in relation to some less-abstract phenomenon.
And fifth, rationalism doesn’t presuppose existence of some magical entities like numbers or “pure forms of understanding” or Platonic ideas. For me it means understanding of the world, and the phenomena of the world as far as they might be taken to fall under certain general notions. To give an example, I think that 1+1=2, is properly understood as “whenever there is a pair of things, there is one and one more thing”, or “whenever three objects form a right angle triangle, there will be such and such relations between those things”, and so on… Are those truths about the world (given the idea that whatever is necessary truth it is not truth about the world)? Well, yes, as far the world falls under those abstract notions. Given the holistic take that I mentioned before, a rationalist can of course deny that those abstractions will be perfectly applicable to the worlds, and argue that there will be something always missed. But *as far* things fall under those notions, I don’t think there is a reason to deny that those truths are about the world.