I'm currently reading the first book of Hume's Treatise, after having read Berkeley major works (Principles and the Dialogue). I'm having a really hard time to understand their arguments against abstract ideas, and how this critique is coherent with Hume's principles as described in the first sections of the Tratise. Unfortunately, since I'm reading the work in an italian translation, I don't think I will be able to directly quote Hume or Berkeley, so I will try to explain my perplexities as clearly as I possibly can.

From what I understand, the only mental contents that Hume recognize are impressions and ideas. Impressions are subdivided in external impressions, derived by the five senses, and internal impressions, which I still don't understand if are comprised of only irrational, emotion related content, or if they include also cognitive content. It seems to me that Hume only includes the former.
That being said, ideas are just copies of the impressions. But then he quickly specify that this should be said only of simple ideas, because there are complex ideas which cannot be reduced to a particular impression or a collection of impressions. In fact, complex ideas includes not only substances/objects, like a cat, which can be easly be reduced to a collection of impressions, but also modes and relations. Now, especially relations are the ones I'm struggling with. Hume's accept different kind of "philosophical relations", such as resemblance, contiguity and causality, and they ougth to be seen as complex ideas. But, being Hume an empiricist, he doesn't believe in innate ideas. So even complex ideas should derive from experience. But:

1) How can a relation between impressions or ideas be derived from experience?

Now, probably Hume would say that experience is necessary for the mind in order to perform operations between ideas, but he seems to imply that not only is necessary (in that case he would had the same position Leibniz had on this matter, who is considered a rationalist), but is also sufficient. And currently I'm not able to make sense of this thesis, assuming I'm not misinterpreting empiricism as a whole. In fact, he seems to introduce what he calls "principles of association" to explain "ideas" like space, time and causality, but I don't understand if these principles of association are ideas or not. If they are ideas, how and where could the mind get them? Not from experience, of course. Experience is passive. The principles described by Hume requires, instead, activity from the mind. If, on the contrary, these principles are not ideas, but just our mean to describe the way our mind "arrange" our percpetions, than how can this position be defined "empirist" while it is clearly assuming that experience per se is not sufficient to derive all our mental operations, but that "innate principles" like the association principles should be assumed? If this is the case, I'm unable to see any difference between Leibniz and Hume position on this topic.

Than, another difficulty, closely related to the first one: the Berkeley/Hume discussion of abstract ideas. These general abstract ideas are accepted by Locke. He says that we are able to form general ideas by means of abstraction, hence by isolating particular aspects of our perceptions from all the other aspects. So we have an idea of a general triangle, or of a color without any shape, or a shape without any color. Berkeley and Hume attack this position by showing that we cannot form in the imagination (!) any object of this type. Every triangle that I imagine is a particular triangle. Every shape comes with a color. Every color comes with a shape. Hence abstract ideas are unintelligible, and then they provide their notorious nominalist theory about generalisation. But this position seems to assume that to THINK about an idea is to form an IMAGE of that idea. Now, this is where I start to be really confused, because now Hume start to argue like if the "copy principle" of impressions and ideas is valid for EVERY idea, even complex ideas! But he spent an entire paragraph explaining that there could be complex ideas which had nothing to do with our impressions, hence our imagination. And in fact space, time and causality have nothing to do with our "mind's eye".

2) So why now the idea of triangle in general should be a problem? Why cannot be considered a complex idea? Why the burden of the impressions?

This position seems also to imply that I don't have a clear and dinstict idea of high numbers, like 2567, cause I clearly not form in my mind the IMAGE of 2567 apples. Does it mean that the idea of "2567" is unintelligible? Then how come that I can perform math operations with this unintelligible ideas without any problems? It seems obvious to me that "thinking" does not always requires mental representation.

Please note that my questions and statements do not have the intention of attacking Hume's theories to prove something. My aim is to understand. My feeling is that these problems arise more from my lack of understanding. In fact Berkeley and Hume seem to recognize withouth problems the difference between mental representation and "pure" conceptualization. So I assume there is something that I am missing.