Some good stuff from Zahavi's book on Husserl (pdf not hard to find, paperback well worth the price):
According to Husserl, reality is not simply a brute fact detached from every context of experience and from every conceptual framework, but is a system of validity and meaning that needs subjectivity, that is, experiential and conceptual perspectives if it is to manifest and articulate itself. It is in this sense that reality depends on subjectivity, which is why Husserl could claim that it is just as nonsensical to speak of an absolute mind-independent reality as it is to speak of a circular square (Hua 3/120).
This is obviously not to deny or question the existence of the real world, but simply to reject an objectivistic interpretation of its ontological status. What does it mean to be a transcendent object? For Husserl, this question can only be answered critically, that is, undogmatically, by turning to the phenomenologically given, namely to the objects qua appearing. To speak of transcendent objects is to speak of objects that are not part of my consciousness and that cannot be reduced to my experience of them. It is to speak of objects that might always surprise us, that is, objects showing themselves differently than we expected. However, it is not to speak of objects as independent of or inaccessible to my perspective in any absolute sense.
On the contrary, Husserl believes that it only makes sense to speak of transcendent objects insofar as they are transcendent for us. The objects only have significance for us through our consciousness of them. To be real, to be an objectively existing object, is to have a specific regulated structure of appearance, it is to be given for a subject in a certain way, with a certain meaning and validity, not in the sense that the object can exist only when it actually appears, but in the sense that its existence is connected to the possibility of such an appearance. To claim that there are objects that are not actually experienced—stones on the backside of the moon, plants in the Amazon jungle, or colors in the ultraviolet spectrum, for instance—is to claim that the objects in question are embedded in a horizon of experience and could be given in principle (though there might be empirical or anthropocentric difficulties connected to this). It is precisely for this reason that every transcendent object is said to remain part of the phenomenological field of research.
Occasionally, Husserl describes his idealism as an attempt to comprehend and clarify the richness and transcendence of the world through a systematic analysis of constituting intentionality (Hua 1/34). In this sense, Husserl's transcendental idealism can be seen as an attempt to redeem rather than renounce the realism of the natural attitude. Or, to put it differently, Husserl would claim that the transcendental reduction enables us to understand and account for the realism that is intrinsic to the natural attitude. In fact, Husserl writes that his transcendental idealism contains natural realism within itself (Hua 9/254).41 [T]he transcendent world; human beings; their intercourse with one another, and with me, as human beings; their experiencing, thinking, doing, and making, with one another: these are not annulled by my phenomenological reflection, not devalued, not altered, but only understood (Hua 17/282 [275]). That the world exists, that it is given as an existing universe in uninterrupted experience which is constantly fusing into universal concordance, is entirely beyond doubt. But it is quite another matter to understand this indubitability which sustains life and positive science and to clarify the ground of its legitimacy (Hua 5/152-153). There can be no stronger realism than this, if by this word nothing more is meant than: 'I am certain of being a human being who lives in this world, etc., and I doubt it not in the least.' But the great problem is precisely to understand what is here so obvious' (Hua 6/190-191 [187]).
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In making these claims, Husserl is not only approaching Kant's famous dictum about the compatibility of transcendental idealism and empirical realism, he is also getting close to what has occasionally been called internal realism.
To a certain extent, it might actually be said that Husserl's criticism of representationalism does support a kind of (direct) realism. We are ... directed at real existing objects, and this directedness is not mediated by any intramental objects. But if one wants to call this position realism, it has to be emphasized that it is a realism based on experience. It is an experiential realism or an internal realism not unlike the one espoused by Hilary Putnam, having no affinities with a metaphysical realism. In the same breath, and perhaps even more appropriately, one might say that Husserls criticism of representationalism can be seen as a criticism of both realism and idealism. If one defines the opposition between realism and idealism with the use of the doublet internal representation/external reality, idealism claiming that the only entity existing is the intramental representation, while realism claims that the mental representation corresponds to an extramental and mind-independent object, it is obvious that Husserl must reject both.