Read this article and consider what Heidegger means by "care". How is Heidegger's notion of care different from how we usually understand the concept of care? What role does care play in Heidegger's analysis of our own being? What about this notion of truth makes it radically different from how you might commonly think of truth?
On the Scandal in Philosophy (from Sein und Zeit)
Reality as a problem of Being, and whether the 'External World' can be Proved
Of these questions about Reality, the one which comes first in order is the ontological question of what "Reality" signifies in general. But as long as a pure ontological problematic and methodology was lacking, this question (if it was explicitly formulated at all) was necessarily confounded with a discussion of the 'problem of the external world'; for the analysis of Reality is possible only on the basis of our having appropriate access to the Real. But it has long been held that the way to grasp the Real is by that kind of knowing which is characterized by beholding [das anschauende Erkennen]. Such knowing 'is' as a way in which the soul - or consciousness - behaves. In so far as Reality has the character of something independent and "in itself", the question of the meaning of "Reality" becomes linked with that of whether the Real can be independent 'of consciousness' or whether there can be a transcendence of consciousness into the 'sphere' of the Real. The possibility of an adequate ontological analysis of Reality depends upon how far that of which the Real is to be thus independent - how far that which is to be transcended - has itself been clarified with regard to its Being. Only thus can even the kind of Being which belongs to transcendence be ontologically grasped. And finally we must make sure what kind of primary access we have to the Real, by deciding the question of whether knowing can take over this function at all.
These investigations, which take precedence over any possible ontological question about Reality, have been carried out in the foregoing existential analytic. According to this analytic, knowing is a founded mode of access to the Real. The Real is essentially accessible only as entities within-the-world. All access to such entities is founded ontologically upon the basic state of Dasein, Being-in-the-world; and this in turn has care as its even more primordial state of Being (ahead of itself - Being already in a world - as Being alongside entities within-the-world).
The question of whether there is a world at all and whether its Being can be proved, makes no sense if it is raised by Dasein as Being-in-the-world; and who else would raise it? Furthermore, it is encumbered with a double signification. The world as the "wherein" [das Worin] of Being-in, and the 'world' as entities within-the-world (that in which [das Wobei] one is concernfully absorbed) either have been confused or are not distinguished at all. But the world is disclosed essentially along with the Being of Dasein; with the disclosedness of the world, the 'world' has in each case been discovered too. Of course entities within-the-world in the sense of the Real as merely present-at-hand, are the very things that can remain concealed. But even the Real can be discovered only on the basis of a world which has already been disclosed. And only on this basis can anything Real still remain hidden. The question of the 'Reality' of the 'external world' gets raised without any previous clarification of the phenomenon of the world as such. Factically, the 'problem of the external world' is constantly oriented with regard to entities within-the-world (Things and Objects). So these discussions drift along into a problematic which it is almost impossible to disentangle ontologically.
Kant called the inability to prove the existence of an external world the "scandal" of philosophy
Kant's 'Refutation of Idealism' shows how intricate these questions are and how what one wants to prove gets muddled with what one does prove and with the means whereby the proof is carried out. Kant calls it 'a scandal of philosophy and of human reason in general' that there is still no cogent proof for the 'Dasein of Things outside of us' which will do away with any scepticism. He proposes such a proof himself, and indeed he does so to provide grounds for his 'theorem' that 'The mere consciousness of my own Dasein - a consciousness which, however, is empirical in character - proves the Dasein of objects in the space outside of me'.
We must in the first instance note explicitly that Kant uses the term 'Dasein' to designate that kind of Being which in the present investigation we have called 'presence-at-hand'. 'Consciousness of my Dasein' means for Kant a consciousness of my Being-present-at-hand in the sense of Descartes. When Kant uses the term 'Dasein' he has in mind the Being-present-at-hand of consciousness just as much as the Being-present-at-hand of Things.
The proof for the 'Dasein of Things outside of me' is supported by the fact that both change and performance belong, with equal primordiality, to the essence of time. My own Being-present-at-hand - that is, the Being-present-at-hand of a multiplicity of representations, which has been given in the inner sense - is a process of change which is present-at-hand. To have a determinate temporal character [Zeitbestimmtheit], however, presupposes something present-at-hand which is permanent. But this cannot be 'in us', 'for only through what is thus permanent can my Dasein in time be determined'. Thus if changes which are present-at-hand have been posited empirically 'in me', it is necessary that along with these something permanent which is present-at-hand should be posited empirically 'outside of me'. What is thus permanent is the condition which makes it possible for the changes 'in me' to be present-at-hand. The experience of the Being-in-time of representations posits something changing 'in me' and something permanent 'outside of me', and it posits both with equal primordiality.
Of course this proof is not a causal inference and is therefore not encumbered with the disadvantages which that would imply. Kant gives, as it were, an 'ontological proof' in terms of the idea of a temporal entity. It seems at first as if Kant has given up the Cartesian approach of positing a subject one can come across in isolation. But only in semblance. That Kant demands any proof at all for the 'Dasein of Things outside of me' shows already that he takes the subject - the 'in me' - as the starting-point for this problematic. Moreover, his proof itself is then carried through by starting with the empirically given changes 'in me'. For only 'in me' is 'time' experienced, and time carries the burden of the proof. Time provides the basis for leaping off into what is 'outside of me' in the course of the proof. Furthermore, Kant emphasizes that "The problematical kind [of idealism], which merely alleges our inability to prove by immediate experience that there is a Dasein outside of our own, is reasonable and accords with a sound kind of philosophical thinking: namely, to permit no decisive judgment until an adequate proof has been found". But even if the ontical priority of the isolated subject and inner experience should be given up, Descartes' position would still be retained ontologically. What Kant proves-if we may suppose that his proof is Icorrect and correctly based-is that entities which are changing and entities which are permanent are necessarily present-at-hand together. But when two things which are present-at-hand are thus put on the same level, this does not as yet mean that subject and Object are present-athand together. And even if this were proved, what is ontologically decisive would still be covered up-namely, the basic state of the 'subject', Casein, as Being-in-the-world. The Being-present-at-hand-together of the physical and the psychical is completely different ontically and ontologically from the phenomenon of Being-in-the-world. Kant presupposes both the distinction between the 'in me' and the 'outside of me', and also the connection between these; factically he is correct in doing so, but he is incorrect from the standpoint of the tendency of his proof. It has not been demonstrated that the sort of thing which gets established about the Being-present-at-hand-together of the changing and the permanent when one takes time as one's clue, will also apply to the connection between the 'in me' and the 'outside of me'. But if one were to see the whole distinction between the 'inside' and the 'outside' and the whole connection between them which Kant's proof presupposes, and if one were to have an ontological conception of what has been presupposed in this presupposition, then the possibility of holding that a proof of the 'Dasein of Things outside of me' is a necessary one which has yet to be given [noch ausstehend], would collapse.
Heidegger thinks the only scandal is that philosophers keep looking for a proof
The 'scandal of philosophy' is not that this proof has yet to be given, but that such proofs are expected and attempted again and again. Such expectations, aims, and demands arise from an ontologically inadequate way of starting with something of such a character that independently of it and 'outside' of it a 'world' is to be proved as present-at-hand. It is not that the proofs are inadequate, but that the kind of Being of the entity which does the proving and makes requests for proofs has not been made definite enough. This is why a demonstration that two things which are present-at-hand are necessarily present-at-hand together, can give rise to the illusion that something has been proved, or even can be proved, about Dasein as Being-in-the-world. If Dasein is understood correctly, it defies such proofs, because, in its Being, it already is what subsequent proofs deem necessary to demonstrate for it.
If one were to conclude that since the Being-present-at-hand of Things outside of us is impossible to prove, it must therefore 'be taken merely on faith' , one would still fail to surmount this perversion of the problem. The assumption would remain that at bottom and ideally it must still be possible to carry out such a proof. This inappropriate way of approaching the problem is still endorsed when one restricts oneself to a 'faith in the Reality of the external world', even if such a faith is explicitly 'acknowledged' as such. Although one is not offering a stringent proof, one is still in principle demanding a proof and trying to satisfy that demand.
Even if one should invoke the doctrine that the subject must presuppose and indeed always does unconsciously presuppose the presence-at-hand of the 'external world', one would still be starting with the construct of an isolated subject. The phenomenon of Being-in-the-world is something that one would no more meet in this way than one would by demonstrating that the physical and the psychical are present-at-hand together. With such presuppositions, Dasein always comes 'too late'; for in so far as it does this presupposing as an entity (and otherwise this would be impossible), it is, as an entity, already in a world. 'Earlier' than any presupposition which Dasein makes, or any of its ways of behaving, is the 'a priori' character of its state of Being as one whose kind of Being is care.