Can one believe without faith?

In several Indian texts, the fact that the ṛṣis have seen dharma and, hence, authored the Veda has been "proven" on the strength of statements of the Veda itself. This sounds obviously flawed to a contemporary audience: the authority of a text (even this of the Veda) depends on its author, hence one cannot rely on a text's statement until one has independently established its author's authority. In other words, the text itself has not an independent epistemological power to establish the characteristics of the one who authored it.

Similarly, Ernst Steinkellner and Masatoshi Nagatomi (and Tilmann Vetter before them, see Vetter 1964) argued that there is a similar circularity at the foundation of the validity of Buddhist thought:

the path taught by the Buddha is valid ––» because it is established by instruments of knowledge ––» the validity of these instruments has been established by the Buddha


Hence, the very instruments which should prove the Buddha's authority are only justified through His authority:

The testing of the validity of the Buddha's words requires a tool which was for Dignāga and and Dharmakīrti the pramāṇa, the valid means of cognition. Such a tool, at least in principle, may be expected to be one which is universally acceptable to all and free from dogmatic premises and presuppositions. Both Dignāga and Dharmakīrti struggle to achieve that end by polemically refuting the number and definitions of pramāṇas of the non-Buddhist schools which were contradictory to their own. We must note, however, that the final authority by which they claimed the validity of their pramāṇa system was none other than the Buddha's words which they accepted as authentic by faith (Nagatomi 1980, 245-6).

The issue is more than controversial among Buddhologists and Eli Franco and Tom Tillemans strongly disagree with this view. See for instance Franco 1999 and Tillemans 1999.
Whatever the case, a naif Western reader may overestimate these cases, forgetting to look at comparable instances in Western thought. For instance, let me point out common statements in Christian sermons, such as "God is love, as stated in the second letter of St. Paul to the Corinthians". In fact, that God is love is presupposed by the existence of his Revelation. Hence, the Revelation itself cannot independently prove it.

The above discussion is not meant in order to censure religious thought. In fact, circularity is not a flaw for a believer —who already trusts the Sacred Texts and is hence not disturbed by an appeal to their authority. One can imagine that an emotive commitment is used in order to found an epistemological one, so that one cannot strictly speak of circularity. Moreover, it might be suggested that religious thought cannot avoid such a commitment and is, hence, inextricably linked with a decision which cannot be a priori explained through epistemology (which can, however, a posteriori justify it).

On this topic, you might look at this post by Jayarava. On Dharmakīrti's agenda in regard to faith (as seen by V. Eltschinger), see this post. On the problem of the boundaries of religious thought (and of philosophy, by the way), see this post.