Thank you all for the thoughtful replies.
Perhaps I should have expressed my point without using loaded words such as "faith". In posing the question I'm not particularly interested in the translation of saddha, the actual mechanism of stream-entry, or how one has to let go of the concept of "I".
Furthermore this discussion is not motivated to any particular problem that I have with my practise. Discussions such as this, I feel, do little to advance my practise. However, they can be an interesting diversion and may shed light on other discussions that go on here and elsewhere.
The point I am trying to make is that, despite the statement that in Buddhist practise one should "test for oneself", the advertised goal of Arahantship (or even Stream Entry) is, in fact, unverifiable until achieved. (See, for example, MN 27 Cula-hatthipadopama Sutta, The Shorter Elephant Footprint Simile, which I quoted above.)
Personally, I keep practising because I can see that it does give improvements. I can see that my teachers are living the holy life and it appears to be working for them. I can verify certain signposts from the Suttas, Commentaries, Dhamma books and talks, and discussions with my teachers.
However, I cannot actually state that I have "verified the teachings" in the sense of verifying the ultimate goal (Nibbana). And I suspect that there are few, if any, here who can.
Of course, it is possible to "redefine" the goal as something along the lines of: "Being reasonably happy and content in this life". Well, if that's the goal, I could say that I've verified it too. However, from my reading of the Teachings, it's not...