With G-d’s Help
Does the phrase b’ezras Hashem make sense philosophically and if so, what does it mean?
B’ezras Hashem implies to me that a person can do things himself, but Hashem helps. In what sense is it true that we have a sort of independent ability to do things? How does that interplay with God’s “help”?
(It seems to me that b’ezras Hashem is used as a replacement for ‘hopefully’ or the like when ‘frum‘ people talk, but that is a side point.)
There are two similar expressions: (אם ירצה ה׳ (אי״ה – if G-d so Desires / Wills) and (בעזרת ה׳ (בע״ה – with G-d’s Help. It seems from your question that you have no problem with the former, אי״ה, as it leaves the future in G-d’s “Hands” with no other factors under discussion.
Saying “בע״ה”, however, brings up issues of bechirah chofshis (free will) and hashgachah peratis (personalized Divine Providence). See the question “Free choice versus the Will of G-d“. (My own answer is here.) I think it is there that you will find answers to the fundamental dilemma underlying your question.
But the bottom line is “אין סומכין על הנס — we do not rely on miracles”, and even the resolutions of free will vs providence that give providence the most expansive role acknowledge that there is a role for human effort. That success and failure are in G-d’s “Hands”, but it is still fair to also acknowledge that we’re talking about success or failure of our efforts.
בע״ה is thus a good counterfoil for taking too much credit for those successes. While leaving אי״ה a great attitude to take when the situation leaves us little to do, we don’t run such risks. We can still avoiding losing hope by placing our trust in Him.