Begging the Question:  Hume's Example

The Scottish philosopher David Hume (1711-1776) famously observed that almost everything we do is based on the following principle:

The future will resemble the past (in significant ways).
E.g. When you go home after class, you (usually) act on the assumption that your home is the same place it was this morning.  Likewise, you (typcially) assume that people's names don't change from moment to moment.

Question:  What reasons can we give to support our belief in the above principle?

The most popular answer:  Believing in the principle has worked well up to now.  This makes it reasonable to believe the principle will continue to work.

What's wrong with this answer?
As Hume pointed out, this answer begs the question. Citing things that have happened in the past as evidence for what will happen in the future is only helpful if we make the assumption that the future will resemble the past.  But that assu