This is quite the interesting question. If we can't trust our senses and/or our logic then we're in deep trouble. We would not be able to trust anything that we experience (not to mention the entire scientific enterprise), nor would be able to trust that we would be able to find any form of truth.
I'm going to look at three different worldviews and what they say about this. (Due to the desire to be brief, this post is in no way a comprehensive or nuanced understanding or treatment of these worldviews or the challenges I raise.) Let's start with the eastern worldviews.