1. "There is an objective reality". 2. "Reality is consistent". 3. "The human mind is capable of knowledge about reality".

These all need to be taken as axioms if any further knowledge is going to be possible.

There's a book called Introduction to Objectivist Epistemology which covers this in much more detail. (Ayn Rand gets a bad rep, but few people know about her theories of concepts and knowledge. They indicate the path to solving many of the issues in philosophy of science).