Not to get too deep into philosophy, but I imagine it has to do with observed cause and effect. For example, you may not realize it, but you think in a paradigm where 2 + 2 = 4. There is no good reason why 2+2=4 has to be true; we only believe it is true because we observe 4 objects every time we aggregate 2 and 2. Every time.

We break out of a paradigm when we push it to the extremes and notice effects that hadn't been observed before. For example, in quantum dynamics when something can pop up out of nothingness and 2 + 2 can sometimes equal 5.

The difficult part of escaping our paradigms is that we can't just assume any random thing in our current paradigm is false. (e.g., My sky is not blue.) You need to find the key ingredient in order to come up with a new paradigm that is actually useful.