And this is why I keep on disagreeing with you! Logic is meaningless without a worldview.
2+2=10 is not logical if the worldview used is base 10. It is logical if the worldview being used is base 5. Your logic comes out of your worldview.
I think you are causing confusion by being hung up on this worldview business. Trouble is, the term is poorly defined, and you are using it in a particular way that confuses people who use it in a more regular way. For instance, you say "
Your logic comes out of your worldview". To my way of understanding these terms, that is completely wrong. Logic is not relative or subservient to any more profound epistemic system. Worldviews are personal and messy things that owe to cultural baggage, time and place. A worldview might derive, in part, from logic, but logic is logic is logic and it does not derive from a worldview. Your arithmetic base analogy is trivially misleading.