1. Computationalism – in the philosophy of mind, computer science: this is the view that the physical brain can be, should be, or is describable as a manipulator of digital information; that all brain processes are algorithmic, and this algorithmic level has an even higher logical (or axiomatic) language of description. I’ve seen Dawkins in places adopt this kind of view, and for philosophers working in contemporary areas, it seems like a harmless assumption (like assuming modus ponens is valid an inference).
2. Mathematicisation desideratum: Another thing we seem to take for granted is, in our acceptance of predominantly recieved notions in the physical sciences, we also take the wholesale acceptance of the assumption that physical reality can be mathematically formulated, or to state this in less rigid terms; that there is an a priori constructablity constraint hinged upon anything that may count as ‘science’. A corollorary thing to note is how people associate natural sciences with numbers and ‘data’, with the arts and humanities, by contrast, with ‘words’. But that’s a whole other issue!
Not to say that these are bad things to assume; but these are powerful assumptions that people hardly come to question. That said, there are some well rehearsed objections to mathematical representation pace Newton. But that’s another story!