I conceded that by stating that both were axiomatic positions. I also feel my position is more justifiable. Language in this case is a formal system of using an

I conceded that by stating that both were axiomatic positions. I also feel my position is more justifiable. Language in this case is a formal system of using and manipulating symbols to enable implication. If the ‘laws of physics tell us’ some hypothetical alien being ‘would discover’ Pi, that just means said aliens had to discover a logically consistent meaning of the natural numbers, and I would contend any species sufficiently abstractly intelligent enough to do so would also ‘discover’ Boolean logic. The fact that some species can reason using implication on the Natural numbers or some isomorphic inductive structure does not mean that the logic which enable those implications is anything other than the product of the mind, i.e. an invented thing. If following the logical inference chain that leads to determining the geometric concept of a circle and then inferring the ratio between the circumference and radius is a discovered thing, then any and all logical inferences which can be proved are then discoveries, but I don’t think that argument can be taken seriously.