>>16601945
That's not a unique problem with mathematics but with all language. All reason starts from axioms. Besides there's the structuralist versus essentialist debate. How can a biologist prove that a cat is a cat? Is it not a cat anymore when we cut its tail, whiskers and legs? That's sophistry. The fundament of all knowledge is very simple: even before any thoughts arise there are shapes and colors and sounds and all the rest. There are things to discern, this, that and the other. Next we put words on these discernments: this = boob, that = cat, such = Firefox and so on. Now we have our axioms. The next step in knowing is how the things we have discerned and labeled are related to eachother. That's all we're doing all day every day: discerning things, measuring things, comparing measurements of things. We are all born mathematicians. Ask a woman and she'll tell you exactly the status of everyone in her social circle. That's her way of doing mathematics. Ask a biology about the functioning of an ecosystem: the word system should already reveal to you that the biologist way of understanding how all life forms relate to eachother is again another form of mathematics. All is mathematics.