>>12266273>Well we don't have anything else that is directly observable.Ultimately you're right that everything we know is purely empirical and rely on the existence of physical objects. But the fact that we distinguish Mathematics from Physics is pretty telling that some truth strike us as more fundamental than others.
The existence of sets, numbers and other mathematical structures is fundamental, they seem to be consequences of pure logic, they rely on self evidence: numbers exists because I can enumerate in order.
The laws of Physics, the existence of the reality we find ourselves in, seem important as well, but also feel much more arbitrary, like if they had been derived from additional axioms. That is, our world follow equations, and those equations are the expression of a set of mathematical axioms concomitantly with physical axioms.
Math are all the equations, Physics is the restriction to some equations to explain reality.
That is why I think basing the definition of information on Mathematical grounds is more useful than just making it a property from our (very) arbitrary physical world. Information is relationship, and relationship in its purest form is intrinsically mathematical.
