Some differential equations that model physics admit singularities and multiple solutions. Therefore, functions are not the most general way of describing relations. Functions are a subset of relations.

Although "non-deterministic" and "stochastic" are often used interchangeably, they are not equivalent. Probability is applied analysis whose objects are distributions. Analysis is a form of deductive, i.e. mechanical, reasoning. Therefore, it's more accurate (philosophically) to identify mathematical probability with determinism. Probability is a model for our experience. That doesn't mean our experience is truly probabilistic.

Humans aren't exceptional. Math modeling and reasoning are human activities.