Nature of mathematical knowledge

Axioms are the foundations of all mathematics, which makes it comparatively different to science. Science is largely based on our interpretations of our surroundings and basing rules off of them. While there are axioms in science, for example, that quarks are the smallest particles and they are able to do a specific set of things, these axioms are mostly found through experimentation with our environment, and also can be challenged if new data is found. In mathematics, it is completely different. The axioms in math are more difficult to challenge because rather than being based on nature, they are axioms mathematicians have developed on paper. Theorems are generally what is challenged in mathematics and in this way it is more similar to how science approaches theories. Theorems are merely logical deductions by mathematicians, which anyone can attempt to disprove, similar to science, where anyone can challenge laws with evidence. Another thing that is different about mathematics is that with the axioms of science, they are attempting to define truth in our reality, whereas in mathematics, it isn’t as much about finding a truth, but rather finding certainty in what we are trying to prove.

Print Friendly, PDF & Email

One thought on “Nature of mathematical knowledge”

  1. Thanks Alex.

    “While there are axioms in science, for example, that quarks are the smallest particles and they are able to do a specific set of things, these axioms are mostly found through experimentation with our environment, and also can be challenged if new data is found.” So this is misunderstanding the nature of axioms; if they are experimental and subject to revision, then they are not axioms. Axioms have to be the BASE, not the conclusion of a process (though it is a little more complex than that – but we can chat easier than I can write about it).

    Your last point about truth-certainty is well put. And it is related to this idea that axioms are not subject to ‘truth’ as such.

    Well done for catching up; nice to have you back in class.

    N

Leave a Reply

Your email address will not be published. Required fields are marked *