When it comes to the point of view stating that science starts with the senses, a common objection is that is starts with maths.
No it doesn't.
Aristotle saw subtleties on frogs with his eyes that we saw more with microscopes, Galileo saw planets first with his eyes and studied them more with his telescope.
Similarly, we first need to feel stars and planets before talking about the mathematics of the true alignements of the famous zodiacal signs.
Maths do have a role to play in science, but it's more of a tweak with the data phenomenon, it's closer to the end than the beginning of the process.