Science an empirical endeavor. The world determines what is, not logic, or math. Logic and math are great tools for making sense of observations, but they do not determine what will be observed. Otherwise, there would have been no need to carry out experiments. People, armed with only logic, could have deduced any truths about the world from their arm chairs.
Some, like Aristotle, did try to do that. To be fair, it was a mix of observation and first principles, but it was lacking adequate experimentation, as humans later found out.
> People, armed with only logic, could have deduced any truths about the world from their arm chairs.
Fair enough. I'm probably giving too much of my own spin to the word "logic".
I'm thinking of logic as being somewhat grounded in empirical observations. I agree that armchair logic completely removed from reality is of questionable value.
At this stage of my understanding, I would argue that our notion of logic and math largely stems from us creating models about the world that lead to abstract deductions, which often are eventually used in new models about the world... and so on. This cycle probably got started as early humans acquired better mental models for categorizing objects of different types and their apparent boundaries, and then began to "count" like entities.
If math wasn't useful for describing the world, I doubt we would have done much with it.
