Should add that logic and mathematics are tools, not philosophical constructs. Logic works to a point, but every once in a while counterintuitive situations arise, and logic changes with new information. Logic and math are key to the scientific method for the physical world. If I build a space probe, I need to get it into space. So I call a company that makes rockets, and give them the weight, dimensions, and where I'm sending the probe (orbit, or Saturn, or elsewhere). The company can tell me over the phone what what kind of rocket, and how many rockets I'll need, and how much fuel to use. That is logic and math and science doing their dance. The only hard number the rocket guy cannot give me is the final costs, and a firm delivery date. Rockets take time to build, parts need to be ordered or made, shipping can be an adventure, and diesel fuel prices have been a circus this year. So best the rocket guy can do is estimate the cost, and the delivery date. That part is not empirical science, just an educated guess.
And since I know nothing about rocket making, or space probe building what I wrote above is an educated guess based on my years in shipping and receiving, and model rocketry. I know it's more complex, but I think it's a decent illustration of a real world situation where science does all the main work, but can't give an exact number for the out-the-door price, or when the rocket(s) will be available for delivery. That's the real world.