Hmm, I will consider this, I'm not sure I buy it yet though, it is close getting me to change my mind.
Philosophy is interesting for people who are interested in philosophy, and generally for few others.
Here's some more to ponder. The relationship
C = π⋅
d is, of course, a sentence in a mathematical structure in which concepts like the field ℝ and the operations + and ⋅ are defined, complete, and consistent. Especially in the 20th century, people burned a lot of neurons coming up with a foundation for mathematics that makes this possible.
But consider what it's trying to say. The sentence is true for all circles. But what do we mean by "circle?" It's the set of all points in a plane that are equidistant from a fixed point. What's a point? What's a plane? What is a distance? What does it mean to measure a distance and thereby assign it values that we represent with
C and
d? Why do we get to measure diameter one way and circumference another way? Do circles that fit this description actually exist in the real world or are they purely objects in the mind? Yes, there are
circular objects, but what does it mean for the sentence to hold for those objects?
Before we can assure ourselves that
C = π⋅
d is a deductively reliable sentence, the brain has to invent a lot of things to hang some simple facts on.
Might engineers bias, I use math to eventually influence physical reality daily.
I sympathize. I am also an engineer, which I described to prospective students as, "Weaponized calculus." In another thread on quantum mechanics I said I generally don't become interested in something until it's big enough to hit with a hammer.
My biggest problem with circles was to properly position holes along the circumference of something that's 144 ± 0.004 inches in diameter and the holes have to line up to a tolerance of ±0.001 inch. Oh, and if you get it wrong, people might die. And—in fact—did.