@Neil D,
No, I'm still confused, nevertheless I appreciate the painstaking efforts.
You wrote two paragraphs.
I agree with the content of the first one. If I had to pick something to argue about (and I do), then I'd disagree with usage of words like "pure" and "perfect". When we consider nicely shaped triangles in the course of learning trigonometry, we don't dwell on the molecular crooks and crannies. Our conceptions or calculations are either perfect or imperfect? Or that real triangles are different from imagined triangles in some philosophically important way? Mathematics is about measuring and measuring is about being precise or imprecise. I think the science of math can handle rounding numbers off and I don't find significant digits particularly challenging philosophically.
It is the second paragraph that I find interesting.
Zetetic11235;71229 wrote:Now, the concept of the frog that we have is not necessarily complete, because the concept of the frog can only approximate the reality of the frog. This seems to be an inversion of the logic applied above; but it is in fact not. When we try to take a triangle, a geometric object, and try to make one out of some material, we are in fact, doing the reverse of what we do when we take a real object, say a frog, and try to make a purely logical/linguistic representation or mental ideal out of it. Our definition can only approximate what a frog really is. This is why a description can be interpreted different ways by different people, it is an approximation and we fill in the details with our past experience.
I do not understand. That is not completely true; I understand that you are comparing the abstraction of an idea of frogs with the concretization of a triangle from an idea of triangles. I'll agree that the two processes are different, but it doesn't convince me there is a difference between the logicical possibilities of either triangles or frogs morphing into a Chevron-with-Techron commerecial.
It gets silly(-ier) after this, so feel free to skip to the bottom.
Consider the cup of coffee and the donut. I can make a donut, a geometric object, out of an idea of the donut shape and the proper materials. I can also form linguistic representations from cups of coffee, which are real objects.
Or I can do the reverse. I can make a cup of coffee, which has it's own unique geometry, out of some clay and beans and form ideas about donuts while I dunk them in aforementioned geometry.
I don't think I can make a frog. Maybe a puppet of a frog.