(April 14, 2016 at 9:35 pm)Simon Moon Wrote: Math may just be a concept of the mind.
It's a bit more complicated than that. To say something is simply a concept in the mind does not account for its objectivity. How is it that various people can come to complete agreement with respect to some concepts like the nature of mathematical objects. I think most people would say that mathematics is objective. But in what way is it objective?
Something is objective if it exists and could be known independently of who knows about it or even if no one learns anything about it at all. People can know about physical things because they are objects. For example, when different people see various apples, those apples serve as the basis for what anyone could learn about apples: rounded, nutritious, grows on trees, etc. That’s real knowledge about a type of actual objects, in this case apples. The meaning of objective is obvious when talking about physical things. The objectivity of other types of things is less clear, but philosophically justifiable; things like forms are objects of knowledge.
People also know about mathematical objects. Just like apples, everyone can agree that triangular form share common features. It does not matter that the triangular form never exists apart from something shaped like a triangle. If it has a triangular form, it has three sides, encloses an area, and the sum of its angles is 180 degrees.
Some things are better examples of the triangular form than others. Those examples are objectively better or worse to the extent that they conform to the triangular form, despite what other accidental features they may have. For example a glass prism is a better triangle than a yield sign, but being made of clear glass versus painted metal, has no bearing on the fact that both, objectively speaking, are triangular. The principle here is that most everything is also a kind of thing something. Every particular apple is still a kind of apple. Every expression of the triangular form is a kind of triangle.
The only way I could continue would be to explain the difference between conception and imagination, but it probably wouldn't actually interest you anyway. I have never met an intellectually inclined atheist than wasn't also a nominalist, even if they didn't realize it. The two seem to go hand in hand. I suspect that there is an unconscious recognition by atheists that allowing for any kind of actual objectivity could undermine the fundamental assumptions of atheism.
