issuevoter wrote on Sep 4
th, 2018 at 6:29pm:
Super Nova wrote on Aug 31
st, 2018 at 4:33pm:
Plato claimed that numbers exist in some mind-independent abstract heaven. Nominalists claim that there is no such heaven. Clearly, we can't see, hear, taste or feel numbers. But if there are no numbers what is mathematics all about?
Actual numbers: 0, 1,2,3 et cetera are part of written language, and are used to express concepts. Therefore, they are human constructs, but if we are talking about the concepts they express, they appear to be borne out in physics. If we say we cannot sense them, I am not sure that is so. I can hear musical intervals, perhaps not as well as some, but I easily hear 1, 3, 5 in the major scale. Its like when the Three Stooges do that Hello, Hello, Hello, routine.
I think many of the concepts they express are representations of the physical world. However, there are concepts that are not.
Simple example of a number that is represented would be PI. The ratio of the diameter to the circumference. A number derived by observing the physical world. Very useful number.
Concepts that I would challenge that are useful to mathematics but may not be represented in the physical world IMO are:
- Infinity – there is not evidence that anything is infinite in the universe…. Just a handy concept
- Imaginary numbers based on SQRT(-1). Useful but does not exist.
- Higher dimensional maths. Purely conceptual, very useful as pure thought and extending to other problems…. But do they exist