If by "numbers" you mean concepts like "two," "five", and "million", then yes: of course numbers are abstract because concepts are abstract.
If by "numbers" you mean, say, these three pencils or those five eggs, then no: in themselves concrete things aren't abstract -- they're merely concrete things.
The key you will learn as you continue reading is that abstractness lies solely in our perspective on things -- aside from such a perspective things like pencils and eggs in themselves are nothing but brute concretes.
answered Sep 11 '12 at 00:38
Greg Perkins ♦♦
Yes, numbers are abstract, because numbers are concepts of quantity. Concepts are abstractions.
It's informative to compare numbers with colors. If you observe an apple and stoplight, you'll notice that they are both red.
If you observe the fingers on a hand, and the toes on a foot, you'll notice they are both five.
Just as color is an attribute of an entity, number is an attribute of a group of things.
An attribute is something about something. An attribute is an aspect. An aspect is a way of observing something.
Observation is the act of relating something to something else, to see how they differ (differentiation) or how they are the same (integration).
These hows are aspects. The fingers on your hand, and the toes on your foot, are the same in number. The apple and the stoplight are the same in color.
We have concepts for entities, concepts for aspects, concepts for relationships, concepts for actions, etc. Every concept is an abstraction, though some concepts are more abstract than others. For instance "integer" is more abstract than "three" and "molar" is more abstract than "tooth", and "color" is more abstract than "red".