There are things with names which I can pick up, see, feel, or if too radioactive then at least observe and measure…..this is the reality we have (though some philosophers, and neuroscientists would have us believe otherwise). But what with numbers?
I can see three coconuts, I can count them, and match the count to the quantity, but the number THREE is not real, it is an abstraction from all the occurrences of three object that I have seen or can visualize.
Well, if THREE is not real then MINUS THREE hasn’t got a chance at being real, it is in fact a second stage abstraction, as negative numbers were invented by humans to deal with situations not adequately described with “ordinary” numbers. It gets worse, as complex numbers were invented to get over the difficulties with “real” numbers (the positive and negative numbers). It is a shame about the use of the word “real” in this situation (see above). They should have been called “simple numbers”.
Abstraction is also the basis of geometry. Euclid says “A line is that with extent but no breadth”, which does make it difficult to see!