On Tuesday, 4 March 2014 16:09:32 UTC+2, Peter Percival wrote: > John Gabriel wrote:
> Is magnitude a mathematical thing?
It all depends on what you mean by a "mathematical thing". Ideas do not belong only to mathematics, but to all knowledge.
> Because if so I would hesitate to define it as an idea of any kind.
There is no other way to define it except as an idea or concept.
> Mathematical thing seem to have a life of their own: so if I add the "ideas" 2 and 3 I get the "idea" 5, and so do you.
2 and 3 are not ideas. They are symbols for rational numbers. In this case natural numbers. These are the reification of the measurement of magnitudes. A magnitude can refer to a line distance or mass or volume or any other concept requiring measure.
> How is that possible? Then there is Wigner's > "unreasonable effectiveness of mathematics in the natural sciences". > Whatever mathematical things are (and don't ask me, I haven't a clue) > they seem to be rather more than just ideas.