What does that prove? Merely that some mathematical truths are the result of arbitrary axioms and rules but it is absurd to suggest that all mathematical truths fall into that category.
Is the difference between positive and negative imaginary? If one animal had one eye and another two there was no difference between them?
Before there were humans there was no such thing as mathematics or any mathematical truths.
There was no such thing as mathematics but mathematical** facts** existed. There were the same number of planets around the earth - not created for any human purpose.
Your solution to the nature of mathematics is simplistic. Do you believe numbers are arbitrary? Is the speed of light a human invention? Forget about the units of measurement: the ratio of the distance travelled to the time taken is not arbitrary or devised by man. Neither is the proportion of hydrogen atoms to oxygen atoms in water. Nor is the number of planets in the solar system nor the mathematical value of physical constants.
numbers are not arbitrary. neither are tractors. both are human creations.
Did men create the** proportion** of hydrogen atoms to oxygen atoms in water? That is a numerical
relation which exists independently of man.
The word or symbol 2 is a convention but what it refers to is a fact! Unity or duality don’t depend on us for their existence.
what need could there have been for such concepts before there were human beings who could wield them?
There was no need for them but the
reality to which the concepts refer existed nevertheless. Things or facts don’t cease to exist just because no one needs them or is aware of them. Science doesn’t consist solely of inventions but mainly of discoveries. And it is not primarily the existence of things but
how they are related. Seeing things is not enough. You need to **interpret **and
understand what you see. There is far more in life than the evidence of your senses…
where would these concepts have been before humans existed?
Where was the** fact **of gravitation before humans existed? In the mind but not only in the mind because knowledge exists only in the mind. We don’t know or understand things themselves. We know and understand
facts about things. We don’t create or invent facts: we discover them.
you speak as though 2-ness is a fundamental platonic essence or something. plato thought sick people have an excess of “fever” and that odd numbers lack “duality.” thankfully, philosophy has finally gotten past plato in the past hundred years or so.
It has nothing whatsover to do with essences but facts. If you deny facts exist you are left without knowledge because knowledge is composed of facts. In other words if truth doesn’t exist you cannot reach any conclusions. An illusion is not a tool, let alone a reliable tool. If only material objects exist there is no such thing as meaning, so it does not even make sense to say everything is meaningless! Reasons disappear and all that is left are physical causes. The inevitable outcome of materialism is total scepticism - which of course is self-destructive because the theory of materialism is not a material object!
it is one thing to think that the invention of 2-ness was as inevitable for humanity as the invention of the wheel or the incline plane, but quite another to think that such a concept could exist without minds to invent it and to contain it.
So according to you there was no difference in quantities or velocities or forces or proportions before humanity existed? There weren’t two atoms of hydrogen and one of oxygen in water?
words and numbers are tools like wheels and hammers that humans invented to help meet human needs.
So you believe a number is an illusion? What then do the binary, decimal and hexadecimal systems refer to? Imaginary units? No. They are different methods of counting** the same variations in quantity**. Different languages express the same ideas. We don’t think with words but with concepts which refer not only to tangible things but intangibles like persons, emotions, relations, principles and purposes. Thought cannot be reduced to mechanical activity. That is a programmers’ myth…