Philosophy of (2 + 2 = 4)

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It is said (2 + 2 = 4) is always true. Yet this is not true at all. At least under the current mathematical construct. For example....

2 tiny apples plus 2 tiny apples equals 4 tiny apples.

2 large apples plus 2 large apples equals 4 large apples.

If you think these two sets, are the same 4 apples....then ask a starving man. He will point out to you the difference.

So then to fix this problem we must assign dimensional quantities to abstract numbers. The same way we assign dimensional units to concrete numbers.

All abstract numbers....should be assigned an abstract quantity of dimension.
 
$2+2 = 4$ is about abstract objects called "natural numbers". These objects can be used to calculate an amount of any objects as long as every object counts as $1$. The fact that a large apple is more food that a tiny apply is completely independent from the fact that 2 tiny apples + 2 tiny apples = 4 tiny apples.
 
$2+2 = 4$ is about abstract objects called "natural numbers". These objects can be used to calculate an amount of any objects as long as every object counts as $1$. The fact that a large apple is more food that a tiny apply is completely independent from the fact that 2 tiny apples + 2 tiny apples = 4 tiny apples.

It is not independent. Again ask a starving man. Further large and tiny, are not units. They are abstractions. This shows philosophically that absract numbers NEED absract units.

2 is not 2 necessarily. There can be abstractly, a large 2, and a tiny 2.

Consider how 1/2 is the inverse of 2/1. If it were not for the cardinality of the given numbers....ergo their value. Then this would be an example of a tiny 2, and a large 2.
 

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