On logic and mathematics
Only logically valid mathematical operations are universal.
Consider a simple mathematical operation like 1+1 is equal to how much? Any nursery going child will answer it as 2.
Yes, so simple.
Now consider adding 1 apple and 1 apple, how many? Obviously 2 apples.
Now consider adding 1 apple and 1 orange, how much?
Not so simple isn’t it ?😀
We cannot add two dissimilar objects because they don’t belong to same set of fruits. They belong to different sets.
Now consider sets.
Sets are mathematical collection of objects with similar qualities. For example a set of odd or even numbers or a set of fruits.
We can carry out all mathematical functions in between the objects of a single set because it’s objects have similar qualities.
Hence two apples can be added but an apple and an orange cannot be added unless you consider a larger set consisting of all fruits.
So, in order to conduct all mathematical operations, the first thing we have to do is; remove distinctions between all objects and consider only the universal set.
This allows all possible operations to be carried out among entities and let them have different qualities at the same time.
So 1+1 is 2 only when both the 1 belong to same set or it is an operation in a universal set.
The principles and operations of mathematics have to follow logical rules to have a universal application.
Did you get the logic of the discussion?
Only logically valid mathematical operations are universal.