Let’s consider the mathematical equation 1 = 1.
Now let’s try to compare it with 1-1 = 0.
If we compare these two equations with concrete reality, we are forced to conclude that 1 = 1 means, for example, that an apple is equal to itself, not that it is equal to another apple. If we have an apple in our hand and we want to obtain the result of zero, we must subtract exactly that precise apple we have in our hand; we cannot subtract an apple other than the one we are holding.
Now let’s consider 1 + 1 = 2.
In this case, if we consider the concrete reality, we are forced to conclude that 1 = 1 means that an apple is equal not to itself, but to another apple that is not itself. If we have an apple in our hand and we want to get the result of 2, we have to add a different apple. If we add an apple to itself, we don’t get 2, but 1.
Now the question: does 1 = 1 mean that an apple is equal to itself or does it mean that an apple is the same as another one different from itself? In both cases we run into a contradiction: if we say that 1 = 1 means that an apple is equal to itself, we have problems with 1 + 1 = 2, because an apple added to itself does not give 2 as a result. If we say that 1 = 1 it means that an apple equals another one different than the one we have, we find problems with 1-1 = 0, because, if we have an apple in our hand, we cannot subtract a different one from the one we have.
Like other paradoxes, this proves to be a paradox only if we link theory with practice. If we keep theory and practice separate, there is no contradiction, there is no paradox. We can also say that mathematics is not concerned with material apples, but with their quantities. But this means keeping ourselves strictly within the theory, without connecting it with practice. In this case we are forced to conclude that mathematics cannot be related to material objects, it has no relevance, it has no correspondence with reality! In reality, we are not dealing with abstract quantities, but with very specific objects.
If you know of somebody else having already described this paradox, let me know.