Did I discover “Angelo Cannata’s paradox”?
Posted: Thu Sep 14, 2017 11:36 am
Let’s consider the mathematical equation 1=1.
Now let’s compare it with 1-1=0.
If we connect these equations with practical reality, we must conclude that 1=1 means that, for example, an apple is equal to itself. If we have an apple and we want to obtain the result of 0, we must subtract precisely that one apple that we have in our hand; we cannot subtract an apple that is a different one.
Now let’s consider 1+1=2.
In this case, if we consider practical reality, we must conclude that 1=1 means that an apple is equal not to itself, but to a different one. If we have an apple and we want to obtain the result of 2, we must add a different apple. If we add an apple to itself, we don’t obtain 2, we obtain 1.
Now the question: does 1=1 mean that an apple is equal to itself or does it mean that an apple is equal to another one? In both cases we obtain some 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 summed to itself does not give 2 as a result. If we say that 1=1 means that an apple is equal to another one, we have problems with 1-1=0, because, if we have an apple in our hand, we cannot subtract a different apple.
Like other paradoxes, it reveals its being a paradox only if we connect theory and practice. If we maintain separated theory and practice, there is no contradiction, no paradox. We could say that maths does not consider material apples, but their quantity. But this means to maintain ourselves strictly into theory, without connecting it to practice. In that case, we should conclude that maths cannot be connected with material objects, maths has no relevance, no correspondence with reality!
Now let’s compare it with 1-1=0.
If we connect these equations with practical reality, we must conclude that 1=1 means that, for example, an apple is equal to itself. If we have an apple and we want to obtain the result of 0, we must subtract precisely that one apple that we have in our hand; we cannot subtract an apple that is a different one.
Now let’s consider 1+1=2.
In this case, if we consider practical reality, we must conclude that 1=1 means that an apple is equal not to itself, but to a different one. If we have an apple and we want to obtain the result of 2, we must add a different apple. If we add an apple to itself, we don’t obtain 2, we obtain 1.
Now the question: does 1=1 mean that an apple is equal to itself or does it mean that an apple is equal to another one? In both cases we obtain some 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 summed to itself does not give 2 as a result. If we say that 1=1 means that an apple is equal to another one, we have problems with 1-1=0, because, if we have an apple in our hand, we cannot subtract a different apple.
Like other paradoxes, it reveals its being a paradox only if we connect theory and practice. If we maintain separated theory and practice, there is no contradiction, no paradox. We could say that maths does not consider material apples, but their quantity. But this means to maintain ourselves strictly into theory, without connecting it to practice. In that case, we should conclude that maths cannot be connected with material objects, maths has no relevance, no correspondence with reality!