if you don’t mean any ontological import you might want to phare it as “integers is system that works”. The negation would be things that dont’ work. For example a triangle with a right corner with angles summing over 180 degrees. But even then you have to specify the background assumptions as those kinds of triangles actually work out. Usually a mind defaults to a euclidean mindset while the applied concepts could apply to non-euclidean context too.
That integers exist could mean a number of things. Like that x + y = y + x for every x and y that is a value. However the logic of non-commuting values has been figured out. Therefore that sentence would be false. There are things that don’t fall under this rule meaning this is not an universal rule. Having some assumtion that you need not have violated in your life doesn’t mean such a violation would be impossible. The only way back would be to explicitly declare the delineation of that context ie the various properties needed. But then “integers exists” becomes just “assuming integers integers is all there is” which isn’t very surprising or would need any explanation.
if you don’t mean any ontological import you might want to phare it as “integers is system that works”. The negation would be things that dont’ work. For example a triangle with a right corner with angles summing over 180 degrees. But even then you have to specify the background assumptions as those kinds of triangles actually work out. Usually a mind defaults to a euclidean mindset while the applied concepts could apply to non-euclidean context too.
That integers exist could mean a number of things. Like that x + y = y + x for every x and y that is a value. However the logic of non-commuting values has been figured out. Therefore that sentence would be false. There are things that don’t fall under this rule meaning this is not an universal rule. Having some assumtion that you need not have violated in your life doesn’t mean such a violation would be impossible. The only way back would be to explicitly declare the delineation of that context ie the various properties needed. But then “integers exists” becomes just “assuming integers integers is all there is” which isn’t very surprising or would need any explanation.