Comment by paganel

I’m a Marxist on this and I’m saying that a “big enough quantitative change equals a qualitative one”, meaning that in the first example if you stretch that cup long enough in order to almost change it into a plate then the cup is actually not a cup anymore (because of the quantitative “long enough”) and trying to answer the question “does a cup have a hole?” by presenting as a counter-example a “long enough” stretched out cup (which is not a cup anymore) serves no purpose. The second example with the straw which can be seen at the limit as a doughnut is similar. Granted, I’m not a topologist, just an admirer of Hume and of his fascination for mathematical induction and of people’s blind faith in it (stretching a cup until it’s no longer a cup can be seen as similar to some mathematical induction operations).