XYZKLUB: Beginning in the Fall of 1959

XYZKLUB Earman, John and Norton, John (1996) Infinite Pains: The Trouble with Supertasks. It was devised in 1954 by British philosopher James F. Thomson, who used it to analyze the possibility of a supertask, which is the completion of an infinite number of tasks. Now mathematicians do say that this sequence has a sum; they say that its sum is 1⁄2. And this answer does not help us, since we attach no sense here to saying that the lamp is half-on. It seems impossible to answer this question. It cannot be off, because I did in the first place turn it on, and thereafter I never turned it off without at once turning it on.|Synthetic Biological Circuit