On Mar 12, 12:58 am, "DavidW" <n...@email.provided> wrote: > Transfer Principle wrote: > From these lecture notes by Harvey Friedman comes one of the best > metamathematical anecdotes I've ever heard (and yes, I've heard my share). > Apparently Friedman was attending a talk by the "ultra-finitist" Alexander > Yessenin-Volpin, who challenged the "Platonic existence" not only of infinity, > but even of large integers like 2^100. So Friedman raised the obvious "draw the > line" objection: in the sequence 2^1,2^2,.,2^100, which is the first integer > that Yessenin-Volpin would say doesn't exist? > Yessenin-Volpin asked Friedman to be more specific. > "Okay, then. Does 2^1 exist?" > Yessenin-Volpin quickly answered "yes." > "What about 2^2?" > After a noticeable delay: "yes." > "2^3?" > After a longer delay: "yes." > It soon became clear that Yessenin-Volpin would answer "yes" to every question, > but would take twice as long for each one as for the one before it.
Do these 'finitists' deny that R is closed under multiplication or addition? What about Z?
This business of waiting twice as long as the previous question carries absurdity to a new exterme. If 2^3 exists, and they accept closure, then 2*2^3 exists and it doesn't take twice as long to determine it.