Harvey M. Friedman on his meeting with Alexander Esenin-Volpin
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Imagine this is a pic:
"I have seen some ultrafinitists go so far as to challenge the existence of 2^100 as a natural number, in the sense of there being a series of "points" of that length. There is the obvious "draw the line" objection, asking where in 2^1, 2^2, 2^3, … , 2^100 do we stop having "Platonistic reality"? Here this … is totally innocent, in that it can be easily be replaced by 100 items (names) separated by commas. I raised just this objection with the (extreme) ultrafinitist Yessenin-Volpin during a lecture of his. He asked me to be more specific. I then proceeded to start with 2^1 and asked him whether this is "real" or something to that effect. He virtually immediately said yes. Then I asked about 2^2, and he again said yes, but with a perceptible delay. Then 2^3, and yes, but with more delay. This continued for a couple of more times, till it was obvious how he was handling this objection. Sure, he was prepared to always answer yes, but he was going to take 2^100 times as long to answer yes to 2^100 then he would to answering 2^1. There is no way that I could get very far with this. "
— Harvey M. Friedman, "Philosophical Problems in Logic"
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Imagine this is a pic:
"I have seen some ultrafinitists go so far as to challenge the existence of 2^100 as a natural number, in the sense of there being a series of "points" of that length. There is the obvious "draw the line" objection, asking where in 2^1, 2^2, 2^3, … , 2^100 do we stop having "Platonistic reality"? Here this … is totally innocent, in that it can be easily be replaced by 100 items (names) separated by commas. I raised just this objection with the (extreme) ultrafinitist Yessenin-Volpin during a lecture of his. He asked me to be more specific. I then proceeded to start with 2^1 and asked him whether this is "real" or something to that effect. He virtually immediately said yes. Then I asked about 2^2, and he again said yes, but with a perceptible delay. Then 2^3, and yes, but with more delay. This continued for a couple of more times, till it was obvious how he was handling this objection. Sure, he was prepared to always answer yes, but he was going to take 2^100 times as long to answer yes to 2^100 then he would to answering 2^1. There is no way that I could get very far with this. "
— Harvey M. Friedman, "Philosophical Problems in Logic"
Forgot to attach the pic?
