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SecondWind comments on Second-Order Logic: The Controversy - LessWrong
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Hmm.
So, it's not sufficient to define a set of steps that determine a number... it must be possible to execute them? That's a rather pragmatic approach. Albeit it one you'd have to keep updating if our power to compute and comprehend lengthier series of steps grows faster than you predict.
No, ultrafinitism is not a doctrine about our practical counting capacities. Ultrafinitism holds that you may not have actually denoted a number by '3^^^3', because there is no such number.
Utlrafrinitists tend no to specfify the highest number, to prevent people adding one to it.
Hence "may not"