Nicely done. The math will never work, i.e., the second of your two possibilities seems to me correct, and for reasons you suggest. The objects in question are not of the same order (the sets are messy), and can be deemed so only for brief periods and with large numbers. Even things that appear stable and countable, paradigmatically units of a currency, in fact fluctuate with the price of and confidence in that currency. So we're back to Keynes, constantly checking the formalization against the world, or even Robinson, just talking about the world. Sigh. :)
But there's something else at work: right now, and for the foreseeable future, the academic and indeed financial game is big data and big compute. So "right enough" will rule.
Nicely done. The math will never work, i.e., the second of your two possibilities seems to me correct, and for reasons you suggest. The objects in question are not of the same order (the sets are messy), and can be deemed so only for brief periods and with large numbers. Even things that appear stable and countable, paradigmatically units of a currency, in fact fluctuate with the price of and confidence in that currency. So we're back to Keynes, constantly checking the formalization against the world, or even Robinson, just talking about the world. Sigh. :)
But there's something else at work: right now, and for the foreseeable future, the academic and indeed financial game is big data and big compute. So "right enough" will rule.