https://www.youtube.com/watch?v=6UWhPnbZv-o
created by drinka40tonight on 22/01/2015 at 01:11 UTC
19 upvotes, 2 top-level comments (showing 2)
Comment by Bitfroind at 22/01/2015 at 08:03 UTC
3 upvotes, 1 direct replies
If we abstract from all special features of an individual to get cantors units, isn't it impossible to tell how many of them we have? Would we not get only ONE unit if we abstract all properties that make them individuals and therefore nothing we could count? I don't get it.
Comment by x-ok at 22/01/2015 at 15:44 UTC*
1 upvotes, 1 direct replies
In the speakers example, the bank account he describes would have two dollars, but the 2 dollars would not have the properties of occupying any 2 points in any space. They would be approaching Cantor's ideal, undifferentiated objects in that they could not be distinguished from one another, but they would still have the property of being dollars and so would not be numbers in Cantor's sense. You can't allow them to collapse into one dollar just because the two dollars are not distinguishable from one another. You still have the two dollars no matter what ATM you visit. Therefore dollars are things that do not have the property of occupying points in space. They can be anywhere. They could be exchanged at a specific ATM for 2 distinct objects called bills that themselves each represent one dollar. The two bills therefore each have the property of occupying two points in space but they are not dollars, because dollars do not have the property of occupying points in space. The two dollars no longer have the property of being in the bank account, however. The 2 dollars have the property of being represented by the two bills which are 2 distinct objects occupying 2 points in space. Take the 2 dollar bill objects back to the bank. Give the two bills to the bank and tell them to deposit the 2 dollars represented by the 2 bills back into your bank account. Now the two dollars are back in your bank account. The bank performs the service of storing the 2 dollar bills. Meanwhile, the bills represent nothing while the bank holds them. They cannot be spent. Suppose a teller works at the bank for a period of time sufficient to earn 2 dollars. If the teller wants payment in dollar bills, the bank must transfer 2 dollars out of its account and allow those 2 dollars to be represented by the 2 dollar bills and then gives the bills to the teller. But suppose something else happens before the bank can do that. While the bank is storing the 2 bills, a bank robber who has no dollars robs the two bills from the bank. This is then a fraud because now, even though the bills are not in the bank, they still are the property of the bank and as such they still do not represent any dollars. Now, the robber is a double criminal if he purchases something with the 2 bills. First, he stole bills that are the property of the bank and don't represent any dollars. Second he deceives a merchant into exchanging goods and/or services for dollars that don't actually exist.