fom
Posts:
1,969
Registered:
12/4/12


Re: Distinguishability of paths of the Infinite Binary tree???
Posted:
Dec 26, 2012 4:47 PM


On 12/26/2012 9:49 AM, WM wrote:
> http://planetmath.org/?op=getobj&from=objects&id=12607
The example is really cute.
I just finished reading through a great deal of Leibniz. He portrayed his logic as being oppositely oriented from that of scholastic thinking. So, the hierarchy of genera in the two logics is opposed.
Scholastic logic is extensional, but Leibniz logic is intensional. Curiously, he also attributes the principle of identity of indiscernibles to Thomas Aquinas. The summary statement was
"an individual is the lowest species"
This may clearly be interpreted along the lines of Cantor's intersection theorem with vanishing diameters.
Set theory, itself (along with the Fregean "extension of a concept"), is based on extensionality.
So, while I will take a little more time to weigh your example, it does reflect precisely a mismatch in the historical development.

