fom
Posts:
1,968
Registered:
12/4/12


Re: Matheology § 233
Posted:
Mar 27, 2013 10:12 PM


On 3/27/2013 4:56 PM, WM wrote: > > So the structure of the tree is something very special. Uncountability > seems to be a matter of how numbers are written. >
No. Uncountability is a logical delineation.
The justification for making that delineation is an argument scheme that applies to syntactic representations intended to prove a specific claim.
The fact that syntactic representations cannot faithfully represent the claim leads to defining systems in which the substance of the claim may be subjected to mathematical analysis.
Thus one obtains a definition of countability.
Thus one obtains the logical form of genus and species.
Genus  number system
Species  countable number system
Coordinate species  uncountable number system
"For falsity and truth involve combination and division."
Aristotle
Not that WM could understand a word of the above.

