Wednesday, April 29, 2015

An ontological feedback loop. Interesting!

Every ring is a group so groups are more general than rings.


Every group is an object within a formal system, so formal systems are more general than groups.


Every formal system is a grammatical system, so grammatical systems are more general than formal systems.


The space of all grammatical systems is a set[*], so sets are more general than grammatical systems.


Every set is an object "within" a grammatical systems, so grammatical systems are more general than sets.


Therefore, grammatical systems are as general as sets.

Since the word set is atomic, given the previous line, the term "grammatical system" is also atomic.




[*] the most questionable step