True of False: All the worlds knowledge can be placed into only these two catagories

[SuperDemocrat]

I was wondering can we have some other category besides true of false to place all the world's knowledge into? We can take everything that is said or thought and either place it in the true or the false category. I could be wrong on this so is there must be another category to place any of the world's knowledge into? And if that is possible are we not saying that the idea that their can only be true of false is false and therefore we are using a binary system of logic to prove that binary systems of logic doesn't exist? if it doesn't exist then how do can we use it to prove it doesn't exist?

 

[Pogo]

People can be divided into two types:
Those who divide people into two types, and those who do not.

 

[SuperDemocrat]

People can be divided into two types:
Those who divide people into two types, and those who do not.

For the people who don't aren't they kind of contradicting the fact that people can be divided into two groups? Then people can't be divided into two groups so we can't have those that divide people into two groups and those that don't.

 

[Pogo]

People can be divided into two types:
Those who divide people into two types, and those who do not.

For the people who don't aren't they kind of contradicting the fact that people can be divided into two groups? Then people can't be divided into two groups so we can't have those that divide people into two groups and those that don't.

Aye but that's from the perspective of the former group. The latter doesn't believe it. Which must mean the latter doesn't believe the former exists.