I have been thinking of sylogisms.
Supose that one set out a sylogism:
If: A
And: B
Then: C
And another:
If: D
And: E
Then: F
We know that A, B, D, and E are all true.
But what happens when C contradicts F?
Lets analyze a paradox with that:
"This sentence is false."
A: The sentence is either true or false.
B: it is false.
C: Then it is true
That logic is faulty since it cannot be both true and false. Therefore we must change one of the assumptions. Lets try again:
A`: The sentence is either true or false.
B`: it is true.
C`: Then it is false.
That logic is faulty since it cannot be both true and false. Therefore we must change one of the assumptions.
Can we change assumption A or A`?
Can the sentence be both false and true? No.
Can it be neither false nor true? I don't know but that would solve the dillemma. Lets set that up and ask?
D: The first sylogism is not logical
E: The second sylogism is not logical
F: at least one sentence that is either true or false cannot be either.
Hmmm? That can't be.
I don't know if there are any paradoxes that we could apply this logic to and come up stumped while not making any mistakes (I can the mistake I made above). But if we do then logic must be ilogical. (kind of in the way that 2 feet +2 feet =4 feet except at light speeds or in the big bang)
I am not particularly interested in knowing if that paradox is solved or not but in knowing if there are any that have not been solved. If any one has not been solved then the door is open to the possibility that the resolution is that logic is not logical.
