NationStates Jolt Archive

a thumbs up for those that see the error:

Z and A both stand for sentences:

A: everything i say is true.
Z: If this sentence is true, then everything i say is true.
Z: if Z then A
Z: Z -> A
so:

1: Z <-> ( Z-> A) (Z is equivalent to ( Z-> A), this is true)

2: Z -> (Z -> A) (from 1)

3: Z -> A (from 2)

4: (Z -> A) -> Z (from 1)

5: Z (from 3 and 4)

6: A (from 5 and 3)

So in a nutshell: everything i say is true!

a thumbs up for those that see the error:

Your error is in your definition for "Z." In sentential logic, only simple sentences get a letter of their very own. "Z" is not a simple sentence, it is a compound sentence of the form A->B. So you have something like,

X="This sentence is true."
A="Everything I say is true."

You are left with the mere assertion that X->A... but no way to prove it, or to prove A. Notice that your original definition is inconsistent. If Z were logically identical to (Z->A), that is, if they were the same statement, then they would have identical truth tables, but of course they do not:

A....Z.... \ ....Z....Z->A

T....T.... \ ....T....T
T....F.... \ ....F....T
F....T.... \ ....T....F
F....F.... \ ....F....T

Everything you say cannot be true because there's several snipers pointing guns to your head and waiting for you to acknowledge that YOUR WRONG!

Ok, I agree with you, everything you say is true, now go to bed...snore

Ok, what the hell is up with this A and Z stuff? What ever it is, I don't care. Your wrong though, if I read the original post correctly.