MHB What does it mean for G to be consistent with Q?

[agapito]

My text if Smith's Godel book. We establish that G (Golbach's conjecture and a Π1 wff of Robinson's Arithmetic Q) is true if and only if Q cannot prove ¬G.

That much is clear. But then it goes on to say:

G is true if and only if G is consistent with Q.

We know that Q is sound (and thus consistent), so can someone please explain what "consistent with Q" means.

Thanks for all help.

 

[HallsofIvy]

"G is consistent with Q' simply means that G and Q do not contradict each other. That, in turn, means that we cannot use G and Q to prove both statement "T" and statement "not T".

 

[agapito]

"G is consistent with Q' simply means that G and Q do not contradict each other. That, in turn, means that we cannot use G and Q to prove both statement "T" and statement "not T".

Greatly appreciate your help with this, agapito