Guessing w/ Shorter Truth Tables for Consistency

Mr. Nance,

Two questions:
1.  If you guess on consistency must you guess again as in validity and equivalence?
2.  If you find it inconsistent once does that trump consistency no matter what?

Thanks so much in advance for your help.


1.  If you guess on consistency and get no contradiction, then you do not have to guess again. This is also true for validity and equivalence. In all three, if you guess, fill in truth values, and get no contradiction, then the question is answered (either that they are consistent, as in this case, or that the argument is invalid, or that the propositions are not equivalent).

2.  No, if you guess and get a contradiction (which looks like an inconsistency), then you must guess again, because the contradiction may mean that you just guessed wrong.

If you think about what consistency means, then all this makes sense. Consistency means the propositions can all be true. So if you assume they are true and can fill in the truth values without contradiction (even when you need to guess), then you have shown that they can be true.

Below is a short video in which I explain how shorter truth tables are used to determine consistency. 


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