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>The statement "a sea-battle will be fought tomorrow" is either true or false. How would you prove such a statement? You can give it as an axiom, but you have
by ernst_klim 7y ago
>The statement "a sea-battle will be fought tomorrow" is either true or false.
How would you prove such a statement? You can give it as an axiom, but you have to admit it true or false in advance.
You can't have a statement in classic logic which is not an axiom and couldn't be proved true or false. This
> You just don't know which one.
means that your statement is neither true nor false in a given model. How would you even reason using such a statement?
- drdeca 7y ago> You can't have a statement in classic logic which is not an axiom and couldn't be proved true or false. Hm? What of Gödel sentences though? Or, like, the continuum hypothesis? I think I might be misunderstanding you.
- AnimalMuppet 7y agoToday, we make the statement "a sea-battle will be fought tomorrow". Two days from now, the equivalent statement is "a sea-battle was fought yesterday". That statement is either true or false. As far as I can see, this leaves two possible views. First view: The statement today is true or false, just as it will be two days from now. But today we don't know whether it's true or false. Second view: The statement today is neither true nor false, but it will become true or false tomorrow, and will therefore be either true or false two days from now. Pick whichever view you like. The argument is going to come down to differences of (unstated) definition of what it means for a statement to be true.