2011-04-15, 04:52 AM
I think you're misrepresenting how the hypothesis and implications are related.
The hypothesis is not part of the logical statement - it is the logical statement itself.
Hypothesis: (P -> Q)
This hypothesis (P -> Q) is either true or false. You test it experimentally by producing P and seeing if Q occurs. The hypothesis is correct if for all states of P (true/false), the results Q fit.
If it turns out P & ~Q can be achieved, this hypothesis is wrong. If only P & Q, or ~P & ~Q, or ~P & Q, are possible, then the hypothesis is correct.
You "prove" the hypothesis by demonstrating that (P -> Q) is always true. Someone disproves it by demonstrating a case where P->Q is false.
The hypothesis is not part of the logical statement - it is the logical statement itself.
Hypothesis: (P -> Q)
This hypothesis (P -> Q) is either true or false. You test it experimentally by producing P and seeing if Q occurs. The hypothesis is correct if for all states of P (true/false), the results Q fit.
If it turns out P & ~Q can be achieved, this hypothesis is wrong. If only P & Q, or ~P & ~Q, or ~P & Q, are possible, then the hypothesis is correct.
You "prove" the hypothesis by demonstrating that (P -> Q) is always true. Someone disproves it by demonstrating a case where P->Q is false.