ABSTRACT
This chapter distinguishes two important uses – establishing a conclusion, and disestablishing a set of premisses. Now to prove a proposition is not merely to show that it follows from some set of premisses –– reader must show that the proposition is true. But if they can show that it follows from true premisses, then it must be true. For if the conclusion follows from the premisses, the inference is valid; and the key feature of a valid inference is that if its premisses are true, the conclusion cannot be false. Or to put it another way: Whatever follows from true premisses is itself true. The combination of false premisses and a valid inference may yield a true conclusion, but falls short of giving us reader the guarantee of truth of the conclusion that look for in a proof. Equally, the combination of true premisses and an invalid inference may yield a true conclusion, but does not guarantee its truth.
