Tag: deduction

The power of logic

Most people think that the purpose of an argument is to justify its conclusion — and to thereby establish its certainty — and that the problem with inductive arguments is that they fail to establish their conclusions with objective certainty since their conclusions may be false even if all of their premises are true. But this entirely confuses the issue, and it has even enabled inductivists to take the high ground in the debate, arguing that objective certainty is an impossible dream, and that inductive arguments are not, as a consequence, at fault for failing to achieve it.

But if the uncertainty of their conclusions were the problem with inductive arguments, then we would also have a similar problem with deductive arguments. For the premises of a deductive argument may be false. And the conclusion of a deductive argument may be false as well.

Contrary to what most people think, logical arguments cannot establish the truth, let alone the certainty, of their con­clusions. And so contrary to what most people think, the problem with inductive arguments has nothing to do with the uncertainty of their conclusions.

The best that a logical argument can do is test the truth of a statement. But it can do this only by showing that its falsity is inconsistent with the truth of other statements that can only be tested and never proved. Our so-called ‘proof’ methods are really techniques for testing consistency. And the demonstration that a ‘conclusion’ follows from a ‘premise’ shows only that the falsity of the ‘conclusion’ is inconsistent with the truth of the ‘premise.’

That is all that is involved.

But so long as we regard contradictions as unacceptable, it is really quite a lot.

The inconsistency that marks a valid deductive argument — the inconsistency, that is, between the truth of is premises and the falsity of its conclusion — cannot force us to accept the truth of any belief. But it can force us, if we want to avoid contradicting ourselves, to reexamine our beliefs, and to choose between the truth of some beliefs and the falsity of others — because the falsity of the conclusion of a valid argument is inconsistent with the truth of its premises. …

And this is just another way of saying that what we call a proof actually presents us with the choice between accepting its conclusion and rejecting its premises. …

We construct logical arguments in order to persuade others of our beliefs. But the best we can do is to clarify a choice that they have to make. Inductive arguments, however, cannot even do this. [86-7]