Logical reasoning

Explaining how logical reasoning can sometimes reach wrong conclusions

Is logic a complete and infallible method for approaching the truth?

Logic does not necessarily give us truth, but allows us to see what we already know in a new light.

No amount of logic will substitute for missing knowledge.

The primary usefulness of logic is to uncover contradictions and to simplify our theories about the world.

Logical reasoning is always correct. When wrong conclusions are reached, we say that either the logic was invalid (i.e., not logical) or that some of the axioms and premises were false.

Logic is universal. It applies in all possible worlds.

These points will be better illustrated with examples.

I can have as axioms and premises:
(1) If it rains, I will get wet
(2) It will rain today

Conclusion: I will get wet today.

If I do not get wet today, either (1) or (2) must be false.
(1) could be false by my having an umbrella and raincoat, or by my not going outside into the rain.
(2) could be false because it is not raining today.