The Art of Logic

The key is to remember that it is both statements “A” and “A implies B” that together allow us to infer statement B. So if statement B is not true it is either because A isn’t true or because “A implies B” isn’t true. The possibility of the implication being untrue is often overlooked.

It doesn’t make more things true, it just uncovers more true things than we saw before.

The two are linked, but in mathematics they are particularly cyclically linked.

The idea of logic is to have clear rules so that conclusions can be drawn unambiguously and consistently by different people.

many arguments in real life go wrong because of problems with the groundwork rather than with the argument per se.

Like time, logic has a direction and we must not try to violate it.

soundly but starting from different basic beliefs. So two people can both be logical but still disagree about things.

It is important to note that this is logically different from concluding that the hypothesis is false, which would be the opposite rather than the negation. If you have insufficient evidence to support a hypothesis, it means that the truth value is still unknown. Maybe you need more data. Maybe you need a better experiment.

encapsulate the most important building block of logical arguments: logical implication.