The Art of Logic

A powerful aspect of abstraction is that many different situations become the same when you forget some details.

Mathematics is the logical study of how logical things work.

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

In that situation the key would be to change someone’s mind about that core principle rather than anything else.

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

It doesn’t mean that you won’t ever try, and that nobody else will, it’s just that right now you’ve decided this is your starting point and is the basis of your logical system, or your belief system.

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.

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

Time and causation flow in one direction only, and so does logic, and we must be careful not to make errors in direction.