The Art of Logic

Mathematics is the logical study of how logical things work.

A implies B. B is implied by A. • If A then B. B if A.

for now it’s important to note that the grey area should be included somewhere, otherwise we’re just ignoring part of reality.

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.

be true, not by cause and effect, not by probability, not by observation, but by something inherent that will never ever change.

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

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.

A is a sufficient condition for B. B is a necessary condition for A. • A is true only if B is true. Only if B is true is A true.

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