Although it may seem boring (it’s not!), understanding logical symbols and concepts is crucial if one is to learn how to think. The concepts in the images below, known as the rules of implication, are used in nearly every philosophical argument, so knowing them is extremely valuable. Below are three pictures that will equip you with the essential logical concepts to engage with and read complex philosophical writing. They derive from a philosophy professor’s course titled, “Logic and Critical Thinking“.
A note on symbols:
- ^ and • both mean “and”
- v means “or”
- ~ means “not” or “it is not the case that”
- –> or a sideways-U means “if ___ then ___” or “implies”. For example, P –> Q means “If P, then Q”, or “P implies Q”.
- Treat :: as meaning “is identical to”
- Treat three lines on top of one another as “if and only if”. This is also signified by a bidirectional arrow (since it is a biconditional): <–>