Sublime

To determine whether an argument is valid, one method is to try your best to imagine or describe a situation in which the premises are true and the conclusion is false. If you can describe a situation with this combination of truth values, then the argument is not valid.

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

If I were to say: “All golden mountains are mountains, all golden mountains are golden, therefore some mountains are golden,” my conclusion would be false, though in some sense my premisses would be true. If we are to be explicit, we must therefore divide the one statement “all Greeks are men” into two, one saying “there are Greeks,” and the other

Contradictory propositions do not merely go against one another. They unsay one another. They cancel one another out. The only logical way to read a writer who rejects the law of noncontradiction, who freely and openly contradicts himself, is mentally to insert the words, “or not” after each of his sentences.