On good and bad arguments

at our disposal, and truth-tables tell us that (3) is a valid argument form of classical sentential calculus (CSC); hence, (2) is valid. Essentially the same procedure can be repeated for many other valid arguments; indeed, for all the valid arguments that can be so paraphrased as to fall under the scope of an extant (correct) logical system. No such procedure, however, is available to establish the invalidity of invalid arguments. Consider for example the argument