We laid out two criteria for a persuasive argument: that the conclusion follows from the premises, and that the premises are all true. But what does it mean for a conclusion to “follow from” the premises? In deductive inference, we want to know whether an argument is valid and whether it is sound. What do these terms mean and how are they used?
Truth Tables are a useful tool for analysing propositions and arguments alike. They allow us to give precise definitions for our logical connectives. They also allow us to show systematically that a proposition is a tautology or contradiction, and to prove that an argument is valid or invalid. How do we create truth tables?
What does it mean for two propositions to be logically equivalent? When can we swap out a proposition for another? Using the method of Truth Tables, we can formalise a way to discover whether two propositions are logically equivalent, and deploy this method to transform our claims into the most useful form to deploy them in arguments.
Test your skills at formalising arguments by trying your hand at this quiz. Can you identify which sentences have which basic propositional forms?
This quiz will test your ability to formalise more complex sentences into propositional form. You should try this after you’re confident in formalising basic propositions.