Propositional Logic - Using Truth Tables to Evaluate the Validity of Complex Arguments

In our previous lesson on propositional logic, we learned that we can take arguments in natural language (English, Spanish, German, whatever) and translate them into symbolic form through the use of variables to represent statements, and connectives to represent relationships between statements. This helps us set aside irrelevant considerations such as the content of an argument (what the argument is about), or the language used to express that content, and focus instead simply on its formal aspects to evaluate its validity (whether the conclusion follows necessarily from its premises).

The claim was that these basic concepts can be applied to a wide range of arguments, including indefinitely complex ones, and that logicians have developed systematic methods for evaluating the validity of such arguments in a systematic way: it's not just a matter of personal opinion or subjective point of view but of objectively demonstrative rationality.

So, let's take a look at one example of a complex argument, and go through these systematic steps to figure out whether it makes logical sense or not.

For more related posts, check out our logic tag.