Propositional Logic - Connectives and Truth Tables

The Stoic philosophers bequeathed us with an important theory of ethics and a very respectable account of the nature of the good life. What's less well known, outside of philosophical circles, is that they are also responsible for developing a theory of logic that can impressively deal with most forms of everyday reasoning. Logicians and mathematicians, especially over the pasts two hundred years, have come up with more sophisticated theories of logic, but the stoic propositional logic is good enough for most ordinary purposes.

Part of the stoic insight comes from the fact that they devised methods for organizing, systematizing, formalizing and evaluating compound statements (such as "if it's raining, then it's wet, but since it's not wet, then it can't be raining"). Sure, that one may seem obvious, but their brilliance comes from the fact that no matter how long or complex an argument is (or what the argument is about), it can be systematically broken down into simple statements, allowing us to do a thorough analysis of each of its parts, and then systematically evaluating whether the argument as a whole makes logical sense or not.

But before we learn how to do that, we need to have a little introduction to the idea of connectives and truth tables. Once you know these basic ideas, we'll start to apply them to complex arguments of the kind you are likely to come across daily.

Click here for the next lesson: using truth tables to determine the validity of complex arguments, no matter how complex they are.

If you're interested in how the stoics contributed to the study of logic, how they departed from Aristotle's logic of predication, and why this was important for their materialistic philosophy, you'll find the following audio fascinating:

And don't forget to check out all our related posts in the logic tag, especially our hilarious primer on logical fallacies.