Doing first-order logic

Now that we are familiar with some of the ins and outs of first-order syntax and semantics, we can start covering the central notions of first-order logical systems. As you will see, the account will be eerily similar to the zeroth-order one above. In fact, first-order logic is an extension of zeroth-order logic, in the sense that every valid argument of zeroth-order logic is also valid in first-order logic (but not vice versa!). As with zeroth-order logic, logical notions can be formulated in two ways; semantically and syntactically. Thankfully, since first-order logic is sound and complete, just as zeroth-order logic is, we can be sure that validity and satisfiability will coincide, whether formulated semantically or syntactically.