Separate chapters on derivations in sentential and quantificational logic.
The main change I made to Magnus’s text is breaking up derivations in sentential logic and quantificational logic and move the material on sentential derivation earlier. Magnus’s original textbook featured an opening chapter on the basics of argument, a chapter on symbolizing into sentential and logic, a chapter on truth tables, and chapter on quantificational logic, a chapter on models for quantification, and then a combined chapter on derivations in sentential and quantificational logic. Derivation is the most important part of a traditional formal logic course, and to get it all at once using advanced quantificational concepts was too much for my students. Separating derivations in sentential logic gives the text a nice symmetrical structure. After introducing the basic ideas of argument, you get sentential logic, models for sentential logic (that is, truth tables) and the derivations in sentential logic. The whole pattern is then repeated for quantificational logic. Along the way, we can talk about the difference between syntax and semantics and at least introduce the concept of completeness proofs.
A separate section on proofs with subproofs.
The Magnus text uses a true system of natural deduction, with introduction and elimination rules for each connective. This makes for an elegant system, but it means that if you introduce all the rules at once, students have to digest the concepts of direct proof, indirect proof, and conditional proof all at the same time. To get around this problem, I first introduce the six rules that don’t require the introduction of subproofs. Then I have exercises that only require these six rules. After students get practice with those proofs, I introduce conditional proofs and the accompanying inferences rules. Indirect proofs and their inference rules are in still another section. A more gradual introduction of techniques in derivation makes things much much easier for students.
More exercises on individual component skills.
Within each section I have tried to introduce exercises developing the individual component skills that go with each section. Mostly my changes were modeled on techniques used in Hurley’s A Concise Introduction to Logic. For instance, following Hurley, when introducing truth tables I have separate exercise for identifying the main connective in a sentence. Then I have exercises that ask the student fill out single lines of truth tables assuming that some letters represent true sentences and others false. Only then do you go on to do complete and indirect truth tables to discern important properties like validity.
Similarly, when introducing derivations, I follow Hurley in having the student spend time identifying substitution instances of different sentence forms, and then of different argument forms, before stringing them together in deductive proofs, and even then I begin with filling in the blanks on existing proofs.
For a full version history of the text, click here.