This guide covers many different topics and specialties related to logic so it may help to introduce a taxonomy so we don't get intimidated by the breadth of Dr

This guide covers many different topics and specialties related to logic so it may help to introduce a taxonomy so we don't get intimidated by the breadth of Dr. Smith's scholarship. Let's break it down into 5 topics: 1. Using a well-known and widely accepted system of logic to produce proofs and solve problems. A working man's logic is propositional logic (AND, OR, NOT, and the material conditional) plus first-order predicate logic (quantifiers "there exits" and "for all" over bound variables), natural deduction, and ZFC set theory. 2. "non-standard" logic systems which are somehow "better" or "more expressive:" 2nd order logics, modal logics, many-valued logics, etc. 3. Meta-mathematical investigations into the properties of different formal logic systems: model theory, proof theory, forcing, consistency, completeness, etc. 4. The philosophy of logic: Semantics, sense/reference, truth, nominalism/realism, theory of descriptions, etc. 5. Logic and computability: lambda calculus, recursive functions, turing machines, complexity classes, etc. This is somewhat tangential to logic proper but there are connections and Dr. Smith has a section on it so it's worth enumerating. While everyone will need to know (1) as a working man's logic, the other topics are more or less independent and can be approached independently. For people just starting out and finding this study guide pretty overwhelming, let me re-emphasize two of Dr. Smith's suggestions for starting points: Smullyan's First Order Logic and Halmos's Naive Set Theory. These two books will get you to the same depth of understanding that 95% of working mathematicians need or apply in their day-to-day work, and it's a fact that 95% of modern mathematical theories are built on (formalized within) ZFC set theory and first order logic. https://en.wikipedia.org/wiki/Naive_Set_Theory_(book) https://en.wikipedia.org/wiki/Naive_Set_Theory_(book) http://store.doverpublications.com/0486683702.html http://store.doverpublications.com/0486683702.html I also suggest the online game The Incredible Proof Machine. It's extremely helpful to have a computer formally check your proofs when you're just starting out in logic because it's incredibly easy to "cheat" and skip steps or use rules that "make sense" but aren't part of the formal system your using. TIPM lets you do that without learning any specialized syntax. http://incredible.pm/ http://incredible.pm/