[Phil 151, First-Order Logic](http://web.pacuit.org/classes/phil151winter09.html), is the second term of Stanford's undergraduate logic sequence. [First-order logic (FOL)](first_order_logic) refers to a logical system which includes the propositional connectives, variables, functions, relations, and quantifiers. In a sense, FOL is powerful enough to describe all of mathematics, yet its syntax and semantics can be defined precisely enough to say quite a lot about it.
While the course is listed in the philosophy department, it's really more like a math course. It formally defines the syntax and semantics of FOL, and most of the class is concerned with proving things about the logical system itself. It's a required course for the [symbolic systems](https://symsys.stanford.edu/) major, and has a reputation as a weeder course because, for a lot of students, it is their first course that requires writing rigorous mathematical proofs. The class roughly follows the first two chapters of Enderton's [A Mathematical Introduction to Logic](http://www.amazon.com/Mathematical-Introduction-Logic-Second-Edition/dp/0122384520).
This roadmap roughly corresponds to the course as it was taught in 2005.
## Background: logical languages, proof techniques
The course assumes that students are already comfortable working with [propositional logic](propositional_logic) and [first-order logic](first_order_logic), at the level of understanding what the symbols mean, being able to express statements in those languages, and being able to write [formal proofs](propositional_proofs) (in some formal system).
It also assumes knowledge of a few concepts in set theory:
- * basic [operations on sets](operations_on_sets)
* how to [represent functions and relations as sets](functions_and_relations_as_sets)
* the distinction between [countable and uncountable sets](countable_sets)
* [Russell's Paradox](russells_paradox), and why it justifies the need for a system of axioms for set theory (e.g. the [Zermelo-Frankl axioms](zermelo_frankl_axioms)).
Finally, it requires a certain level of comfort with several mathematical proof strategies: [direct proof](http://en.wikipedia.org/wiki/Direct_proof), [proof by contradiction](http://en.wikipedia.org/wiki/Proof_by_contradiction), and [mathematical induction](http://en.wikipedia.org/wiki/Mathematical_induction).
## Weeks 1-3: propositional logic