Logic is a third branch of philosophy, although it is more properly considered to be the introduction to the rest of philosophy, since it provides the methods used in the other two branches. In this sense, logic is less a division of philosophy than the science or art of which the rest of philosophy makes use. The two main branches of logic, one called formal or minor logic, the other material or major logic, are quite distinct and deal with different problems. Material logic is concerned with the content of argumentation. It deals with the truth of the terms and the propositions in an argument.
Formal logic is interested in the form or structure of reasoning.
The truth of an argument is of only secondary consideration in this branch of logic. Formal logic is concerned with the method of deriving one truth from another. Logic is concerned merely with the fidelity and accuracy with which a certain process is performed, a process which can be performed with any materials, with any assumption. Briefly, you can only find truth with logic if you have already found truth without it. This last remark of Chesterton's is important.