Introduction

Logic, like mathematics, psychology, history, physics, and many other academic fields is a broad subject with many specialized areas and sub-disciplines. The aim of the first part of this text is to introduce you to the main ideas behind what is called philosophical logic in an informal way.

In general, philosophical logic is the study of the principles of correct reasoning. This study includes all the tools one can use in deciding how well a claim is supported by a set of reasons given to support the truth of that claim.

For readers of Part 1 of this text, this will include a study of relations between statements (in the sense of how the truth of a statement or set of statements affects the truth of another statement), arguments both strong and weak, the distinction between proof and strong arguments, the principle of induction as used in reasoning and an examination of some common bad arguments known as fallacies.

Part 2 of this text will cover a formalization of propositional logic which will allow us to examine relations between propositional statements and the validity of arguments in a formal way, as well as evaluate and construct proofs of propositional statements and prove theorems by using rules of inference and equivalence statements.

Part 3 of this text will expand on our treatment of propositions by including propositions which use quantifying terms such as 'all', 'none', 'at least one'. This will be accomplished by first examining sets and set operations which will give us a powerful group of tools and extend our ability to prove arguments and relations between statements which are categorical in nature.

Finally Part 4 of this text will make use of the sets and theorems about sets we learn in Part 3 to examine the theory of probability for finite equiprobable sample spaces as well as concepts related to statistical analysis (learning about a population from a sample of its members) and statistical fallacies.