Introduction to Philosophical Logic/Prolegomena

What is logic?

Logic is the study of the consistency of beliefs. For beliefs to be consistent it must be possible for them to obtain at the same time. For example, it is illogical to believe that the sky is completely blue and that the sky is completely red because the sky being entirely blue is inconsistent with its being entirely red, i.e. it is not possible for the sky to be entirely red at the same time as its being entirely blue.

Logic is also a study of "logical consequence", i.e. what follows by necessity from something else. By studying inconsistency of beliefs, philosophers are able to study the validity of arguments, as will be shown later. Methods of finding whether certain arguments are valid is described later.

The symbolisation of these sentences, known as formalisation, simplifies and quickens this process. It also enables the philosopher to clarify ideas using an unambiguous language in which to represent thoughts. The sophistication of the language used enables greater insights into the significance of these thoughts (and a cursory analysis of more logical languages is described in Other Logics.

Aims of this book

This book aims to give the reader a basic understanding of logic and its relationship with philosophy, rather than a more mathematical approach to advanced logic. It is designed to provide the reader with a grasp of terms such as "valid", "consistency", "entailment", which often arise in philosophy, to help the reader comprehend the philosophical issues that use them. Philosophical debates of certain issues are not developed here, and are at most briefly mentioned. Certain assumptions are made; the reader is advised to consider them.

The final part of this book (Other Logics) is a development and extension of the principles described herein. It is designed to interest rather than fully inform the reader of these matters.