1. Introduction

1.1. Formal deductive logic

1.1.0. Overview

In this course we will study reasoning, but we will study only certain aspects of reasoning and study them only from one perspective. The special character of our study is indicated by the label formal deductive logic, and we will begin our study by seeing what this label means. Each of the terms formal and logic indicates something about the way in which we will study reasoning while the term deductive indicates the sort of reasoning we will study. In the subsections listed below, we will look at each of these three terms in a little more detail.

1.1.2. Inference
The key form of reasoning that we will consider is inference.

1.1.3. Arguments
The input and output of an inference together form an argument.

1.1.4. Deductive vs. non-deductive inference
An inference is deductive when its conclusion extracts information already present in its premises, and such an inference is risk free.

1.1.5. Bounds on inference
The sentences that constitute risk-free conclusions from given premises form a lower bound on what can be reasonably concluded, and sentences that are absolutely incompatible with those premises form an upper bound.

1.1.6. Entailment and exclusion
Entailment is the relation between the premises and conclusion of a deductive inference, and it will be our main concern. But studying it will involve studying its negative counterpart, exclusion.

1.1.7. Inconsistency and exhaustiveness
Other bounds limit the alternatives that can be maintained together—on pain of being inconsistent—or assure that there is always one available when a set of alternatives is exhaustive.

1.1.8. Formal logic
Many cases of entailment can be captured by generalizations concerning certain linguistic forms, and we will use a quasi-mathematical notation to express these forms.

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