1. Introduction

1.1. Formal deductive logic

1.1.0. Overview

The topic of this course is the study of 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 our first task will be to see what this label means. The terms formal and logic specify the way in which we will study reasoning while the term deductive specifies the sort of reasoning we will study. In the course of the subsections listed below, we will look at each of these three terms in a little more detail.

1.1.1. Logic
Logic is concerned with features that make reasoning good in certain respects.

1.1.2. Inference and arguments
The key form of reasoning that we will consider is inference; the premises and conclusion of an inference make up an argument.

1.1.3. Notation for arguments
We will often use some compact ways of referring to arguments and their components generally without identifying particular examples.

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. Deductive bounds on inference
The sentences that constitute risk-free conclusions and those that are absolutely incompatible with the premises form lower and upper bounds on what can be reasonably concluded.

1.1.6. Entailment, exclusion, and inconsistency
Entailment is the relation between the premises and conclusion of a deductive inference, and the terms of exclusion and inconsistency are tied to the idea of absolute incompatibility.

1.1.7. 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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