Logic

An Introduction

Greg Restall

• Publisher: Routledge
• Year: 2004
• ISBN:
  9781134145980
• Edition: 1
• Topic: Philosophy
• Subtopic: Philosophy History & Theory

The methods of logic are essential to an understanding of philosophy and are crucial in the study of mathematics, computing, linguistics and many other subjects. Introducing the major concepts and techniques involved in the study of logic, this authoritative book explores both formal and philosophical logic, and the ways in which we can achieve good reasoning. Individual chapters include:

* Propositions and Arguments
* Truth Tables
* Trees
* Conditionality
* Natural Deduction
* Predicates, Names and Quantifiers
* Definite Descriptions.

This exceptionally clear introduction to the subject is ideally suited to students taking introductory courses in logic.

PART 1
Prepositional logic

Chapter 1
Propositions and arguments

Logic is all about reasons. Every day we consider possibilities, we think about what follows from different assumptions, what would be the case in different alternatives, and we weigh up competing positions or options. In all of this, we reason. Logic is the study of good reasoning, and in particular, what makes good reasoning good.

To understand good reasoning, we must have an idea of the kinds of things we reason about. What are the things we give reasons for? We can give reasons for doing something rather than something else (these are reasons for actions) or for liking some things above other things (these are reasons for preferences). In the study of logic, we do not so much look at these kinds of reasoning: instead, logic concerns itself with reasons for believing something instead of something else. For beliefs are special. They function not only as the outcome of reasoning, but also as the premises in our reasoning. So, we start with the following question: What are the sorts of things we believe? What are the things we reason with?

Propositions

We will call the things we believe (or disbelieve) propositions. The particular name is not important here, but the distinction between propositions and other sorts of things is important. We express propositions by using sentences. If I ask you what I believe about something, you will most likely respond by using some sentence or other. Of course expressing propositions is but one of the things we do with sentences. We do lots of other things with sentences too—we ask questions, we express feelings, desires and wishes, we command and request. In the midst of this diversity, the acts of stating and believing are central to the practice of reasoning, so propositions are at the heart of reasoning and logic. We are interested in claims about the way things are, and reasons for them, so propositions, which express how we take things to be, or how we take things not to be (or which express matters upon which we are undecided), are the focus of logic.

We will illustrate the difference between sentences that express propositions and those that do not by exhibiting the contrast. Here are some examples of sentences expressing propositions:

I am studying logic. If you like, I will cook dinner tonight.

Queensland has won the Sheffield Shield.

The moon is made of green cheese. Most wars are horrible.

2+7=9. The mind is not the brain.

Euthanasia is justifiable in some circumstances.

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