notes2 - Philosophy 220A Symbolic Logic I Department of...

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1 Philosophy 220A: Symbolic Logic I Department of Philosophy University of British Columbia 2. Arguments We saw in Section 1 that logic is the study of propositions, i.e. both thoughts and possible states of affairs. In this course we are mostly concerned with human thinking, or reasoning, and with arguments in particular. 2.1 What is an argument? The purpose of an argument is to add more truth to one’s stock of beliefs, hopefully without admitting any more false beliefs. Arguments, handled carefully, are a way of getting more knowledge. The most important part of an argument is the conclusion . This is a proposition. The aim of an argument is to persuade the listener to believe the conclusion, i.e. to think that the conclusion is true. Not just any means of persuasion counts as an argument, however. Bullying, for instance, is a form of persuasion that is quite different from argument. Also, emotional appeals can be persuasive, but these are not arguments either. An argument is an attempt at rational persuasion, an appeal to the listener’s logical faculty, helping him to see for himself that the conclusion must be true, or is at least likely to be true. Usually an argument begins with some agreement between the two parties involved. They share some assumptions, or beliefs, in other words. The person making an argument will often appeal to some of these shared beliefs as evidence to support his case. These shared beliefs, which are accepted without argument, are known as premisses of the argument. They are the starting point of the argument. If two people have such different opinions on a particular subject that they hardly share any beliefs concerning it, then it will be difficult (if not impossible) for them to argue about that subject. Nearly every argument has premisses, or starting assumptions, which must be accepted by all parties if the argument is to be persuasive. Examples 1. The clearest, most rational arguments are those found in mathematics. Indeed, many people have learned to reason logically from a mathematical training. Here is an example of a mathematical argument that is easy for all to understand. The argument concerns prime numbers. A prime number is a (positive) whole number that can only be divided by one and itself. For example, five is prime, since it can only
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2 be divided into one and five. Five will not divide (without remainder) into 2, 3 or 4. Six is not prime, as it can be divided into 2 or 3. The prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, . .. One question is: Do the prime numbers ever end? Or do they go on forever, like the even numbers? We shall argue that the prime numbers go on forever. Before we start, we need two simpler results that will be used to prove the main result. Such a supporting result is often called a
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notes2 - Philosophy 220A Symbolic Logic I Department of...

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