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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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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 Spring '09
 James
 Logic, Betty

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