When I was doing my PhD at the University of Otago, Madeleine and I would try to save up for a “date night” once a fortnight. Often we would go to the movies. On more than one occasion we would stand in the theatre and look at various options. Madeleine would suggest we see one movie and give some reasons, I would suggest another. After a few minutes we would settle on a movie and then buy a ticket.
In the technical sense, in amicably settling on which movie we would see Madeleine and I had ‘had an argument.’ Now, in everyday language when we say a husband and wife have ‘had an argument’ we mean they have quarrelled, had a fight, come into conflict with each other and so forth. In logic, however, the phrase is more precise. An argument is defined as a set of reasons in support of a conclusion.
This definition suggests an argument has two features:
A Conclusion: the claim being proposed as true; and,
Premises: a set of propositions or statements being made in support of a conclusion.
It is important to note that these features are not the same thing. Simply asserting your conclusion is not an argument, it is a statement. Asserting random facts does not constitute an argument either, unless these facts are offered in support of some conclusion. Grasping the distinction between a premise and a conclusion is important because it is possible, and in many cases likely, that you will come across an argument which has a conclusion you agree with and yet the premises offered for it are either false or do not support this conclusion. Consider the following:
Premise  The sun is divine;
Premise  Whatever is divine would exist in the centre of the solar system and have all other planets orbiting it;
Conclusion  The sun is at the centre of the solar system and all the other planets orbit it.
Pretty much all of us would accept the conclusion of this argument. However, few of us would accept the premises. It is important to note this because one real problem that exists in our current society is that people fail to draw the distinction between premises and conclusions.
Because they agree with the conclusion of an argument and because it advances a cause they believe in, they accept the argument regardless of its merits. This is a terrible mistake, you should want to believe and support a position for good reasons not bad ones. And if you are trying to persuade others you should want to offer them good reasons, not bad reasons for coming to agreement with your position.
A final point to note here is that premises can be implict or unstated. Sometimes a person who offers an argument will take certain things for granted and assume that others will accept them. In this instance the premise will be unstated and you will need to look for it.
An example illustrating these points is a famous quote by Winston Churchill
“I am an optimist. It does not seem too much use being anything else.”
Churchill here provides some reasons for why he is an optimist; hence, this quote expresses an argument for why Churchill thinks he should be an optimist.
The argument can be set out as follows:
Premise  There does not seem too much use in being anything else but an optimist;
Conclusion  I should not be anything else but an optimist.
These are the stated or explicit premise and conclusion of Churchill’s argument. However, this argument has an implicit premise, which is: “if there is not much use in being anything else I should not be anything else.”
So the full argument, with the implicit premise included, is:
Premise [1a] There does not seem too much use in being anything else but an optimist;
Premise [1a] If there is not too much use in being anything else then I should be an optimist;
Conclusion [2a] I should not be anything else but an optimist.
So to recap, an argument is a set of reasons given for a conclusion. Arguments have two components: premises and conclusions. When assessing an argument it is important to distinguish premises from conclusions and also to identify both implicit and explicit premises. One cannot assess or examine an argument until we have accurately identified what it is.
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