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Sound and cogent arguments

A sound argument is a valid argument that has true premises. A cogent argument is a strong non-deductive argument that has true premises.
© Patrick Girard, University of Auckland
So far we have talked about the kind of support that can be given for conclusions: deductive and non-deductive.
We defined an argument as being valid if it’s a deductive argument for which the premises succeed in providing conclusive support for the conclusion.
And we defined an argument as being strong if it’s a non-deductive argument in which the premises succeed in providing strong support for the conclusion.
By that, we mean that, if the premises are true, then the conclusion would be given the appropriate support for also being true.
But we haven’t said anything yet about whether the premises are true or not. This is what we do when we evaluate whether arguments are sound or cogent.
Validity and strength of arguments do not on their own tell us whether arguments are good or bad. We’ve actually seen rubbish arguments that were valid. That’s why we need to introduce two further concepts for arguments: being sound and being cogent.

Sound Arguments

  • Definition: A sound argument is a valid argument that has true premises.
Firstly, a sound argument is a deductive argument. It’s trying to establish conclusive support for its conclusion. Secondly, the argument is valid: the premises, if true, would guarantee that the conclusion is also true. And on top of all that, the premises are actually true. Therefore, a sound argument guarantees that its conclusion is true.

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We say that a sound argument is a good argument. It is a good argument because it guarantees that the conclusion is true. It would be irrational for you not to believe the conclusion of a sound argument.
Of course, sound arguments are very rare, because they’re very hard to establish. But, some arguments are sound.
For example:
The province of Québec is part of Canada. Patrick was born in Québec. Therefore, Patrick was born in Canada.
This is a valid argument. Can you see why?
Furthermore, the premises are true: Québec is indeed part of Canada, and Patrick was indeed born in Québec. Hence, you can be absolutely certain that Patrick was born in Canada, and you ought to believe that Patrick was born in Canada. There’s no way around it.
Here are some more examples of sound arguments:
I drank coffee this morning; therefore, I drank something this morning.
Patrick got married on January 4, 2014. Patrick has not been divorced, and Patrick is not a widower. Therefore, Patrick is not a bachelor.
It is true that Patrick got married on January 4, 2014, that he has not divorced and that he is not a widower. So Patrick is not a bachelor because a bachelor is an unmarried male, by definition.

Cogent Arguments

Now, what about non-deductive arguments? For non-deductive arguments, we introduce the notion of a cogent argument.
  • Definition: A cogent argument is a strong non-deductive argument that has true premises.
And again, we say that cogent arguments are good. A cogent argument is by definition non-deductive, which means that the premises are intended to establish probable (but not conclusive) support for the conclusion.
Furthermore, a cogent argument is strong, so the premises, if they were true, would succeed in providing probable support for the conclusion. And finally, the premises are actually true. So the conclusion indeed receives probable support.
Here’s an example:
Patrick was born in North America and Patrick wasn’t born in Mexico. It’s thus quite probable that Patrick was born in the USA.
That is a cogent argument. If all you know about Patrick is what’s contained in the premises, and those premises are true (they are!), then that’s a fairly strong argument, because the population of the USA is over 300 000 000, whereas that of Canada is under 40 000 000. This means that the odds that Patrick was born in the USA are roughly 88%, which makes the support for the conclusion quite strong. Furthermore, the premises are true. Therefore, the argument is cogent, and so it is a good argument.
This means that we can have good arguments that have false conclusions!
Here’s another example:
I had coffee this morning. Therefore, it’s quite likely that I drank something this morning.
This is a strong argument with true premises, so it is cogent and therefore, good. But the conclusion is not guaranteed. It may be that I had coffee this morning by eating it, or by some other means. But of course, this is very unlikely, so the argument is strong, though it’s still possible that the conclusion is false. Still, this is cogent and therefore, a good argument.
© Patrick Girard, University of Auckland
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Logical and Critical Thinking

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