And there will be a payoff – you’ll be able to see how true conclusions don’t always mean that what you (or someone else) said was logical.
Let’s talk about the most basic structure of a logical argument:
Don’t run away! Come back.
This is just a fancy way of saying:
In practice, that looks like this:
Because there is already a base of mutual knowledge, we don’t have to get any more detailed than this right here.
But, what if we were talking about something we’re not all familiar with? Like a ‘wug.’
We could say:
Why say it like that?
Because then we can fit it into a nice little sentence, like this:
If p, then q.
In this case, it’s: If p1 and p2 and p3, then q. The ‘p1,’ etc makes it LOOK confusing, but ignore that. It’s a premise. If this, then that.
So here’s the thing – sometimes q (your conclusion) is true, but your premises aren’t.
Why is that a problem? Because people often get into arguments where they feel that something is correct, but they make a fallacious (that is, illogical) argument in support of that feeling. Then, when they’re told that the argument is a fallacy, they say, “nuh-uh,” and then insert a total different premise.
We could also that as:
We could look at that argument and find it invalid – it certainly is.
What you see above is not a logical conclusion.
But, then we find out that Dave really is blue and small:
Does that suddenly make our argument logical?
Whoever said that Dave was small and blue just happened to be right. It had nothing to do with their reasoning.
Sometimes you can be right for the wrong reasons. That might mean that things worked out this time, but if you want to solve problems next time, you need to be smarter.