A True Conclusion Does Not Mean a Valid Argument

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Alright guys, I’m going to get all technical for a minute – BUT I promise to break it down so that anybody (yes, anybody) can follow it.

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:

If p, then q.

Don’t run away! Come back.

This is just a fancy way of saying:

If this, then that.

In practice, that looks like this:

If Dave is a unicorn, then Dave is a horse-like creature with a horn on his forehead.
p = Dave is a unicorn.
q = Dave is a horse-like creature with a horn on his forehead.

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:

p1 = All wugs are blue.
p2 = All wugs are small.
p3 = Dave is a wug.
q = Dave is small and blue.

Why say it like that?

Because then we can fit it into a nice little sentence, like this:

If all wugs are blue, and all wugs are small, and Dave is a wug, then Dave is small and blue.

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.

Follow?

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.

For instance:

p1 = All wugs are blue
p2 = All wugs are small
p3 = Dave is NOT a wug.
q = Dave is blue and small.

We could also that as:

If all wugs are blue, and all wugs are small, and Dave is NOT a wug, then Dave is blue and small.

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:

Dave is a blue tree frog

Does that suddenly make our argument logical?

No.

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.

Author: A. Primate

Mammal. Organizes itself into complex social hierarchies. Very particular about objects - even those that can't be eaten or used for shelter. Seemingly aware of itself as separate from the environment.

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