Basics of logical arguments

Since I’m trying to cram some smarts in my brain pan, I thought learning about the basics of logical arguments would be a good thing.

Those that have internalized this, could you point out any mistakes I might make? Thanks.

For the rest of us, here are the 4 basic forms for arguments.
p and q are premise and conclusion, respectively.
~means not.

Two are valid forms, two are invalid. “Valid” doesn’t mean “true” or “sound”. It is just a valid form. The soundness, what people call truthfulness, of an argument still needs to be examined, but eliminating the invalid arguments from the start saves time and effort.

Valid
If p then q, but ~q, therefore ~p. This valid move is called Denying the Consequent.

Invalid
If p then q, but q, therefore p. This invalid move is called Affirming the Consequent.

Valid
If p then q, and p, therefore q. This valid move is called Affirming the Antecedent.

Invalid
If p then q, but ~p, therefore ~q. This invalid move is called Denying the Antecedent.

Remember, an argument can be valid and still be untrue, and a true argument can be invalid in its presentation.

Knowing how argument is presented helps us to see if it valid or not. If it is valid, we can verify the veracity of the premises. If it is invalid, we don’t need to concern ourselves with it.

Let’s run a few examples, trite as they may seem.

Valid: Denying the Consequent
If I am Chinese, then I am Asian. (If p then q)
But I’m not Asian. (But ~q)
Therefore I’m not Chinese. (Therefore ~p)

Invalid: Affirming the Consequent
If Socrates is human, then he is mortal. (If p then q)
He is mortal. (But q)
Therefore Socrates is human. (Therefore p)

The problem with this lies in that Socrates doesn’t have been human. He could be a dog, for example. Still mortal, but not human.

Valid: Affirming the Antecedent
If Mary knows the answers to the quiz, then she will get an ‘A’. (If p then q)
She knew the answers. (And p)
So she got an ‘A’. (Therefore q)

Invalid: Denying the Antecedent
If p then q, but ~p, therefore ~q.
If I am in California, I ‘m in the United States. (If p then q)
But I’m not in California. (But ~p)
So I’m not in the United States. (Therefore ~q)

You can see how this is wrong, since I could easily be in another state, like Arizona, so I would still be in the United States.

These four basic arugment forms are the foundation of logical thought and argument. When I’ve learned more, I’ll do a follow up posts on sound arguments vs unsound, inductive and deductive reasoning.

It should be fun! Well, at least educational. And isn’t education fun?