Brief Lessons in Logic, Part 3

Now in the previous lesson we discussed two different ways of reasoning - induction and deduction. From this point forward however, we're going to focus on deduction.

Now we said that deductive arguments are either valid or invalid, and either sound or unsound.

Before I discuss what a sound argument is, I'm going to speak a little more about validity.

In the previous post I wrote:

An argument is valid if and only if, it is impossible for it to have true premises, lead to a false conclusion.

Or you could think about it this way:

An argument is valid if the conclusion necessarily follows from the premises.In other words, in a valid argument, given that the premises are true, then the conclusion must be true also. It necessarily follows. There's no way around it.


Here's another example of a valid argument.

Premise 1: All Presbyterians are Christians.

Premise 2: All Christians believe in God.
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Conclusion: All Presbyterians believe in God.

This argument is valid.

Why? Because the conclusion "All Presbyterians believe in God" is unavoidable, it necessarily follows from the the two premises. That is, if an argument is valid, then, assuming that the premises are true, then the conclusion must also be true.

Here's another example:

Premise 1: All Spiders have Ten legs.

Premise 2: All Ten-legged things can Fly.
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Conclusion: All Spiders can Fly.



Is this argument valid?



yes!


Now we all know that spiders don't have ten legs, and that ten-legged things don't exist, and that spiders (thank God) can't fly!

Then if all three propositions in this argument are obviously false, how could the argument be valid?

It's because validity doesn't deal with the truth or falsity of the premises or conclusions in an argument. Validity has to do with the structure of the argument; it has to do with the relationship between the premises and conclusion.

So a person can have a valid argument for a certain position, and we can honestly say that the person has reasoned their argument fairly well, but that still does not mean that the person's position is true.

This brings up the issue of soundness.

An argument is sound when it is valid, and it has true premises.

You might say that a sound argument is a "perfect" argument. That is, not only is the relationship between the premises valid (the conclusion is what naturally follows from the premises), but the premises are also known to be true.

So fortunately, the previous argument about flying spiders is valid, but it is unsound.

Here's another example:


Premise 1: If Abortions don't kill a Human person, then Abortion is not Wrong.

Premise 2: Abortions do not kill a Human person.
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Conclusion: Abortion is not Wrong.

This argument is valid.

Now, if you were an anti-abortion advocate, and you know that this argument is valid, how would you attack it? You would attack it, not on the basis of its structure (since the structure is logical), but on the basis of its soundness.

You might say in response, "Yes I agree with your first premise which states that if abortions do not kill a human person, then abortion is not wrong. That statement is true. But your second premise which states that abortions do not kill a human person is not true. Therefore, your argument is valid, but it is not sound."

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OK. That's validity and soundness. I'll leave it at that for now. Feel free to post any questions, comments, etc.