Valid and Invalid Arguments

Once we are able to recognize an argument, the next step is to learn what differentiates a good argument from a bad one. We have two crucial attributes for judging arguments. They are validity and soundness. The beautiful thing about logic is that there is no grey area. An argument is either valid, or invalid. It is either sound or unsound. And, in order for an argument to be sound, it must be valid.

Consider the difference between the following two arguments:

1. 1. All birds have wings.
   2. Penguins have wings.
   3. Therefore, penguins are birds.


2. 1. All winged things are birds.
   2. Airplanes have wings.
   3. Therefore, airplanes are birds.

Which one do you prefer?

What if I told you that they are both problematic arguments?

Let's look at argument A first: Although it conforms to what we know about birds (even the little kiwi has cute stubby wings), There is a problem with the logical structure of the argument. This might be easier to recognize if we remove the features we are familiar with, and replace the parts with algebraic symbols.

Take another look at the argument now:

1. 1. All (every subset of) B has W.
   2. P has W.
   3. P is a subset of B.

Although P has the attribute of W, there is nothing that links that to being a member of B.

The conclusion does not follow from the premises, and so we say that the argument is invalid.

Contrast this with a valid argument:

1. 1. All birds have wings.
   2. Penguins are birds.
   3. So, Penguins have wings.

Here, the conclusion does follow from the premises, and so the argument is considered valid.

A valid argument is an argument where the conclusion necessarily follows from its premises. It is such that, if all of the argument's premises are true, then the conclusion must be true.

What about Argument B?

2. 1. All winged things are birds.
   2. Airplanes have wings.
   3. Therefore, airplanes are birds.

Or,

2. 1. Anything with the attribute W is B.
   2. A has the attribute W.
   3. So, A is B.

Or, even more simplified,

2. 1. X=Y
   2. Z=X
   3. Z=Y

The conclusion follows from its premises - if 1. and 2. are true, then 3. must be true. So, the argument is valid.

However, premise 1. is not true. And because of this untruth, 3. is not true. So, the argument is considered unsound.

Remember that if an argument is valid, when its premises are true the conclusion must be true. Soundness is the way we refer to valid arguments which pass this check. If an argument is valid, and all of its premises are true, then the argument is considered sound.

Simple examples aside, it is much harder to find sound arguments than one might think. This is because except for situations where truth is a function of language (something that is true by definition), such as, "All bachelors are unmarried." If we were to say, "All swans are white", we might think that the premise is true... until someone discovers a black swan.

For now, let's focus on validity (and just try to make the premises as true as possible).

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