Invalid vs Incorrect

There’s a common myth that arguments which are valid always have a correct conclusion. The best Critical Thinking students know better. Invalid arguments can be correct, and valid arguments can be incorrect. Here are some examples:

Invalid argument with correct conclusion

IF: All cats have fur,

IF: Pingu is a cat,

THEN: Lassie the dog has fur.

If we didn’t like this argument, we could completely refute it. Imagine an alien from outer-space coming across this argument. They could say something like:

“This argument is invalid because it is illogical. There is no reason from the argument why Lassie should have fur; Lassie is not even mentioned in the premises.”

They could then go on to make a counter argument:

IF: Lassie is often in the water,

IF: Water animals from earth often do not have fur,

THEN: Lassie probably does not have fur.

This argument is valid, because the conclusion logically flows from the premises.

The strange thing is however, that the first (invalid) conclusion was correct, and the new (valid) conclusion is incorrect. Lassie the dog has beautiful fur!

Let’s look at another valid argument with an incorrect conclusion:

Valid argument with incorrect conclusion

IF: The median average UK income is £27,600

THEN: Everyone probably earns around £27,600.

This kind of argument, just like the second Lassie argument above is called an inductive argument because it leads from a specific argument into a more general conclusion. Inductive arguments are not necessarily true, even when they are valid. We add a “probably” to the conclusion to show this. This is an excellent example of a strong, inductive argument, with good evidence. It is a valid argument.

Unfortunately, the conclusion is still incorrect. We can argue against it like this:

“Many people in the UK are not in paid employment at all, or are in part time work and they will not earn an income at all. In the UK there is also great wage inequality. Some people will earn much more than that, and some workers, particularly from minority groups, will earn less.”

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Refuting Arguments

Whether an argument is valid or invalid is especially important because it affects how we respond.

To properly argue a case, we need to explain why we disagree with the original argument, before we make our new argument to replace it.

When the argument is invalid, we can do this simply by explaining its logical inconsistencies. When an argument is valid, but just incorrect, we have to find a way to explain the evidence better using our new argument.

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