Tuesday, September 10, 2013

Valid arguments vs. sound arguments

Validity and soundness are one of the most important terms in logic. How to distinguish between deductively valid and invalid arguments as well as between sound and unsound arguments? The definition is very much straightforward and it is all that is needed to grasp the idea. However, this post will also give you a brief description of a few examples which will provide you with a more practical approach to the problem. And at the end of the post I will reveal to you a little secret which will turn this logical issue into a piece of cake!

Valid argument means an argument whose conclusion cannot be false if its premises are true. Consider the following example:

Immanuel Kant was born in 1724 in Königsberg.
In 1724 Königsberg was in Prussia.
Therefore, Immanuel Kant was born in Prussia.

The conclusion follows from the two premises so the argument is deductively valid. Provided the two premises are true (and by the way – they are), the conclusion cannot possibly be false. Now consider the following argument:

Plato was born in Greece.
Everybody who is born in Greece have two heads.
Therefore, Plato had two heads.

Does the conclusion follow from the premises? It certainly does. Is it possible for the conclusion to be false when the premises are true? It is not. Therefore, the argument is valid. However, something seems to be wrong with the above argument – obviously, its second premise is not true! This argument is unsound. The argument is sound only if all its premises are true and the argument is valid. Therefore, the argument about Plato is a deductively valid and unsound argument (the argument about Kant is both valid and sound). Now let’s deal with the last example:

Products containing sugar are sweet.
Bananas are sweet.
Therefore, it shouldn’t rain tomorrow.

You didn’t expect that conclusion, did you? Both premises are true but the conclusion does not follow from the argument’s premises. Undoubtedly, this argument is both invalid and unsound (although the premises are true, the conclusion is false).

Just in case you want to be sure that you are able to correctly classify arguments, here is the promised surprise – a little diagram which will make the whole process much easier. And remember – there are no false or true arguments – arguments are either valid/invalid or sound/unsound. The argument may have true/false premises and conclusion but in logic terms true and false do not apply to arguments! Never!

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  1. To the author, Sir / Madam, could you please help me consider this statement: if it is sound?

    A. All birds are animals.
    B. All koala bears are animals.
    C. Therefore, all koala bears are not birds.

    Thanks in advance.

  2. Sound since the premises are false.
    But not valid since possibly all Koala bears are birds.
    I call it silly :)


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