Key terms and concepts

The definition that the course has been using over the years is the standard definition used in logic courses:

A slightly more wordy version is:

A slightly less precise definition is:

The reason this is less satisfactory as a definition is that it doesn’t tell you about those cases where the premises are not true.

It is important to explain to pupils that this is a technical use of the word and it differs from the everyday use of the word which means something like ‘fit for use’ as in having a valid bus ticket. The reason why this is important is because, although the technical use of the word is well established in logic courses, elsewhere the nontechnical use of the word is often applied to arguments and this has caused problems for pupils. People might say ‘that’s a valid point’ or ‘that’s a valid argument’ but be using the word in the nontechnical sense. This doesn’t mean they are wrong it is just that they are using the word in a different way in a different context. 

The mandatory documents don’t address this issue and it would be helpful if they stated the definition that candidates are expected to learn. Better still, it would be good if pupils were required to know and explain how the technical use of the word differs from the more casual use of the word.

Previous versions of the Higher course made it clear that ‘valid’ and ‘invalid’ were terms that applied to deductive arguments. This is no longer the case and that is unfortunate for there are books that use the terms differently. Firstly, there is the issue that some definitions of ‘deductive’ equate deductive arguments with valid arguments which would mean there is no such thing as an invalid deductive argument. But, secondly, some books adopt the nontechnical use of the word ‘valid’ and so talk of inductively valid arguments. The following is from Logic and Contemporary Rhetoric: The Use of Reason in Everyday Life by Nancy M. Cavender, Howard Kahane.

Again, it would be helpful if the mandatory documents stated clearly what the Higher Course required.

There are two unusual consequences of the formal definition of validity that may be of interest but shouldn’t have any significant impact on the course. Consider the following two arguments:

I am in this room. I am not in this room. Therefore, the moon is made of cheese.

The world is flat. Water is dry. Therefore, two is two.

Very surprisingly, both of these are valid arguments! Recall the formal definition of validity: an argument is valid if there are no possible circumstances where the premises are true and the conclusion false. In the first of the arguments the premises are contradictory so cannot both be true. In the second, the conclusion cannot be false. So, in the first argument there are no possible circumstances where the premises are true. Since there are no possible circumstances where the premises are true it has to be the case that there are no possible circumstances where the premises are true and the conclusion false! Anything validly follows from contradictory premises. Whilst this may have some uses in formal logic it can be dismissed as a quirk of the system when dealing with everyday arguments. Interestingly, whilst technically valid they would probably be dismissed as invalid if one was using the everyday use of the word ‘valid’. It is at least a reminder that validity isn’t enough for a good argument.