# Logic is not the complete answer

When I am in a supermarket it is a frequent occurrence that, when scanning a particular item, the cashier (I avoid the self-service tills like the plague – why would I want to give a machine an opportunity to shout at me!) informs me that the item I am purchasing is on offer and I could buy a second or a third one at a reduced price. Sometimes this is helpful; I may not have noticed the offer sign and saving money on a second or third item is of benefit in the long run. Occasionally, however, I do not want a second or third item and so I thank the cashier for the information and inform them I just want to buy the one.

This is all well and good – or so you would think. There are times when the cashier does not believe you and thinks that you are being a little slow on the uptake or that you are throwing money away and so repeats the special offer information. It then becomes a battle of wills as you try to convince them that you are of sound mind and you really do just want the one item. The cashier is only applying logic, the same logic that the supermarkets are exploiting in putting special offers on items: if you buy one item then you will buy a second or third at a reduced price because it saves you money. But I am also applying logic in refusing to buy a second or third because, although they are at a reduced price, I still have to pay something for an item I do not want.

The term ‘logic’ implies ‘good reasoning’ but, as can be seen above, logic can be applied to arrive at two diametrically-opposed actions, depending on the particular circumstances. Children are good at logic: ‘So and So’s parents let them do/have X, so you should let me do/have X also’. Their reasoning is simple and is based on a black and white view of the world. In the black, white and grey world, refutation is not necessarily simple and is not always easy for the child to understand: they end up disgruntled and you end up being the bad guy.

Evidently, a form of reasoning (logic) in which a conclusion is drawn from two given or assumed propositions or premises is called a syllogism – another word that is not commonly heard. An example is as follows: all men are human; all humans are mortal; therefore all men are mortal. A middle term is present in the two initial statements, in this case ‘human(s)’, but not in the conclusion. If the two statements are true, then the conclusion must be true. This example is called a categorical syllogism. The conclusion is based on logical reasoning and thus it does not always have to represent the ‘truth’.

There are other forms of syllogisms, referred to as conditional syllogisms, which are less likely to be valid. My experiences at the checkout are conditional syllogisms, as the supermarkets rely on the following reasoning:
• Major premise: If I buy one, I will want to buy more.
• Minor premise: I want to save money.
• Conclusion: I will buy more than one in order to save money.
However, my reasoning is as follows: I want one; I want to save money; I will save money by not buying more than one!

An appreciation of syllogisms could help us in the application of reliable NDT. The conditional syllogism presents an if… then argument, which can be usefully applied in the assessment of indications. The challenge NDT faces is deriving the correct premises to use and which conclusion to draw, because there are often any number of reasons why a signal presents in a particular form.

We may predict that if the 45° probe gives a large signal response and smooth planar defects give large responses, then the response is from a smooth planar defect. But we know that this is not necessarily sufficient as there could be other reasons for the large response. So we have to test this further with another if… then argument. The analysis of an indication requires any number of if… then loops in order to achieve the desired level of confidence in the final sentencing.

When we look at automating the analysis process, the software needs to include all possible eventualities and, hence, syllogisms. Something that our experience tells us is not easy to accomplish.

Poor knowledge management costs money. I propose to write about knowledge management in the September issue of NDT News. You will not want to miss reading this column next month!

Please note that the views expressed in this column are the author’s own personal ramblings for the purpose of encouraging discussion within the NDT Newspaper. They do not represent the views of Amec Foster Wheeler or the HSE who funded the PANI projects.

Letters can be mailed to The Editor, NDT News, Newton Building, St George’s Avenue, Northampton NN2 6JB. Fax: 01604 89 3861; Email: ndtnews@bindt.org or email Bernard McGrath direct at bernard.mcgrath@amec.com