Necessary And Sufficient Conditions

I was interested to read this comment from Vince Cable (UK Secretary of State for Business, Innovation and Skills) on the UK economy:

“I think it is right and necessary that we have budget discipline. That is the path we have embarked on and we must stick with that. …

What we are putting in place is called Plan A-plus, which is that we do the budget discipline – which is absolutely necessary but is not sufficient – and we have to put in place measures supporting infrastructure and housing. They are coming through.”

I first came across the idea of ‘necessary and sufficient conditions’ when I was taking an undergraduate course in maths. It’s very helpful in getting ideas straight, such as whether a system is stable to small changes or not.

The comment above made me think about non-science applications of the approach. Thinking through whether actions or initiatives are (really) necessary to achieve an aim (maybe there are simpler or different ways?) and whether the sum of the activities is actually likely to be sufficient could be very helpful.

Whilst it’s obviously not watertight (in maths you make sure a problem is well-defined whilst in business many activities are and always will be fuzzy, dynamic and highly interconnected) it may still yield qualitative insights or at least encourage consideration of other viewpoints (as above).

From the point of view of logic theory:

A necessary condition of a statement must be satisfied for the statement to be true.

A sufficient condition is one that, if satisfied, assures the statement’s truth.

A condition can be either necessary or sufficient without being the other.

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