How does this tripartite (3-part) definition of knowledge hold up? Have you identified any problems with it? Before going further we need to look at some useful terms.

If and only if

Like our use of the words 'knowledge' and ' belief', the word 'if' has different uses. Sometimes when we use it we only want to convey a loose connection between statements: "I will come with you to the pictures if you go on Friday". In this example, the two statements - your going to the cinema, my coming with you - are not absolutely connected. I may go to the cinema with you on another evening if you suggest it - in other words, other things are possible.

However, if I say, "I will come with you to the pictures if, and only if, you go on Friday", I am excluding other possibilities (such as going on Tuesday). This distinction is important for philosophers because it allows them to be more precise about the relationship between certain statements.

Exercise

Indicate which of the following are examples of 'if' and which are examples of 'if and only if'.

Statement	If If and Only If?	Reason
I will die if I stop breathing		No, there are umpteen other ways to die!
I can make a hot cup of tea if I have hot water		Yes, it is difficult to make tea without hot water (unless you have iced tea, I suppose...).
I will pass my exams if there is a miracle		No, you might actually study!
If I eat any more I will be sick		No, you may be sick anyway.

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Necessary and Sufficient Conditions

When we talk of something being true 'if and only if' something else is true, this can happen in one of two ways. For instance, if we take the example, "I will grow up to be strong and healthy if I exercise and eat sensibly", in what way might this be true? Will I be strong and healthy only from eating sensibly and exercising? Or can these things be achieved in other ways?

So, in this example:

1. These would be necessary conditions for health if it could not be achieved without them.

2. These would be sufficient conditions for health if that were all that needed to be done in order to be healthy.

Another example might be learning to drive. Passing my theory test is a necessary condition of getting a driving license, but it is not a sufficient condition (you also need to pass your practical test).

Exercise

Take the following situations and list both necessary and sufficient conditions for something to be the case in each of them. The first example is given for you.

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As you can see, a necessary condition is like a prerequisite for doing something - but not enough to actually do it. A sufficient condition, on the other hand, requires actually achieving that thing.