Consider Mrs Green, the greengrocer, who discovers that a customer has left their shopping behind. She has served five customers so far that day - Mr Red, Mrs Pink, Mr Orange, Mr Yellow and Mrs Blue. She has no reason to suppose that any one of them is any more forgetful than any of the others. None of them is in the habit of forgetting their shopping, for instance. Mrs Green concludes that one of the men left the shopping behind. She does have some justification for forming this belief: of the five customers three were male, so on the balance of probability the forgetful shopper is more likely to be a man. That is to say, she does have an argument for that conclusion which is somewhat rationally persuasive for her. But, intuitively, we may feel that this probability is somewhat slim justification for her belief. Even if it turns out that the shopping belongs to Mr Orange, we don't feel inclined to say that she arrived at her true belief via the right route; that is, that her true belief is really justified. So even if she's right, we don't feel that she knows that the forgetful shopper is a man. This is not to say that probability as a justification for true belief should be ruled out per se. The problem here is that the probability is not strong enough. If there had been four male shoppers and one woman, we would be more inclined to allow that Mrs Green's belief is justified. If there had been ninety-nine men and one woman, we would certainly be so inclined.

There are occasions when there is far more at stake in having the proper justification for forming a true belief than simply making sure that someone gets their groceries. An obvious case is where principles of justice are involved, where evidence is required to demonstrate beyond reasonable doubt that a defendant is guilty of an alleged crime. Suppose Jones is accused of the murder of Brown. In fact, Jones is guilty: he strangled Brown to death. Smith is called as a prosecution witness to Jones' crime. He is called as a witness because he has given a police statement in which he claims to have seen Jones emerging from Brown's house carrying a knife. If this is all the evidence the jury has, is it, by itself, sufficient reason for jury members to form the true belief that Jones is guilty of Brown's murder? Clearly not, even though Jones is in fact guilty of the murder. Brown died of asphyxia, not from stab wounds, and probably the evidence would have been too weak even if Jones had stabbed Brown rather than strangling Brown. So although the jury members may have reached their true belief about Jones' guilt on the basis of Smith's evidence, they do not have a justified belief about Jones' guilt. If this is the only evidence they have for reaching their verdict, then they should not convict Jones of Brown's murder. Note that this holds even though, as it happens, Jones is guilty.

How strong must our evidential support be, if a belief is to be justified? How strong must it be if a true belief is to qualify as knowledge? Unfortunately, there is no precise answer to this question. The terms 'justified' and 'knowledge', like 'bald', are somewhat vague: just as there is no exact quantity or proportion of cranial hairlessness required for baldness, there is no exact strength of evidence for a belief short of which it is not knowledge, and beyond which it is knowledge. But this should not trouble us too much. In practice, we are adept at recognising the cases where our degree of justification is borderline. This does not change the nature of our task as critical thinkers: we know that our task is to fashion sound arguments that are rationally persuasive for ourselves or for their intended audiences. By paying attention to the reasons why we are entitled to form true beliefs, we are able to achieve the firmest possible grasp upon what we can legitimately claim to know.

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