Sometimes mis-evaluation of evidence leads us to form irrational beliefs, even in cases that are not so extreme as Smith and his hallucinations. In such cases we over-estimate our evidential support: we think that the evidence supports a belief when it doesn't. This is an error that people who attempt to persuade by devious means can often exploit to their advantage. For instance they might describe one or two vivid examples of some alleged phenomenon with the aim of getting us to form generalisations for which the examples do not provide adequate support. An example that should be familiar to readers and observers of the UK tabloid press is that of a vivid description of a recipient of state benefit or of an asylum seeker, which apparently supports the claim that they enjoy an undeservedly luxurious lifestyle. Such examples are rolled out in an attempt to persuade readers to believe that the majority of benefit recipients and asylum seekers are undeserving cheats. Often, the details of such examples and the manner of their presentation are so rhetorically powerful that they cause us to mis-evaluate the significance of the evidence presented to us. In particular, we make an unjustified inductive inference (one with very low force). When we are led to make such mistakes and form irrational beliefs, we allow ourselves to be distracted by factors other than principles of good reasoning.
There is another type of irrational belief. Sometimes we allow ourselves to accept false beliefs because we believe doing so will benefit us in some way. In such cases we not only lack evidence for the belief, but we also seem not to care that we have none. For instance, someone might believe that the predictions of their astrologer will come true; they might believe in faith-healing; ESP; life after death; that everything in the Bible is literally true; that their terminally-ill grandparent will make a recovery; that a certain alternative healing method will cure cancer. We often feel that it would be unfeeling to point out that such a person's beliefs are irrational. Indeed, we often admire their faith and sincerity. However, it would be a mistake to retreat into relativity and conclude that their belief is 'true for them'. The belief is false, that's that. Indeed, such people can sometimes paradoxically be described as believing that which they know to be false - self-deceived.
However, we should not be too cold-blooded. It's not usually the case that such people are intentionally deceiving themselves, but rather that they are trying to deal with their plight by having faith that their hopes (however unlikely) will be borne out.7 So it's rather unfair and unfeeling to accuse such people of being irrational, even though strictly speaking they are. Whilst we should try to avoid irrationality, we must also accept that as human beings, it is sometimes psychologically better for us if our beliefs and behaviour fall short of rationality.
7 There are, of course, cases where people are guilty of self-deception. A classic case is the parent who knows (for they witnessed the act) that their child stole sweets from the supermarket, but refuses to believe that they did.
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