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Fuzzy Truths and the Probability Fallacy Help

By — McGraw-Hill Professional
Updated on Oct 25, 2011

Introduction to Fuzzy Truths and the Probability Fallacy

Probability

Probability is the proportion or percentage of the time that specified things happen. The term probability is also used in reference to the art and science of determining the proportion or percentage of the time that specified things happen.

The Probability Fallacy

We say something is true because we’ve seen or deduced it. If we believe something is true or has taken place but we aren’t sure, it’s tempting to say it is or was “likely.” It’s wise to resist this temptation.

Belief

When people formulate a theory, they often say that something “probably” happened in the distant past, or that something “might” exist somewhere, as-yet undiscovered, at this moment. Have you ever heard that there is a “good chance” that extraterrestrial life exists? Such a statement is meaningless. Either it exists, or it does not.

If you say “I believe the universe began with an explosion,” you are stating the fact that you believe it, not the fact that it is true or that it is “probably” true. If you say “The universe began with an explosion!” your statement is logically sound, but it is a statement of a theory, not a proven fact. If you say “The universe probably started with an explosion,” you are in effect suggesting that there were multiple pasts and the universe had an explosive origin in more than half of them. This is an instance of what can be called the probability fallacy (abbreviated PF), wherein probability is injected into a discussion inappropriately.

Whatever is, is. Whatever is not, is not. Whatever was, was. Whatever was not, was not. Either the universe started with an explosion, or it didn’t. Either there is life on some other world, or there isn’t.

Fuzzy Truths

If we say that the “probability” of life existing elsewhere in the cosmos is 20%, we are in effect saying, “Out of n observed universes, where n is some large number, 0.2 n universes have been found to have extraterrestrial life.” That doesn’t mean anything to those of us who have seen only one universe!

It is worthy of note that there are theories involving so-called fuzzy truth , in which some things “sort of happen.” These theories involve degrees of truth that span a range over which probabilities can be assigned to occurrences in the past and present. An example of this is quantum mechanics , which is concerned with the behavior of subatomic particles. Quantum mechanics can get so bizarre that some scientists say, “If you claim to understand this stuff, then you are lying.” We aren’t going to deal with anything that esoteric.

We Must Observe

Probability is usually defined according to the results of observations, although it is sometimes defined on the basis of theory alone. When the notion of probability is abused, seemingly sound reasoning can be employed to come to absurd conclusions. This sort of thing is done in industry every day, especially when the intent is to get somebody to do something that will cause somebody else to make money. Keep your “probability fallacy radar” on when navigating through the real world.

If you come across an instance where an author (including me) says that something “probably happened,” “is probably true,” or “is likely to take place,” think of it as another way of saying that the author believes or suspects that something happened, is true, or is expected to take place on the basis of experimentation or observation.

Find practice problems and solutions for these concepts at: Probability Practice Test.

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