appeal to probability
The appeal to probability is a logical fallacy, often used in conjunction with other fallacies. It assumes that because something could happen, it is inevitable that it will happen. This is flawed logic, regardless of the likelihood of the event in question. The fallacy is often used to exploit paranoia.
This has the argument form:
- Possibly P.
- Therefore, P.
Equivalently, using modal logic and logical connective notation:
→ 
Some examples are:
- "There are many hackers that use the internet. Therefore, if you use the internet without a firewall, it is inevitable that you will be hacked sooner or later."
- "AMD has been catching up to Intel in recent years. In a few years they will definitely take over Intel's position, and eventually put them out of business altogether."
- "When soccer becomes popular in a town, hooliganism will become a major problem. Thus, if we allow a soccer team in our town, we will be overrun by hooligans." (also a False cause fallacy)
While not considered a "true" fallacy by some (because it is rarely used by itself), the appeal to probability is a common trend in many arguments, enough for many to consider it a fallacy of itself.
The logical idea behind this fallacy is that, if the probability of P occurring is approaching 1, it is best to assume that P will occur, since it will (almost) almost surely happen. The fallacy incorrectly applies a common tenet of probability: given a sufficiently large sample space, an event X of nonzero probability P(X) will occur at least once, regardless of the magnitude of P(X). This is derived from the definition of probability. The operative term is "given a sufficiently large sample space". Virtually all events are considered for probability within a finite number of samples, and the chance that X will occur in a given finite space S is directly proportional to S. Given a finite number of events S, each of which is X or not X, a sample space Y = 2PrS exists where one possibility is that all events in S are not X. Therefore, P(X in Y) = (Y-1)/Y. Because Y-1/Y < 1 for all finite Y, P(X in Y) < 1 regardless of P(X) or Y. There is thus always a chance that X will not occur, and therefore, no proof that X will occur given its probability.
The 'umbrella joke' is a twist on this fallacy: if someone ever forgets his or her umbrella, that will be the one day that it actually rains.
| Formal fallacies | |
|---|---|
| Argument from fallacy • Fallacy of modal logic • Masked man fallacy • Appeal to probability • Bare assertion fallacy | |
| Fallacy of propositional logic: | Affirming a disjunct • Affirming the consequent • Commutation of Conditionals • False dilemma • Denying the antecedent • Improper Transition |
| Fallacy of quantificational logic: | Existential fallacy • Illicit Conversion • Quantifier shift • Unwarranted contrast |
| Syllogistic fallacy: | Affirmative conclusion from a negative premise • Negative conclusion from an affirmative premise • Exclusive premises • Necessity • Four-term Fallacy • Illicit major • Illicit minor • Undistributed middle |
| Other types of fallacy | |
This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)
