A false dilemma, or false dichotomy, is a logical fallacy that involves presenting two opposing views, options or outcomes in such a way that they seem to be the only possibilities: that is, if one is true, the other must be false, or, more typically, if you do not accept one then the other must be accepted. The reality in most cases is that there are many in-between or other alternative options, not just two mutually exclusive ones.
The logical form of this fallacy is as follows:
Premise 1: Either Claim X is true or Claim Y is true (when claims X and Y could both be false).
Premise 2: Claim Y is false.
Conclusion: Therefore Claim X is true.
This line of reasoning is fallacious because if both claims could be false, then it cannot be inferred that one is true because the other is false. This is made clear by the following example:
Either 1+1=4 or 1+1=12. It is not the case that 1+1=4. Therefore 1+1=12.
This fallacy should not be confused with the Law of Excluded Middle, where ‘true’ or ‘false’ are actually the only possible alternatives for a proposition.
It is worth noting that it is not a false dilemma to present two options out of many if no conclusion is drawn based on their exclusivity. For example ‘you can have tea or coffee’ is not a false dilemma. A fallacious form would require it be presented as an argument such as ‘you don’t want tea, therefore you must want coffee.’
For example, if somebody was to appear to demonstrate psychic abilities, one would commit the fallacy of false dilemma if one were to reason as follows: either she’s a fraud or she is truly psychic, and she’s not a fraud; so, she must be truly psychic. There is at least one other possible explanation for her claim of psychic abilities: she genuinely thinks she’s psychic but she’s not.
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