Continuum fallacy
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Continuum fallacy, also called fallacy of the beard is a logical fallacy which abuses the paradox of the heap. The fallacy appears to prove that two states are not different, or do not exist at all, because there is a continuum of states between them; that there is no difference in quality because there exists a difference in quantity.
The fallacy is often described in form of a conversation:
- Q: Does one grain of wheat form a heap?
- A: No.
- Q: If we add one, do two grains of wheat form a heap?
- A: No.
- Q: If we add one, do three grains of wheat form a heap?
- A: No.
- ...
- Q: If we add one, do one hundred grains of wheat form a heap?
- A: No.
- Q: Therefore, no matter how many grains of wheat we add, we will never have a heap. Therefore, heaps don't exist!
Other examples of this fallacy prove that no one has a beard, no matter how long it is (or that everyone has a beard, no matter how cleanly shaven), because a beard can have varying lengths, that no one can be bald (or that everyone is bald) because there are people with varying quantities of hair, or that languages don't exist because they are in a dialect continuum. A variant is that, as an example, it's okay for a 6-year-old to drink because it's okay for a 21-year old and okay for a 20-and-11-months old and so on.
The most common argument against the fallacy itself is one of simple induction: there are bald people and people who aren't bald. The most common argument against the variant is that it's slightly worse for a 20-and-11-months old to drink, and slightly worse than that for a 20-and-10-months old, and the "slightly"s build up. In general, any argument against the sorites paradox itself can also be used on both.
