Loki's wager is the insistence that because two or more categories exist as poles on a spectrum with a grey area in the middle, the distinction between the two cannot be defined.
In the Prose Edda (Norse, Old: [[Skáldskaparmál]] ch. 35), the Norse trickster god, Loki, made a bet with the dwarf Brokkr, in which he wagered his head.
Loki lost. When the dwarf came to collect it, Loki stated that he would relinquish his head on the condition that Brokkr leave alone any part of his neck. After a discussion on the matter, while parts of Loki clearly belonged to the head or the neck, neither side could agree exactly where one ended and the other began. Loki therefore kept his head indefinitely,[1] though afterwards his lips were stitched shut by Brokkr as punishment for using tricky wordplay.[2]
Loki's wager, therefore, is a situation in which a person unreasonably insists that a term cannot be defined, making it impossible to discuss. It has been described as a fallacy[3] [4] [5] and more precisely as a kind of "continuum fallacy".