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Any hints on translating this English sentence into symbolic logic:

Something is between everything.

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    This question is ill-formed and does not really parse. I am having a Russell-paradox headache here.2011-06-06

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Here is a quick list of rule of thumbs for translation:

  • "Some" means $\exists x$
  • "Every" and "All" mean $\forall x$
  • "If x then y" or "x implies y" or "y only if x" mean $x\rightarrow y$
  • "Either x, or y" means $x\lor y$
  • "Both x and y" means $x\land y$
  • "Not x" means $\lnot x$

The actual predicates you would have to fill in on your own.

As joriki and Gadi commented, "Between" is a trinary predicate (i.e. takes three variables, "x is between y and z") and the closest interpretation of the current sentence would be $\exists x\forall y\forall z\operatorname{Between}(x,y,z)$.

(Note the difference in the order I put the quantifiers and joriki put them, in his version between every two elements there is a third; in my version one specific element is between every two others, including itself.)

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    @Henry, assume $x$ is God in the Judeo-Christian tradition, then god is between everything including itself and itself. :-)2011-06-04