I am using the program Fitch from LPL (Openproof Courseware: Language, Proof, and Logic) and for some reason I am getting an error that the statement below "is not a sentence".

The statement is:

∀x∀y∀z(((Cube(x)∧Dodec(y))→Larger(x,y)) ∧ ((Dodec(y)∧Tet(z))→Larger(y,z))) → ((Cube(x)∧Dodec(y)∧Tet(z)) → Larger(x,z))

From my understanding, there are essentially two reasons for why a quantified statement would not be deemed a sentence:

(1) There are unbounded variables (but in this case, there are not, all variables, x,y, and z, are binded to a universal quantifier).

(2) The parenthesis are off (in this case, I think made sure every statement that needed parenthesis included parenthesis).

What am I missing?


1 Answer 1


You are missing parentheses: you need one more at the beginning and one more at the end, like so:

∀x∀y∀z((((Cube(x)∧Dodec(y))→Larger(x,y)) ∧ ((Dodec(y)∧Tet(z))→Larger(y,z))) → ((Cube(x)∧Dodec(y)∧Tet(z)) → Larger(x,z)))


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