To Mock a Mockingbird

Raymond Smullyan

Mockingbird	Mx = xx
Kestrel	Kxy = x
Identity	Ix = x
Lark	Lxy = x(yy) NB: in a forest with a Lark, every bird A is fond of (LA)(LA)

(for all birds x, y)

Fond	A is fond of B if AB = B
Egocentric	A is fond of itself (ie AA = A)
Agree	A and B agree on a bird x if Ax = Bx
Agreeable	A is agreeable if given any B, there exists a bird x on which A and B agree
Compatible	A and B are compatible if there exist x and y where Ax = y and By = x
Happy	A is happy if it is compatible with itself
Normal	A is normal if it is fond of at least one bird NB: in a forest with a Mockingbird and where the composition condition holds, every bird is normal
Fixation	A is fixated on B if for every bird x, Ax = B
Hopelessly egocentric	A is hopelessly egocentric if it is fixated on itself (ie for every bird x, Ax = A)
Left cancellation law for kestrels	if Kx = Ky then x = y