Your definition for religion is somewhat, half baked.
A definition does not need to be correct. It must, however, always be predicatable. You have usefully defined
D, if it is possible to construct a predicate function
isD(x) that will manage to return
true or
false for any
x that you throw at it.
For religion, the predicate function
isReligion(x) must be able to answer
true or
false, for any x that you throw at it.
In that sense, it obviously ok to improve an existing, predicatable definition, as long as the improved version remains predicatable. I started the definition process of religion by claiming that
religion is a
law of metaphysical origin. So, generally, there are two requirements for a set of statements to constitute a religion:
- It must forbid particular behaviour.
- The set of such interdicts may not be of human origin
It is indeed strange that the definition of
definition, aka, the metadefinition introduces the requirement for a function. The definition of
function, is simply a mapping between elements:
a--->r
b--->t
z--->n
r---->k
With only one limitation, a function is not allowed to map an element on the left to more than one element on the right. This definition gives the impression of being predicatable. So, at first glance, it may look possible to define a function
isFunction(f) that will return for any function
f whether it is truly a function or not. However, here we can simply make use of the spectacular result booked by Alan Turing, the proof for
the halting problem, which says that it is impossible to construct a program (or function) which would always be able to determine if another candidate program (or function) will halt. Since we cannot determine if a candidate function will even just halt, it is a fortiori impossible to determine whether such candidate function will always return the same output for a particular input, since this program cannot determine if such function would even finish computing its output.
In that sense, the correctness of a definition is way less important that its predicatability.