From Exercise 2, you have assigned five position numbers.
ones are Richardian and which ones are not?
Consider the characteristic of being Richardian. Calculate
position number in the list of six definitions—five from Exercise
and the definition of Richardian above. We will call this number n
so that we can refer to it.
Propose a way out of the Richard paradox based on a
kind of argument. That is, is being
Richardian an arithmetic property
or something else?
Here is a paradox of Bertrand Russell involving sets. Some
sets (taken as a whole)
are not members of themselves.
For example, a set (i.e. collection) of butterflies is
not a butterfly. Other sets aremembers of themselves. For example, the collection of
all things that are not butterflies is a thing that is not
itself a butterfly, and is hence a
member of itself. Now, consider the set R,
R is the set of all sets that are not members of
Question: Is R a member of itself, or not? Can you propose
a way out of this paradox?