[Nomic02] a vague attempt at summarising
Wed, 15 Jan 2003 20:22:33 -0500 (EST)
On Wed, 15 Jan 2003, Carbol, Roger wrote:
> > I'm going to be a strict constructionist here.
> In my experience, this only leads to madness.
> What is a 'player'? What is a 'vote'? What
> is 'English'? Can we define these things in
> some manner that isn't, eventually, circular?
The words "vote" and "English" do not require definition to preserve the
formality of "the state of the game", as they are not part of the state of
the game. (But I'm glad to have "vote" defined in Rule 10 anyway.)
The word "player" refers to a member of a set established in rule 3.
That's as much definition as you need. (There are currently no
restrictions on what can be added to this set. However, there is also
currently no way to add things to it.)
Again I state: "every primitive notion introduced and *its relationship to
other terms* defined". This is exactly how mathematical axiomatic systems
work. In set theory, for example, you'll never see a definition of the
word "set" beyond how they relate to their elements and to other sets -
because "set" a primitive notion. This does not in any way lessen the
rigor of the axioms of set theory, which is arguably the most formalized
field in all of mathematics.