Proposal: Formation
Self-killed. — Quirck
Adminned at 11 Jun 2013 09:00:24 UTC
Enact a new rule entitled “Formulae”:
A Variable is a single lowercase letter that is either True or False within the context that it’s in. A Connective is a nonalphanumeric symbol that is [monovalent, placed before a Formula] XOR [bivalent, placed between two Formulae]. A Formula is a single Variable XOR a finite sequence of Variables with properly-placed Connectives. Brackets (”[” and “]”) can be placed around Formulae and phrases to disambiguate the order in which a Connective applies.
Enact a new (empty) rule entitled “Definitions”.
Enact a new subrule of “Definitions” entitled “NOT”:
NOT is a monovalent Connective. [x is True] IMPLIES [[NOT x] is False]. [x is False] IMPLIES [[NOT x] is True].
Enact a new subrule of “Definitions” entitled “IMPLIES”:
IMPLIES is a bivalent Connective. [x IMPLIES y] is True unless [x is True] AND [y is False].
I suppose that this is a way to get started. It seems awfully slow (and lame) though. I don’t suppose we could somehow easily import the necessary axioms and deductions?
It shouldn’t be long before we come up with Nomic-specific stuff. That also entails screwing with these definitions, I hope.
in favour of Clucky’s proposal.
Skju:
Perhaps we could just say something along the lines of “a Formula or Connective is assumed to be used according to its normal mathematical or logical usage unless explicitly stated otherwise” instead of building this mundane stuff from scratch, then immediately define things specific to Nomic?