A modern, functioning, bona fide democracy is one that follows a simple formula: Rule by the people.
You need to read the question, find the appropriate formula, rule, etc, and apply.
Two decades later, the "Jaws" formula rules.
And both agree--here is a real breakthrough--that the alternative to first-past-the-post should be a "proportional alternative .The Lib Dems insist this formula rules out a system with which Mr Blair has flirted in the past: the alternative vote (AV), whereby voters exercise a second preference in individual constituencies.
Mathematics, to them, was formulas, rules, and procedures they had to memorize.
When the axiomatic or 'Hilbert' approach is taken, the rules are formula-to-formula rules and the objects proved are formulas.
(We return to this theme below, in connection with Carnap, by which time we will have traded in formula-to-formula rules for sequent-to-sequent rules, allowing for the convenient representation of inferences in which assumptions are discharged).
What the Humanity formula rules out is engaging in this pervasive use of Humanity in such a way that we treat it as a mere means to our ends.
On the other hand, in our initial presentation of natural deduction, before assumption discharging rules got into the act, the rules were again presented as formula-to-formula rules, but with the things proved with these rules were in effect Set-Fmla sequents: meaning that the rules enabled us to pass from a set of initial assumptions to a final formula.
Blok and Pigozzi have in mind the least consequence relation for which φ, φ → ψ ⊢ ψ and φ, ψ⊢ φ ∧ ψ and ⊢ φ for all φ provable in the Fmla logic R. (This third condition can be restricted to all axioms of any axiomatization of R with formula-to-formula rules corresponding to the first and second conditions).
