The Logic of Plurality

A(ti A(tı A(tn atomic sentence boy loves classical logic classical predicate logic classical quantifiers consequence constitute a manifold defined depending disjunction distinct t-variants distinct terms domain of discourse equivalent everything is F existential quantifiers follows formula Fs are Gs further line Fx & Gx girl given Hence I satisfies informal argument interdefinability interpretation intuitionistic logic k+n+1 least number Lemma Let A(v letter of degree logic of plurality lovers M-w-complete maximal consistent Mx)(Fx v Gx Mx)Fx n-termed natural deduction nearly everything Nx)Fx Nx)Gx plural quantifiers predicate calculus predicate letter Proof propositional function propositional variable provable Quakers results of replacing rules of derivation satisfies A iff satisfies B(t satisfies Nv)A(v semantics sequent sequent-expression set of wffs simultaneously satisfiable Suppose symbolism system Wn t₁ true universal quantifier V(Fai VA(ti vacuously vacuously true valid principle w-complete well-formed formulae wff containing