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2.1 Language and Logic

Predicates
in L		 The sub-theory HI is developed within a first-order, multi-sorted language L. Among its primitive signs, L counts two predicate constants;
(1.1) "ex" for exemplification
(1.2) "=" for identity
Variables
in L		 three sorts of variables;
(2.1) variables for individuals: v, w, x, y, z, v1, w2,...
(2.2) variables for haecceities: V, W, X, Y, Z, V1, W2,...
(2.3) variables for particulars: v, w, x, y, z, v1, w2,...
the usual sentential connectives;
(3.1) ¬, if-then, & , or, equivalent
and the universal and existential quantifiers.
(3.2) for all, for some
Formulas
in L		 A formula of L is any expression provided for by the following conditions:
(4.1) ti ex Tk, ti = tk and Ti = Tkare atomic formulas.
(5.1) Every atomic formula is a formula.
(5.2) If alpha is a formula, ¬alpha is a formula.
(5.3) If alpha and beta are formulas, (alphaif-thenbeta), (alpha & beta) and (alphaequivalentbeta) are formulas.
(5.4) If beta is a formula,for alltbeta and for sometbeta are formulas.7
Meta-
language
of L		 In the metalanguage of L, t1, t2,... range over individual variables; T1, T2,... over haecceity variables; t1, t2,... over particular variables; and alpha, beta,... over expressions.

cont.

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