 The connectives of the formal languages of propositional logic are typically expected to exhibit salient features of the sentence-connecting devices of natural languages, and especially such devices as are regarded as items of logical vocabulary (and, or, not, if–then,…), though it will be no part of our concern to inquire as to what their ‘logicality’ consists in. This is an issue which arises for expressions and constructions such as quantifiers, the identity predicate, and so on, and not just for sentence connectives; for this issue the entry “Logical Constants” by John MacFarlane (2015) should be consulted. The formal languages concerned may be taken to agree in constructing their formulas ultimately on the basis of the same countably infinite supply of propositional variables—or ‘sentence letters’—p1, p2,…, the first three of which we write for convenience as p, q, r. Where they differ is in respect of their stock of primitive connectives. So for example, we have the language L = (L, ∧, →, ¬, ⊥) with (set of) formulas L and connectives as indicated, of arities 2, 2, 1 and 0. (We have no qualms in the last two cases in speaking of connectives, even when there are not two or more formulas to ‘connect’. Note that 0-ary or nullary connectives are already formulas—sometimes called sentential constants—in their own right.) As the notation suggests (with boldface capitals for algebras and the corresponding italic capitals for their universes), we are thinking—in the Polish tradition—of languages as algebras, identifying the primitive connectives with the fundamental operations of such algebras, and in particular, as absolutely free algebras of their similarity types (in the present instance, ⟨2,2,1,0⟩) with the pi as free generators. This allows us to speak in the usual fashion of the main connective of a given formula, the variables occurring in and more generally the subformulas of such and such a formula, and so on, without restricting ourselves to construing the formulas as obtained specifically by concatenating various symbols.