Grice e Croce

 As CROCE observes, it is a common-place in philosophy that there is, or appears to be, a divergence in meaning between, on the one hand, at least some of what PEANO call this or that FORMAL device, when it is given a standard two-valued interpretation, and, on the other, what is taken to be its analogues or counterpart in ITALIAN — such expressions as non, e, o, se, ogni, alcuni (almeno uno), il. Some — PEANO, VAILATI, FORTI — *may* at some time have wanted to claim that there is in fact no such divergence. But such a claim, if made at all, has been somewhat rashly made. And those suspected of making it — PEANO, VAILATI, FORTI — have been subjected to some pretty rough handling — notably by CROCE! Those who do concede that such a divergence in meaning (between, say, Peano’s inverted iota and ‘il’) exists adhere, in the main, to one or the other of two rival groups: the formalists and the informalists. An outline of a not uncharacteristic formalistic position may be given as follows. Insofar as we are concerned with the formulation of very general patterns of valid inference, a formal device possesses a decisive advantage over its ITALIAN counterpart. For it will be possible to construct in terms of the formal device a system of very general formulae, a considerable number of which can be regarded as, or are closely related to, this or that pattern of inference the expression of which involves such a device. Such a system may consist of a certain set of simple formulae that must be acceptable if the device has the meaning that has been assigned to it, and an indefinite number of further formulae, many of which are less obviously acceptable and each of which can be shown to be acceptable if the members of the original set are acceptable. We have, thus, a way of handling a dubiously acceptable pattern of inference, and if, as is sometimes possible, we can apply a decision procedure, we have an even better way. Furthermore, from a PHILOSOPHICAL point of view, the possession by, say, ‘il,’ of that element in its meaning, which it does not share with inverted iota, is to be regarded as an *IMPETFECTION*. Such an element is an undesirable excrescence. The very presence of this element has a the double result that the concept which, say, ‘il,’ manifests cannot be precisely or clearly defined, and that at least some statements involving it cannot, in some circumstances, be assigned a definite truth value. The indefinability of this concept — the definite article — is objectionable in itself and leaves open the door to ‘metaphysics.’ We cannot be certain that none of these expressions is metaphysically *loaded.* For these reasons, the expressions of natural speech cannot be regarded as acceptable, as they may turn out to be ultimately UNINTELLIGIBLE or coherent. The proper course is to construct PERFECT, language — RAGIONATO, incorporating the formal device, the sentences containing it will be clear, determinate in truth value, and certifiably free from metaphysical incoherence. The foundations of philosophy qua regina scientiarum will be secured, since the statements of a scientist will be expressible within this perfect language. To this CROCE infamously replied that the PHILOSOPHICAL demand for a perfect language rests on an assumption not be conceded. The primary yard-stick by which to judge the adequacy of Italian is hardly its ability to serve the needs of a particular science. An expression in Italian can be guaranteed as fully intelligible even if a precise definition, of the assertion of a logical equivalence  of its signification has been provided. Italian serves many purposes other than that inquiry in this of that science. Proficient Italian speakers know perfectly well what an expression in Italian means — and what they mean by it — and so, a fortiori, that it is coherent) without knowing its definition. Indeed, the provision of such a definition upon request may (and usually does) consist in the specification, as generalised as possible, of the conditions that count for or the applicability of sheer felicitous use, of the expression in question. Moreover, while it may be granted that PEANO’s inverted iota  may be amenable to a systematic treatment, the facf  remains that there are very many inferences and arguments, expressed with ‘il’ and not with the inverted iota, which are recognisably valid. There is room for an *unsimplified* unreginented, and so more or less free and not systematic, use in conversational discourse of ‘il’. This use may be aided and guided by the *simplified* first-order predicate calculus of inverted iota (with identity) but cannot be legally or officially supplanted by it. Indeed, not only do the two enterprises differ, but sometimes they come into conflict. A rule that may hold for inverted iota may not hold for ‘il.’ On the general question of the place of the reformation of a natural language, I shall here have nothing to say. I shall confine myself to the dispute in its relation to the *alleged* divergence of meaning. In fact, I wish to maintain that the common assumption shared by formalists and informalists that the divergence in meaning — between, say, the inverted iota and ‘il’ — do in fact exist is (broadly speaking) a *mistake* that arises from inadequate attention to the nature and importance of the general conditions that, in one way or another, apply to conversation as such, irrespective of its subject matter.