2.5 Quantifiers and resolving ability of human perception
The number of quantifiers that are denotates of some words of natural languages is very great. And the number of quantifiers described in the logical studies by means of logical symbols is even greater. All these quantifiers are, obviously, understandable to the human mind or, speaking a bit more strictly, to human rational reasoning. This is, however, not the same as if they were acceptable to our immediate perception. Thus, for instance, we are able to use the rays of light with a wide range of wavelength, say, in the electronic microscopes or in the night viewing devices, but the range of wavelength accessible to the human eye directly is much narrower. In linguistics, the same situation is well known in phonology: not all sounds which could be produced by the organs of speech are used by the natural languages, even if we take all the natural languages of the world in their totality. In narratology, it is also obvious that not all understandable modalities are really in use in plot constructing.
Thus, it would be reasonable to suppose that the situation with quantification is the same. Only a relatively narrow class of quantifiers is really in use when the narrative or the language “work.” These “working” quantifiers are only those whose set is a part of the generative grammar of natural language or the “grammar” of narrative. Of course, their number is much smaller than the number of quantifiers which have their corresponding lexical expressions.
This consideration leads us to answer the question at the end of the previous section: why the “working” modalities of narrative apparently ignore quantifier not all, the inner negation of the quantifier some, being, in the same time, heavenly relying on a derivate of the inner negation of some, quantifier all?
This is not a question of narratology. The triplet structure of the corresponding modalities was described by logicians for different situations, but all of them were not interested in subtle distinction in the quantifying with either all or not all.
My answer is that the opposition between all and not all, in human perception, is completely overshadowed by the much more powerful opposition corresponding to the quantifier more than. This quantifier is of type ‹1, 1, 1›, and so, is irreducible to the quantifiers of type ‹1, 1›. It represents, using an Alexander Ivin’s bon mot, a different worldview.
Just now, it is easy to see that the difference between all and not all is easily perceivable in terms of more than. The quantifier more than has basic significance for the logic of preferences, but, outside some specific contexts, its significance is so far mostly overlooked.