Science as cognitive activity is constituted out of collections of acts of judging, validating, verifying. Science as theory is constituted out of the homogeneous fabric of meanings taken in specie. There are different levels of complexity, different varieties of combination of the elements making up this fabric, and only some possible combinations will yield complex meanings possessing that sort of unity which is required if the meanings in question are to be qualified to form part of the subject-matter of logic. It was in relation to this problem that Husserl, in his 4th Investigation, put forward those ideas on meaning categories which were to prove so influential through the work of Leniewski and Ajdukiewicz and in subsequent experiments in the field of ‘categorial grammar’.
The theory of meaning categories as Husserl conceives it is part and parcel of his theory of meanings as species. For Husserl’s use of the term ‘species’ (and of the associated terminology of ‘genera’, ‘instantiation’, ‘lowest difference’, etc.) is no mere historical accident. It was designed to draw attention to the fact – familiar to Aristotle and Porphyry, as also to Brentano and W. E. Johnson – that species form trees: if A is similar to B in some given respect, i.e. if both instantiate some species S, then A is similar to B in all superordinate respects, i.e. both A and B instantiate all S-including species higher up the relevant tree.(14) Each tree of species is crowned by a certain highest species or ‘category’ including all the species lower down the tree. Such highest species are ‘primitive’ or ‘indefinable’ in the strict Aristotelian sense that they do not arise through composition of any specific differences. Husserl’s meaning categories, now, are just the highest species in the realm of meanings, and therefore they, too, are ‘primitive’ in this sense.(15)
Higher and lower level meaning species, as we have already had occasion to note, can be taken either as many or as one, as species or as ideal singulars standing proxy for the relevant instantiating acts. But now each meaning species S, when taken as an ideal singular, bears to its respective category a similar relation to that which the relevant instances of S bear to S itself, taken as species.(16) To investigate the connections and combinations of highest species is therefore also to investigate the range of possible connections and combinations of the relevant lower level meaning species themselves, and therefore also of the underlying acts which correspond thereto.
Categorial grammar is thus for Husserl not a matter of building up a grammatical theory on the basis of a more or less arbitrary selection of convenient and conventional combinatoric units. It is a descriptive theory, a science, taking as its subject-matter the ideal structures obtaining in the meaning sphere itself, and therefore also in the sphere of object-giving acts. The laws of this science, laws governing the objective and ideal possibilities and impossibilities of combination among meanings, are laws relating precisely to such highest species. They set forth ‘the a priori patterns in which meanings belonging to the different meaning categories can unite together to form a single meaning’ (II A287/493), as opposed to those merely possible combinations – ‘and swam if never apple knock’ – which yield only meaning heaps. It is not any merely empirical incapacity on our part which puts it beyond us to realise such a heap as a unity: ‘the impossibility is rather objective, ideal, rooted in the pure essence of the meaning realm’. (II A308/511)
Husserl’s science of meaning categories is the science which deals with combination-possibilities among meanings purely from the point of view of their intrinsic well-formedness and abstracting from any possible cognitive employment and from all questions relating to truth and reference. There is however a further level of possibility and impossibility among meanings which we encounter when we consider meanings in respect of their having or not having objects or in respect of their corresponding or not corresponding to states of affairs. The first level is the level of grammar, a matter of the presence or absence of sense or meaning as such in given meaning-combinations (and of correspondingly unified complexes of instantiating acts). The second level is the level of logic proper, a matter of the presence or absence of objectual correlates for meanings already established as unified. To the impossibilities on the first level belong cases such as ‘a round or’, ‘a man and is’. To the impossibilities on the second level belong cases such as ‘a round square’ or ‘this colour is a judgment’.
Impossibilities of the first sort are such that their constituent part-meanings cannot even come together to form a unity on the level of meaning alone. We cannot fit together corresponding presentations in such a way as to yield a unified directedness to any sort of object, whether existent or non-existent, possible or impossible. At most we can patch together ‘an indirect presentation aiming at the synthesis of such part- meanings in a single meaning, and at the same time have insight into the fact that such a presentation can never correspond to an object’ (II A312f./517). Impossibilities of the second sort, in contrast, clearly do in fact yield unified meanings, reflecting a corresponding unity on the level of objectifying acts, a unity of complexity within a single act, of ‘part-presentations and dependent presentation-forms within an independently closed presentation-unity’ (II A295/500f.). But it is no less evident that there could be no object which would correspond thereto: ‘An object (e.g. a thing or state of affairs) in which there is unified all that the unified meaning on the strength of its “incompatible” meanings presents as unitarily pertaining to it does not and cannot exist’ (II A312f./517).
There are, then, simple meanings and complex meanings, and both can be combined together in different ways, governed by necessary laws into which we can have insight of the kind that is enjoyed e.g. by the theorems of geometry. At the one extreme we have a unity of several meanings within a single complex whole. At the opposite extreme we have a mere meaning heap. Between these two extremes we have various ways in which the combination of meanings can be merely partial, ways in which instantiating acts are capable of being combined together but in such a way that they do not and cannot constitute a complete and self- contained unity of judgment or presentation: ‘John is nearly’, ‘If John were’, ‘+ 2 =’. Such combinations require, as a matter of categorial law, a larger surrounding context within which they can be brought to a completion of an appropriate sort. Simple meanings, too, above all the various connective forms: ‘and’, ‘if’, ‘but’, etc., may be partial in this sense, and there are also partial meanings which include as parts whole meanings which are in themselves capable of making up ‘the full, entire meaning of a concrete meaning act’ (II A303/506): ‘John is swimming but’, ‘Before she opened the door’. In this way we obtain an opposition between dependent meanings, both simple and complex, which stand in need of a larger meaning context, and independent meanings, where the process of completion has been successfully brought to an end. Dependent and independent meanings, like all combinations of species are subject to necessary laws. The opposition between the two sorts of meanings ‘has its objective ground in law in the nature of the [meanings] in question.’ (II A302/506).
Expressions, correspondingly, are divided into syncategorematic and categorematic. The former are not meaningless. They carry a determinate though characteristically modified moment of meaning even when they occur in isolation. And when they occur normally, i.e. in the context of an independently complete expression, they have as their meaning a certain dependent part or moment of the total thought.(17)
Barry Smith, Logic and Formal Ontology