We are now in a position where we can say something about Husserl’s theory of dependence, which is all of a piece with his theory of species. For Husserl recognised that there are, in addition to the vertical (inclusion) relations between species, certain sorts of lateral relations, sharing with them important modal properties. Examples of the vertical relations would be:
every instance of the species red is also an instance of the species colour;
every instance of the species mammal is also an instance of the species animal;
every instance of the species judgment is also an instance of the species mental act.
Such relations involve moving from one species to another along given branches of a single species-tree. They can be more or less satisfactorily captured by means of the familiar inclusion relation of standard set theory. Lateral relations, in contrast, involve moving from one branch to another, or perhaps even moving to a wholly different tree. Such relations, even when conceived merely extensionally, fall outside standard set theory or any of its more usual extensions. Examples of such lateral relations are:
no instance of the species funeral occurs, without a prior and associated instance of the species death;
no instance of the species colour exists, without a simultaneous and associated instance of the species visual extension;
no instance of the species phoneme is also an instance of the species edible thing;
no instance of the species red coincides with (occupies the same spatio-temporal area as) an instance of the species green.
These relations are, in Husserl’s terminology, relations of dependence and of necessary exclusion or incompatability. Such relations are of course in a certain sense trivial (no less trivial, indeed, than the vartical or analytic relations which are captured in the arbor porphyriana of the traditional sort). This does not mean, however, that they can be ignored, and nor, either, does it mean that there is not a great advantage to be derived in embedding them within a theoretical framework within which their status can be clarified and their character of apparent arbitrariness removed.5 The theory of such relations has indeed been shown, in as yet unpublished work by Kit Fine, to yield a mathematical framework of some elegance and complexity, though it would take us too far from our main concerns to develop the details of the theory here.6 Suffice it to point out that Husserl distinguishes between one-sided and reciprocal dependence, e.g. between the one-sided dependence of an instance of the species musical tone on an instance of the species temporal duration, and the three-sided mutual dependence of instances of the species pitch, timbre and loudness within a given tone.
Such n-fold dependence relations correspond to n-fold dimensions of variation in the space of objects governed by the relations in question. Husserl’s own 4th Investigation, now, is precisely an application of the theory of dependence to the relations structuring the space of meaningful uses of language. Uses of language can be divided, at different levels, into (relatively) dependent and (relatively) independent, in a way that can be shown to generate a categorial order of types of such uses (i.e. of the various ‘parts of speech’). Thus Husserl’s work on the laws governing dependent and independent meanings influenced the development of categorial grammar by Stanisaw Leniewski (1886-1939) and Kazimierz Ajdukiewicz (1890-1963) (see Smith and Mulligan, 1982, § 5.) The idea of a grammatical theory built up on the basis of a theory of the dependence relations between parts of sentences has since been developed formally by linguists such as A.J. Melcuk and R.A. Hudson as alternatives to grammars of the more familiar transformational sort. (For references see Melcuk 1979, Schachter 1980.) All of these grammars, however, exploit theoretical resources weaker than those available to Husserl, since they employ exclusively the notion of unilateral dependence or its equivalents. The idea of a dependence or categorial grammar utilising also relations of mutual dependence is currently in process of investigation by William Haas.
Husserl’s theory of dependence was employed also by the linguist Roman Jakobson, above all in his work on distinctive features in phonology and on implicational universals of language acquisition. (See Holenstein 1976.) But its most thorough-going application was carried out by the Munich phenomenologist Adolf Reinach in his “Die apriorischen Grundlagen des b}rgerlichen Rechts” of 1913. Reinach’s work is, notwithstanding its somewhat misleading title, an investigation of the ontology of those complex structures which are actions of promising, commanding, forgiving, questioning, and so on, structures which straddle the borderlines not only of linguistics and psychology but also of jurisprudence and the theory of action. A good case can indeed be made for the claim that Reinach, already in 1913, had set forth the essential elements of what later came to be called the theory of speech acts. His work even contains a discussion of the various ‘infelicities’ to which speech acts can be subjected, not, however, in terms of any quasi-logical ‘conditions of satisfaction’, but rather in terms of a theory of the various possible sorts of ontological modifications which structures involving speech acts may undergo, a theory which is then applied also to throw light on the ways in which such structures may be affected by determinations of the positive law. (See Mulligan ed., and also Smith 1986 and 1986a for further details.)
Barry Smith, Husserl, Language, and the Ontology of the Act