The knowledge of the commonsense metaphysics slowly intrudes in our existing
theoretical setup. One can not ignore this metaphysical necessity, in course of attaining ‘a
meaning algebra by introducing a rich type structure’ (Saba 2005). Later, while
discussing linguistic semantics, we will talk about the same cumulative effect.
From our above discussion, what we can actually infer is that logic, as an
axiomatic form, was not necessarily self-evident / self-consistent. As a result, it has been
augmented into formal semantics - a voyage has been set up from the epistemological
concern to the metaphysical one! This developmental scenario will be clearer, in a while,
as we start to sail down the sections.
2.1 The Birth of Ontology
2.1.1 Formal Semantics
The genesis of formal semantics is a result of the augmentation to the existing version of
the philosophical logic. Otherwise, it has the same theoretical apparatus, which has been
inherited from Descartes. Philosophical logic works by and large on the basis of the bare
minimal semantics of the Syncategorematic symbols, such as ‘—’, '∨', '∧', '→' etc.,
which are not basic expressions, in the sense that they are not members of any syntactic
category. They are limited in number and hence constitute the closed class, which is
‘logical’ in nature. Categorematic symbols are assigned to syntactic categories, such as
names, n-place predicates etc. (Dowty, Wall & Peters 1981: 16). These symbols are
infinite in number; constituting an open class. Semantics of this closed class
syncategorematic symbols governs the logical computation.
In addition to this, in formal semantics, as we have already seen, the point of
interest shifts toward the propositional form. Since, the study of propositional form
requires some extra attention to the categorematic symbols, formal semantics starts to
feel the necessity of an ontological support, ultimately resulting into the
conceptualization of the higher order type-theoretic logic. These types are syntactic in
nature.
In spite of having traditionally held syncategorematic and categorematic
distinction, we have the corresponding categorical specifications, in terms of ‘e’ and ‘t’,
representing a term and a formula respectively, along with the law of cancellation
(Dowty, Wall & Peters 1981: 83-85). Now the system becomes much more general and
adequate in comparison to its earlier versions, since it is minimally designed. The process
of augmenting the traditional logic to formal semantics has been done by blurring the
distinction between the syncategorematic and categorematic elements. Therefore,
categorial specification of a lexical item, irrespective of its syncategorematic or
categorematic nature, in terms of ‘e’ and ‘t’, ultimately preconceives a nascent form of
ontology.
Even after introducing higher order type-theoretic mechanism, formal semantics
remains far away to fulfill the criteria for a self-evident / self-consistent system; since
the concept of type, irrespective of its degree of richness, has a very insignificant
contribution, to the ontological studies, primarily because of its syntacto-centrism.