Page 396 - Encyclopedia of Philosophy of Language

Formal Semantics
John loves Mary. She loves him.
John' :e
love' :e-»(e-»0 Mary':e
love' (Mary'): e -»/
love' (Mary') (John'): /
Modus Ponens Modus Ponens
markers, for example, are a means of linking one local piece of reasoning with another—through some unifying variable. Suppose, for example, we wish to link together two pieces of information, that a man fainted and that that man smiled. We can do so through the relative clause structure:
A man who smiled fainted. (25)
The relative marker provides a means of constructing such linked pieces of information, through common use of some unifying variable. Reflecting this, wh- can be characterized as initiating, from the lexicon, a database to be so linked. The logic defines a concept of linked databases, two databases being linked if and only if some free variable in each is replaced by some common unifier. And we assign to wh- the lexical specification that it impose the requirement that its containing proof structure lead to a conclusion of type t labeled by some open formula containing a variable, a structure which can then be linked through some associated determiner:
wh-{ }h«(u):r
The lexical content of wh- does not itself constitute a premise to be manipulated in any proof structure— rather it provides a restriction on the form of con- clusion that must be established.
We now have a new construal of the nature of interpretation—lexical items contain specifications which constrain the building of a proof-structure from which the more orthodox concept of truth-content will be derivable. The essence of linguistic content so defined is that it is meta to any such level and hence essentially syntactic. Furthermore, the building of this configurational structure is not characterized as a grammar-internal process but as a process of central cognitive reasoning. We have arrived at a conclusion which not only blurs syntactic and semantic dis- tinctions but sets a different boundary between gram- mar-internal and central cognitive processes. Yet despite the apparent merging of syntax and logical deduction, the language faculty itself remains as a discrete construct. The input information, char- acterized as the lexicon, is the necessary input to the deduction process, its own internal statements encap- sulated from and not affected by any subsequent pro-
cesses of deduction. We abandon the concept of the language faculty as a body of knowledge entirely div- orced from our faculty for reasoning, but we retain the concept of encapsulation vis-a-vis its a priori nature, the essential input to any cognitive processing of linguistic stimuli. The apparent interaction of syn- tactic and cognitive constraints is now unproblematic. The linguistic input severely underdetermines the out- put structure constituting its interpretation, and the entire process of actually building that structure is a process of reasoning. Many so-called syntactic phenomena emerge as consequences of the proof disci-
u :e
condition: 0u I local proof-structure female(0u)
[0 an instantiation func- tion]
Reiteration
0u I local proof-structure male(0f)
Reiteration
Modus Ponens Modus Ponens
Mary' :e
CHOOSE 0u = Mary' love' :e->(e-»/)
»
:e
: e
condition:
John'
CHOOSE 0»=John' love' (John'): e -»/ love' (John') (Mary'): t
Reconstructed this way, anaphoric linkage is a relation established across structure—proof-theoretic structure. Locality restrictions on this process, whether to some non-local domain as with pronomi- nals, or to some local domain as with anaphors, are naturally expressible as side conditions on the process of instantiating the initiating assumed variable. We have principle A and principle B of the binding theory stated directly as a specification given in the lexicon as definitional of anaphors/pronominals but implemented on proof structures as part of the process of arriving at some labeled conclusion, here:
love' (John') (Mary'): t.
Utterance interpretation can now be defined as a pro- cess of natural deduction from some initiating set of premises to some conclusion a: t, a being the prop- osition expressed, with some of the words presented as premises to that conclusion, others determining how the conclusion is reached. With this mode of explanation the concept of interpretation is essentially structural: linguistic content is characterized in vari- ous ways according as the lexical item contributes to this process of proof-unfolding. Lexical items such as love contribute labeled premises:
love love': e -* (e -* t).
Items such as pronouns and anaphors contribute premises labeled by a metavariable with some associ- ated side condition determining how that variable is to be identified:
he u:e
CONDITION
0u I local proof structure
male(0u) (0 an instantiating function)
And some expressions contribute solely by providing some constraint on the proof process. Relative clause
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