Indexical Semantics in the Language of Thought
Accepting that there is an innate and universal language of thought, we can inquire into its formal characteristics. It will have two components: a syntactic component and a lexical component. These components will be found in every human being’s cognitive-linguistic repertoire (barring pathology), like any other innate human trait. There is no problem about this with respect to the syntactic component: there is no reason to doubt that each person uses an identically structured internal language. Nor is there any obvious problem about large tracts of the lexical component: people share a large number of basic concepts because they live in a common world of space and time, colors and shapes, other minds, plants and animals, logical and mathematical truth, ethical demands, etc. That is, the universality implied by the idea of an innate species-wide internal language is not contradicted by the facts of human psychology. However, there is a segment of the lexical component that does appear to present a problem for this picture—the words that refer to specific local objects, artifacts, and natural kinds in the individual’s environment. It is not plausible to suppose that people in foreign lands have names for the places, people, artifacts, and animal species found in this land. Generally, it can hardly be that words for local entities are genetically encoded in our species and enter the thoughts of every human on the planet. Yet we do use such parochial concepts to think about the world. So either the language of thought is not fully innate and universal or it innately covers a lot more than it is plausible to suppose that it does. How do we get out of this problem?
The problem can be put like this: how do we find an interpretation for all such locally bound lexical items that is consistent with the absolute universality of the language of thought? What kind of semantics would allow us to declare that the “referential component” is universal to humans? It can’t be a semantics that simply assigns a unique entity to each such term, on pain of assigning the same entities to terms no matter the location of the individual in question—people from the jungles of the Amazon don’t have a name for London! Clearly we need a semantics that provides a uniform inner linguistic structure that combines with a contribution from the local environment. One way to do this would be to suppose that the innate language contains interpretation-free terms as well as interpretation-bound terms; the free terms pick up reference from the way the individual is contingently embedded in the world. The genes supply these initially meaningless terms, which are common to everybody, in order to allow for the future possibility of local reference, relying upon the embedding of the individual to provide them with an interpretation. Thus a single symbol S in the language of thought can come to refer in one land to London and in another land to a certain Amazonian village, having no intrinsic fixed meaning at the outset. We could call this the “interpretation-free component”—the part of the lexicon that requires a suitable embedding before it acquires any meaning.
But there is another approach, akin to this one but without the assumption of initial meaninglessness, namely that the innate language of thought is heavily indexical. The form of this type of theory allows us to say that the lexical component is universal and semantically interpreted, while accepting that not everyone shares the same range of references. What we have is a universal language that gets tied down to particular entities by virtue of the context in which that language finds itself located. Semantically it’s like the word “I”: everyone has the same indexical word but context determines to whom it refers. Names are then introduced on the back of indexical expressions, as in, “Let ‘London’ denote this city”, where the name “London” is not part of the genetically given language of thought but the demonstrative “this city” is. The Amazonians and us share the underlying indexical apparatus but not the local terms that are subsequently tied to it. This solves the problem of reconciling linguistic universality with referential locality: the language is universal but its referential interpretation is local. The words of the language mean the same thing for everyone everywhere, but context links these words to different entities (which can subsequently be given names). Thus there is no interpretation-free (meaningless) component to the innate language, yet words of this language can receive different referential interpretations in different environments. That is how the genes solved the problem of parochial reference in a common language: they invented indexical semantics. Some sort of mutational and selective history led to a semantic structure that can deliver variation from uniformity, thus preserving the commonality of the language while combining it with referential diversity. The apparatus is common to all humans, though that apparatus gets applied to different entities in different contexts. It is the apparatus that is encoded in the genes, but that apparatus allows for non-genetic factors to fix reference in specific contexts. Thus the indexical component of the language of thought is what enables us to solve the problem of referential diversity.
What is the evidence for the indexical theory of the language of thought? The indexical character of natural languages of course: natural languages are heavily indexical, and this reflects the character of the underlying language of thought. I won’t repeat all the arguments for recognizing the ubiquitous role of indexical expressions in natural languages (all natural languages); my point is just that the role of indexical expressions in solving the problem of universality is mirrored in the manifestly indexical character of spoken languages. Arguably, natural languages cannot perform their referential function without relying on indexical reference; it turns out that the underlying language of thought could not exist without a similar reliance. The use of an indexical apparatus is what is needed to make that language both biologically universal and environmentally variable. The lexical component needs an indexical component if it is to be possessed by all humans alike. Natural languages make this component visible. We are born indexical thinkers. 
 Thus the language of thought will not be a context-free logical language like first-order predicate calculus; it will be a context-dependent indexical language exhibiting the semantics of content and character in the style of David Kaplan.