Now as it's formulated here, this argument doesn't rule out the view that 'that'-clauses refer to mentalese sentence types, but the argument can be extended to rule out that view as well (e.g., one might do this by talking not of an American and a Russian but of two creatures with different internal languages of thought).
They present various features such as simulation environments, connection to DNA-sequence databases, internal languages (e.g. Eugene [ 34], Antimony [ 35]), and rule-based grammars [ 36, 37] for circuit specification and design automation.
A topos is said to be Boolean if its internal language is classical.
In the internal language of a Boolean local topos, the logical connectives and quantifiers have their natural meanings.
Big firms are making English their internal language, even if it is not the native tongue of most of their workers.
In the same spirit, an amplified version of Gödel's completeness theorem would say that every topos may be viewed as a continuously variable local topos, provided sufficiently many variables (Henkin constants) are adjoined to its internal language.
While it was fine for a company to have English as its internal language, said Diane Wood, chief judge at the United States Court of Appeals for the 7th Circuit, companies often had to reach out into the society where they were doing business, and for that they needed languages.
Growing disquiet among the German-speaking politicians, especially those from Bohemia, exploded in 1897 when the Austrian prime minister Kasimir Felix, count von Badeni in order to win Czech votes to renew the compromise with Hungary agreed to make Czech equal to German as the internal language of administration in Bohemia and Moravia.
Note that, in the internal language of the free topos, and therefore in pure intuitionistic type theory, the substitutional interpretation is valid for existential quantifiers, by virtue of the free topos being local, but that it fails for universal quantifiers, in view of the absence of ω-completeness and the fact that in the free topos all numerals are standard.
As it turns out, a Boolean local topos may be described more simply, without referring to the internal language, as a topos with the following property: if f, g : A → B are arrows such that fa = ga for all a : 1 → A, then f = g.
One strand of representationalism, endorsed by Fodor, takes mental representations to be sentences in an internal language of thought.
