Philosophy Concordance - online philosophical quotations

A part-whole system can be considered as a set U of items plus a set of certain 'operators' each of which maps an n-tuple of items of U (parts) on an item of U (whole).

It maps multi-directionally (in production and comprehension) among systems: recursive semantic representations, recursive communicative intentions, and hierarchial phonological signals.

Finally, the suggestion that the recursive power of language arose as a simple co-opting of recursion in other cognitive systems such as navigation or number encounters numerous problems: that navigation is not discretely infinite; that recursive number cognition is parasitic on language rather than vice-versa; and that language maps among recursive systems rather than being a straightforward externalization of a single recursive system.

The intension of a singular term maps a possible world to the referent of a term in that possible world: the intension of 'Don Bradman' picks out whoever is Bradman in a world.

The intension of a general term maps a possible world to the class of individuals that fall under the term in that world: the intension of 'cat' maps a possible world to the class of cats in that world.

So the diagonal intension of 'water' maps the H2O-world to H2O, the XYZ-world to XYZ, and so on.

So the character of 'I am hungry' maps the first context above to the proposition that Joe is hungry at t1, and the second context above to the proposition that Diana is hungry at t2.

Extending this idea to subsentential indexical terms, we can say that the character of 'I' maps the first context to Joe and the second context to Diana; more generally, it maps any context into the speaker in that context.

Similarly, the character of 'now' maps any context into the time specified in that context.

But to a rough first approximation, one can say that the character of an expression maps a context to the content that the expression would have if uttered in that context.