"It really is a nice theory. The only defect I think it has is probably common to all philosophical theories. It's wrong."
Saul Kripke
Saul Kripke
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This point was implicit in the original critique of the denoscription theory of names. The rejection of the internalist picture was not a rejection of the idea that reference was determined by the speaker's intentions and beliefs: rather it was the rejection of the assumption that intentions and beliefs need to be explained in terms of the grasping of purely general concepts. In the sketches by direct reference theorists of an alternative account of reference, intentions played a prominent role, but it was assumed that intentions could be directed to particular individuals, and need not be explained in terms of a purely conceptual content. A causal theory of reference was not a theory that explained reference independently of intentions, but a theory that explained intentions in causal terms.
(с) Context and Content, Stalnaker
(с) Context and Content, Stalnaker
Kohei Kishida, in Chapter 8, uses category theory to develop a model theory for modal logic by focusing on the familiar Stone duality. Specifically, he aims to bring together Kripke semantics, topological semantics, quantified modal logic, and Lewis’ counterpart theory by taking categorical principles as both mathematically and philosophically unifying.