What's the point of 'dthat'?

Question

David Kaplan famously formulated a logic for demonstratives (including terms like 'I', 'now', 'here' 'actually' etc.), LD, which is a version of first-order two-dimensional logic. Very roughly and very informally, LD's model theory defines two components: Firstly, an expression relation between formulas, contexts (tuples of contextual parameters such as worlds, individuals, times etc.) and propositions (sets of world-time pairs). Secondly a truth relation between indices (world-time pairs) and propositions. So, LD's model theory amounts to defining 'formula A is true with respect to context c and world w (relative to model M and assignment g)'.

Now LD also involves a one-place operator, called dthat. Syntactically, dthat takes terms to produce new terms. Semantically, dthat is a 'diagonal' operator from term intensions (functions from indices to individuals) to term intensions in that it shifts its argument intension along its 'diagonal': For s a term the denotation of dthat(s) w.r.t. c,(w, t) = the denotation of t w.r.t. c, (w', t'), where w', t' are the world and the time of c, respectively. Kaplan furthermore says that dthat(s) is directly referential: Its truth-conditional contribution amounts to the individual it (rigidly) denotes.

Kaplan thinks dthat is a quite useful operator. But I never understood its significance; can someone set me straight?

Answer 1

In the Stanford entry we have this explanation:

Kaplan (1989a) uses dthat-terms to represent the demonstrative ‘that’ together with a type of demonstration. Kaplan holds that a type of demonstration presents a demonstratum in a particular way, and a definite description (that may contain indexicals) can capture the way in which the demonstration presents the demonstratum.

The content of ‘dthat[t]’ in a context c is the object to which the term t refers in c. For example, the content of ‘dthat[the dog I see now]’, in a context c, is Fido iff: there is exactly one dog in the world of c whom the agent of c sees at the time of c in the world of c, and that dog is Fido. If Mary utters ‘That is larger than that’ while pointing first to a dog to her left and then to a dog to her right, then Kaplan might use the formal sentence (12) to represent Mary’s sentence-plus-demonstrations.

(12) Dthat[the dog I see to my left] is larger than dthat[the dog I see to my right].

Answer 2

Kaplan explored 'indexicals', which are words with context dependent referents. They are typically adverbs: here, there, now, then, previously, currently, ...; or pronouns: this, that, these, those, they, them, he, him, you, we, us, .... They have a meaning to the language process: proximal, distal, neuter, gendered, male, female, singular, plural, ...; and they have an antecedent noun or event (to be stored in memory) such as: Fido, Fido burying a bone, .... Some can be used demonstratively, where the context depends on cues from the speaker ('This is a pen'); otherwise the antecedent is to be found in memory ('John thinks he is smart', or 'Every boy thinks he is smart'). Note that the context can change during an utterance ('That is on top of that'). It is possible that the brain first stores a demonstrative antecedent as a snapshot of the raw sensory data, and incrementally refines it to lexical memory.

Answer 3

Well according to this 1998 paper by Mark Textor it serves a confused purpose. According to Textor it is used by Kaplan as both a "demonstrative surrogate"[para 31] and an "operator on definite descriptions"[para 32].

I can't find a secondary reading on `dthat' that translates it into ordinary English. Sorry. Maybe reading dthat paper I linked to will help you.