The Relational Theory of Meaning

Barwisean situation theory provided a semantic for utterances in natural language. Situoid theory does the same. Because utterances are always temporally extended, they have to be viewed in the domain of situoids, and not situations.

Before we can explain how the meaning of a term is modelled in situation theory, we have to explain the ``categorization devices'' we introduces in section 5.2.8. A categorization device is a universal. Only universals are instances of a categorization device, so it is a universal of universals. It has been introduced by Sacks in sacks1 as a non-empty collection of categories together with rules of application. As an example there may be a categorization device ``gender'' with two universals as its instances, ``$male_H$'' and ``$female_H$''. The index $H$ means here that these universals are applied to humans. Now we could formulate rules of application, like in devlin1: ``If some population of persons is being categorized, and if a category from some device has been used to categorize one member of the population, then that category, or other categories of the same device, should preferentially be used to categorize further members of the population.'' or Sack's Economy rule: ``A single category from any device can be referentially adequate.'' Several more preferential rules, for example for category-bound activities, can be found in devlin1.

The meaning of a referring word or term $\phi$ is a relation $\Vert\phi\Vert$ between pairs $(d,u)$ of situoids and pairs $(T_{\phi},T_{dev})$ of universals. The situoid $u$ contains the utterance of $\phi$, while the situoid $d$ is the context in which $\phi$ has been uttered. The universal $T_{\phi}$ is the universal that $\phi$ is an instance of, while $T_{dev}$ is a ``categorization device determined by the contextual features in $d$.''devlin1. $T_{\phi}$ is a member of $T_{dev}$. As in devlin1, we will call $T_{dev}$ the outer device, the connection between the context $d$ and $T_{dev}$ the outer link, the universal $T_{\phi}$ the inner type and the connection between $u$ and $T_{\phi}$ the inner link.

Categorization devices are associated with situoids using the relation $ass$, with $ass \subseteq Universal \times Situoid$.

How can this be used to give meaning to a referring word, such as ``man''? There are several meaning for the term ``man'', such as husband, human being with a certain gender or a stage in life.

Let us focus a situoid $d$. We know the following things about $d$:

• $d \models \langle\langle Student,John;1\rangle\rangle$
• $d \models \langle\langle Sits-in-biology-class,John;1\rangle\rangle$
• $d \models \langle\langle Teacher,Mary;1\rangle\rangle$
• $d \models \langle\langle Teaches-about-sexual-reproduction,Mary;1\rangle\rangle$
• $d \models \langle\langle Movie-of-reproduction,m;1\rangle\rangle$
• $d \models \langle\langle Watches,John,m;1\rangle\rangle$
• $d \models \langle\langle Utters,John,u;1\rangle\rangle$

So our context is a situoid with at least two people, John and Mary. John is attending Mary's biology class about sexual reproduction. Apparently some kind of instructive movie has been shown to the class, and John is giving a report on what he saw. This context establishes a categorization device $T_{sex}$, and $T_{man}::T_{sex}$. The categorization device $T_{sex}$ has universals as instances that are relevant in the context of sexual reproduction. $T_{man}$ is such a universal. When John utters ``The man is more muscular than the woman'' ( $u \models \langle\langle More-muscular,man,woman\rangle\rangle$), the meaning of the word ``man'' is expressed as $(d,u)\vert\vert man\vert\vert(T_{man},T_{sex})$. The same would hold for ``woman''.

Adjectival terms like ``muscular'' can be given a meaning, too. The meaning of an adjectival term $\phi$ is the relation $(d,u)\vert\vert\phi\vert\vert(T_{\phi},T_{item})$ between pairs of situoids $d$ and $u$ and pairs of types, $T_{\phi}$ and $T_{item}$. As in devlin1, $T_{\phi}$ is the universal with all the entities that can be referred to as $\phi$ as instances. $T_{item}$ is the universal the item referred to by the utterance $u$ in $d$ is an instance of. So in our previous example, the meaning of ``muscular'' would be $(d,u)\vert\vert muscular\vert\vert(T_{muscular},T_{man})$ and $(d,u)\vert\vert muscular\vert\vert(T_{muscular},T_{woman})$ respectively.

Figure 6.1: Word meaning (from (Devlin, 2003))

The relation between the context, the utterance, the uttered term, the universal of the uttered term and the categorization device has been illustrated in figure 6.1.