How states of affairs are constituted

Since Wittgenstein has been one of the most influential philosophers researching states of affairs, let us examine, what he wrote about states of affairs:

A state of affairs (a state of things) is a combination of objects (things). [...] The configuration of objects produces states of affairs. In a state of affairs objects fit into one another like the links of a chain. In a state of affairs objects stand in a determinate relation to one another.

This is close to Barwise, who defined a state of affairs as being constituted by a relation $R$ holding amongst objects, the arguments of $R$. However, in barsit, states of affairs do not contain only a relation and objects, but also a polarity, distinguishing between positive and negative states of affairs. We are not prepared to commit ourselves to negative states of affairs yet. However, we will commit ourselves to the belief, that a state of affairs is a configuration of things. Therefore, a state of affairs is made up of at least a characteristic relation $R$ and a number of objects, the arguments of $R$.

The question still is, what those objects are, that make up a state of affairs. There are two separate ways of how to conceive states of affairs, described in soas:

• Contingently existing, structured chunks of reality, embedded in the causal net of nature, and composed of concrete particulars, the features they exhibit, and relations among them. Call this concrete compositionalism.
• Necessarily existing abstract entities, existing outside space-time, without concrete particulars or other contingent entities as constituents. Call this situational abstractionism.

For an in-depth discussion of those two views, see soas. Here we will only state the fundamental differences in both theories, and how we will apply their results in this thesis.

Adopting the viewpoint of concrete compositionalism, we would state the following axiom:

Axiom 5.1  

• If $a$ is any concrete particular and $F$ is a property $a$ has, then $a$ and $F$ are constituents of the state of affairs consisting in $a$ having $F$.
• If an $n$-place relation $R$ holds among concrete particulars $a_1,...,a_n$ then $a_1,...,a_n$ and $R$ are all constituents of the state of affairs consisting in $R$'s holding among those relata.

Also, in the compositionalist view, a state of affairs $S$ would not exist, if one of its constituents does not exist.

Situational abstractionism views states of affairs as necessarily existing, abstract entities, which are necessarily not dependant on contingently existing entities. Even if there were no things, there would be infinitely many states of affairs. An abstract entity is an entity that necessarily exists, and is not dependant on concrete things. A possible motivation behind this view is the need for accepting possible, but non-obtaining relations among things, therefore possible, but non-actual states of affairs, and simultaneously rejecting the view on possible, but non-actual worlds with possible, but non-actual existing objects. If rejecting the existence of non-actual, possible worlds, this view solves several problems, as discussed in length in soas.

In this thesis, we will adopt another view about states of affairs. We believe, that states of affairs exist in reality and are constituted by any existing entity, concrete or abstract. In the terms of GOL, states of affairs are constituted by the relation between sets, urelements or relations themselves. We will acknowledge the existence of abstract, non-actual worlds in reality. Those worlds will contain situoids, and situoids are the entities that make states of affairs factual. Therefore, states of affairs are made up of existing entities, which may exist in an abstract, possible world.

Using GOL-terms, we can formulate the following axiom:

Axiom 5.2  

• If an $n$-ary relation $R$ holds among entities $a_1,...,a_n$ then $a_1,...,a_n$ and the relator $r::R$ are all constituents of the state of affairs consisting in $R$'s holding among its relata and we will write $\langle\langle r::R,a_1,...,a_n \rangle\rangle$.

For simplicity reasons, we will from now on simply write $\langle\langle R,a_1,...,a_n \rangle\rangle$ for such a state of affairs, and ignore the relator, except when we need it. We did not limit the arguments of the relator of a state of affairs in any way, and thereby allowing states of affairs such as $\langle\langle r::R,a_1,\ldots,r,\ldots,a_n\rangle\rangle$. However, whenever the relator of a state of affairs occurs as an argument, too, we will never use the short notion for writing states of affairs.

We can, of cause, classify states of affairs further, by the entities that are its constituents. Then we end up with a class of states of affairs that is made up by concrete individuals, a class that is made up of abstract entities and a class of mixed entities. However, a detailed classification is left open in this thesis.