The problem on negative and non-basic states of affairs

The question remains whether there are states of affairs that do not obtain. Are there states of affairs, configurations of things, that do not exist? Exist non-existant states of affairs? This is closely related to the question, whether there are things, concrete entities, that do not exist.

Imagine the state of affairs ``Bugs Bunny's being a rabbit''. Now there are several problems with this state of affairs (if we could call it that). The main problem appears to be, that Bugs Bunny is a cartoon character, and does not exist in real in our world, except perhaps as some concept of a cartoon rabbit. This concept, however, is something different than a rabbit. Therefore, Bugs Bunny is not a rabbit, but something else.

Some philosopher suggest, that there is another state of affairs, namely the negation of ``Bugs Bunny's being a rabbit'', that obtains. Barwise would denote ``Bugs Bunny's being a rabbit'' with $\langle\langle Rabbit,BugsBunny;1\rangle\rangle$ and the negative state of affairs $\langle\langle Rabbit,BugsBunny;0\rangle\rangle$. But what does the latter mean? There are two ways of looking at this. Either it is the absence of a configuration of things, the non-existence of a state of affairs, or it denotes ``Bugs Bunny's being a non-rabbit''. We reject the first view as it contradicts our belief that states of affairs are real, existing configurations of entities, and not the absence of such a configuration. The second view seems more plausible on the first, but the question arises, what a ``non-rabbit'' would be. Are there any non-rabbits in our world? We will deny this question, too, until someone can show us a non-rabbit.

There may be occasions, when negative relations occur, as in $having$ and $non-having$ or $lacking$, and they may perfectly make sense. Is this then some kind of negative state of affairs, that is formed by negating the relation? We take the standpoint, that those are fundamentally different relations, and they are not related.

If there were negative states of affairs, then there would be an imbalance between the number of positive and negative states of affairs, as for every positive state of affairs exists a possibly infinite number of negative states of affairs. Image the state of affairs $\langle\langle Rabbit,BugsBunny;1\rangle\rangle$, saying Bugs Bunny's being a rabbit. Now there is only one positive state of affairs, but we could state a number of negative ones: $\langle\langle Dog, BugsBunny;0 \rangle\rangle$, $\langle\langle Snake, BugsBunny;0 \rangle\rangle$, $\langle\langle Tree, BugsBunny;0 \rangle\rangle$, et cetera.

In this thesis, we will deny the existence of non-obtaining states of affairs. States of affairs exist in the configuration of entities. They are the configuration (or relation) of real, existing objects. It is nonsensical to speak of the existence of non-existent configurations of things. Therefore, states of affairs are made up of exactly one relator $r::R$ and a number of entities $a_1,...,a_n$.

We believe, this also answers the question whether there are non-basic states of affairs, like disjunctive or conjunctive states of affairs. Because states of affairs consist of exactly one relator (and therefore one relation) and a number of object which this relator mediates, there are no non-basic states of affairs.

The relation may be composed of several relations. For example, consider the location of three red dots, $d_1, d_2, d_3$, on a white sheet of paper. Then each two of those dots stand in a relation $R_1$, $R_2$ or $R_3$ to each other, designating their spacial location to each other. There is also another relation, maybe $D$, stating that those three dots stand in a different, spatial relation to each other. The holding of relation $D$ is a consequence of the holding of $R_1$, $R_2$, and $R_3$, but only with regard to a background theory. If we had an ontology of relations and a theory of the relations $R_i$ and $D$, we could deduce the holding of $D$. But even then, $D$ is a relation in its own right.

States of affairs, that are constituted by only one relator holding amongst a number of objects are called basic.

We take on the viewpoint of logical atomism in this thesis, and therefore state, that there are only basic states of affairs. We will also consider states of affairs of the form $\langle\langle R,a_1,\ldots,\langle\langle P,b_1,\ldots,b_m\rangle\rangle ,\ldots,a_n\rangle\rangle$, which have other states of affairs as constituents, as basic.