Dependence relations of situoids and states of affairs

An interesting aspect is whether infons or situoids can exist on their own, or if they need other entities, before they can come into existence. This relation between entities is called existential dependence.

Definition 5.14 (Existential dependence)   An entity $A$ is existentially dependent upon the entity $B$ if and only if it is logically impossible for $A$ to exist if $B$ does not exist. The category $C$ is existentially dependent upon the category $D$ if and only if for every instance of $C$ it is logically impossible to exist if not at least one instance of the category $D$ exists.

Now, what is the relation between situoids and states of affairs, and the relation between situoids and infons. One part of this question can be answered by researching whether there could be an empty situoid, namely a situoid $s_0$, such that $\forall \phi ( \neg (s_0 \models \phi))$. What would such a situoid behave like? Let us consider some region of empty space over some chronoid. Are there any infons that obtain in this situoid?

Is there a special class of infons, that does obtain in every part of existence, in every part of the world, of reality? Those would be logical tautologies. As an example, consider the infon $\langle\langle =,p,p;1\rangle\rangle$, stating the logical tautology $p=p$. This infon would be true in every part of reality. Wherever there is existence, the laws of logic obtain. However, consider the following excerpt from Wittgenstein's Tractatus:

Tautologies and contradictions are not pictures of reality. They do not represent any possible situations. For the former admit all possible situations, and latter none. In a tautology the conditions of agreement with the world -- the representational relations -- cancel one another, so that it does not stand in any representational relation to reality. tractatus

This explains our -- suspicious -- feeling when we considered the infon $\langle\langle \rightarrow,p,p;1\rangle\rangle$. In this infon is no information about a situoid, but it rather defines a frame for any possible situoid. Even worse, there is no state of affairs corresponding to this infon. However, if it was an infon, it would obtain in every part of reality, in every situoid in every possible world.

We believe that there is no such thing as an empty situoid, there are always states of affairs present in every part of reality. The reason for this are again due to Wittgenstein. If reality is the collection of all the facts, all the states of affairs, then any part of reality, which we believe situoids are, must contain some states of affairs.

Axiom 5.17  

$$\forall s (Situoid(s) \rightarrow \exists \phi (s \models \phi))$$

This answers one part of our question: Situoids are existentially dependant on infons.

Now we will focus on another question.

Can infons exist outside a situoid? Are there states of affairs, that do exist in reality, but not in any situoid?

If we use alternative 5.5 in section 5.1.5 and assume that there are states of affairs that cannot be pictured, then certainly the above is true. But what if we use the other alternative, 5.6?

States of affairs mediating abstract entities like numbers or sets would be another possibility for states of affairs that are not part of any situoid.

We will leave again two alternatives here, and leave it open for the user of this theory to choose amongst them. The first asserts that all states of affairs exist in some situoid. The second assumes that there is at least one state of affairs outside all situoids. Note the similarity to the alternative axioms 5.5 and 5.6.

Axiom 5.18   Alternative 1

$$\forall \phi (Infon(\phi) \rightarrow \exists s(Situoid(s) \land s \models \phi))$$

Axiom 5.19   Alternative 2

$$\exists \phi (Infon(\phi)\rightarrow \forall s (s \not\models \phi))$$

There is another class of infons that never obtains (and their negations always obtain). Those are infons about natural sciences. The infon stating that the gravity constant is $1.5$, $\langle\langle =,gravity-constant,1.5;1\rangle\rangle$ is never true in the current world. In this sense, it could serve as a class of never-obtaining infons. However, it is possible to obtain in some world, it does not deny existence. Therefore there could be some part of reality, some world made up of situoids, where it obtains. The relation between situoids and worlds will become clear later. For now we assume that these are infons with pictural states of affairs and corresponding states of affairs.