An example on infons, states of affairs and pictures

To make things more clear, we will investigate a longer example using states of affairs, infons and pictural states of affairs. We will use some sketches to make things more clear.

First, what are the relations between the categories $Infon$, $SOA$ and $picSOA$? Figure 5.1 shows their relations. Pictural states of affairs are specialized states of affairs. They are a part of infons. The $partof$ relation is not specified more closely, but we defined infons above, and believe this to be sufficient. It may have been better to use ``constituent part-of'' in out sketch, but it does not suffice either, so we refer to the previous definition and discussion. The correspondence between states of affairs and their pictures is missing. This is shown in more detail in figure 5.2.

Figure 5.1: Relations between Infons, states of affairs and pictural states of affairs

Figure 5.2 shows the pictural representation of a state of affairs. To create a picture of a state of affairs, an agent is needed. The box on the left represents the agent's mind. The circle on the right represents some part of the world. In reality, two objects, represented as small circles, stand in relation $R$. The two objects standing in relation $R$ are a state of affairs. In the agent's mind, two representations of these two objects, noted as small crossed, are created, and the assignment function $a$ (dotted line) assigns them the objects in reality. The structure of the picture in the agent's mind and the structure of the state of affairs is isomorphic, so the relation $R$ exists in the state of affairs and in the picture. The dashed polygon designates the picture of the state of affairs in reality: The picture elements, small crosses in the agent's mind, the structure of the picture as the relation $R$, and the assignment function $a$, but not the objects in reality. As can be seen, in the agents mind are also objects standing in some relation to each other, and therefore the picture is a state of affairs on its own.

Figure 5.2: Correspondence between pictural states of affairs and states of affairs

We have mentioned, that pictural states of affairs may be about possible, but non-actual worlds. How do they enter the actual world, or the human mind, and what are their relations to states of affairs in the actual world? This is shown in figure 5.3. The box represents the agent, or more specifically the agent's mind. The small crosses are pictures of states of affairs, while the larger crosses represent states of affairs. Dotted lines designate the correspondence relation.

The circles are worlds, and only one of them is the actual world. The agent is a part of the actual world. Again, we do not like to define what ``part of'' means in this specific case, because here it is unnecessary. It suffices to know that the agent exists in the actual world. The other worlds are possible worlds. We do not want to say anything about the mode of being of possible worlds, as it is still a controversial issue in philosophy nowadays. For more information on possible worlds, see barsit, lewis1, lycan.

It suffices for us to know, that there are alternative possibilities, possible worlds, that are accessible to a rational agent's mind. Those worlds contain states of affairs, and the agents mind has access to those states of affairs. The agent can create pictures of states of affairs in possible but non-actual worlds. Because the agent exists in one world, the actual world, the pictural states of affairs corresponding to states of affairs in possible worlds are facts of the actual world. This is how possibilities enter the actual world: The world is as it is, without any possibilities or alternatives, complete in itself. An agent has access to alternative, possible worlds, and can create pictures of their states of affairs. While the states of affairs present in possible but non-actual worlds are absent in the actual world, pictures of them exist, if an agent able to access other worlds with its mind exists.

Figure 5.3: Pictures of states of affairs and their relation to possible worlds

Now the only missing category we need are infons. Infons contain a pictural state of affairs plus a function assigning it to 0 or $1$. But how are they related to worlds? How do they enter reality? Figure 5.4 demonstrates some of these aspects. Again is the box an agent's mind and the big circles are possible worlds. There is a state of affairs, noted as a big cross in one world. This state of affairs is called $s$. The agent created a pictural state of affairs corresponding to $s$. This picture is called $p$. When focusing on a part of a world or a world, the agent perceives information present in this part. The smaller circles inside the world-circles represent parts of the world. Some of them will later be called situoids.

Information present in the world or its parts is information about the presence or absence of states of affairs. This information is expressed through infons. Those are sketched in the dotted boxes. The agent then recognizes the presence of this information in some parts of reality. There are two parts of which the agent believes the positive infon to obtain, the small circle around the state of affairs $s$ and the world $s$ is a part of, while the agents believes the negative infon to obtain in the entire other world with its parts and some part of the world $s$ is a part of.

Figure 5.4: How infons enter reality