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When we look at the modeling scheme, we see four nodes representing
'states of affairs', or 'states of the world'. What are those states?
To answer this question let us ask ourselves: if action is the primary
reality, how do we distinguish between various states of the world?
The answer can be: by being able to do various different actions.
For example, if the state of affairs is such that there is an apple
on the table in front of me, a can reach it and pick it up. If there is
no apple this is impossible. If the moon is on the night sky, I can
execute the action of observing it. For this purpose I rotate my head in a
certain way and keep my eyes open. Observation is a kind of action.
Thus we could define a state of the world as a set of actions that I
(the subject of knowledge) can take.
But there are states of another type,
which do not fit this definition. If I feel pain, or am frustrated, or
elated, angry, or complacent, this has no effect on the actions I can
take. It affects only the choices I am going to make selecting from the
same set of possible actions. Indeed, if my hand is over a gas heater
and hurts (say, gently, for plausibility), I still have the choice between
keeping the hand where it is, or withdrawing. But, obviously, the more it hurts, the more likley I am to withraw it.
Thus we come to distinguish between:
(a) a physical state, which is a set of possible actions for the
subject 'physical' actions; and
(b) a mental state, which influences the choices to be made by the subject,
but does not alter the set of possible choices.
When speaking of "states" without any of the two adjectives, we shall
mean physical states.
The distinction between (a) and (b) reflects the fundamental distinction
between "I" and "not-I".
Why should we consider action as more basic and primary than state?
After all, we register an action when the states of the world changes.
The reason is this: a state can be understood and characterized
in terms of actions -- we have just defined it as a set of possible actions.
An action, however cannot be defined through states. When we define
an action as a change of the state, we introduce something new, which is
not present in the idea of a state; change is, essentially, an action
abstracted from the actor that executes it.
The following observation confirms the primacy of action
over state. When we start thinking about constructing a model of the world
on the basis of these concepts, we tend to believe that we will need
a relatively few types of actions, while the set of possible states of the
world is expected to be much greater and much more complex.
In our mathematical model of semantics we shall denote the set of all
possible action by A. We do not yet know what this set is, or rather
what it should be for our further models to be successful. It is possible
that various models of the world will start with various different sets A.
But with any A, the set of possible states of the world, which we shall
denote as W, is the powerset of A, W = P(A), i.e. the set of all subsets
of A. Thus an individual state w is an element of W. w \el W, and
a subset of A, w \subs A.
