## The deflationary defintion of power - a recap

In my last post on the topic of power, I proposed a deflationary definition of power, according to which the power that a person or group A possesses in a certain situation C is equated with their scope of action in that situation, that is, with what A can do in C:

(1)

A has the power to do H in context C iff A can do H in context C.

If we accept this as a starting point, then attributions of power translate into modal statements of the form "A can do H." We can analyze modal statements more deeply if we look for a semantics that can deal with the variety of interpretations that expressions like *can* possess. For this purpose, I relied on Angelika Kratzer's theory of relative modalities.1

What affords a modal verb like *can* such diverse interpretations is - according to Kratzer - the fact that the interpretation depends on a **conversational background**: what we know in a certain situation, what would be morally required in a certain situation, what range of actions we have in a certain situation, etc. The nature of these various backgrounds then determines the reading of this expression.

A conversational background (or a so-called *modal base*) can be represented as a function **f** which maps possible worlds (or situations, or contexts) to sets of propositions, which comprise what is assumed within a certain situation. In the context of power attributions the conversational background includes propositions which express the **scope of action** an actor has at a certain situation.

Propositions can be modeled as sets of worlds (the ones in which they are true), and the intersection of this set of sets of worlds - represented as **⋂f(w)** - is a set of worlds in which all the assumptions made are realized. In this case, it is the set of worlds that comprises the scope of action of a person or a group within a certain situation.

According to this framework, the truth conditions of sentences of the form "A can do H." can be formulated as follows:

(2)

[[Can(Ha)]] = 1 in w iff ∃w' ∈ ⋂f(w) such that [[(Ha)]] = 1 in w’.

A sentence like

(3)

I can bend my index finger.

in which A is me, and H is the action of bending my index finger - then would express something like:

(4)

Among the set of worlds that comprise the actions currently available to me - i.e. my current scope of action -, there is at least one world in which I bend my index finger.

If there is such a possible world among those that comprise my current scope of action, then this sentence is true; and it would therefore - according to my definition - also be correct to say that it is within my **power** to bend my index finger.

Whether the movement of my index finger represents a trivial or a non-trivial form of power essentially depends on the context. If my index finger is close to the trigger of a weapon pointed at another person's head, then this implies a more significant degree of power than if I am sitting at the kitchen table doing finger exercises in the air, because the consequences of my actions would be very different.

The difference in the consequences of both actions, which at a basic level consist in the bending of the index finger, gives rise to various possibilities of description. While Peter is doing finger exercises at the kitchen table, Paul pulls the trigger, which leads to the death of another person.

In this situation, Paul’s action is more consequential than Peter’s, and this is due to the fact that Paul’s index finger bending can be correctly described as ‘killing someone,’ while Peter’s can’t. Killing a person is, therefore, part of Paul's range of action, while it is not part of Peter's.

With a definition of power that is based on scopes of action, such differences can certainly be mapped. But there seems to be an issue that appears to be more serious. To assert that Paul has the power to shoot someone - by bending his index finger - not only presupposes that Paul hasn't done this yet (but could), but also that Paul has **alternative courses of action**, i.e. for example, that he could instead refrain from it and lower his weapon.

The possession of alternative actions is an essential characteristic of power. One could perhaps even say that the more alternatives are available to us in a situation, the more power we possess. This is not entirely true, but could serve as a good rule of thumb.

Among the myriad alternative actions we possess in any given situation, some inherently contradict each other. Paul, for instance, cannot simultaneously shoot and abstain from shooting his victim, yet he possesses the power to execute either action. Therefore, when we strive to outline what someone can do as a measure of power, it seems to inherently imply the capability to undertake actions that are mutually exclusive.

## How you can do mutually exclusive things

Some actions can be performed simultaneously. Paul talks to his neighbor while he is cleaning his car. Susan buys an ice cream and winks seductively at the seller. Peter loads the dishwasher and sings a song.

However, this doesn't apply to all combinations of actions. Peter throws a dice, and it lands on three. It could not have landed on six at the same time. Paul is playing chess. He can either advance the pawn or move the bishop across the board, but he cannot do both - at least, not if he abides by the rules of chess. A runner in a 100m race cannot both win and lose.

Some actions are mutually exclusive. And this seems to pose a problem for my approach. Let’s see why.

Imagine that an actor A in world w stands at a fork in the road. A could turn left, or he could turn right. Let's say "A turns right." expesses proposition P1, while "A turns left." expresses proposition P2.

Now, we would like to say that both alternatives belong to A’s scope of action: A can turn right, and A can turn left, but if these two propositions both belong to the modal base in w, then ⋂f(w) seems to be empty, because there is no world w' in which A turns right and A turns left *at the same time*, i.e. the intersection of P1 and P2 is empty.

(5)

f(w) = {P1, P2}

⋂{P1, P2} = ∅

This is a horrible result, because our model would predict that “A *can* turn left.” f.i. is false, because there is no world in ⋂f(w) in which A turns left, precisely because there’s another alternative available to A. And similar things are true with respect to all possible actions of A in w that are mutually exclusive. How can we deal with the problem of mutually exclusive actions?

One way around this issue could be to understand the modal base not as including both P1 and P2, but as including a broader proposition P3, such as "A turns either right or left." P3 would be true in all worlds where either P1 or P2 is true, and the intersection of the modal base would then include all such worlds.

In other words, instead of (5) we would have (6):

(6)

f(w) = {P3}

⋂{P3} = {w: P3 = 1 in w}

If proposition P3 is true in the set of worlds in which either "A turns right" or "A turns left" is true, the intersection of the modal base, ⋂f(w), would not be empty. This is consistent with Kratzer's theory and allows us to handle situations where there are mutually exclusive possibilities.

The proposition P3 is - in a sense - the *union* of P1 and P2, and the maneuver to utilize P3 seems just to be a clever way to "smuggle" a union into an intersection. I think, however, there's a deeper point here related to the nature of modality and the way we represent knowledge and possibilities.

In a more real-world context, it's worth noting that the actual determination of what propositions are in the modal base would depend on the specific knowledge and assumptions of the speakers in the situation. If we know that "A will turn right or left", but we don't know which way A will turn, then it is *accurate* to say that the modal base includes a proposition like P3. This is not so much a trick as it is a reflection of the state of our knowledge: we know that one of the two possibilities (right or left) will occur, but we don't know which.

Including P1 and P2 but not P3 in the modal base would lead to an *inconsistent* set of propositions, which might not accurately represent the state of our knowledge or assumptions.2 This is not to say that our assumptions can’t be inconsistent. We are human, after all, and we don't always hold perfectly consistent beliefs or assumptions.

If we, however, include inconsistent propositions in the modal base, the intersection of these propositions will be empty, and this essentially means that there are no possible worlds consistent with our assumptions, which doesn't provide a useful foundation for further analysis.

For references, see my original post.

*Mutually exclusive* and *inconsistent* are similar concepts in that they both indicate that two things can't both be true at the same time. However, there are subtle differences in how these terms are typically used. "Mutually exclusive" is often used to refer to events or outcomes in a probabilistic or statistical context. Two events are mutually exclusive if they can't both occur at the same time. For example, if you're rolling a six-sided die, the events "roll a 1" and "roll a 2" are mutually exclusive—you can't do both on a single roll. "Inconsistent", on the other hand, is often used in a logical context to refer to propositions, beliefs, or sets of beliefs. Two propositions are inconsistent if they can't both be true at the same time. For example, the propositions "it is raining" and "it is not raining" are inconsistent - they can't both be true at the same time. In the context of our discussion, the propositions "A turns right" and "A turns left" could be described as either mutually exclusive or inconsistent, since they can't both be true at the same time. However, "inconsistent" might be the more appropriate term in this context, since we're dealing with propositions and their logical relationships.