This is the fourth installment in my series on power. I will explore the intricacies of power attributions, building upon the perspective of power introduced in the second part of this series. My earlier understanding, henceforth referred to as the coarse-grained view of power, is a useful model but fails to capture the full complexity of power ascriptions.

Throughout this piece, I will illustrate that the coarse-grained perspective is not sufficient to unpack all the subtle nuances involved in attributing power. To demonstrate this, I will present a variety of scenarios that highlight the limitations of this view.

In response to these limitations, I propose an enhancement: the addition of a second conversational background, or what Angelika Kratzer calls an 'ordering source.' By integrating ordering sources into the model, we can use them to further analyze power attributions and thus move towards a more refined, or: fine-grained view of power. This progression is the main goal of this article.

However, it's crucial to acknowledge that this fine-grained perspective isn't necessarily superior to its coarse-grained counterpart. Instead, they supplement each other, each one being more appropriate in different situations or under specific viewpoints.

Given that power attributions can be seen as true according to one view and false under another, it's clear that power is not a wholly objective feature of reality. This point underlines one of the primary arguments I hope to establish: power is an inherently fuzzy concept. The process of attributing power often resembles a negotiation, dependent on the immediate stakes and the strength of the claims involved.

With this understanding, let's delve into what has been proposed so far.

The coarse grained view of power

Statements about power can be reduced to statements about what actions are available to a person or group, i.e. what they can or cannot do. I called this thesis the deflationary definition of power:

(1)

Deflationary Definition of Power: An actor A has the power to do H in w iff A can do H in w.

According to this definition, we can reduce sentences about power to sentences about what can be done. The non-relational “A has power.” can be reduced to “There is something A can do.”

Furthermore, I suggested analyzing statements in the form of “A can do H” (the explanans) through the lens of relative modality, as introduced by Angelika Kratzer.1 In this approach, modal expressions such as 'can' or 'must' are evaluated against what Kratzer describes as conversational backgrounds. These backgrounds encompass implicit and explicit assumptions about our knowledge, norms, typical scenarios, etc.

I proposed that when we’re interpreting "A can do H." in the context of attributing power, the conversational background pertains assumptions about A's scope of action at the situation we are evaluating (i.e. in w).

Kratzer termed this conversational background a ‘modal base’. A modal base comprises propositions that articulate facts about A’s range of actions in the situation or world under scrutiny. Essentially, a modal base is a function that takes a world w (the scenario where A is placed) as an input and produces a set of propositions (assumptions about A’s scope of action in that scenario) as an output. Formally, this can be represented as:2

(2)

Modal Base: f(w) = {P: P is a proposition expressing A’s attributes, resources, positions, connections, situational aspects, abilities, skills, etc., that enable A to perform H in w}

In semantics, it’s customary to employ the concept of possible worlds to represent propositions. Here, a proposition P refers to a set of possible worlds where P holds true. The intersection of the propositions that belong to a modal base, viewed as sets of possible worlds, results in a set of worlds that are consistent with all the assumptions or conditions we consider to be part of w. This set is denoted as ⋂f(w), and is referred to as the modal base set.

This shift from a collection of propositions (modal base) to a modal base set is warranted because the context for evaluating modal statements should satisfy all our assumptions.

Consider an analogy: pondering if we can bake a cake right now. To bake a cake, essential ingredients such as eggs, milk, flour, yeast, and sugar are required. The modal base, in this instance, would be a checklist indicating the availability of ingredients for each day. For example, if eggs, milk, and flour are available on Monday (represented as "w1"), each item corresponds to a proposition like “I have eggs” or “I have milk,” and so on.

Each item, taken individually, holds true on different days. For instance, “milk” might be true on Monday but not on Tuesday. Within this analogy, propositions can be visualized as lists of days. If milk is available on Monday, Thursday, and Saturday, the entry “milk” can be represented as {Monday, Thursday, Saturday}. Similarly, the entry “eggs” could be represented by another list like {Monday, Tuesday, Friday, Sunday}.

If each necessary ingredient is represented as such a list, we can compute the intersection of these lists, generating a final list of days that are common to all ingredient lists. If Monday and Tuesday are common across all lists, the final list (representing our modal base set) would be {Monday, Tuesday}. These are the days when all the ingredients are at hand.

With this groundwork laid, we can elucidate what is meant by “A can do H”. This explanation hinges on the notion of 'truth conditions', which delineate the circumstances under which a statement is true or false. If my definition of power is accurate, it clarifies what it implies for someone to possess or lack power—that is, under what conditions he does or does not have power.

I have already touched upon truth conditions here, but I will reiterate them for clarity. For reasons that become apparent later, I would like to call this explanation of power the coarse-grained view of power:

(3)

Truth Conditions (coarse-grained view of power): [[A can do H]] in w = 1 iff there is a world w' ∈ ⋂f(w) such that [[A does H]] = 1 in w’.

Returning to the cake-baking example, the ability to bake a cake in a specific situation (on a particular day or in a possible world w) hinges on the availability of all the ingredients on that day. This implies that the question can be affirmed for those situations in which this is the case.

If our final list (the base modal set) includes Monday and Tuesday, then these are the days when baking a cake is feasible. On days not on this list (e.g., Saturday), baking a cake is not an option.

In this analogy, the truth condition would state: You can bake a cake on days that are included in your final list (and on other days, you cannot). Therefore, this example clarifies the circumstances under which baking a cake is possible. Correspondingly, if my definition of power is correct, it also explicates under what conditions one has the power to bake cakes. If you have grasped this concept, you have understood my approach thus far.

Susan’s predicament

Consider this scenario: Susan has invited Paul to her apartment for a glass of wine after their second date. The ambiance takes a romantic turn, and Susan is faced with the choice of either allowing the night to progress or asking Paul to leave. Eventually, she gives in to the moment and spends the night with Paul. The following morning, Susan confides in a friend, admitting that she felt unable to ask Paul to leave.

We can represent Susan's statement to her friend as follows (using the third person perspective and ignoring tense):

(4)

Susan can’t send Paul home.

At first glance, it seems that Susan indeed had the capacity to ask Paul to leave. She has the ability to communicate verbally, the mental capacity to make decisions, and the social authority as the host to ask a guest to depart.

Let's dissect whether Susan’s statement is a fabrication or an expression of her experience.

This discussion - just to make this clear - is not an examination of Susan’s conscious or subconscious decision to stay with Paul. The focus is not on her choices or actions. The point is that, despite having the option to act differently, she felt powerless to do so. I hope this distinction will be clear as we continue.

We must recognize that when evaluating an individual's capabilities, our assumptions about their skills and competencies are integral. These form part of the conversational background and should be taken into account when assessing Susan’s power in this situation.

The modal base here is a set of propositions representing the pertinent facts during the conversation between Susan and Paul. For instance:

• P1: Susan communicates fluently and both she and Paul converse in a shared language.

• P2: Susan has the cognitive ability to form intentions and make decisions, including the decision to ask Paul to leave.

• P3: Susan, as the host, has the social authority to request her guest to leave - a norm that both acknowledge.

The modal base set incorporates all scenarios in which P1, P2, and P3 hold true. For instance:

• In world w1, Susan is overwhelmingly attracted to Paul, with her emotions dominating any intention to ask him to leave.

• In world w2, Susan is attracted to Paul but has reservations. After a brief internal struggle, she asks him to leave.

• In world w3, Susan’s attraction to Paul is mild, and she resolutely asks him to leave.

The modal base set is thus:

(5)

⋂f(w) = {w1, w2, w3}

Since this set includes scenarios where Susan does ask Paul to leave (specifically, w2 and w3), statement (4) would be deemed false if we adopt the coarse-grained view of power. In such a case, we would have to conclude that Susan lied to her friend.

However, my intuitions suggest that Susan wasn’t lying. Her emotional state, characterized by arousal, seemingly barred her from accessing a scenario akin to w2 or w3. These scenarios were incongruent with her emotions towards Paul at that moment.

A balanced evaluation of Susan’s predicament would recognize the dual nature of her capacity: theoretically, she could have asked Paul to leave, but emotionally, she couldn't. She could have done it, but still, she couldn’t. Both perspectives hold a measure of truth, contingent upon the lens through which the situation is analyzed.

Indeterminate modal base sets

In analyzing scenarios like Susan’s, it is possible to argue that the spectrum of actions we attribute to her is ambiguous or indeterminate, encompassing various assumptions. We might consider her capabilities and skills, such as her capacity to communicate and make decisions, while also accounting for her emotional states and desires. Whether statement (4) is true or false hinges on our focus.

The proposition that we are toggling between distinct modal bases when evaluating Susan’s range of actions might elucidate our quandary in discerning what is genuinely within her power. Saying that she could have sent Paul home reflects one conversational background, whereas saying she couldn't reflects another.

I don't think this is a good strategy. Firstly, desires and emotions do not define a scope of action. What one is capable of doing at any given moment is not contingent on one's emotional or volitional state. For instance, an intense craving for sushi does not enable one to eat sushi if it is unavailable. Similarly, one can consume noodles despite a distaste for them. This aligns with the coarse grained view of power, according to which power is predicated on what one can do, not what one desires to do.

Additionally, Susan’s emotional state did not create new possibilities but constrained an existing choice. She had the option to either send Paul home or spend the night with him. Her emotional state influenced her preference but did not create these alternatives. Transitioning to a different modal base set is distinct from narrowing an existing modal base set.

So, what we're trying to say here is that given certain circumstances, one of the options became more probable than the other, and not that there were - depending on one's perspective - different types of options, which can be attributed to different sets of assumptions about Susan.

What we are attempting to articulate is that under certain circumstances, one alternative became more likely than the other. This is not indicative of disparate types of options attributable to varying assumptions about Susan.

To aptly express the subtleties in attributing power, we require a mechanism to appraise different alternatives based on certain criteria.

What we are grappling with here is a commonplace phenomenon. While we often have an array of options in most situations, bestowing us with considerable potential power, these options are not all equivalent. Some actions are more accessible, evident, or immediate, while others are demanding, carry grave consequences, or conflict with our self-concept and values.

With regard to this latter cases, there are instances where, contingent upon the circumstances, we might assert that it is beyond our power to execute the corresponding actions despite technically possessing the ability to do so. I believe this is what Susan was trying to convey to her friend.

Entering ordering sources

With the machinery that I have introduced so far, we cannot model such differences and nuances. However, we can do this within the framework provided by Kratzer. She posits that, when interpreting modals, there is a second conversational background, which I have so far neglected: an ordering source. This background allows us to capture finer distinctions.

Both conversational backgrounds play distinct roles when interpreting modal expressions. The modal base set includes a set of possible scenarios or ‘worlds’ consistent with our knowledge or assumptions. The ordering source ranks these worlds based on some standards, norms, likelihoods, or constraints. These also can be expressed as propositions.

Regarding power ascriptions, the ordering source could reflect the degree to which certain circumstances, f.i. A's volitional and emotional state, the social norms A contends with, and perhaps the risks associated with executing H, align with A’s performing H. We can represent this as:

(6)

Ordering Source: g(w) = {Q: Q is a proposition expressing how A's volitional and emotional state, the social norms A contends with, and the risks associated with executing H are aligned with A’s performing H in world w}

Consider Susan again. She is sexually aroused and finds Paul overwhelmingly attractive. This is an important piece of information that should be taken into account in assessing the present case. Let’s, therefore, assume the ordering source g in this situation contains the following proposition Q1:

(7)

g(w) = Q1 = Susan is sexually aroused and finds Paul overwhelmingly attractive.

Now, let's take the intersection of all propositions within g(w), denoted as ⋂g(w), which we call the ordering source set. In our case, g(w) contains just one proposition, so this set includes worlds in which Q1 is true.

We want to use the ordering source set ⋂g(w) to find the “best” worlds within the modal base set ⋂f(w) that align with ⋂g(w). This set of best worlds is denoted as MAX(w, f, g), defined as:3

(8)

Best Worlds: MAX(w, f, g) = {w' ∈ ⋂f(w): ∀w'' ∈ ⋂f(w) (if w'' ∈ ⋂g(w), then w' ∈ ⋂g(w))}.

This means we select worlds from the modal base set that are also in the ordering source set.

To illustrate, let's discuss baking cakes again. I am considering baking a cake. My world contains variables like the ingredients I have at home on different days. These variables create a set of possible scenarios. The intersection of these scenarios, represented as ⋂f(w), is a list of days I have all ingredients for baking a cake, for example, {Monday, Tuesday}.

We introduce the ordering source g(w), which refers to constraints and considerations when deciding to bake a cake, like my schedule and the rule that I can't bake if I have more than 3 appointments. The scenarios aligning with these constraints form ⋂g(w), represented as a list of days with at most 3 appointments.

For example, on Monday, I have the day off and all the ingredients. This scenario is part of ⋂f(w). Because I have no appointments, this scenario also aligns with ⋂g(w). Therefore, Monday belongs to MAX(w, f, g). On Tuesday, I have all ingredients but four appointments. While part of ⋂f(w), it does not align with ⋂g(w). Therefore, Tuesday doesn’t belong to MAX(w, f, g).

MAX(w, f, g) contains scenarios where I can bake a cake, and these scenarios meet the constraints of my schedule and rule about appointments. Here, only Monday fits into MAX(w, f, g), because for any other scenario in ⋂f(w) to be in MAX(w, f, g), it must also exist in ⋂g(w). Only Monday's scenario meets this criterion.

This example illustrates the concept of ‘best worlds’. The set (MAX(w, f, g)) is a subset of the modal base set (⋂f(w)) where the constraints in the ordering source set (⋂g(w)) are met.

Let’s return to Susan. Assume our modal base set includes the worlds w1, w2, and w3, as introduced above. We use Q1 to check whether it is true in w1, w2, and w3. As Q1 is clearly false in w3, w3 doesn’t belong to the set of best worlds. There might be some dispute over w2, as having reservations might not align with finding someone “overwhelmingly attractive.” Thus, Q1 likely isn’t true in w2 either. In w1, however, Q1 is true.

Thus, our set of best worlds contains only one world:

(9)

MAX(w, f, g) = {w1}

The final step to elucidate the fine-grained view of power is to state the truth conditions for "A can do H in w," utilizing the set of best worlds:

(10)

Truth Conditions (fine-grained view of power): [[A can do H]] in w = 1 iff there is a world w' ∈ MAX(w, f, g) such that [[A does H]] = 1 in w'.

This definition captures the intuition that A can do H if (i) A's comprehensive set of resources, capacities, skills, etc., enables A to do H, and (ii) H aligns with constraints relevant for A, f.i. his emotions, the social norms A accepts, and the risks A is willing to take.

Let’s revisit the question of whether I can bake a cake. This is determined by whether there exists a world within MAX(w, f, g) in which I bake a cake.

We established that only Monday aligns with my rules, schedule, and the ingredients that enable me to bake a cake. Thus, Monday falls into MAX(w, f, g), where I have all the ingredients, the day off, and no appointments. This means there’s a day on which me baking a cake is possible, and therefore, “I bake a cake.” is possible.

Note that the truth conditions require this to be true and not just possible. In this example, we only considered a small set of actual days, and didn’t consider every possible course of days. While the analogy breaks down here, the concept should be clear.

What about Susan? Did she lie to her friend? If she did, (4) should be false:

(4)

Susan can’t send Paul home.

Let’s apply our truth conditions to this case:

(11)

“Susan can’t send Paul home.” is true when she had Paul in her apartment after their second date iff “Susan doesn’t send Paul home.” is true in w1.

As this is the case, (4) is true. So, she didn’t lie. This demonstrates that the fine-grained view of power captures our intuitions more effectively, especially in cases where a more nuanced judgement is required.

The role of enabling and constraining conditions

Evidently, these two perspectives – the coarse and fine-grained views of power – differ in the metrics we utilize to assess what someone is capable of. The fact that the set MAX(w, f, g) is a subset of ⋂f(w) implies that a more fine-grained assessment leaves fewer options available than a coarser assessment, thereby reducing power.

This distinction has profound implications in everyday life. Once you acknowledge these differences, you begin to recognize them everywhere. At times, we exhibit a dash of heroic arrogance and boast about our capabilities – thus applying the coarse-grained view of power. Conversely, we occasionally adopt a victim mentality, complaining about our lack of options and frequent failures, thereby utilizing the fine-grained perspective.

Consider an ardent Trump supporter named John, who had to make a choice in the 2020 US presidential election. Technically, John had the power to vote for Biden. This action would merely involve marking his ballot differently. Here, we are taking the broad, coarse-grained view of power, which assesses possibility based on basic prerequisites, while ignoring emotional, psychological, or social factors.

On the other hand, John might find the idea of voting for Biden so abhorrent that he cannot bring himself to do it, despite having the technical ability. This is the fine-grained view of power, which takes into account not just John's physical capacity to vote for Biden, but also his emotional and psychological state, social pressures, and obligations to his chosen identity.

Essentially, within the broad set of all possible worlds that are consistent with the circumstances of the 2020 US predsidential election, ⋂f(w), there might exist a world where John votes for Biden. However, this world may not be part of the narrower set, MAX(w, f, g), which only includes the worlds that are additionally in alignment with John's emotions, social norms, and self-identity.

This distinction resonates closely with our intuitions. We want to make sure - and expect - that every voter can vote for every candidate on the ballot. And we also assume that this is irrelevant for some voters. For them, every day is a Monday, whatever the calendar says.

Now, let's consider Maria, in a similar situation but contemplating starting her own business. For Maria to entertain this idea, certain prerequisites exist. These include her business acumen, financial resources, professional network, societal status, and other situational elements enabling her business venture.

Simultaneously, Maria must contemplate several constraints. Does launching her own business align with her aspiration of self-sufficiency? Is she compliant with societal norms surrounding entrepreneurship? How risk-averse is she? Can she withstand the financial risks involved in entrepreneurship, even if she secures the necessary funds?

Are there considerable obstacles that impede Maria from realizing her goal? Could insurmountable risks, unbearable social pressure, or significant deviations from her plan deter Maria from starting her business, despite possessing the required 'ingredients' or resources?

With the fine-grained view of power, the emphasis lies on those worlds where these elements harmonize in a way that doesn't restrict Maria from accomplishing her goal. Conversely, the coarse-grained view focuses on those worlds where the necessary prerequisites for achieving this goal are fulfilled.

To employ more engaging terminology, I suggest calling the assumptions (propositions) utilized in determining the modal base set "enabling conditions," and the additional assumptions used in establishing the ordering source set "constraining conditions."

Enabling conditions must be met for there to even be a chance of performing H. Constraining conditions, however, vary significantly and can be either strong or weak. These conditions can – in theory – be overcome. You can't win a marathon if you're paraplegic. But if your athletic performance is average? That's debatable!

In what follows, I will discuss three features that can help us understand the nature and characteristics of these conditions:

a) You can, but you can’t

In various examples, I have addressed the question of whether someone possesses the power to perform a specific action. Could Susan have sent Paul home? Could I bake a cake? Could a die-hard Trump supporter vote for Biden? Could Maria start her own business?

In each of these deliberations, the conclusion could be that both scenarios are plausible if the following initial conditions apply: the enabling conditions are fulfilled, but there exist (strong) unmet constraining conditions. Under these circumstances, you can, but can’t.

Consider:

(12)

Susan: “Sure, I could have sent Paul home because he was my guest. But I couldn't. His charm was irresistible.”

Me: “Sure, I could have baked the cake because I had all the ingredients. But I couldn't. Time was against me.”

John: “Sure, I could have voted for Biden. His name was on the ballot. But I couldn't. That would have plunged me into a deep personal crisis.”

Maria: “Sure, I could have started my own business because I had a loan approval. But I couldn't. The financial risk was too high, and I didn't want to risk bankruptcy.”

b) C’mon, you can!

Constraining conditions are more susceptible to criticism than enabling conditions. Often, we justify our inaction by listing reasons that prevented us. These reasons are typically more accepted if we cite unfulfilled enabling conditions. However, if we cite constraining conditions, they are more likely to be challenged.

(13)

Susan: I couldn’t have sent Paul home because I was his guest.
Betty: I understand. You should host the meeting next time!

Susan: I couldn't sent Paul home, because his charm was irresistible.
Betty: C’mon, he's not that charming, and he stutters!

Me: I couldn’t have baked the cake because I had no eggs.
My friend: I understand. Be better prepared next time.

Me: I couldn't have baked the cake because I didn't have time.
My friend: C’mon, it seems other things were higher on your priority list!

John: I couldn’t have voted for Biden because he wasn’t on the ballot.
Mandy: I understand, but I wonder why he wasn’t.

John: I couldn't have voted for Biden because that would have plunged me into a deep personal crisis.
Mandy: C’mon, you're exaggerating. Your vote wouldn't have tipped the election, and you know it!

Maria: I couldn’t have started my own business because I didn’t get a loan approval.
Her husband: I understand. You could approach other banks. Maybe you haven't exhausted all your options yet.

Maria: I couldn't have started my own business because the financial risk was too high for me.
Her husband: C’mon, the risk isn't that high. You're being too pessimistic!

Additionally, constraining conditions can come in many colors, they can be strong or weak, or even not acceptable at all. Consider the following two dialogues:

(14)

Susan: I couldn’t send Paul home after he complimented me.
Betty: That's ridiculous!

John: I couldn't vote for Biden; his name reminded me of someone I dislike.
Mandy: You can't be serious!

This demonstrates that when we talk about constraints, we are in a gray area. Not all the things we perceive to limit our power actually do. The extent of the limitation often depends on the context. A coach of a slightly inferior team won't accept his players giving up; he'll motivate them to try harder. But when there's less at stake, minor constraints can be more acceptable.

c) The hero’s journey

A popular narrative device is the hero's journey, which hinges on the protagonist overcoming multiple obstacles and confronting various challenges. In wrestling with himself and tackling these impediments, the hero exceeds his limitations and eventually achieves his goal.

The story is a power game; our hero aspires to something but initially lacks the power to realize it. He only succeeds after overcoming the obstacles. These could either belong to the enabling conditions or the constraints of his actions. Most of the time, however, obstacles tend to be the latter. While ensuring that enabling conditions are met may seem uneventful, overcoming constraints usually leads to a more gripping story:

(15)

Story 1: It's my wife's birthday, and I want to make her happy. I know she would love a homemade cake. Unfortunately, I had no eggs in the fridge (obstacle). So, I went to the nearest supermarket and bought some. At last, I baked the cake and surprised my wife, much to her delight.

Story 2: It's my wife's birthday, and I want to make her happy. I know she would be thrilled with a homemade cake. My day was filled with important meetings and negotiations, and time was against me (obstacle). It took considerable effort, but I managed to keep the meetings short. The negotiation didn't go as smoothly as planned, but promising to write the minutes helped us conclude earlier than expected. Despite the time crunch, I managed to bake the cake. My wife was thrilled.

Neither story is a literary masterpiece, but that's not the point. The second story seems more engaging, right? Of course, the allure of a story greatly depends on the storyteller's skill. A skilled author can make even the overcoming of enabling conditions a compelling narrative.

Still, I believe that in most stories, the hurdles resemble strong constraints. Maybe this is because constraints inhabit a gray area, and thus it's not always clear whether the hero can overcome them. This ambiguity creates suspense. Enabling conditions, however, are more binary. Either I have eggs in the fridge, or I don't. Once the eggs are there, no additional effort is needed, and the suspense dissipates.

Power is an inherently fuzzy concept

The attribution of power is often a matter of "negotiation" and depending on what is at stake, we bring into play claims of varying strength.

Let's consider an example: Imagine a large, white square piece of paper, representing all potential actions one could undertake. Now, visualize a black circle within this white square, symbolizing the scope of actions a certain actor 'A' can perform within a specific situation. This black circle is a manifestation of A's power.

If this could be done, then the concept of power would behave like an ordinary set. The coarse-grained view of power provides - at least approximately - such an image. The modal base set is a black circle on a white sheet of paper.

My discussion so far has hopefully shown that the matter is not quite so simple. This is because it is often literally not so simple to do something that I - looking at it soberly - could do. The black circle is therefore not a circle with a sharp, but with a blurry edge, a gradient from dark to light, which embodies the varying challenges or obstacles involved in performing certain actions.

The lightest part of the gradient denotes tasks with substantial constraints, mostly outside the sphere of our power. As we move towards the center of the circle, the gradient becomes darker, signifying tasks with decreasing hurdles. Actions at the very center are easily accomplished with little to no effort.

Thus, power can be perceived as a fuzzy set, rather than a binary one. The variegated shades of gray depict the space where we possess some power, yet simultaneously face restrictions. These zones are often the subject of debates, disputes, and intriguing narratives.

Attempting to quantify someone's power is a futile exercise, as the nuances and subjectivity make it impossible to objectively measure. What seems feasible to one might appear impossible to another.

For instance, bending my index finger falls in the black area of absolute power, while time travel is in the unreachable white. Winning a kickboxing championship is a very light grey endeavor for me, suggesting the steep challenges. Conversely, mowing my lawn today would be a darker grey task, relatively easily accomplished.

Furthermore, the distinction between enabling and constraining conditions is itself blurred. What if I choose to bake a cake without milk? In a vegan perspective, this would be an obvious choice. Here, perhaps milk, usually considered an enabling condition, becomes a constraint, while another ingredient like flour is the enabler. This begs the question, is flour truly necessary for a cake? The possibilities are endless and the boundaries fluid.

I hope it's clear where this is going. Figuratively speaking, we can move the gray areas more and more into the white areas, which would mean that we take the stance that more is usually possible than we would assume.

But it also works the other way around. Perhaps what represents an overcomeable constraint for someone is an insurmountable hurdle in my eyes? Perhaps my meetings and negotiations always take longer than expected. Maybe too much depends on me really taking the time for it. And after all, baking a cake requires time. It can't be done without. We are moving the gray areas more and more into the black area. Perhaps I have much less power than I think I have?

These two different attitudes and maneuvers are sometimes called optimism and pessimism. An optimist thinks that more is possible - that more is within our power - than we believe. A pessimist claims the opposite. Who is right? I think, neither of them. Or maybe both!

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.

Our world is full of gaps. Something is missing everywhere. We have holes in our socks. There are gaps in arguments. Shadows. Trenches are gaps in the ground. Valleys are places where the mountain is missing. Silences are stretches of time in which nothing is said. Talking about what is not there belongs in our conversations like the gaps in a picket fence. Something is missing after every slat.

We owe a peak of grotesque-comic poetry to Christian Morgenstern (1871-1914), the master of eccentricity. His famous poem "Der Lattenzaun" (The picket fence), published in the Galgenlieder (Gallows songs) in 1905, is less about the peculiarities of the instrument for garden or property demarcation, than about the withdrawal of "nothingness" - so to speak:1

Memories also have gaps and do not differ so much from picket fences. Some pickets are prominent, jutting out like sore thumbs, while others are smaller, blending in with the background. The gaps between the pickets can be vast and wide, leaving plenty of room for forgetfulness or uncertainty. Our identity - what we believe ourselves to be - is like a continuous fence built by trying to fit the pickets and gaps together to delimit a field in which an I is at home.

Everyone's picket fence is different. Some people have many pickets closely spaced, while others have pickets that are far apart. My own fence of memories has few pickets that are loosely connected by large areas of nothingness. At times, this can be a curse, making it difficult to tell stories about myself since there is little material to work with. However, it can also be a blessing, as the baggage is lighter, and it's easier to move the fence when I need to.

One incident that I still vividly recall dates back to the 1980s, around 1986 or 1987. Allow me to share the story with you.

A conversation at the beach

One beautiful summer day, a few friends from my high school class decided to go for a swim together. As we lay on the beach, we found ourselves contemplating the meaning of a "hole." I can no longer recall how the topic came up, whether it was prompted by one of us digging a hole in the sand or meditating on a slice of cheese or or maybe someone was wondering why trouser legs have an inside and an outside. Whatever it was, the question had taken hold of us and refused to let go.

At first glance, holes seem like such a simple phenomenon, made up of conceivable simple components, easy to identify. You can see them, point to them, even describe and depict them because right there, where something is missing, there is a hole. That's the frustrating thing about holes. How can there be something that is not?

Holes certainly exists. They are a part of our world. They have a certain size and spatial topography. They have a dimension both in space and in time. Holes can arise and disappear. We are able to point to them, count them. We can create and destroy holes. Holes are a part of the causal network of our world. We can dig, punch, drill, or cut them. They collect water or let light in.

Holes have already existed long before us. And holes are useful: sieves, funnels, handles on beer cases, windows, doors, and trouser legs. How could we even exist without holes? Holes are not fictions but real. They are everywhere. Physics even speaks of "black holes," but that's another story.

What then are holes? We came up with various possibilities. A hole - we started with the obvious - is something where there is nothing. But this seemed contradictory. Something cannot be nothing!

Another one was that a hole is something that is (partially) enclosed by something else. Holes are things that have a boundary. That also seemd obvious and sounded much better. But then we saw a ball floating on the water. Obviously, this was something (a ball) that was partially enclosed by something else (water). But there was no hole. Just a ball in the water.

The ball, however, made a dent in the surface of the water - we also saw dents as holes. If we could freeze the water in its current state and remove the ball, then we would see a hole, in a certain sense.

Holes can be filled, but not every filling is acceptable. Holes are picky. We then thought that it could have to do with the density of the materials. A hole exists when a denser material partially encloses a less dense material. The "dimple" in the water is a hole because water is denser than air and partially encloses the air.

But that can't be right either. We can make a hole in Styrofoam and then pour water into it. We would still have a hole in the Styrofoam, but the filling (the water) is denser than what surrounds it (the Styrofoam).

If I remember correctly, we finally agreed that if we assume that there are only three states of matter (gaseous, liquid, solid) that are ordered in this sequence, then a hole is a region consisting of a substance in a lower state of matter than the substance that partially surrounds it.

Clouds that consist partly of liquid water are therefore not holes, but they can have some, if the water is missing. If we submerge a solid object in water, we don't have a hole at that point. A hole would only exist if we’d replace the solid object with air (provided that the water remains in the same configuration). A drop of oil floating on the water surface and making a small dent is also not a hole. And if we stuff an apple-filled goose at Christmas and then roast it, it doesn't have a hole, but a filling.

This definition seemed useful to us and we moved on to the more mundane things that young people do at the beach in good weather.

Today I think, that our reasoning had some weaknesses. We weren’t talking about holes, but about something else. The most obvious problem is that a hole is not identical to what it fills. If we go into the garden and dig a hole with a spade, then we substitute one volume of earth with one volume of air. But the hole is not that air! We could fill it with water afterwards, another substitution, but this doesn’t change the identity of the hole. It remains the same.

The second problem is that holes are also not identical to what surrounds them. A hole in a piece of cheese is where cheese is missing. A piece of non-cheese, so to speak. So we had tried to characterize holes by what they are not.

Let’s call the thing or material that surrounds a hole the host of a hole. The host is what the hole is “in”. Every hole is inside something, as all holes are filled with something.2 Let's call that filling the guest of the hole. A hole - every hole, therefore, has a host as well as a guest, but it is neither one nor the other. A hole is where there is a host that can accommodate a guest. It’s a gap, a possibility of substitution.

In most cases, it is easy to locate a hole. It is there, and yet, it is not what it consist of. Are holes (or shadows, moments of silence, valleys, the gaps of a picket fence) therefore nothing? Places that are defined by the absence of something? Nonthings that exist?

Piggeldy’s plan

The probably most philosophically interesting (and interested) pigs in children's literature, Piggeldy and Frederick, have extensively circled around holes.3 “What are holes?” the piglet Piggeldy asks his big brother Frederick, after which the peripatetic but equally clueless Frederick invites his little brother for a walk with the words: "Nothing easier than that. Come with me."

The two set out and first try to approach the problem phenomenologically, searching for examples of holes (sock holes, mouse holes, puddles) and their qualities (you can fall into them).

But Piggeldy is dissatisfied with the result of the search. Because in the puddle there is water, in the mouse hole there is a mouse, and in the sock hole there is still more sock than hole. “Always a hole is something where something else belongs,” he complains, “a hole is never just a hole.”

To which his brother Frederick replies: “There will never be a hole without something around it." "Aha,” Piggeldy rejoiced, “a hole is only a hole because there is always something around it.” Frederick nodded. He could have quoted Kurt Tucholsky to support his insight:4

There is no such thing as a hole by itself, as sorry as I am to say.

“When I grow up,” said Piggeldy ignoring his bigger brother as well as Tucholsky, “I will invent a hole without anything around it.”

Piggeldy seems to have an absurd plan, and his remark makes us smile. I think, however, Piggeldy might be onto something. We could make a distinction between a criterion for holes, which could include their host, and what holes themselves are - as holes, ontologically speaking.

Without a host, we cannot identify holes, but they themselves are something else. Think of a mother. It is not possible to identify a mother without considering her offspring. A mother is always a mother of someone. There is no such thing, Frederick and Tucholsky would say, as a mother by herself.

But wait a moment! Isn't a mother herself a female person who exists at a specific space-time location, independent of her offspring? This example highlights the difference between identifying mothers and defining what mothers are, in and of themselves.

Similar things apply to holes. To identify a hole in a cheese, we need to consider the cheese. But not a single particle of a hole in a cheese is made of cheese! It seems, therefore, that Piggeldy wouldn't need to invent holes without something around them. Holes already are excluding the stuff that surrounds them. But, hey, what the heck are we talking about here?

Having clarified this, the question remains: What are holes? Unsurprisingly, there is a philosophical debate about this issue. There are always philosophical debates. But this one is especially interesting. Let’s dive in.

Hole Ontologies

If we assume that there are holes, then they seem to be specific to a certain place and time, similar to concrete physical objects like mountains or pencils, and unlike abstract entities such as numbers or values. They possess a particular shape, size, and location, and they have origins and histories. They can undergo changes and be subject to various events.

If we view holes as particulars (lets call this position naive realism about holes), which seems to be an obvious move, then we run into a diffuculty: holes are different from more familiar particulars. Holes seem to be immaterial, not made of matter but rather made of nothingness, if they are made of anything at all.

To accept a naive realism about holes, therefore, means to acknowledge the existence of concrete immaterial objects (let’s call them nothings).5 Given this challenge, most philosophers lean towards a reevaluation of commonly held beliefs abut holes rather than accepting a straightforward realist view.

So we are now entering the field of the ontology of holes, where all kinds of fruits grow. Some of these fruits could be given classical names, such as nominalism, materialism, physicalism, or universalism, as they recycle ideas from these currents. I will not discuss these positions as such, but will only examining the different strategies for avoiding the assumption of concrete nothings and what costs these strategies have. There are always some costs …

Holes don’t exist

What if there are no holes at all, but only perforated objects? Instead of saying that a cheese has a hole, we could just as well say that it is perforated. That would imply that there is cheese. Perhaps that it has properties, such as being yellow, having a certain weight, or being perforated. It would, however, not imply that there are holes. Certainly not that there are nothings!

That’s the old strategy of nominalism. If I say that my sock has a hole, then I am referring to my sock only. And my utterance would be true, if it would be correct to apply the predicate “has a hole” or “is perforated” to my sock. Let's imagine two sheets of paper. Now, let's take a hole puncher and perforate one of them. In what way do the two sheets differ? Instead of saying that one has a hole and the other does not, we could say instead that one is perforated and the other is not.

One might object that these predicates can only be correctly applied if there really is a hole in my sock or in the sheet of paper. A nominalist would respond that we do not need to assume this, but can simply stop at establishing norms of language usage.

This strategy comes down to the claim that all sentences that seem to imply the existence of holes could be rephrased to eliminate the implication of the existence of holes, while still being able to serve the same purposes as the original sentences.

The philosophical debate about holes started in 1970 when David Lewis and his wife Stephanie published a paper about this problem.6 This paper was presented in a unique format - that of a fictitious dialogue between two philosophers named Argle and Bargle, who engage in a thought-provoking discussion about the holes in a piece of Gruyère cheese.

Argle defends the position of nominalism:

When I say that there are holes in something, I mean nothing more nor less than that it is perforated. The synonymous shape-predicates “… is perforated” and “there are holes in …” – just like any other shape-predicate, say “… is a dodecahedron” – may truly be predicated of pieces of cheese, without any implication that perforation is due to the presence of occult, immaterial entities.

Argle doesn't hold out for long, however. Bargle points out that we can count holes and compare the number of holes with other, more common objects. While we could paraphrase a sentence like "The cheese has two holes" as "The cheese is doubly perforated," we would have to assume that our language has an infinite number of such predicates (doubly perforated, triply perforated, etc.) to account for all holes. Besides this, we would have to explain how we could learn such a language that includes so many words. This leads to a dead end.

Moreover, we can compare the number of holes in a cheese with the number of other ordinary objects, such as the crackers on the plate next to it: "The cheese has the same number of holes as there are crackers on the plate." A nominalist should prohibit such sentences. And that is the price we would pay if we deny the existence of holes. We would have to restrict our language concerning holes massively, and this would probably render it useless.

Holes are portions of spacetime

Another strategy is to hold that holes are just regions of spacetime rather than material objects. Wake, Spencer, and Fowler, for instance, argue that the traditional view of holes as objects with a physical boundary is problematic because it raises questions about what exists on either side of the hole's boundary. By contrast, the authors propose that a hole should be understood as a region of spacetime in which the properties of matter and energy differ from the surrounding spacetime.7

According to this view, a hole is not a thing, but rather a region in which the properties of things are different.

One could object that we want to know more about these different properties. Not every region of spacetime that differs from the surrounding region is a hole. In front of me is a chest. It occupies a certain region of spacetime and its properties differs from its surroundings. But my chest is a chest and not a hole.

Remember our day at the beach? We spoke about regions with different properties as well and were pondering what this difference consists in (density or state of matter for instance).

This criticism is, however, not entirely fair, as we could argue that the exact nature of these differences only matters in identifying holes, not in determining what holes are. Once we have identified a hole, what it is, could be just a region in space and time.

This means that there is nothing special about the portions of spacetime that constitute a hole, compared to other portions of spacetime that are occupied by ordinary material objects. It is not fundamentally more difficult to determine the conditions under which a portion of spacetime should be considered a hole than it is to determine the conditions under which it should be considered a pencil, a mug of coffee, or any other kind of object.

A more important objection to this position has to do with the fact that regions of spacetime can overlap or that one region can be part of another region. Let's take a toilet paper roll. It has a hole. Now let's turn it clockwise. The hole moves with it. We could now insert another, narrower toilet paper roll into this one and turn it counterclockwise. The spacetime region of the hole in the smaller roll is a part of the spacetime region of the larger roll. Does the smaller hole now rotate both clockwise and counterclockwise?

The problem - expressed more generally - is that regions that overlap cannot have mutually exclusive qualities in the area where they overlap. If one region is completely black and another is completely white, they do not overlap; they cannot have common parts. This has to do with the identity of regions of spacetime.

Holes, however, can contain other holes, and it seems that it doesn't matter whether the properties of the individual holes exclude each other or not. Does it follow that holes are, therefore, not spacetime regions?

Holes are ordinary things

Argle has another card up his sleeve. Holes are ordinary objects, he says:8

The matter isn’t inside the hole. It would be absurd to say it was: nobody wants to say that holes are inside themselves. The matter surrounds the hole. The lining of a hole, you agree, is a material object. For every hole there is a hole-lining; for every hole-lining there is a hole. I say the hole-lining is the hole.

Be prepared: Argle isn’t claiming that this is what we would say. A hole in a cheese is where there is no cheese. We would say that the host doesn’t belong to the hole. The hole starts where the host ends.

What Argle is proposing instead, is that we should say that a hole is identical with its lining. This would avoid the assumption of concrete nothings, but presumably preserves everything what we want to say about holes, because there’s a 1:1 relation between a hole and its host.

What would it mean to identitfy holes with their hosts? First of all, we could no longer say that hosts (partially) surround or enclose a hole. “Surround” and “enclose” would mean something else (“identity”) when we speak about holes.

Then, we would have to change our language with regard to to what we say about what’s inside a hole. A point on a hole-lining would then be inside the hole, but the filling wouldn’t.

Moreover, ordinarily speaking, holes and hole-linings often have different volumes. When we were children at the seaside, we sometimes looked for so-called chicken gods. These were stones that had one or more holes. Often the stones were more voluminous than the holes they had. If a hole is the same as the surrounding material - here the stony material - then we would have mostly been wrong in our assessment of the size of the holes back then.

Or let's imagine we make a small hole in a piece of paper. Then we cut off some of the paper outside the hole. Have we made the hole smaller by that? Would expanding the hole-lining amount to enlarging the hole?

The next difficulty concerns counting. Suppose we have a piece of cheese with two holes. Wouldn't Argle have to say that there is only one hole and not two? That it is impossible for a connected thing - a sieve, for example - to have multiple holes? Argle could respond - and he does - that we do not have one piece of cheese in front of us, but rather two pieces of cheese that overlap each other. Each one is identical to a hole. With a sieve, there would be more overlaps accordingly.

But how do we decide how many overlappings there are? Look at a roll of toilet paper. How many holes does it have? One? Two? Three? How many overlapping parts does the roll consist of? It's hard to say.

It seems that identifying holes with material things is even more costly than simply denying their existence altogether.

Holes are mind-dependent things

In the article "What Angles Can Tell Us About What Holes Are Not," P.J. Meadows challenges the idea that holes can be understood as individual objects or things in their own right.9 He argues that holes are better understood as properties or relations between objects, rather than as entities that exist independently.

Meadows explores the role of angles in understanding holes, arguing that the way we perceive holes is shaped by the angles of the surrounding objects. He suggests that holes are not objective features of the world, but are instead mind-dependent in the sense that they are created through our perceptions and interpretations of the world.

It might be worth noting that Meadows' focus on angles as a key factor in understanding holes may not be universally applicable. The way we perceive holes may also be influenced by other factors, such as lighting, color, texture, and depth perception, among others. But we’re not talking about perceiving holes here.

The central problem with this view, in my opinion, seems to be that the conclusion that Meadows draws isn’t following from his premises. While it is true that our perception of holes is influenced by our surroundings, it does not necessarily follow that holes, therefore, cannot be understood as objects in their own right. For example, one could argue that a hole in a bucket is a physical object and the cause of the water running out, even if its existence is dependent on the material around it. Even if we can’t perceive the hole in the bucket without perceiving the bucket.

Holes are real but not quite

Maybe, there’s some middleground. Maybe that there are not only things that exist and things that don’t. Some things could be more or less real. And possibly holes are such sorts of things.

McDaniel, for instance, examines the concept of almost nothingness and argues that it is a meaningful and important aspect of human experience.10 He suggests that although we often focus on the substantial and concrete aspects of reality, such as physical objects and events, there are also many instances where we encounter something that is not quite nothing, but also not quite something in a substantial sense.

McDaniel tries to clarify his view that holes are things with a kind of diminished reality. Considering the nominalist project, he writes:11

Suppose that we cannot paraphrase statements about holes and other almost nothings in terms of statements about ‘positive’ entities alone. Perhaps this is because of the limits of our language: there are no infinitely long sentences in English, and the only way to paraphrase talk about holes would be via infinitely long constructions. However, suppose we can conceive of how such a paraphrase might go in an augmented version of English. I think this is the case with holes. If we think this augmented version of English would be a metaphysically better language to speak than ours, … then we have a reason to think that holes are mere beings by courtesy. Ontological reduction, on this picture, amounts to identifying some entity as a mere being by courtesy. Ontological elimination, by contrast, consists in denying any sort of reality to the entity in question.

Assuming that it makes sense to talk about different types of things that are differently real, and that holes belong to the things that exist but not quite (beings by courtesy), in contrast to chairs or mountains, then it seems that we can have our cake and eat it too. We could calm our skepticism regarding the existence of immaterial things without having to assume that holes don’t exist or aren’t entities in their own right.

Another possibility is that holes are genuine absences or negative spaces in the world. While they are not physical objects or properties, they can still have an impact on our understanding of the world. C.B. Martin, for instance, argues that entities are not the only things that exist in the world.12 We can conceive of absences and voids as ‘ways things are not,’ and that they can be just as real and important as entities.

He uses the example of a hole in the ground to illustrate his point, arguing that the hole is not just the absence of dirt, but a real and meaningful part of the world. Martin contends that recognizing the ontological status of absences and voids can help us to better understand and explain certain phenomena, such as the behavior of subatomic particles in quantum mechanics.

McDaniel and Martin's views lead to an inflated ontology, where everything that is not present is treated as a separate entity. That makes the question of the existence of holes appear like a decision.

That reminds me a little bit of my six-year-old daughter. She's afraid to go to her room at night when the light is off. That's completely normal at her age. She says there are ghosts in her room. Sometimes I suggest that we could just check to see if that's true. And then she says: Ghosts can't be seen because they're only there in the dark. So ghosts are "almost nothings." They're there, but not really. Not like chairs or socks that we can see even in the light.

Which language do you speak?

If I'm to be completely honest, none of the approaches presented just now impresses me, not even naive realism. Don't get me wrong: I wouldn't say they're wrong with regard to holes. It’s rather that they introduce different ways of speaking. And we are free to chose one. We could roll the dice and deceide to speak as each individual author presented and thereby accept the costs that would come with that.

Alternatively, we could go back to the beginning of the story and see if we've made a mistake somewhere along the line. I think we have.

Let's think again of a sheet of paper with a hole cut into it. If we could give a complete physical description of the sheet, including the hole, we wouldn't find anything astonishing. Molecules, atoms, and subatomic particles are in various relationships to each other and are in different states.

Perhaps the sheet has not only a hole but also a fold and a small dirt stain somewhere. Surely, it's not cut completely straight, the edges are a bit frayed here and there. While this will make our physical description more complicated, it doesn't mean that we would discover any strange entities that don't fit into our physical description.

With this type of description, the sheet itself is no more or less real than the hole in its center. This is because, when we speak about "the world" in our daily lives, we rely on abstractions. When we talk about sheets, we leave out all the folds, holes, indentations, unevenness, etc. in which different things, which we also call sheets, differ from each other. Once we've abstracted over these differences, we can bring them back into the picture by making more detailed descriptions. And this is where slits, gaps, folds, holes, etc. come into play.

Similar considerations apply to mountains. No mountain is like any other. Physically speaking, the concept of a mountain is an abstraction. That's practical. If we want to know more, we bring valleys, cuts, slopes, etc. into play. But that doesn't mean that valleys are less real than mountains. It's just more practical to talk about mountains and valleys than to make a complete physical description of a section of the world.

Holes are like folds or frayed corners - concepts that compensate for the idealizations we've made with other concepts. If I go into the garden and dig a hole, I "transform" a prototypical garden into a less prototypical garden. Strictly speaking, there are neither prototypical gardens nor holes. Or, there are in a certain sense.

We could start with more complicated geometric constellations instead of flat surfaces. Suppose we start with undulating surfaces. A prototypical garden would then look like a stormy ocean. Instead of digging holes, I could then go out and remove accumulations that have formed on its surface. I probably wouldn’t dig a hole then. I would say that this way of categorizing things would result in a less efficient language, but it wouldn't change the world one bit.

Our everyday language is an efficient way of talking about the world, but it's certainly not the only way. We could divide the world according to other criteria and make corresponding - different - adjustments.

So to summarize, holes are deviations from an ideal that exists just as little and as well as the ideal itself. A gap in an argument is a deviation from an ideal argument. A gap in a garden fence is a deviation from the ideal of a continuous, fully closed surface. A hole in a sheet of paper is a deviation from an ideal sheet of paper. One could just as well say that a sheet of paper is an ideal hole filled with cellulose - provided that we adjust our language accordingly in other areas too.

Naive realism about holes is not naive because it assumes the existence of immaterial objects, but because it regards the way we categorize the world in everyday life as unalterable. And nominalism is not rejected because it denies the existence of certain things which seem to “be there,” but because it sees our everyday way of dividing the world as fundamentally wrong. As if it were possible to distinguish a "correct" way of division from a less correct one.

Are holes real now? I would say that this is not a meaningful question. A sheet of paper with a hole is just as real as a sheet of paper without a hole. They are simply two differently filled regions, or - rather - two regions with different correct descriptions within the same language.

What we could do is to consider what kind of deviation holes are. After all, there are not only holes. We also know gaps, shadows, silences, dents, valleys, and so on. As a final suggestion to contribute something constructive here, I would propose the following:

A hole is a spaciotemperal region R such that

(i) R is a real part of a larger region R*,
(ii) R and R* consist of different largely homogeneous stuff S and S*, and
(iii) S is more easily substitutable by another stuff S’ compared to S*.

There are as many holes in a region R* as there are unconnected regions R1, R2, … that fulfill conditions (i) to (iii).

The most interesting part of this account is condition (iii) which is about substitutability (or removability). A hole contains stuff that that can be removed easily compared to its surroundings. The chest in front of me is not a hole in the space which surrounds it. It is easier to substitute the air around the chest than the chest itself. Imagine a sheet of paper within a larger region R*. It’s usually difficult to replace the space the sheet lives in with something else. So, the space the sheet fills out is not a hole.

But we could make a wooden box that can precisely accommodate the sheet inside. In this case, it would be easier to replace the space occupied by the sheet with something else - another sheet of paper for instance - than to replace the space occupied by the box. In this case, the space occupied by the sheet of paper could be considered a hole.

Condition (iii) also adds a modal dimension to holes. Holes are regions in which replacement or substitution is (easily) possible. For water to flow out of a bucket, there needs to be a spot on the surface of the bucket that can be easily replaced by water. If we dig a hole in the garden, we can fill it with potatoes. If there were still soil in the spot, it would be difficult bring in the potatoes.

It would certainly be interesting to investigate this type of modality further. I suppose it won't be quite so easy, and I won’t do it here. Instead, I would like to test my suggestion a little bit. It is, of course, an empirical hypothesis about our language usage, and not about what our world is made of.

It can, nevertheless, turn out to be false. With the assistance of a set of questions, I recently tested my hypothesis. My objective was to determine whether substitutability is a valid criterion for identifying holes. As a guest at a large party, I distributed a questionnaire containing the following items. (The percentage figures refer to the relative frequency with which the respective answers were selected by the guests.)

Imagine we have a piece of styrofoam, about 10 mm thick and as large as an A4 sheet. Now we cut a circular hole in the center of the styrofoam with a knife. Consider the following cases:

1. We insert a wooden rod with the same diameter as the hole and about 50cm long into the hole and move it back and forth.

A) The hole still exists. (57%)
B) The hole no longer exists. (35%)
C) I don't know what to say. (7%)

2. We now shorten this rod to 1cm length, insert it into the hole so that the ends exactly match the edge of the styrofoam, and leave it in place.

A) The hole still exists. (57%)
B) The hole no longer exists. (35%)
C) I don't know what to say. (7%)

3. We remove the wood and take a round, transparent glass rod of 1cm length and insert it into the hole so that we can see through it.

A) The hole still exists. (64%)
B) The hole no longer exists. (29%)
C) I don't know what to say. (7%)

4. We remove the glass and insert the cut-out piece of styrofoam into the hole.

A) The hole still exists. (36%)
B) The hole no longer exists. (50%)
C) I don't know what to say. (14%)

5. Now we take out the styrofoam again, smear the edges with glue, put it back into the hole, and wait for the glue to dry.

A) The hole still exists. (14%)
B) The hole no longer exists. (86%)
C) I don't know what to say. (0%)

6. We take a new, similar piece of styrofoam and cut another hole into it. Now we slit the styrofoam from one side so that the slit reaches from the edge of the styrofoam to the edge of the hole.

A) The hole still exists. (64%)
B) The hole no longer exists. (36%)
C) I don't know what to say, (0%)

7. Now we also slit the styrofoam from the other side so that this second slit reaches from the opposite edge of the styrofoam to the other edge of the hole. We could separate the two sides of the styrofoam, but we keep them together.

A) The hole still exists. (43%)
B) The hole no longer exists. (57%)
C) I don't know what to say. (0%)

8. Now we take the two sides of the styrofoam apart and lay them on the table at some distance.

A) The hole still exists. (14%)
B) The hole no longer exists. (86%)
C) I don't know what to say. (0%)

9. A new piece of styrofoam. We cut another hole into it. At some distance from it, we cut a second hole. Now we take a knife and slit the styrofoam from one hole to the other, connecting them.

A) The first hole still exists. (86%)
B) The first hole no longer exists. (14%)
C) I don't know what to say. (0%)

10. We create another hole. Then we take the knife and cut away a piece from the edge of the hole all around, making it larger - for example, 20 mm in diameter.

A) The original hole still exists. (50%)
B) The original hole no longer exists. (43%)
C) I don't know what to say. (7%)

The first thing that should strike you is that the concept of a hole - like most everyday concepts - is vague. That means that the intuitions of different speakers can differ slightly from each other, especially in borderline cases.

In questions 1 through 5, I tested the effects of the presence of a "solid" guest on our conception of holes. Slightly more than half of the participants indicated that a wooden filling - regardless of whether it fitted the host or not - had no impact on the continued existence of the hole. A transparent filling slightly increased this tendency.

When the filling, however, was the same material as the host, significantly fewer participants assumed that the hole would continue to exist than that it would disappear. If the filling was difficult to substitute (case 5), then most participants changed their assumption from the existence of a hole to its absence.

I have a suspicion that the correlation between the answers to case 1 and case 2 could be explained by consistency considerations. Some of the participants told me that they found it difficult to answer the questions. It might have been better, therefore, to distribute several different questionnaires to neutralize this effect. However, this would have required more participants than I had.

I find the comparison between case 4 and case 5 interesting. Even if the hole has the same filling, the easiness of substitutability seems to be crucial for the conception of holes. If the guest is firmly attached to the host, only very few people seem to want to consider the presence of a hole.

I have no idea how to explain the significant difference in the answers between case 6 and case 9. In both cases, the host is partially penetrated and either connected to its edge or the edge of another hole. While in the first case only 64% assumed that the hole would continue to exist, in the latter, it was a whopping 86%. This was a big surprise.

What surprised me as well - albeit to a lesser extent - is the difference between 6 and 7. Similar case 10. There is - at least in German - a linguistic ambiguity regarding the situation as described in 10. If we remove stuff from the edge of the host a bit, we can express this activity in two different ways:

a) We create a larger hole.
b) We make the hole bigger.

In the fist description we assume that the resulting hole is another hole than the one we started with. The second description assumes a continuity of the hole. The answers to case 10 might reflect this ambiguity more or less.

What this shows is that a hole is not simply a region, but perhaps rather a maximally extended sub-region that possesses a certain characteristic. For people who prefer the second description, a property of the hole has changed (its size). For people who would rather use the first formulation, the identity of the hole has changed, which would mean that the size was not seen as a feature, but as a criterion for the identity of holes.

I had a conversation about this topic with some of the guests (a qualitative field study, so to speak). Most of them had not thought about holes and could not tell me exactly what they are and how they can be individuated. One conversation partner said that, "for him," there are only holes when the host is solid and the guest is gaseous. When I asked if he meant that there are also holes in clouds, he denied it. Another guest said that there are only holes where something is "broken." A woman believed that holes always had to be continuous, with two "entrances." If something only had one exit, like a cave, then it was not a hole in the rock, but rather a pit.

This small experiment shows that there is no consistent everyday theory about holes. This is not surprising. After all, there is also no consistent everyday theory about chairs, containers, or porridge.

This also shows that it doesn't make much sense to ask what holes are. I tried to explain how it comes about that we use this concept. We use it because, when we speak, we initially overlook details and use concepts that contain abstractions and idealizations. Holes are therefore interruptions of "things" because such interruptions are not initially provided for the things we talk about.

We live like Platonists in a world full of ideal forms: an ideal stone has no dents; an ideal leaf has no fringes, and an ideal bucket has no holes. Ideal stones, ideal leaves, and ideal buckets, however, do not exist. Therefore, we need holes (dents, gaps, scratches, bumps, creases) too.

Welcome back to my series on power relations! In my first post, I delved into the nature of authority. Today, I will explore the concept of power.

The notion of power is essential in both empirical and normative investigations. Empirical questions, such as whether a country is controlled by a power elite, whether employers hold power over employees, or how power dynamics are structured within political groups, require a clear conceptual framework for the concept of power. This framework allows us to evaluate such issues empirically.

Normative inquiries regarding power, such as whether power and freedom can coexist, whether power equality should be pursued, and whether justice can be achieved in a society shaped by power dynamics, also rely on a clear understanding of the concept of power.

To embark on empirical and normative inquiries into power, it is crucial to perform a conceptual analysis to understand the essence of power and its fundamental components. Two different questions arise in this context. The first question is conceptual: What is power? The second one is empirical: How can power be assessed?

As we cannot answer the second question without having a good understanding of the concept of power, let us start with the first question. The discussion of assessing power relations must wait for another installment.

Defining power

Having power in the most general sense may seem to imply the ability to achieve something. Someone who achieves something can be considered powerful, to some extent, and someone who achieves more than others can be seen as more powerful.

Another way to articulate this idea is to say that power is control. The more control you possess, the more power you have. Accomplishing something makes you feel powerful. On the other hand, if you continually fail despite your efforts, or if you anticipate failure, you lose control and feel powerless.

One could challenge the notion that power solely belongs to those who achieve something, as true power lies with those who achieve what they desire or want. This voluntative aspect seems to be an essential component of the concept of power.

However, this view is both true and false at the same time. For instance, consider a shareholder who wishes for a stock price to rise in the near future, and the price of that stock rises rapidly. In this case, the shareholder has achieved what he wanted. But it does not necessarily mean that the shareholder has power or control over the stock price.

Simply achieving what one wants does not always equate to power, as a person who adjusts their desires to realistically achievable things may be rational but not necessarily powerful.

Therefore, analyzing the concept of power should not be limited to actual desires and achievements. It must also consider what someone could achieve if he had certain desires, regardless of whether he currently has them or not.

Asserting that someone has power does not necessarily mean that he typically achieves what he wants. Rather, it means that the powerful person could achieve what he desires, regardless of his current wants or desires.

This is why volitions do not play a crucial role in the analysis of power. The more someone can achieve, the greater their power, regardless of their desires.

Another objection could arise by observing that one can achieve a multitude of trivial objectives. For instance, one could make one’s right index finger bend or move a teapot on one’s kitchen table two centimeters to the left. If power is equated with what one can do, then perhaps there is an excess of power in the world, more than what is typically assumed.

However, it would be premature to deny that there are situations where considering such trivial cases of power may be beneficial. When a child feels overwhelmed by its own powerlessness, highlighting the many things it can do and control could be helpful.

Furthermore, whether an action is considered trivial or not depends on the context. For example, let's imagine that Hannes Longfinger has a gun pointed at someone's head and his finger is on the trigger.

In this situation, simply bending his index finger could have severe consequences for his victim. Hannes holds a significant amount of power and can make a life or death decision.

It is highly unlikely that we can identify certain situations that lead to significant exercises of power while others do not. Therefore, it may not be beneficial to differentiate between significant and trivial exercises of power when defining power.

This leads to a simple definition of power: Someone has power if and only if he can achieve something. Denoting anything one can do or achieve as "H," the general definition of power can be expressed as an equation:

(1)

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

The sentence "A can do H" expresses a possibility and is a modal statement that should be analyzed as a relative modality, according to Angelika Kratzer.1 This means that the modality expressed by the modal adverb "can" is interpreted against a conversational background.

As we discussed earlier in the context of authority, sentences expressing relative modalities can be analyzed in a model of the form:

(2)

M = <X, W, f, V>

where X is a set of persons, W is a set of possible worlds, V is an evaluation for each atomic sentence, and f is a function that assigns to each possible world w a set of propositions {pⱼ}, representing the conversational background relevant in the context of an utterance in w.

Let us assume that the scope of action available to a person, x, in a given situation is relevant to the conversation regarding their power. The set of propositions that are the value of f, consists then of all propositions according to which x performs the actions available to him/her given the circumstances in the situation.

The scope of action, in this sense, can be expressed as:

(3)

f(x,w) = {pⱼ: x performs actions within the limits of x’s scope in w}

Since each proposition pⱼ is a set of possible worlds, the intersection of these sets will give us a set of worlds in which x performs all the actions available to him/her:

(4)

∩f(x,w) = ∩{pⱼ: x performs actions within the limits of x’s scope in w}
= the set of worlds in which x performs what is in x’s limits of scope

The truth conditions of sentences of the form "A can do H" can then be formulated as follows:

(5)

[[Can(Ha)]] in M, w = 1 if and only if there is a world w' ∈ ∩f(a,w) such that w' ∈ [[(Ha)]].

= “Can(Ha)” is true in a world w iff there is a world w’ which belongs to the worlds that comprise the scope of action of a in w and a does H in w’.

Looking at power in this way places the responsibility of explaining power on the function f, which determines the scope of action available to a person in a particular situation. While my definition of power offers a framework for modeling power, it does not provide information on what f actually looks like or how we can assess an actor's power.

It is worth noting that while this analysis provides a definition of power, it is not an all-encompassing theory of power. While a definition guides the development of a theory, the real challenge is to construct the theory itself rather than merely defining power.

However, a definition of power is still useful, as it provides a framework for the development of a theory of power. It allows us to model power, identify factors that might affect power, and avoid shortcuts in analyzing power relations.

Many of the "theories of power" currently in the intellectual marketplace offer only a limited view of power. Theories of political power, economic power, structural power, institutional power, and interpretive power are interesting in their own right, but they offer only partial insights into the phenomenon of power.

My definition of power also has a critical aspect. We can evaluate claims about power relations by examining whether these claims are consistent with our judgments about what someone can and cannot do in a given situation.

For example, if someone claims that women are structurally oppressed in our society and have less power than men, this claim can only be true if it can be shown that women have fundamentally fewer options for action than men. It is not enough to demonstrate that there are more men than women in managerial positions in certain fields or that there is a gender pay gap.

Instead, it must be demonstrated that women have fewer opportunities to attain leadership positions or negotiate higher salaries. I do not claim that this cannot be done, but I want to emphasize that a definition of power enables us to better assess claims and justifications for the existence of power imbalances.

Defining power may seem simple, but assessing power in a given situation is much more complex. What determines the scope of action available to a particular person or group in a given situation? I cannot answer this question here, and I doubt that there is a simple answer, but I will discuss some possible misunderstandings and explore some implications of my deflationist definition of power.

Abilities and skills

I have proposed that the power of an individual or a group in a specific context is equivalent to their capacity to act within that context. However, this approach may be perceived as reducing power to a mere set of skills and capabilities, which may seem overly simplistic and incomplete. Although an individual's abilities and skills can contribute to their power, there are - of course - many other factors at play, including social status, cultural norms, institutional structures, relationships between individuals and groups, and much more.

This misunderstanding arises when assuming that "A can do H" simply means that A is able to perform H or has the necessary skills to do so. However, the modal auxiliary "can" has various interpretations, including epistemic, deontic, dispositional, and entitlement.

Regarding power, "can" has what we can refer to as a scope-of-action reading. For instance:

(6)

Putin has the power to end the war between Russia and Ukraine.

- is quivalent to:

Putin can end the war between Russia and Ukraine.

- is equivalent to:

Given the scope of action available to Putin, it is possible for him to end the war between Russia and Ukraine.

When evaluating someone's scope of action, it's essential to consider a wide range of factors, including his abilities and skills, social structures, cultural norms, physical laws, dynamics of relationships and interactions between individuals and groups, and many others.

This deflationist view of power, as we may call it, shifts the burden of a theory of power from its definition to its assessment, which is a more reasonable approach. Attempting to define power based on factors that influence an actor's ability to act in a given situation would be hasty. Such an approach would, at best, result in a partial definition of power, and at worst, lead to overlooking important aspects of power due to an overly narrow perspective.

Ubiquity of power

Unless you are comatose or deceased, you always have some agency. You are never completely powerless. Therefore, power is ubiquitous.

The more we can accomplish, thanks to personal growth, technological advancements, favorable environmental conditions, and political liberties, the more power becomes accessible to us.

At every moment of our lives, we face countless options and choices. Even if we choose not to act on them, our potential for action and power remains significant.

This is not to imply that there are no discrepancies in power among individuals or groups, quite the contrary. Nonetheless, it demonstrates that each of us possesses more power than we might recognize.

Neutrality of power

Power often carries a negative connotation. It is often associated with oppression, inequality, abuse, and manipulation. Although these associations have a basis, they do not necessarily define the nature of power.

One may argue that the expansion of opportunities for action has its positive sides too. Those who possess knowledge and technology that can cure certain diseases have more power, and this benefits many. When one has the power to increase the well-being and happiness of others, it is a positive manifestation of power.

The misconception that power is inherently negative because people tend to exploit it may lead us to believe that it would be better to contain and restrict it.

However, this could come at the expense of our well-being. Power is not a zero-sum game. Limiting the power of one person or group does not automatically transfer that power to others. In many cases, it would be more advantageous to increase power in a targeted way, rather than limiting it.

If we expand our overall scope for action, we all become capable of achieving more. Power is not a finite resource, and it is not always a matter of how the pie is divided fairly. We can expand the cake as a whole, so that everyone gets a larger share.

Increased opportunity leads to more power, which can lead to both good and bad outcomes. Power as such is neutral, and it is up to us to use it wisely.

Degrees of power

Power is not a singular entity, but instead exists in varying degrees. The more one can accomplish in a given situation, the more power one possesses in that moment. This suggests that power is, in principle, measurable and comparable.

However, it is difficult to determine how powerful someone is in a given situation. How many units of power does one gain upon graduating from college, climbing the corporate ladder, or winning the lottery? How many units are lost due to aging or illness? These questions are difficult, if not impossible, to answer.

This is because the scope of action in any given situation is influenced by a vast array of factors that cannot be easily reduced to a formula.

When we compare power, we do so with the assumption of ceteris paribus - that all other things are equal. For instance, if Susi and Marie meet at a fair and Susi has one Euro more in her pocket than Marie, then Susi has slightly more power. She has more options available to her. She could maybe do two laps on the carousel instead of just one.

However, in reality, everything is never equal. Susi and Marie differ in many ways - in their skills, intelligence, social networks, appearance, health, and attire, among other factors. All of these differences affect their respective abilities to act in any given situation.

We may argue that Susi and Marie have different economic power, but economic power is only one aspect of the power available to them when they attend the fair. Therefore, we cannot draw any definitive conclusions about the power dynamic between Susi and Marie based solely on the difference in their pocket money.

Reach of power

Power is not a timeless attribute; rather, it is dynamic and mutable, capable of being augmented or diminished over time. At any given moment, an individual or group may have the capacity to attain certain objectives, while at other times, they may not.

Power, therefore, cannot be considered an inherent trait of a person or group in general, but rather a feature that they possess at a specific moment or over a certain period of time.

Furthermore, power not only concerns what can be done now but also how actions today can influence the future. When we say that a person or group A has power at time t1 concerning a matter E at time t2, we imply that A can bring about E at t2 through their actions at t1. Let’s call this the temporal reach of power.

This temporal aspect of power raises several intricate issues that relate to the relationship between t1 and t2. It is not apparent, for instance, whether A must be capable of ensuring that E occurs at t2 at all times between t1 and t2 to claim power over E at t1.

We are constantly confronted with considerations of the reach of power, as in the climate debate. Can what we do today affect the lives of future generations? Is it in our power to stop global warming? These are difficult questions, requiring valid theories and models, as well as an accurate assessment of our current situation.

What is clear is that we have the power to influence the future. However, our judgments about how what we can do will play out in the future become weaker the further the effects of our actions lie in the future.

It is unclear how long the period between t1 and t2 can be to apply the concept of power meaningfully. For example, can we say that a 10-year-old holds power over a particular issue in the distant future if it is conceivable that they can achieve goals linked to that issue in adulthood? Should he or she care about grades?

The spatial range of power is another issue. In the past, it might have been possible to escape the sphere of influence of a principality and its courts simply by getting a few hundred kilometers away from them. With the availability of telephones, cars, developed roads, airplanes, and international cooperation, this is no longer so easy. Our scope for action has greatly increased.

We could call the temporal and spatial dimensions of power a sphere of influence that becomes increasingly opaque with distance. The sphere of influence of any particular person, group, or humanity as a whole depends on how what can be done here and now will work out in a then and there. While knowledge and technology extend the range of our power, we cannot specify precise boundaries of power in time and space.

Intransparency of power

Not all the consequences of our actions are clear to us. Often, we are unaware of the effects that our actions might have. Additionally, our assessment of our own abilities is not always accurate since we might not know all the circumstances surrounding a particular situation. As a result, a significant part of the power that we possess is opaque to us.

For example, while we could start a business or invite friends over for dinner, there is no guarantee of success or attendance. Similarly, questions about colonizing Mars, curing cancer, winning a war, or doing a handstand are complex and dependent on many factors, making the outcome uncertain.

Since power is dependent on various factors that we cannot fully appreciate, it is often diffuse and elusive. While knowledge can help to make power more transparent, a complete theory of power is impossible. Instead, our understanding of power benefits from knowledge gained in other areas.

Forms and dimensions of power

Saying that having power means being able to do things does not preclude an examination of specific achievements in a particular field, nor does it prohibit comparisons.

Perhaps the most intriguing type of power is social power, which refers to the ability to affect the behavior of others. We humans are social creatures, and the ability to influence behavior, especially during interactions, occupies us from morning till night.

Power can have both negative and positive effects in this context as well. When we consider propaganda, manipulation, bribery, violence, and other such phenomena, we usually focus on the negative aspects of social power.

Conversely, when we examine the lighter side of social power, we see that it can manifest in therapy, assistance, empathy, love, and cooperation.

I refer to these phenomena as the various forms of power, which I will delve into in a future post.

There are various domains of power, including political, diplomatic, elite, interpretive, economic, negotiating, and many more.

These dimensions of power differ from the forms of power in that they are not focused on specific forms of interaction but on the interplay between different resources and their impact on the potential for action in a particular area.

A significant portion of the discourse surrounding power centers around these matters, and I do not intend to duplicate existing work in this area. My definition of power does not preclude such analyses and only makes a minor contribution to them.

Opportunity costs

Paradoxically, one way to diminish your power is by engaging in an activity. When you commit to something, you lose the opportunity to pursue other alternatives that could have been more beneficial. In economics, this is known as an opportunity cost.

The concept of opportunity costs emphasizes the importance of making wise choices about our actions. We must invest our power in activities that provide us with the most benefit and avoid wasting it on frivolous pursuits.

To this end, one effective strategy is to engage in activities that will increase our power. We can enhance our skills, learn new things, prioritize our health through diet and exercise, cultivate new relationships, or invest in our future. By doing so, we can expand the realm of our possibilities and ultimately increase our power.

However, we must also be mindful of the opportunity costs associated with these activities. If we solely focus on expanding our possibilities and fail to take advantage of them, our efforts will have been in vain. Reading is an excellent example of an activity that both expands and utilizes our abilities, making it a highly recommended pursuit.

What I want to reiterate, once more, is that I did not assert that the scope of action is the foundation of power. Rather, I stated that it is power. Consequently, any declaration of an individual's power is equivalent to a declaration of their capabilities and potential achievements.

As such, the term power does not indicate a specific area of phenomena, but rather encompasses the diverse range of actions we, as agents, can take in particular circumstances. In principle, we could consider abandoning the concept of power altogether. However, in practice, the notion of power makes it easier to have meaningful discussions about what we can accomplish or achieve. It facilitates a more efficient and streamlined discussion of these phenomena.

Ultimately, therefore, the term power serves as a linguistic shortcut.

Welcome to the first installment of a series on power relations. I find power to be a fascinating topic because it is complex and integral to our social structures. Although I am uncertain how many posts this series will include, I promise to keep you updated.

We often discuss power, but seldom do we take the time to fully explore its complex and multifaceted nature. Therefore, let us delve deeper and clarify what we mean when we use the term "power."

At its core, power refers to the ability to influence or control others. However, two distinct concepts of power are at play here.

The first, which I consider more fundamental, is the execution of power, whereby an individual asserts their will over others. Power can be executed in various ways, such as coercion, violence, persuasion, manipulation, or bribery.

On the other hand, there is the possession of power, where an individual may not necessarily execute power but has the potential to do so. This is often referred to as the power of influence.

I would like to begin this series by exploring authority, which refers to the power to perform important tasks, such as enacting laws or settling religious disputes.

Authority is a specific form of power and can have two different meanings: executing authority, which means carrying out authorized actions, and having or possessing authority, meaning the ability to do what others cannot.

Both concepts are intertwined and closely related to each other, but I will mainly concentrate on the first concept of authority: What does it mean that someone is authorized to do a range of things?

The reasons why I believe it is more productive to concentrate on influencing instead of having influence will become clearer in later installments. For now, let's start with a closer examination of authority.

Defining authority

Authority is the power or right to make decisions, give orders, and enforce obedience.

It is often associated with positions of leadership, such as a government official, a manager, a captain of a pirate ship or a priest, but can also refer to someone who has expertise or knowledge in a particular area.

Authority can be based on a variety of factors, such as legal or institutional power, social status, or personal qualities like charisma or expertise.

Authority is present in many different fields and contexts. It is an important aspect of social organization, as it allows individuals and institutions to exert control and influence over others in a structured and legitimate way.

It is also an essential part of social institutions and plays a significant role in shaping the norms and values of society.

The exercise of authority can have an impact on individuals and society, and its legitimacy is often a subject of debate and scrutiny.

I will not concern myself with what authority is based on or why it is respected. Those are interesting topics. Here, I want to focus on what authority is, or more specifically: what it means for someone to be authorized to do something.

Here are some examples of actions that require authoriy from various fields:

• Government: The President of the United States issuing an executive order that carries the force of law.

• Education: A teacher setting classroom rules and expectations, and enforcing consequences for breaking them.

• Parenting: A parent setting boundaries and rules for their child's behavior, and enforcing consequences for disobedience.

• Business: A manager making decisions about hiring, firing, promotions, and other personnel matters.

• Law enforcement: A police officer arresting and detaining suspects, and using force if necessary to maintain order and protect the public.

• Religion: A religious leader interpreting and teaching religious doctrine, and making decisions about matters such as marriage, divorce, and excommunication.

These are just a few examples. What they show is that having authority means that you’re entitled to perform certain actions that can bring about specific states or situations.

These states often have a normative status, meaning that certain rights or obligations are linked to the outcomes of authorized actions. For instance, entering into a contract, getting married, convicting a defendant, or being granted custody of a child are all examples of such actions having normative consequences.

The fact that someone has authority, therefore, includes two different aspects: he or she is firstly entitled to perform a specific range of actions (in a certain context), and the consequences or norms brought about by those actions are accepted as “binding” in a certain sense:

(1)

A person a has authority to do H in context C iff

(i) a is entitled to do H (in C), and
(ii) the consequences of H are accepted (in C).

Both conditions are necessary. Let's imagine a mutiny on a pirate ship. A gang of three sailors has conspired against captain Whitebeard, overpowering him and tying him to a mast.

They call the crew together, and the strongest of the three - called “Blackbeard” - orders in a commanding tone, "Set the sails!" The crew hesitates for a moment, but they are intimidated and begin to set the sails.

This means that the conspirator's words are interpreted as an order to set the sails in this situation. If the ship's cook - Sam Teaspoon - had shouted the same thing in a sunny afternoon, it would not have had any binding force and would have been interpreted at best as a playful role-playing game.

So, Blackbeards's words had normative consequences without him yet having the authority to give orders to his crew. He only exercised power over the other members of the crew through his physical strength and demonstration of his determination.

He could acquire authority in the next few days by declaring himself captain, and the others might accept it. But it is also possible that he may not succeed, and someone might throw him overboard to end the mutiny.

Although Whitebeartd tied to the mast still is entitled to give orders at this point, if no one follows him, his words do not count as orders to the crew. Entitlement alone doesn’t install authority.

I suspect that both conditions are sufficient for authority. If someone actually is entitled to perform a certain range actions (in a certain social context), and the consequences of those actions are accepted, then they have authority in that area. Let's examine the interplay between these factors in the following examples:

• Legal authority: A judge has authority in a courtroom if (a) he is entitled to issue a sentence and (b) that sentence counts as legally binding.

• Academic authority: A professor has authority in a classroom if (a) he is entitled to grade assignments and (b) those grades count as a measure of student achievement.

• Managerial authority: A manager has authority in a workplace if (a) he is entitled to make hiring decisions and (b) his decisions count as the official hiring decisions.

• Parental authority: A parent has authority in a household if (a) he is entitled to to set rules and (b) those rules count as expectations for behavior.

• Political authority: A government has authority in a country if (a) it is entitled to to enact laws and (b) those laws count as binding regulations.

• Religious authority: A religious leader has authority in a religious community if (a) he is entitled to interpret scripture and (b) his interpretation counts as the official doctrine.

• Scientific authority: A researcher has authority in a field if (a) he is entitled to conduct experiments and (b) his findings from those experiments count as evidence.

In each of these examples, a person - such as a captain, coach, priest or manager - is granted the right to take specific actions within a particular context, and those actions result in a particular state of affairs or a socially binding norm.

To better understand the concept of authority, we must, therefore, analyze the relationships referred to in the two conditions. We need to examine what it means for a person to have the right to perform a range of actions within a specific context. Additionally, we must comprehend what it means for a particular action to be considered as setting a social norm.

Let's address these questions in this order.

Entitlement

Another way to express that someone has the right or entitlement to do something is by stating that he or she can do it. A judge can issue a verdict, but a lawyer cannot. The government can enact laws, but the local bowling club cannot.

To say that someone can do something involves using a statement with a modal force: it is possible that he or she does it, based on various circumstances and assessments.

Entitlements have certain analogies to permissions, obligations, or abilities. The following comparison clarifies this:

(2)

Peter can conclude the building society contract.

a. For all we know, Peter concludes the building society contract.
b. Peter is allowed to conclude the building society contract.
c. Peter is able to conclude the building society contract.
d. Peter is entitled to conclude the building society contract.

The paraphrases (2.a) to (2.d) suggest that the modal adverb can has not only the well-known epistemic (2.a), deontic (2.b), and dispositional interpretations (2.c), but also an interpretation in which it signifies having the right or entitlement to do something (2.d).

However, this does not yet establish whether entitlement is a distinct concept or not. It could be argued that entitlement is a particular form of permission or that it is similar to the ability to perform an action.

To explore this further, we need to examine whether entitlement constitutes an independent modal category alongside deontic and dispositional modality.

To begin with, it is important to clarify that permissions and entitlements are distinct from each other. Having permission to do H does not necessarily imply having the right to do H, and vice versa.

Makinson (1986, 408) examines a scenario where having the entitlement to do something does not entail having permission to do it:1

... consider the case of a priest of a certain religion who does not have permission, according to instructions issued by the ecclesiastical authorities, to marry two people, only one of whom is of that religion, unless they both promise to bring up the children in that religion. He may nevertheless have the power to marry the couple even in the absence of such a promise, in the sense that if he goes ahead and performs the ceremony, it still counts as a valid act of marriage under the rules of the same church ...

The other case, in which someone is allowed to do something he or she is not entitled to do, arises in all those cases where someone acts on behalf of another person.

The director of the institute, for instance, is authorized to invite the members of the institute to a council meeting. The act of inviting the members to the meeting may, however, be carried out by his secretary, as far as it is apparent that she is acting on behalf of her boss.

This is one of many cases where someone has permission to do something without being entitled to carry out such actions in general. It is not within the power of the secretary to convene an institute council meeting, although she is allowed to do so in certain situations.

The practical ability to perform actions that have a normative situation as a consequence is, again, neither a sufficient nor a necessary condition for being entitled to perform such actions.

An actor may have the practical ability to marry a couple (for example, because he knows how to perform the ceremony) without being entitled to do so. His acting would not count as marrying the couple, because of his lack of entitlement.

It is, on the other hand, possible for someone to be empowered to do something - for instance marrying a couple - without being practically able to do it (cf. Jones & Sergot 1997, 351):2

... one may imagine circumstances in which it is not practically possible for the priest to marry the couple (because, say, he is sick or otherwise incapacitated), although he is still empowered to do so.

Both the actor and the priest could express themselves in a slightly paradoxical manner: "I can marry you, but I can't." However, they would convey different meanings.

The actor would mean, "I am capable of performing the ceremony, but I am not entitled to marry you." The priest, on the other hand, would mean, "I am entitled to marry you, but I am not capable of performing the ceremony." Saying that someone is entitled to do something, seems - therefore - to be a genuine case of modality.

Let's revisit the example we discussed earlier, "Peter can conclude the building society contract." Suppose we interpret this sentence deontically to mean that he is allowed to conclude the contract. In this case, can expresses the modal force of possibility, and a natural rephrasing would be:

(3)

Given the things that Peter is allowed to do: it is possible for him to conclude the building society contract.

Under this interpretation, the modal operator it is possible that quantifies over a subset of possible worlds that is established by the context. This phenomenon is known as relative modality and has been extensively explored by Angelika Kratzer in a series of papers. According to her view, modal operators depend on different types of intensional contexts and are sensitive to the context of their use:3

Modals are context-dependent expressions since their interpretation depends on a conversational background which usually has to be provided by the utterance situation. Only occasionally do we use phrases like in view of what is known … for referring to conversational backgrounds in an explicit manner. (Kratzer 1981, 42)

Our examples can, therefore, be analyzed such that in (1.a) to (1.d), the modality expressed by the modal adverb can is interpreted against different conversational backgrounds. In (2.a), the context is what we know, in (2.b) it is determined by the actions that Peter is allowed to perform, in (2.c) it is determined by what Peter is capable of doing, and in (2.d) it is determined by what Peter is entitled to do:

(4)

Peter can conclude the building society contract.

a. In view of what is known ...
b. In view of what Peter is allowed to do ...
c. In view of what Peter is capable of doing ...
d. In view of what Peter is entitled to do …

… it is possible that Peter concludes the building society contract.

A conversational background is a kind of entity which might be referred to by an utterance of a phrase like in view of what is allowed. What is allowed is different from one situation to another. What is allowed in a certain situation could be represented as a set of propositions. If we consider the different situations as possible worlds, then Kratzer's approach assumes that a conversational background is be construed as a function which assigns sets of propositions to possible worlds.

The meaning of “what is allowed” will then be that funktion from the set of possible worlds W into the power set of of the set of propositions, which assigns to any world w of W the set of all propositions which are allowed in w.

Let's consider the truth conditions of sentences of the form (2.d). From a semantic perspective, such sentences can be analyzed in a model of the form:

(5)

M = <X, W, f, V>

Here, X is a set of persons, W is a set of possible worlds, V is an evaluation for each atomic sentence, and f is a function that assigns to each possible world w a set of possible propositions {pⱼ}, each construed as a set of worlds in which a person x does what he or she is entitled to do in w. This set of propositions, therefore, comprises all the actions that x is entitled to do in a given situation.

The conversational background for a modal utterances expressing entitlements could, therefore, be written as:

(6)

f(x,w) = {pⱼ: x does what x is entitled to do in w}.

Each proposition pⱼ is a set of possible worlds (the worlds in which pⱼ is true). So, interpreting the modal will involve generalizing over the following set of worlds:

(7)

∩f(x,w) = ∩{pⱼ: x does what x is entitled to do in w}
= the set of worlds in which x is entitled to do everything x does

The truth conditions of sentences of the form "A is entitled to do H" can then be formulated as follows:

(8)

[[Entitled(Ha)]] in M, w = 1 iff there is a world w’ ∈ ∩f(a,w) such that w’ ∈ [[(Ha)]].

Assuming, for instance, we live in a world where building society savings are possible, and if Peter is one of the eligible people, then there is a possible world in which Peter concludes the society savings contract. This then makes it true that he can get building society savings, i.e. that he is entitled to conclude such a contract.

Different contexts and worlds generate different functions of the type F. This might not seem exciting, but it is interesting nevertheless because it lets us see that such a function is the sole nature of entitlement.

An institution, whether formalized or not, consists - at least - of a set of roles that are associated with specific actions, and an assignment mechanism that determines who can perform those actions based on their role within the institution.

In informal institutions like family and friendship, roles are typically determined by tradition and mutual expectations. For instance, in a family gathering, the host is typically responsible for inviting the guests, while the guests do not have the authority to do so. Similarly, in a friendship, certain privileges like using informal language may only be extended to close friends and not outsiders.

In semi-formalized institutions like marriage, the assignment of roles as husband or wife requires a formal act, and certain actions are governed by law, such as financial assistance and tax sharing. However, other actions are based on customs and tradition.

In formalized institutions like private companies and public authorities, the assignment mechanism is based on employment contracts and promotions, and the roles are clearly defined in job descriptions and organizational charts. Each role comes with a specific set of actions that can be performed by individuals who occupy that role.

Overall, the assignment of roles and associated actions in an institution can be formal or informal, depending on the context, and the assignment mechanism determines who has the authority to perform certain actions based on their role within the institution.

Formal institutions such as hospitals, for instance, have many different roles, each with specific sets of actions and responsibilities.

Physicians, for instance, diagnose and treat patients. Nurses provide care to patients and assisting physicians in the treatment process. They may administer medication, monitor vital signs, and provide emotional support to patients and their families.

Technicians are responsible for performing various medical tests and procedures, such as X-rays, MRIs, and blood tests. They may also maintain and operate medical equipment, such as ventilators and dialysis machines.

The designation process for these various roles in an hospital involves job interviews, hiring decisions, and promotions.

Pirate ships, on the other hand, were informal institutions that operated outside of the law and were typically organized around a hierarchical structure with a captain at the top. He was the leader of the pirate ship and was making decisions about the ship's course, managing the crew, and overseeing raids.

The quartermaster was managing the ship's supplies, including food, water, and ammunition. He also oversaw the distribution of loot and was responsible for maintaining order among the crew.

The navigator was plotting the ship's course and ensuring that the ship did not run aground or collide with other vessels. He also kept track of the ship's speed and distance traveled.

The gunner was managing the ship's weapons, including cannons and firearms. He oversaw the loading and firing of the ship's guns during raids.

While pirate ships were not as formalized as hospitals, they did have a system of roles and responsibilities that were critical to their success. These roles were designated based on experience, skill, and performance.

The function f, therefore, can be construed as a representation of a certain institutional setting. A number of actions are endowed with entitlements (conprised into roles) and these roles are assigned to specific people.

As one person can be simultaneously assigned to different roles in different formalized and non-formalized institutions, a function of type F can be thought of as a representation of all actions that are part of roles to which a person is assigned in a certain world w.

Functions of type F therefore describe the basic structure of institutions. And these institutions in turn define who is entitled to do what in a certain situation. Institutions, however, involve more than just roles, assignments, and entitlements that follow from them.

My account of authority does not require a comprehensive account of institutions or institutional structures. My hypothesis only requires that there are institutional structures, whether formalized or not, and claims that entitlements rely on them.

The importance of these elements becomes apparent when the legitimacy of authority is a subject of debate. There are at least three different scenarios in which authority can be critizised.

Authority may, firstly, be questioned when a role no longer exists. For instance, after the Russian Bolsheviks overthrew Tsar Nicholas II in February 1917, the position of the Tsar no longer existed, and this meant that Nicholas II was for instance no longer authorized to collect taxes from peasants or give orders to his guard.

Additionally, it is possible to question whether the role in question included a particular action. For instance, in some countries, doctors are authorized to assist terminally ill patients in dying, while in others, they are not. This means that the role of a doctor is codified differently in different countries, and this usually changes over time.

And finally, it is possible to question whether a person is properly assigned to the role that includes a particular action. For example, when Blackbeard tied Whitebeard to the mast, he was not yet the captain. Therefore, when he commanded the crew to set the sails, he was technically doing something he was not yet authorized to do and could be critizised for doing it.

However, on a pirate ship, the processes of role assignment are usually informal, so the crew members may have been uncertain about whether Blackbeard had already inherited the role of Whitebeard. In such a situation, telling someone that he has no say because he is just a cabin boy and not the captain could be dangerous if the matter has already been settled without you noticing.

If we were satisfied at this point, it would mean that authority and entitlement are the same. A person would then have the authority to do what they were entitled to do. This is, however, not the case.

Acceptance

The legitimacy of an action can be disputed based on the underlying institutional framework, as seen in the three previous instances. However, there is also a fourth scenario to consider.

Even if the institutional structure is acknowledged by all parties and the roles are properly defined, the establishment of authority ultimately depends on whether the involved individuals accept the consequences of the action. In other words, even if the rules are clear, it is crucial to consider how the decision will impact the people it affects and whether they are willing to comply with it.

Let's revisit the scenario of Whitebeard being bound to the mast. Despite his status as captain and his entitlement to issue orders, Blackbeard and his allies disregard this and restrain him anyway. As a result, the remainder of the crew may follow suit, effectively rendering Whitebeard's words meaningless.

However, it is important to note that this does not necessarily mean that he has lost his position as captain. Rather, his authority has been temporarily undermined, and it will be up to him to regain control and reaffirm his leadership.

Institutional contexts differ in terms of the effort required to establish authority. Let's think of a classroom. Every teacher is entitled to set classroom rules and expectations, for instance. His or her authority within this settting can be measured by the degree by which those rules really count as expectations for behavior. So you could say that various teachers - despite equal entitlements - are endowed with varying degrees of authority by their students.

What we see in such and similar examples simply has to do with the fact that an institutional structure - even if it is recognized as such - cannot magically turn words into commands or rules. There is no automatism here. Power or authority, even if legitimate, must be enforced.

Entitlement - as I see it - relates to having a right to do something, while authority relates to having the power or control to enforce it.

Authority is, however, not the same as having the power to do something. It refers to the legitimacy to exercise power or control over others, often based on one's position or role. It implies that the actions of a person in authority are generally considered legitimate and appropriate.

Social power, on the other hand, also refers to the ability to exert control over others, but it doesn’t exclude brute force or coercion. It can come from a variety of sources, such as physical strength, wealth, or influence. Unlike authority, power does not necessarily have to be legitimate or accepted by those being governed.

Authority is, therefore, a form of power more closely tied to legitimacy and acceptance, while social power is more about the ability to control others, regardless of whether that control is accepted or legitimate.

Assuming that having authority means having legitimate power, we can understand the "legitimate" aspect of this concept through an analysis of entitlement. Power, on the other hand, is closely related to the ability of the person who holds a right to enforce it.

This ability is influenced by both the individual's own traits and the systemic conditions of the environment in which they operate. For instance, a person's level of determination, assertiveness, and resourcefulness may impact their ability to exercise their rights effectively.

At the same time, external factors such as social norms, legal frameworks, and political structures may facilitate or hinder the individual's authority. When assessing power, it is essential to consider both the personal qualities of the individual and the broader societal context in which they operate.

Consider again the situation in a classroom. The students willingness to accept the teacher’s authority can be influenced by several internal factors, such as knowledge, confidence, and communication skills. External factors such as social norms, political and social structures, school policies, and parental involvement can also have a significant impact on a teacher's ability to establish their authority in the classroom. Similar things apply to Whitebeard and his crew.

We can observe that in some cases, individuals accept a statement and act accordingly, while in other cases, they do not. Ignoring the factors that influence the acceptance of authority, what is the nature of this acceptance?

It cannot be simply reduced to the affected person's compliance. Consider, for example, the following utterance:

(9)

Get off the phone and get to work!

Depending on the context of the interaction, this statement can be perceived as a friendly reminder, an order given under threat, or a direct instruction.

In the first case, a friend may say this to another friend who is distracted while working, and the recipient may see it as a well-intentioned suggestion and start doing their job voluntarily.

In the second case, a gangster may say this to a cab driver after putting a gun to his head, and the recipient may comply out of fear for his life.

In the third case, a supervisor may say this to an employee who is wasting time, and the recipient is expected to accept it as a legitimate demand and start doing his job as part of his work duties.

In all three situations, there’s a compliance of the affected person, but only the third case involves an interaction characterized by authority. The supervisor has the right to give instructions to their subordinates and expect them to be followed. Neither a friend, nor a gangster have a legitimate reason to enforce a certain request or command.

Therefore, accepting authority can be understood as agreeing to receive a legitimate demand from a person or institution that has the right to give it, while not accepting authority means refusing to comply with such demands.

This is my final hypothesis in this post. Let’s summarize this discussion in an updated version of the definition above:

(10)

A person a has authority to do H in context C iff

(i) there is an institution in C according to which H is one of the actions that make up a particular role,
(ii) a holds that role in C,
(iii) a series of claims, legitimized by (i) and (ii), are associated with H and directed at an audience, and
(iv) the audience agrees to these claims through their behavior in response to H.

I'm not entirely satisfied with this definition, mainly for aesthetic reasons. But I believe it contains the essential ingredients. I consider it a little miracle that there is any authority at all, and that it is so easy for people to establish it.

It only takes a group of three hikers, with one - John - being particularly knowledgeable about the area. Once the three agree to consider John as their leader, they have established an institution. Leading a hiking group means determining which path the three will take. And as long as John can do that without anyone complaining, he exercises legitimate power and possesses authority.

Authority is practically everywhere, in the family, in kindergarten, in school, at the doctor's office, at work, on the bus, train, and taxi, in travel groups and choirs. It permeates our entire social life by making cooperation predictable and, therefore, efficient.

Without authority, every encounter with a stranger would be highly marked by uncertainty. Without authority, no ship would ever leave a port, and it probably wouldn't have been built in the first place.

The exercise of authority is an exercise of power. But it is by no means the only form of exercising power. Therefore, I will address the exercise of power separately again. But not now and not here.

Meet Klaus, a man who values his independence and chooses to remain single. However, his aunt Ursula has left him a substantial inheritance in her will, but with a catch: he must be married by the age of 30 to receive it. In need of money, Klaus finds a solution by marrying Berta, a fellow adventurer who shares his passion for archaeology and frequently travels abroad, allowing Klaus to maintain his desired lifestyle.

Consider Klaus' solution to his financial predicament. While it may seem reasonable, we must question its true value. To do so, let's examine the following statements, with the constituent in focus indicated in square brackets:

(1)

It is good that Klaus married [Berta].

(2)

It is good that Klaus [married] Berta.

In Klaus' situation, it seems that (1) holds true while (2) is false. These two sentences, despite their identical wording, convey different meanings.

To understand why, we can explore the reasons behind them. Perhaps, (1) is true because Klaus married Berta, who is frequently away from home, allowing him to maintain his single lifestyle. However, (2) is false because Klaus, a self-proclaimed bachelor, should not have married anyone at all.

These two value statements are related to different reasons, despite their similar wording. Essentially, (1) is equivalent to (3), while (2) is equivalent to (4):

(3)

Given the various people he could have married: it is good for Klaus that he chose to marry Berta.

(4)

Given his commitment to a single lifestyle: it is good for Klaus that he chose to marry Berta.

Assuming we are correct so far, it seems reasonable to suggest that the focus of a statement works to relativize a value statement to a particular set of reasons, which are tied to the emphasized constituent and further specified by the surrounding context.

However, standard semantics cannot account for the nuanced difference in meaning between sentences (1) and (2). Therefore, we require a non-standard semantics capable of accommodating focus-related meanings.

Two theories, in particular, could be applied: the theory of structured meanings, mainly developed by A. von Stechow, and alternative semantics, developed by M. Rooth. For the sake of simplicity, I will utilize the former theory.

The theory of structured meanings proposes that isolating one or more constituents of a sentence through focus partitions the sentence's meaning into two distinct sets: a background meaning and a thematic meaning. The background meaning is obtained through lambda abstraction over the focused constituents, while the thematic meaning is defined as the value of the focused constituents.

By applying this theory to sentences (1) and (2), we can display their focus-related meanings as an ordered pair in the format <background meaning, thematic meaning>. The expressions are as follows ([[α]]f represents the focus-induced meaning of α):

(5)

[[“Klaus married [Berta]”]]f = <λy. marry'(k,y), b>

[[“Klaus [married] Bertha”]]f = <λP. P'(k, b), λxy. marry'(y,x)>

What role do focus-related meanings play in determining the truth conditions of value statements?

Consider example (1), where the focused component, Berta, implies a comparison to all other viable marriage candidates, represented by λy. marry'(k,y). Consequently, the truth conditions of (1) attribute special qualities to Berta that justify Klaus' favorable view towards her.

On the other hand, in example (2), the component "to marry" defines the thematic meaning and necessitates the distinction of all other alternative relationships between Klaus and Berta represented in the background meaning.

If Klaus valued no other relationship with Berta more than marriage, it would justify his desire to marry her. However, as this is not the case, such a sentiment would be unwarranted, which is why (2) is deemed false, in accordance with our intuition.

What is the technical significance of these insights? How can we express the truth conditions of value statements? To begin, we can use the following formula as a useful starting point:

(6)

[["It is good that S"]] in w1 = 1 iff there is a world w2 and a subject a such that

1. [[S]] in w1 = 1 (factivity condition);

2. [[Φ(a, S)]] in w2 = 1, where Φ is a pro-attitude and w1 and w2 are broadly similar (essential condition); and

3. it is appropriate to have a pro-attitude with content p (appropriateness condition).

Condition (1) captures the factivity of propositional value statements. When you utter a sentence of the form “It is good that p.”, you presuppose that p is true. Therefore, the sentence “It is good that the earth is flat.” is neither true nor false because its presupposition that the earth is flat isn't satisfied.

Condition (2) captures the essential requirement for something to be valuable. Namely, there must be someone who values it - i.e. has a pro-attitude towards something described by S.

However, this is not always strictly required. Values don't cease to exist just because nobody values them at a particular moment. Values are dependent on but not identical to appreciation.

For this reason, I added another broadly similar world w2: actual appreciation is not always required, but it should not be an outlandish attitude within the situation under consideration.

You might be wondering why condition (3) is necessary. The proposition p is not specified, and it is unclear how p relates to S. Aren't values simply the things we appreciate?

Unfortunately, this is not always the case. We could appreciate something wrongly that is not worth valuing. Values require justification; they don't appear out of thin air. This is what condition (3) aims to capture.

To further clarify, we can rely on our previous discussion of focus-induced meanings. Assuming background meaning α and thematic meaning β, a plausible assumption would be the following:

(7)

It is appropriate to have a pro-attitude with content p iff: if [[S]]f = <α, β>, then there is a good reason for α(β) = p, such that it there is no good reason for any other proposition α(γ), with γ ≠ β.

The third condition is crucially based on the focus effect, stating that there is an appropriate pro-attitude only towards the proposition that is the object of a value statement, but not towards alternative propositions that we get when we substitute the focus position with other entities of the same type.

In the case of (1), this would mean that Klaus has a good reason to marry Berta (since he gets the inheritance and can still live mostly alone), but no good reason to marry Luise, Andrea, or Brigitte instead.

However, upon closer inspection, this approach turns out to be inadequate. The truth of (1) does not rule out the possibility that it might have been just as desirable for Klaus to marry Hannah instead of Berta, for instance, if Hannah is a famous marine biologist who is never around. Thus, the condition is too strong.

It seems that both Berta and Hannah would be good marriage candidates for Klaus. This, however, does not imply that choosing one necessarily rules out the other.

We must allow for other alternatives, for which equally good reasons could be found. We can do that by weakening (7) to (8):

(8)

It is appropriate to have a pro-attitude with content p iff: if [[S]]f = <α, β>, then there is a good reason for α(β) = p, such that this good reason doesn’t exist for another proposition α(γ), with γ ≠ β.

This suggestion, however, makes sentences like (1) too easily true. For instance, imagine Klaus and all potential marriage candidates are archaeologists, and one of them, Brigitte, is ruled out as a marriage candidate because she is a lesbian.

Under such circumstances, the mere existence of Brigitte would make (1) true since Klaus can't find good reasons for a marriage proposal with her.

This is not the desired outcome, and it shows that (8) is too weak.

To address this issue, we can refine condition (8) by adding a relevance requirement, as follows:

(9)

It is appropriate to have a pro-attitude with content p iff: if [[S]]f = <α, β>, then there is a good reason for α(β) = p, such that it there is no such good reason for any other proposition α(γ), where γ is a relevant alternative to β but ≠ β.

This means that the alternatives must be not only undesirable but also relevant to the value statement in question. This condition strikes a balance between being too weak and too strong, as it allows for appropriate pro-attitudes to be context-dependent and sensitive to the relevant alternatives.

This analysis renders (1) true only if Klaus has a reason to marry Berta that he would not have with respect to other women who are marriage candidates, because they would stay home more often instead.

The presence of an alternative marriage candidate like Hannah, who is too similar to Berta, would not count as a relevant alternative. Brigitte, on the other hand, would not count as an alternative at all, as she is not a marriage candidate.

For (2), (9) would render it true only if Klaus has a reason to marry Berta that he would not have if he married someone else. Since this is not the case, (2) would turn out to be false, as expected.

If we were to exclude focus-induced meanings from our analysis of value statements, then the third condition could be simplified to:

(10)

It is appropriate to have a pro-attitude with content p iff [[S]] = p, and there is a good reason for p.

Let’s assume:

(11)

It is good that Klaus married Berta.

Based on my analysis so far, (11) would be true if (a) Klaus married Berta, (b) marrying Berta isn't undesirable in general, and (c) he had good reasons for doing so.

While all three conditions are fulfilled, this explanation isn't entirely satisfying because the reasons for marrying someone are typically a mixed bag. Klaus likely had reasons for and against marrying Berta, and another person might have been a better match for him.

This creates what I call the "Mixed Bag Problem" (MBP).

The MBP cannot be easily resolved. If the reasons for doing something are mixed, it means there are good reasons for both p and non-p.

Strengthening (10) by requiring there are no good reasons for non-p would result in too few valuable things.

Requiring there be no alternative to p for which there are good reasons would be even worse, as there would be at most one valuable thing, and likely none at all.

Intuitively, if p is good or valuable, then there should be better reasons for p than for non-p. All things considered, it's better for Klaus to marry Berta. He can have his cake and eat it too. This idea is captured in (12):

(13)

It is appropriate to have a pro-attitude with content p iff [[S]] = p, and there are better reasons for p than for non-p, all things considered.

While the initial impression may seem positive, upon closer examination, I believe it falls short. Let us assume that propositions are sets of possible worlds, where p denotes all possible worlds where p is true. The set of possible worlds where non-p is true is enormous.

What could happen to Klaus in these worlds where he doesn't marry Berta? All kinds of extremely positive and extremely negative outcomes could occur, along with everything in between. What reasons could there be for choosing p-worlds over non-p-worlds given such vast sets of possible worlds?

I don't know, honestly.

It appears that utilizing focus in value statements makes the semantics more complex and the decision-making process simpler. Conversely, forgoing emphasis has the opposite effect.

In practice, decisions are critical, not semantics. Therefore, it is advisable to use focus to narrow down the relevant alternatives.

Is truth truly valuable? Assuming we are talking about practical usefulness here, one could argue that truth is valuable because it helps us navigate the world more effectively. For example, if we have accurate information about a situation, we can make better decisions and take appropriate action. On the other hand, if we have false or misleading information, we may make mistakes that could have serious consequences.

We could also look at specific instances where truth has played a role in improving outcomes. For example, scientific discoveries and technological advancements have been made possible by the pursuit of truth and the desire to uncover new knowledge. Similarly, in personal relationships, honesty and transparency are often seen as essential components of building trust and strengthening bonds.

There seems to be some evidence to suggest that truth is generally beneficial and worth pursuing. You may be surprised, dear reader, but I believe that the matter is not so simple.

So far, we have talked about "the truth" as if it were clear what that even means. In order to avoid making things too complicated - and perhaps unanswerable - we could look not at the value of truth itself, but at the value of individual instances of truth - concrete truths, so to speak.

If truth is valuable (practically, epistemologically, perhaps even morally...) in general, then concrete instances of truth should be valuable as well. Isn't that right? For example, if we assert that 'It is true that p', and this assertion is itself true with respect to some specific proposition p, then it must be valuable or good, if truth were generally valuable.

To explore this idea, let's examine some concrete value judgments related to facts (1.a), knowledge (1.b), and truth (1.c):

(1)

(a) It's good that it's raining.

(b) It's good to know that it's raining.

(c) It's good that it's true that it's raining.

Statements (1.a) and (1.b) are well-formed and common. In fact, there may be situations in which (1.a) is false but (1.b) is true. For example, we might be indoors and not need to worry about getting wet. But (1.c) is more interesting, as it challenges the so-called truth conditional:

(2)

Truth conditional: It is true that p if and only if p.

By applying the truth conditional to (1.c), we arrive at (1.a), meaning that (1.c) is true if and only if (1.a) is true. In other words, if it's good that it's raining, then it's good that it's true that it's raining.

This might seem like a circular argument, as it suggests that the value of truth is derived solely from the things we value firsthand, rather than being an intrinsic value. To put it another way:

(3)

The value of truth: If p is good, then it is good that it is true that p.

This raises the question of whether we truly value truth as an abstract concept. Could it not be the case that we do not value truth as such, but that what we really care about are beliefs? Should we not strive to possess true beliefs and avoid false ones?

After all, we make better decisions when our beliefs are accurate. When our beliefs are wrong, it can lead to all sorts of negative consequences. So, perhaps it's not the value of truth as such that we should be concerned with, but rather the value of true beliefs. Let's examine this claim in more detail with a specific example - an instance of a true belief, so to speak:

(4)

It is good that the belief that it rains is true.

If the belief that it rains is true, then this seems to be valueable. But this is not what (4) says. It appears as if (4) is only true if it is good that it is raining - and that has nothing to do with the value of truth or the value of true beliefs, but with the value of rain.

Let’s again have a closer look on some principles that should apply here:

(5)

True beliefs: The belief that p is true iff p.

Applying the principle “True beliefs” to (4), we can derive the following:

(6)

It is good that the belief that it rains is true iff it's good that it's raining.

That's what we already suspected: the supposed value of a true belief consists in the value of what it is about. This can be summarized as follows:

(7)

The value of true beliefs: If it is good that p then it is good that the belief that p is true.

And this shows that true beliefs don’t have value in themselves. It’s the things we value, and not (true) beliefs about them.

There are no controversial assumptions in this discussion, and it is not overly complex. It simply combines value statements with two different forms of the truth conditional without heavy use of logical machinery.

Yet, the conclusions are surprising. Are we willing to accept that neither truth nor true beliefs hold any value in themselves? Contrary to what most of us might assume?