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Your Nibling Knows the Logic of Decision-Making: Visualizing Beyond Obligation

Posted in logic, math, philosophy, and reasons

Description: We can solve problems around all-or-nothing thinking and paradoxes around actions above and beyond the call of duty. To do so, we need to learn the logic of reasons and decision-making.

Estimated reading time: 12:14 (238 wpm)
Estimated reading time range: 8:31 (342 wpm) to 21:43 (134 wpm)

cw: abuse, gaslighting, immersive description of life-or-death dilemma

Shoulda

I had an abusive roommate seven years ago. One common tactic she used to wear me down was to always convince me I wasn’t doing enough. For any thing I was doing (e.g. taking a break after class), wasn’t there something else I had more reason to do (e.g. using my time to finish assignments due later this month)? In some sense, she had a point. I didn’t know how to defend myself against these arguments.

I want to make a clear disclaimer first. Coming up with ways to point out flaws in arguments from gaslighters is not always going to be the most effective way of resisting them. But there are many cases where learning these flaws can and, in my experience, has helped. Many people fall into traps in thinking about what they have a reason to do, with or without an external, active abuser. Sometimes we give ourselves funny, frustrating ideas we have a hard time shaking off our tail.

In this post, I’ll be talking about two problems people often face. The first problem is “in for a penny, in for a pound” mentality and how people defend this sort of mentality. The second problem is the reasoning behind always trying one’s hardest and never chilling out. This problem is sometimes known as a paradox of supererogation.

That last one sounds technical and complicated. But take a moment to imagine a nibling of yours—a child of your sibling or cousin. Niblings can be any age, with any background. And yet the nibling you have in mind probably already has the tools to solve both of these problems. They are tools we intuitively gain from a very young age. I’ll make those solutions generalizable and visually accessible so we can use them to avoid making mistakes in general.

First Problem: Static All or Nothing

Each day is a list of tasks that can be quite daunting. An ideal morning involves getting out of bed, taking a thorough shower, and so on. But what if you don’t want to go through the trouble of taking a thorough shower? Then it’s easy to fall into the trap of not making effort to do anything at all. After all, it feels like you’ll fail either way.

If this sounds familiar, you may have a thinking pattern characterized by the following:

  • All-or-nothing thinking.
  • Seeing the threshold of permissibility as static.

It’s easy to have a gut feeling there’s something wrong with this all-or-nothing approach. It’s hard to dig out of this way of thinking without an alternative. I will offer that alternative.

An Alternative: Dynamic All or Some or Nothing

The solution is to note that these properties—obligation and permissibility—can be broken down.

They’re made up of reasons. Linguists and philosophers think we already naturally and unconsciously grasp this. Sometimes, but not always, we consciously think in terms of reasons. “Does that have more pros and less cons than the alternative? Do I have more reason to play this move or that move?”

What I am proposing is we deliberate this way explicitly, with visual aids.

Reasons for action that can weigh against one another explain how obligations and permissions work. What exactly is going on when I should go to bed rather than play a video game like Infinifactory some more? Well, I have stronger or heavier reasons in favor of going to bed than playing some more. I shouldn’t keep playing, because my reasons are weaker there!

So as a first pass, we get something like this:

  • An action is obligatory only if it has the most reasons counting in favor of it. We weigh the pros and cons, and the obligatory action has the most pros over cons.
  • An action is impermissible only if there’s another action with more reasons in favor of it. We weigh the pros and cons. Once we find some action has more cons than another action, we think “Okay, we shouldn’t do that then!”
  • An action is permissible if and only if it isn’t impermissible.

So even when we do what we shouldn’t do, there are still some actions we have more reason to do than others.

We can visualize and work with obligation really well when we see this property as composed of reasons. One heavy reason to sleep is I’m sleep deprived and it would prevent any long-term damage to my health. One light reason to sleep is sleep feels nice, and I’m in the mood for it, regardless of my health.

One light reason to play Infinifactory is it’s relaxing to play. Another light reason to play Infinifactory is there’s a competitive element, and it feels good to beat my peers. We can represent this with a scale, with a line showing where the lowest scale goes. That line represents the threshold for what an agent is allowed to do. Anything above the line, I don’t have enough reason to do. Anything below the line, I do! In this case, I shouldn’t play Infinifactory—the reasons to sleep outweigh the reasons to play Infinifactory!

Seeing the decision this way explicitly is helpful.

First, this makes it clear our obligations aren’t a static list of commandments. There is no “thou shalt sleep at 9pm.” Instead, we should be sensitive to what reasons for actions there are around us, including how many spoons 44 we have for the day. If we wake up and have fewer spoons than usual, that’s a reason to do less than we might’ve otherwise done.

People often get in the habit of internalizing a static rules for life, and often follow these rules even in cases where it would be unhealthy for them. But obligation and permissibility break down into reasons. So we have a dynamic list of things to do which depends on how many spoons we have, what the situation is, and so on.

Second, this makes it clear acting reasonably is not all or nothing! Say you do something impermissible. Plenty of people then find themselves with a “in for a penny, in for a pound” mentality. But it’s important to remember that between various impermissible actions we have, we can still have stronger reasons to decide to do some than others! We can still deliberate between the best action we’re willing to do!

There are many cases in which it’s important to resist the “in for a penny, in for a pound” mentality many of us are prone to. We often feel as if we’ve crossed a line that puts us in a different mode of decision-making. But we should continue weighing reasons even if we really are only willing to choose between impermissible actions!

This can help people who need to a reminder. Only somewhat taking care of themselves is an option.1 Taking a haphazard shower is better than no shower at all.

Or someone may cheat on a promise they made with their roommate to not go out during a pandemic. They don’t sufficiently protect themselves, contract a disease, and then hide it from their roommate. People contract and hide transmissible diseases they have all the time in this fashion.

There are many interesting factors behind why people end up doing this. But part of what helps people get out of the trap of building on their mistakes with more mistakes is thinking in terms of reasons.

In this case, certainly, I have much more reason to not cheat on a promise than to cheat on a promise…

Visualization of reasons for and against cheating being weighed.
Image description linked here.

…but I have more reason to cheat on a promise safely than I have reason to cheat on a promise unsafely.

This means if I’m only willing to do one of these two actions, I should cheat in a way that doesn’t get anyone sick.

Explicitly working with reasons and weighing them against each other has other advantages too, which I’ll discuss in a future post.

Second problem: Trying your hardest

The second problem occurs when people start to think about actions that are above and beyond the call of duty. Actions you don’t have to do, but have more reason to do than the other options. Such actions are often called ‘supererogatory.’

If we should do whatever we have most reason to do, it sounds like we should always try our hardest. On this view, any time we do anything less, we’re doing something we shouldn’t do.

Comic about trying your hardest.
Image description linked here.
Credit: Sarah’s Scribbles.

Once you think just in terms of reasons, everything you’re doing can seem wrong. Because isn’t there always something you have more reason to do than what you’re doing now?

So we have the following paradox! Reasons and their weights alone provide no room for actions being above and beyond the call of duty. But to the contrary, it seems like someone running into a burning building to save someone’s life is going above and beyond the call of duty. They’re not obligated to risk their life like that, it’s just better that they did.

We can make this problem clearer. Consider three choices you can make when you see the burning, collapsing building. Your digital clone pipes up from your backpack, “I’ve run the calculations. If you run in there, you’ll have to press a polka-dotted or a striped button, equal effort and risk each. Then, the burning will collapse in a way that will probably crush both of your arms, and may kill you. The polka-dotted button has a high chance of saving a person you hear ramming their horns against the door , and the striped button certainly saves two people you hear clucking from the building.”

Now, it’s well beyond your duty to have to lose your arms and risk your life to save others. If you did, you’d be a hero, but heroic actions are actions above and beyond the call of duty.

But notice something interesting. Say you see the two people you could save on the side of the building. One leans out the window desperately holding onto the other, who’s flailing and kicking wildly, feathers coming off and falling down below. You muster up your courage and run in.

You have a choice. You hear the person you could save by pushing the polka-dotted button, bellowing and roaring. You hear the two you could save with the striped button squawking more and more desperately. You can push the polka-dotted button to maybe save one. You could have used the exact same amount of effort at the same risk to push the striped button and guarantee saving two people. Pushing the polka-dotted button doesn’t seem like the right choice here.

Notice the issue. How do we make:

  • staying outside and watching the flames permissible,
  • running inside and maybe saving the one whose loud footsteps you hear behind the door impermissible, and
  • running inside and saving the two whose eyes and beak you see twisted in effort and distress above and beyond the call of duty?

Let’s really spell out the paradox here. Say you have as much reason to stay outside as you have reason to save maybe one. Then, either you have more reason to save two people than to stay outside, or you have equal reasons between the two actions. If you have more reason to save two people, how is staying outside obligatory? If you have an equal number of reasons to stay outside and to save two people, how is saving maybe one impermissible?

To make this easier to visualize, see the table below. ~ between two actions shows that either action is permissible. > between two actions shows that one should do one action over the other. This is saying that in a pairwise choice between doing nothing and saving two people, either action is permissible. Between doing nothing and saving maybe one, either action is permissible. But between saving two people and saving maybe one, you should save two people.

Do nothing~Save two people
>
Do nothing~Save maybe one

To solve this problem, we need to recognize a property other than reasons. Where reasons favor, justify, and require actions, we need a property that only justifies actions. We can call these justifiers so it’s easy to remember. Justifiers don’t favor or require an action at all, so on the scale, they don’t pull the scales down to the red line. However, if you have enough justifiers, you can justify an action that you have less reason to do.

A good way to imagine this is little weightless blocks that attach to the underside of the scales. Attach enough of them, and you’re now dipping past the red line of permissibility.

To make this a little more concrete, imagine the unit of measurement for reasons is kilograms. Each reason-block is a kilogram, which weighs down the scale by an inch. So, if you put two reason-blocks, the scale goes down by two inches. We’ll assign some arbitrary weights in this example to deepen our understanding. Each justifier-block is an inch tall. Let’s say you have:

  • One kilogram of reason to stay outside and do nothing.
  • Three kilograms of reasons to run inside and save maybe one person.
  • Five kilograms of reasons to run inside and save two lives.
  • Six inches of justifiers to stay outside and do nothing.

So, between doing nothing and saving maybe one, we have more reason to save maybe one by a margin of two kilograms. The scale weighing saving maybe one is pushed down by three inches, and then only pulled up by one. The reasons and justifiers for staying outside reach down by a gross total of seven inches, which reaches past the line of permissibility.

Anything that can dip down below that line is permissible. But these justifiers don’t pull the scale down. So doing nothing is permissible, but not obligatory. Saving maybe one is still permissible. In fact, it would be preferable over doing nothing since there are more reasons for it.

Between doing nothing and saving two people, we have more reason to save two people by a margin of four kilograms. But even here, the justifiers are still reaching past the line of permissibility. There would have to be more reasons on the save two people scale before it became obligatory.

Visualization of reasons for doing nothing and saving two people.
Image description linked here.

Here, even with all the extra reasons to run into the building, it’s still permissible to do nothing and not risk one’s life or arms. It’s a closer race now—with enough additional reasons to run inside, you’d have a duty to run in. But for now, it’s still permissible to hang outside. Even so, it sure would be great if you did run inside and saved two people!

Finally, there’s the pairwise comparison between saving two people and saving maybe one. Here, the reasons for saving two people outweigh the reasons for saving maybe one by a margin of two kilograms.

Straightforward. Saving two people is pushing the line of permissibility down too far for saving maybe one to reach!

Keep in mind again that I assigned arbitrary weights for concreteness. This isn’t meant to represent genuine comparative measurements between these actions.

So once we make it explicit for our second pass:

  • An action is obligatory if and only if there are:
    • greater reasons for it than justifiers and reasons for all alternatives.
  • An action is impermissible if and only if there are:
    • fewer justifiers and reasons for it than reasons for some alternative.
  • An action is permissible if and only if there are:
    • greater justifiers and reasons for it than reasons for all alternatives.
  • An action is supererogatory, or above and beyond the call of duty, if and only if there are:
    • greater reasons for it than reasons for permissible alternatives, and
    • fewer reasons in for it than justifiers and reasons for some alternative.

By making the situation concrete, we can see introducing justifiers into our visualization helps us make sense of how it’s possible that:

  1. Saving two people is required over saving maybe one.
  2. Saving two people is better than doing nothing.
  3. Both saving two people and doing nothing are permissible.
  4. Saving maybe one is better than doing nothing.
  5. Both saving maybe one and doing nothing are permissible.

Conclusion

As I mentioned before, I had an abusive roommate. She gaslit me for years into thinking I was always doing something wrong. To this day I have to remind myself how reality works: we don’t always have to try our hardest.

We don’t have a culture that gives us a lot of tools to understand we don’t always have to try our hardest. So, I’ve met many others who face this problem. Among people in certain religious denominations, I’ve seen even more of a tendency to be this way. The mentality and culture behind the phrase “What would Jesus do?” drives people to go above and beyond recklessly. But Jesus earned so much reverence precisely because what Jesus did was much more than They had to!

I’ve taught this to many people. So I know what understanding the logic of reasons and getting used to visualizing it in one’s everyday life does. It helps improve well-being and ability to take care of oneself. It’s another cognitive tool in your arsenal you can use when you feel like you always have to fulfill a static list of commandments or give up. When others make you feel like you need to always risk your well-being for others, or when you make yourself feel that way.

I hope this helps!

The rest of the series

I made this series (and this blog) with a set of goals.

  • To give people the logical tools they need to deal with very common problems.
  • To resist pessimism about people’s ability to deal with those problems.
  • To generalize from what most of us already know to help deal with those common problems.
  • To enter into the Summer of Math Exposition 1 (SoME1) competition.

Here is a link to the rest of the series.

Endnotes

  1. In many cases where someone can’t find it within themselves to do something for their own well-being, they actually aren’t doing anything unreasonable. Perhaps they have a reason to conserve some spoons for later or perhaps they simply currently aren’t able to do the thing. Thinking in terms of reasons is only a genuine antidote to cases where someone:
    • is acting against their own well-being,
    • has the ability to do otherwise, and
    • has more reason to do otherwise.

Further resources

  • While just about all of the visualizations are original, and correspond to what I saw in my head when I first studied the logic of reasons, nearly all of the raw information can be found in Daniel Muñoz’s “Three Paradoxes of Supererogation.” There’s much more in that paper I find worth reading, along with the sources therein. 🙂
  • cw for discussion of sex
    Regarding the many complicated factors behind transmissible diseases being undisclosed, a good example of some stuff we know on the matter is in Phil Hutchinson and Rageshri Dhairyawan’s philosophy and science paper, “Shame and HIV: Strategies for addressing the negative impact shame has on public health and diagnosis and treatment of HIV.”

Acknowledgments

Thanks so much to The_Passenger_, insurgentrat, Olivia Roberts, L Morden and Lani Franz-Kindred for their thorough and helpful notes and questions.

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