To Do or To Not Do?
The meaning of not doing something
🧠 What It Means to Not Do Something
—or, the surprisingly complex world of nothing happening on purpose
Let’s begin with a humble sentence that could appear in court testimony, therapy sessions, or on your passive-aggressive roommate’s whiteboard:
“He didn’t do it.”
Sounds simple, right? But hang on. Did he (1) not do it because he wasn’t able to? Because he chose not to? Because he forgot? Because someone else got there first? Or because it never occurred to him?
Welcome to the deceptively thorny philosophical territory of not-doing—a phrase that looks like empty space but is teeming with implications. Today, we’re going to untangle the logic behind “did not do” using formal tools, and maybe a few informal winks.
The Problem with Not Doing
In casual language, did not do can mean several very different things:
Neutral absence: The thing simply didn’t happen.
Intentional refraining: The agent actively chose not to do it.
Failure to act: They were supposed to, but didn’t.
Lack of ability: Poor soul never had a chance.
In philosophy and logic, this ambiguity is deeply unsatisfying. (Philosophers, you’ll have noticed, are the kind of people who get itchy if two meanings share a toothbrush.)
To fix this, we need a formalism that lets us separate the couldn’t, the wouldn’t, and the should’ve but didn’t. And for that, we bring in the star of our show:
👀 Enter: STIT Logic
STIT stands for "See To It That" logic—pronounced like you're shushing someone ("shhh-TIT"), but more judgmental. It was designed to reason about agency: when people actually do things, and crucially, when they choose not to.
In STIT logic, we write:
[a stit: φ]
This means: Agent a sees to it that φ happens. It’s like assigning credit (or blame) for a result. Not just “φ happened,” but “a made φ happen.”
So how do we say “did not do φ”? Easy:
¬[a stit: φ]
Translation: Agent a did not see to it that φ. That’s our basic “did not do”—but we can now get precise about why they didn’t.
🎭 The Many Faces of Not Doing
Let’s look at a few common disambiguations, dressed up in logic but friendly in spirit.
1. Didn’t Do and Didn’t Care
Your average passive bystander.
¬[a stit: φ]
They didn’t make φ happen. That’s it. Maybe φ happened anyway, maybe it didn’t—but agent a wasn’t involved. Could be laziness, could be indifference. Could be napping.
2. Could’ve Done It, But Didn’t
This is refraining. Often called “omission with options.”
¬[a stit: φ] ∧ ◊[a stit: φ]
Agent a refrained from φ, even though they could have. The moral philosophers start warming up here. Did they mean not to? Are they responsible? This is where free will and popcorn enter the conversation.
3. Should’ve Done It, But Didn’t
This one stings. It’s the logical form of a disappointed parent.
O([a stit: φ]) ∧ ¬[a stit: φ]
Agent a ought to have done φ—but didn’t. This isn’t just refraining; it’s failure. Or to put it formally: an act of deontic delinquency. (Say that out loud at parties to sound intimidating.)
4. Didn’t Do It, and That’s a Good Thing
A righteous inaction!
¬[a stit: φ] ∧ O(¬[a stit: φ])
Agent a correctly refrained from φ because refraining was required. This is your moral hero—who heroically did nothing. (Honestly a great role model for social media.)
5. Didn’t Do It—Because They Couldn’t
Now we’re into excused inaction territory.
¬[a stit: φ] ∧ ¬◊[a stit: φ]
Agent a didn’t do φ, but also had no choice in the matter. They were locked out, overruled, unconscious, or existentially irrelevant. You can’t blame someone for not painting the Sistine Chapel if they were never in Rome.
Why This Matters
“Did not do” isn’t just a philosophical toy—it plays a role in ethics, law, AI responsibility, and even daily life:
Did the AI fail to alert the pilot, or was it never designed to?
Did the officer choose not to intervene, or were they unable to?
Did your partner forget your birthday, or did they decide to ignore it?
These aren’t just semantic quibbles. They’re at the heart of moral and legal accountability.
📌 TL;DR
“Did not do” could mean:
✅ wasn’t involved
✅ didn’t want to
✅ failed in duty
✅ couldn’t
✅ refrained nobly
To make this precise, we use STIT logic to distinguish among them using combinations of:
[a stit: φ] (agent did it)
¬ (not)
◊ (can do)
O (ought to do)
So next time someone says, “I didn’t do it,” pause. Don’t yell. Instead, raise an eyebrow and calmly ask:
“Yes, but was it a permissible omission, a dereliction of duty, or merely a case of modally foreclosed agency?”
(Then run, because they will either be confused or throw something.)
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