Deontic logic facts for kids

Deontic logic is a special part of philosophical logic. It studies important ideas like what we must do (our obligations) and what we are allowed to do (our permissions). Think of it like a set of rules for how we should act.

In deontic logic, people often use symbols to make these ideas clear.

• OA means "it is obligatory that A." This means you must do A.
• PA means "it is permitted that A." This means you are allowed to do A.

Sometimes, different people (called "agents") have their own duties and permissions. For example, if we say , it means "Adam has an obligation for B to happen." B could even be an action by someone else, like "Bob doesn't crash the car."

What Does "Deontic" Mean?

The word deontic comes from an old Greek word, Ancient Greek: δέον, romanized: déon. This word means "that which is binding" or "that which is proper." So, it's all about rules and what's right.

Standard Deontic Logic (SDL)

One of the most common types of deontic logic is called Standard Deontic Logic (often shortened to SDL). It helps us understand how obligations and permissions work together.

SDL uses a few basic rules:

• Rule 1 (Necessitation): If something is always true (like "2+2=4"), then it ought to be true. This means you can't be told to do something impossible or contradictory.
• Rule 2 (Distribution): If you ought to do A, and A leads to B, then you ought to do B. For example, if you ought to study for a test, and studying leads to good grades, then you ought to get good grades.
• Rule 3 (Permission from Obligation): If you ought to do something, then you are allowed to do it. You can't be forced to do something that's not permitted.

We can also define what it means for something to be forbidden.

• FA means "it is forbidden that A." This is the same as saying "it is obligatory that A does not happen" (). Or, it means "it is not permitted that A happens" ().

What if "Ought Implies Can"?

Some people believe that if you ought to do something, then you must be able to do it. This idea is often called "ought implies can." In logic, this means if something is an obligation, it must also be possible.

Conditional Obligations

Sometimes, an obligation depends on a certain situation. For example, "If you smoke, then you ought to use an ashtray." This is called a "conditional obligation."

It's tricky to write these rules in simple logic. If we just say "If you smoke, then you ought to use an ashtray," it can lead to strange conclusions. For instance, if you do something wrong, like smoking where you shouldn't, the logic might accidentally say you ought to do other unrelated things too.

To fix this, some logicians use a special way to write conditional obligations:

• means "it is obligatory that A, given B."
• means "it is permissible that A, given B."

This way, the obligation (A) only applies if the condition (B) is true.

Other Types of Deontic Logic

There are many other types of deontic logic that try to solve different problems. Some deal with situations where rules might change, or where there are conflicts between rules.

A Brief History of Deontic Logic

People have thought about the logic of rules for a very long time.

• Even ancient Greek thinkers and philosophers in India noticed how ideas like "allowed" and "forbidden" are connected.
• In the 1600s, a famous thinker named Gottfried Wilhelm Leibniz saw that "permitted," "forbidden," and "obligatory" were similar to "possible," "impossible," and "necessary."

Early Attempts and Modern Beginnings

The first person to create a formal system for deontic logic was Ernst Mally in 1926. He tried to use symbols to show how "A ought to be the case" works. However, his system had some strange results. For example, it seemed to say that "A ought to be the case if A is the case," which isn't very useful for telling us what we *should* do.

The first truly useful system of deontic logic was created by Georg Henrik von Wright in 1951. He was the first to use the term "deontic" in English for this type of logic. Von Wright's work was a big step forward, but it also faced new challenges.

For example, "Ross's paradox" showed a problem: If "It is obligatory that the letter is mailed," von Wright's logic could also imply "It is obligatory that either the letter is mailed or the letter is burned." This sounds like it's okay to burn the letter, which isn't right!

Another problem is "Chisholm's paradox." It's hard to make these four statements work together in a simple logic system:

• Jones ought to help his neighbors.
• If Jones helps, he ought to tell them he's coming.
• If Jones doesn't help, he ought not to tell them he's coming.
• Jones doesn't help.

These paradoxes show that creating a perfect system for deontic logic is very difficult!

Jørgensen's Dilemma

Deontic logic faces a big puzzle called Jørgensen's dilemma. It's like a three-part problem: 1. For logic to work, the things we're talking about (like "premises" and "conclusions") usually need to be either true or false. 2. But statements about rules or "norms" (like "Close the door!") don't seem to be true or false. They are commands. 3. Yet, it feels like there are logical connections between these rule statements.

So, how can we have a logic of rules if rules aren't true or false?

People try to solve this in different ways:

• Some say that logic doesn't always need things to be true or false. It can still show how ideas connect.
• Others say that while a command itself ("Close the door!") isn't true or false, a statement *about* the command ("It is obligatory to close the door") *can* be true or false. This is how Standard Deontic Logic works.
• A third option is to say there simply isn't a logic for rules, but most philosophers disagree with this.

See also

• Deontological ethics: A type of ethics that focuses on duties and rules.
• Imperative logic: Logic that deals with commands.
• Modal logic: A broader type of logic that deals with possibility, necessity, and other "modes."
• Moral reasoning: How we think about right and wrong.
• Norm (philosophy): A rule or standard of behavior.