What Does 'Or' Really Mean? The Logic of Choices
A Fork in the Road: The Everyday ‘Or’
Imagine you finish your homework and your dad says, “You can watch a movie or play video games.” What do you think he means? Probably that you can pick one, but not both. And you assume he doesn’t know which you’ll choose. The little word “or” seems to carry a lot of hidden information.
Philosophers and logicians have spent centuries trying to figure out what “or” really means – and whether the rules of logic match the way we actually use it. The story involves future sea battles, fuzzy boundaries, free ice cream, and a debate about what we say versus what we mean.
The Logic of ‘At Least One’: Classical Disjunction
To a logician, “or” – called disjunction – is a tool for combining two statements. In classical logic, the meaning of “or” is simple: the whole sentence is true if at least one part is true. If both parts are true, it’s still true. This is called an inclusive or.
We can picture this with a truth table, a chart that shows all possible combinations. If A is “you watch a movie” and B is “you play video games”, the table looks like this:
- Both true: “A or B” is true
- A true, B false: true
- A false, B true: true
- Both false: false
This seems straightforward. But you might already see a problem: in real life, if your dad says “you can watch a movie or play video games,” would he be happy if you did both? Probably not. The logical “or” allows both, but everyday “or” often suggests “not both” – an exclusive or.
Logicians also accept certain ironclad rules. One is the law of excluded middle: for any statement A, “A or not A” is always true. Either it’s raining or it isn’t. Either you have a pet dog or you don’t. This rule seems undeniable. But is it always?
Grice’s Idea: What We Say vs. What We Mean
The philosopher H.P. Grice (1913–1988) had a clever solution to the gap between logical “or” and everyday “or”. He argued that the literal meaning of “or” is just the inclusive one. The extra ideas – “not both” and “I don’t know which” – arise from general rules of conversation, not from the word itself.
Grice pointed out that conversation is a cooperative game. When someone speaks, we assume they are trying to be informative, truthful, and relevant. If your dad knew you could have both, he’d probably say “you can watch a movie and play video games.” Since he didn’t, you infer he doesn’t want both to happen. That inference is an implicature – something hinted at but not literally said.
The proof: you can cancel these extra hints without contradiction. Imagine your dad adds, “In fact, you can do both if you finish the movie early.” That doesn’t feel like he’s changing the meaning of “or” – just the unspoken hint. Grice’s view became hugely influential, showing that much of what we “hear” in language is actually pragmatics, not pure logic.
When ‘Or’ Breaks the Rules: Vagueness and the Future
Even if Grice solved the everyday puzzle, deeper problems with “or” remained. One of the oldest comes from Aristotle (384–322 BCE). He asked: is the statement “There will be a sea battle tomorrow” true or false now? If it’s already true, then the battle seems fated to happen; if false, it’s fated not to. But the future feels open. Aristotle suggested that perhaps such statements are neither true nor false – violating the principle of bivalence, which says every statement must be either true or false.
Centuries later, logicians developed systems where statements could be “neither” or “both” or have truth-values on a scale. In some, the law of excluded middle fails: “A or not A” isn’t always true, because if A is neither true nor false, the whole disjunction may be undefined. The Polish logician Jan Łukasiewicz (1878–1956) created three-valued logic partly inspired by Aristotle’s puzzle.
A modern version of this appears with vague words like “tall”. If someone is exactly 170 cm, is the statement “She is tall or she is not tall” clearly true? It seems true, but some philosophers use supervaluationism to explain: they say “A or not A” is supertrue (true on every precise way of drawing the line), even though neither “A” nor “not A” is supertrue individually. So the law of excluded middle can be saved, even when bivalence fails. These debates show that the simple word “or” forces us to think about the nature of truth itself.
Free Choice: The ‘Or’ That Gives Permission
A more recent puzzle about “or” comes from permission sentences. Imagine a sign in a park: “You may swim or fish in the lake.” You’d naturally think you’re allowed to swim and you’re allowed to fish. But that doesn’t follow from the standard logical rules of “or”. In deontic logic (the logic of permission and obligation), “You may do A or B” does not automatically mean “You may do A and you may do B”. Yet we all infer that.
This is called the free choice effect. If we add it as a logical rule, paradoxes pop up: from “You may swim” we could deduce “You may swim or fly to the moon” (by a valid logical move called addition), and then by free choice, “You may fly to the moon” – nonsense. So philosophers had to find another way.
Some, like the contemporary linguist Thomas Ede Zimmermann, argue that “or” itself carries a modal meaning: it says that each option is possible. Under this view, “or” doesn’t just combine truth values; it opens up alternative possibilities. More recent alternative-based semantics treats a disjunction like “swim or fish” as generating two separate options, and the permission word “may” applies to each individually. This neatly explains free choice without making absurd predictions. The debate is still lively.
So What? Thinking About ‘Or’ in Your Own Life
You might not be a logician, but you use “or” dozens of times a day. Every time you make a plan, describe a rule, or even just wonder about the future, you’re relying on the logic of disjunction. Understanding the hidden complexity of “or” can make you a sharper thinker and a more careful communicator.
When your friend says, “We’ll go to the park or the pool,” do you assume both are possible? Do you think they know which? Are they offering you a choice or just stating what might happen? Philosophy trains you to hear these subtle signals. And when you hear promises like “You’ll get cake or ice cream,” knowing about free choice might even prevent a tantrum.
The word “or” might be tiny, but it carries a world of meaning – and centuries of arguments. Next time you face a fork in the road, you’ll know the philosophers are standing right beside you.
Think about it
- If you say “I’ll do my homework or watch TV,” do you think you’re breaking your word if you end up doing both? Why or why not?
- Can a statement about someone’s future, like “They’ll be a parent one day,” be definitely true or false right now? Why might it matter whether we think so?
- If a sign says “You may eat an apple or a banana,” and you eat both, have you followed the rule? What might your answer tell us about how rules work?
