Could There Be a Purple Elephant? Ruth Barcan Marcus Says No
The Night the Morning Star Became the Evening Star
You learn in school that the Morning Star and the Evening Star are the same thing: the planet Venus. For a moment it feels like a trick — how can one object be called two different names? Did Venus have to turn out to be Venus, or could it have been a completely different star? That’s not just a question for astronomers. It’s a question for logicians: what makes a name stick, and when is something necessarily true?
Ruth Barcan Marcus (1921–2012) spent her career answering those puzzles. She was a philosopher and mathematician who built the first full systems of modal logic for quantifiers — the part of logic that handles words like “must” and “might.” While other thinkers were afraid that mixing “possibly” and “all” would break logic, Marcus dove straight in. Her proofs, her big debates with Willard Van Orman Quine, and her fierce belief that only actual things exist changed the way we talk about names, necessity, and possibility.
Why Two Names for Venus Can’t Point to Different Planets
In 1947, as a young PhD finishing her dissertation at Yale, Marcus published a proof that still startles people. She asked: if two terms — say “Hesperus” and “Phosphorus” — refer to the exact same individual, does that identity have to be true in every possible situation? Her answer was yes.
She distinguished two kinds of sameness. Material identity means two things share all their actual properties — everything true of one is true of the other right now. Strict identity (what we normally just call identity) requires something stronger: that they must share those properties, no matter how the world could have been different. Marcus proved that in strong enough modal systems, material identity and strict identity are equivalent. That means if Hesperus and Phosphorus are identical in the actual world, they are necessarily identical — there’s no possible world where they split apart.
This wasn’t just a puzzle about the stars. It meant that once you fix what an object is, you can’t imagine a world where that thing is a different thing. The necessity of identity became one of the pillars of modern metaphysics, and Marcus had proved it before many of her famous colleagues were even writing about it.
Names Are Just Sticky Notes
So how does a name like “Hesperus” manage to be necessary? Marcus offered a simple picture: tags. A proper name, she said, “has no meaning. It simply tags.” While many philosophers at the time thought names were hidden descriptions (like “the brightest object in the evening sky”), Marcus argued that ordinary names work more like a direct label you stick on an object.
If “Hesperus” and “Phosphorus” are both tags for Venus, then the sentence “Hesperus is Phosphorus” doesn’t report a surprising discovery about two descriptions that happen to match up. It records that the very same taggable thing wears both tags. And since a thing is always itself, the identity couldn’t have been otherwise. That cleared up a famous puzzle: why substituting one name for another inside a “must” claim doesn’t cause logical trouble, but substituting a description like “the number of planets” does. Descriptions can pick out different objects in other possible worlds; tags cannot.
Marcus refined this tag idea over decades, anticipating the direct-reference revolution that would later sweep through the philosophy of language. By the 1970s she welcomed the causal picture of names advanced by Saul Kripke, but the core insight — that a name doesn’t come with a built-in definition — had been hers all along.
The Rule That Keeps “Might” From Making Up New Things
If you say “There could have been a purple elephant,” does that mean a possible-but-not-actual purple elephant exists somewhere in a shadow universe? Marcus thought that idea was a mistake — the kind of bloated unreality that turns logic into fantasy. Her earliest papers, written in 1946 while she was still Ruth C. Barcan, included a principle that would later be named the Barcan formula. In plain language it says:
If it is possible that there exists something with a property P, then there actually exists something that possibly has P.
At first glance that seems strange. Suppose no real elephant is purple. Is it still possible that a purple elephant exists? The Barcan formula demands that there be an actual thing that is possibly a purple elephant — maybe an ordinary elephant that could have been dyed. But if no actual elephant or proto-elephant can play that role, then the statement “It is possible that a purple elephant exists” would be false.
Marcus took this rule seriously because of actualism — the view that only real, actual things exist. Merely possible objects, like unicorns or the golden mountain, don’t exist anywhere; talk about them is talk about properties of actual things. When logicians built models with different sets of objects for different possible worlds, Marcus objected. The Barcan formula forces the set of objects to stay the same across all worlds, so you can’t smuggle in new entities just by saying “might.” It’s a tough restriction, but for Marcus it kept logic honest about reality.
The Big Quarrel Over “Must”
No one pushed back harder than Willard Van Orman Quine (1908–2000), the most influential American philosopher of his time. Quine thought that adding modal operators to logic created a swamp of confusion: problems with substitution, mysterious commitments to “essences,” and ontologies full of shadowy intensional entities. He originally misread Marcus’s identity results and later, even after correcting the record, remained deeply skeptical.
Marcus didn’t retreat. She argued that Quine’s attacks bundled together very different kinds of intensional talk — belief, quotation, necessity — and dumped them all onto one “referentially opaque” shelf. That, she said, simply ignored the richness of the world. Scientists speak of essential properties all the time: gold must dissolve in aqua regia; a sample of gold cannot lose that disposition without ceasing to be gold. That’s not ancient mysticism (Quine called it “Aristotelian essentialism” as an insult); it’s built into how we carve nature into kinds.
She also countered Quine on names. Where Quine claimed we could always swap ordinary names for descriptive phrases, Marcus insisted that real names act as tags, capable of plugging into modal sentences without any twistiness. Her confidence in logic — “I for one have no aversion for any kind of logic” — stood firm against Quine’s dismissal of modal systems as philosophically useless. Their duel pushed both sides to sharpen their arguments, and it still shows up in textbooks.
Why Possibility Still Puzzles Us
Marcus didn’t stop at names and possible worlds. Later in her career she tackled moral dilemmas — situations where any choice you make leaves a genuine obligation unmet — and argued that a consistent ethical code doesn’t need to erase those conflicts. She also challenged the idea that believing something requires squeezing it into a sentence. Infants and animals have beliefs, she pointed out; rationality is about coherent action, not just tidy sentences.
Today, modal logic is everywhere: from computer scientists verifying that a program must terminate, to philosophers analyzing what it means to be a person across possible lives. Marcus’s rulebook for “might” and “must” keeps the conversation grounded — when you imagine a world where you skipped dessert, you’re still talking about your actual self, your actual family, your actual kitchen. No ghostly alternate you has to pop into being.
That purple elephant you imagined at the beginning? It never existed. It never needed to. And you can still talk about it perfectly well.
Think about it
- If you name your pet “Biscuit,” does that name describe the pet, or is it just a tag like a sticky label? Could you have given the same animal a completely different name without changing who it is?
- Some people say there are possible worlds where you are a superhero, or a pirate, or a famous singer. Do you think those versions of you actually exist somewhere? Why or why not?
- When a scientist says “Gold must dissolve in aqua regia,” is that the same kind of “must” as when your parent says “You must clean your room”? If not, what is the difference?
