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My daughter asked whether a square circle could exist on another planet. How do I answer?

Thamarai Raman Fellow
· 4 replies
Possibility & necessityAnalyticSaul Kripke#logical-necessity#metaphysical-necessity#philosophy-for-children#physical-necessity
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Its coordinates: 1.6 Modality · 1.6.1 Possible Worlds

My nine-year-old has decided that "anything could be true somewhere in space". Last week it was square circles, this week it is a planet where two and two make five. I said no, and she asked why a planet with no gravity is fine but a planet with square circles is not. I did not have a good answer.

I have been reading a little and I gather philosophers separate different kinds of "could". Something like:

  • things that are impossible because of logic or meaning (a married bachelor),
  • things that are impossible because of what something is (water that is not H₂O?),
  • things that are impossible because of the laws of physics (going faster than light).

Is that roughly right? And how would you explain the difference to a child without it turning into "because I said so"? I am especially stuck on the middle kind. Why can't water be something else, if a scientist had to discover what it was made of?

I would like an answer I can actually use at the dinner table, but I also want to understand it myself.

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4 answers

Accepted answer

  1. Tomasz Szewczak

    ✓ Accepted answer Fellow

    Your list is right, and it is the most useful distinction in this whole area. Here is the version I give beginners, simplified.

    Logical impossibility: the description cancels itself. A square circle is a shape with corners and without corners. You don't need to go to another planet to check; there is nothing there to look for, because the words have already contradicted each other. Same for 2 + 2 = 5 once you fix what the numerals mean.

    Physical impossibility: the description is coherent, but our universe's laws rule it out. A planet with no gravity, or a rocket faster than light, is something you can describe without contradiction. Physics just says it won't happen here. Different laws, different verdict.

    Metaphysical impossibility is the strange middle case. The idea, which Kripke made famous, is that once you have found out what water is, a stuff with a different chemistry would not be water at all, just something that looks like it. So "water that is not H₂O" is not a contradiction in the words (people said it for centuries without contradicting themselves), but it is still not a way water could be.

    For a nine-year-old: logic is about whether the sentence makes sense, physics is about the rules of our universe, and the middle one is about what a thing really is underneath its looks.

Other answers

  1. Vikram Sethi

    Fellow

    Teacher's trick that works with my students: for each "impossible" thing, ask "what would you need to change to make it happen?"

    Faster than light: change the laws of physics. Possible in a story, so physical impossibility.
    Square circle: there is nothing to change except the meaning of the words, and then you are not talking about squares any more. Logical.

    Children are surprisingly good at feeling the difference between "change the world" and "change the words".

    Helpful · 1
  2. Lars Eriksen

    Fellow

    A small caveat from physics for the dinner table: physical impossibility is only as firm as our current laws. Faster-than-light travel is ruled out by relativity as we understand it, and I would bet heavily on that, but it is a different kind of confidence from the square circle. Nobody will ever revise their way to a square circle. So your daughter is half right: there may be things we now call impossible that turn out to be fine somewhere, but only in the physical column.

    Helpful · 2
  3. Thamarai Raman

    Fellow

    Vikram's "change the world or change the words" worked. She thought for a while and said the square circle is "a word mistake, not a space mistake". I'll take it. The water one I am still chewing on myself, so I may be back.

    Helpful · 3