Does Math Objectively Exist, or Is It a Human Creation? A New PBS Video Explores a Timeless Question

in Math, Philosophy | June 5th, 2013

In a famous scene from Boswell’s Life of Samuel Johnson, the biographer and his subject come to discuss the bizarre theories of Bishop Berkeley, who posited that everything is immaterial—nothing has any real existence; it’s all just ideal concepts held together by the mind of God. If God should lose his mind or fall asleep or die, everything would fall to pieces or cease to exist. Boswell insists there’s no way to refute the idea. Johnson, kicking a large stone with such force that his foot rebounds, cries, “I refute it thus.”

Johnson’s little demonstration doesn’t actually refute Berkeley’s radical idealism. It’s a conundrum still with us, like Plato’s Euthyphro stumper, which asks whether the rules governing human behavior exist independently of the gods, who simply enforce them, or whether the gods make the rules according to their whims. In other words, is morality objective or subjective? A similar problem occurs when we consider the existence of the rules that govern physical laws—the rules of mathematics. Where does math come from? Does it exist independently of human (or other) minds, or is it a human creation? Do we discover mathematical problems or do we invent them?

The question has engendered two positions: mathematical realism, which states that math exists whether we do or not, and that there is math out there we don’t know yet, and maybe never can. This position may require a degree of faith, since, “unlike all of the other sciences, math lacks an empirical component.” You can’t physically observe it happening. Anti-realists, on the other hand, argue that math is a language, a fiction, a “rigorous aesthetic” that allows us to model regularities in the universe that don’t objectively exist. This seems like the kind of relativism that tends to piss off scientists. But no one can refute either idea… yet. The video above, from PBS’s Idea Channel, asks us to consider the various dimensions of this fascinating and irresolvable question.

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Josh Jones is a writer and musician based in Washington, DC. Follow him at @jdmagness

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Comments (12)

  1. Laroquod says . . .
    June 5, 2013 / 6:30 am

    Is there any way you could STOP republishing every recent article, every day? Every day I go to check my RSS, and every single Open Culture article has been republished into the feed, even the ones I’ve read before. So even if you only published one article today, I have to flip through 20 Open Culture entries today in order to find that single new article. The other 19 are all reposts (updates? refreshes? it matters not) of all of the previous posts I have already read this week. Some of your articles crop up as ‘fresh’ in your RSS feeds literally a dozen times.

    This is a great site and all, but seriously it’s not THAT great that I should wade through 95% reposts every single day. It all adds up to a giant waste of time. RSS is difficult enough to manage without you reposting *everything* *every* *day*.

    So, to sum up: RSS, you are doing it wrong. You are doing it very, very wrong. Thank you for your attention. I give it about a week or two before my patience finally gives with your RSS feed. Maybe I will follow your Twitter account instead. (Of course I hardly ever read Twitter so you should not take this as a good alternative.)

  2. Sha says . . .
    June 5, 2013 / 6:53 am

    In reference to RSS: I don’t have this problem with my RSS reader. Something else may be going on?

  3. JCA says . . .
    June 5, 2013 / 10:16 pm

    My RSS feed always displays 2 of the same article. Which means the list is twice is long for the same thing. I agree with Laroquod — something is the matter.

  4. Rebecca W says . . .
    June 6, 2013 / 6:44 am

    What rss reader do you use? I recently switched to Feedly and have had good luck. I also like the optional magazine format.

    PS: To the webmaster: Could you enable the options on comments for “notify me of new comments on this post” AND “notify me of new posts by email”. Thanks!

  5. Brannon says . . .
    June 6, 2013 / 8:29 am

    This reminds me of the argument that Stephen Hawking makes in his “The Elegant Design” book, which, IMHO as a former scientist and a current science teacher, is a full load of crock…

  6. Andrew Suttar says . . .
    June 8, 2013 / 6:53 am

    Maths is a language. It exists in our minds. It is used to articulate relationships. The relationships may well be ontological though.

    And yet this blows my mind:

    Make a mobius strip. It now has 1 surface. Draw a single line down the middle until it becomes a continuous loop. Cut along this line. The mobius now has 2 surfaces.

    Make another mobius. Draw 2 parallel continuous loops now. Cut down these loops in parallel. It now makes a mobius looped through a double mobius, (i.e 3 surfaces)

    Try it with 3, 4 and 5 parallel lines and we have creating the number series.

    What is amazing is that they are always looped through each other and can be reassembled back into 1 mobius with only one surface.

    I wonder what Vihart has to say about all this .o?

  7. Theis Peter says . . .
    June 10, 2013 / 12:15 pm

    All of human knowledge is approximation — our attempt to create/impose a grid on something wiggly, organic. Though we like to feel and think otherwise, we mostly fumble through the dark. Objectivity seems to be the main issue — does it even exist? We humans attempt to define objectivity, but we are attempting to do so with our very limited capacities. As Deleuze/Guattarri wrote, it´s like trying to “seize a blade of grass and hold fast to it when it begins to grow only from the middle.” It´s not “you can´t step in the same river twice,” instead it is probably more like “You can´t step in the same river once.”

  8. lee says . . .
    June 13, 2013 / 11:13 am

    This is a foisted dialectic. The dualism arises in failing to see that everything is a process, including reality itself. Our conscious experience exists only as a process, but as a property arising out of its substrate.

    Maths are the same thing, only different.

  9. We needed says . . .
    December 8, 2013 / 8:37 am

    Math exist . In the same way that psychology exists.nHumans correlated language to describe the interactions of the universe. formulas and concepts are created by humans to communicate abstract ideas of thing that actually exist . nnUntil Freud’s theories of the psych, we still would not fully understand the brain’s full capacity. A biologist can tangibly note the aspects of the brain, but the measurers of the brain’s full functioning capacity is paired with “meta-cognition” or thinking. The concept of a human’s brain capacity and how it impacts on their over all mental and physical well-being is abstract (intangible ) but real. nnMathematicians are discovering the inter-relatedness of things in the universe, and devising a formula to communicate that universal discover to all. n

  10. asdf says . . .
    April 14, 2015 / 10:05 am

    But… math does have an empirical component. It’s called proofs. The results of a computation, which are isomorphic to proofs, are unknown until after the computation has completed.

  11. Sam says . . .
    August 1, 2015 / 2:01 pm

    I’m a linguist writing a paper on the theory of maths for my research at an Institute of Neuroscience.

    Maths is a human language. Yes, maths with an ‘s’, I’m British.

    Human language is used to explain metaphysics.

    Metaphysics exists even without being perceived.

    Therefore mathematical language is created (not real) but mathematical meaning is discovered (real).

    Animals don’t understand theoretical maths but many understand practical maths (like geometrics and basic physics). Prey seeing a predator and running fast in the opposite direction? They’re using maths!

    The opposite of empiricism is ontology and the opposite of science isn’t faith, it’s logic.

    If a tree falls down and no human is there to hear it, does it make a sound? Yes! Because sound comes from sound waves which are electromagnetic. Electromagnetic activity happens even in the furthest reaches of our Universe. It’s a question of logic, not faith.

    Fiction is a form of metaphysics but it’s different. You have to remember how James Bond likes his drink, as opposed to understand it. It needs context. Pythagoras’s theorem can be understood, even out of context. That’s why it’s true.

    But it’s possible that I’ve just lost my mind.

  12. Mike Deutsch says . . .
    January 15, 2016 / 1:04 am

    Sound is created by vibrations through a medium (i.e. Air, water etc.) that affect a hearing apparatus, as an ear. Electromagnetic radiation (ocillating electric and magnetic fields) will propagate thru a total vacuum (space) @ the speed of light (vs sound thru air @ Mach 1) solids (x-ray, *limited solids* & gamma *will pass thru your body* & other solids), atmosphere
    (visible light, ultraviolet, radio waves) etc.

    Back to the question of a tree falling, if there was absolutely no entity capable of hearing or feeling the vibrations (no observer) including measuring devices then how would you prove it makes a sound ? You might infer a sound is made with or without the observer
    based upon scientific laws. The tree hits the ground producing vibrations in the earth, air or nearby water producing sound waves regardless of an observer.
    How would you prove it in the absolute
    without a measurement or more exactly an observer ? More to the point sound is only meaningful to those with the ability to detect it. The sound of a falling tree is meaningless when no thing hears it.

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