Depth 1 · 35 s
What is three?
Three isn't three apples, and it isn't the sign 3 - those are things and names. It's what every group of three shares, which you can see when you match the groups one to one.
About this video
We use numbers all day, but what is a number? This short animation asks it about three. Three can't be three apples, because three stars or three claps are three too, and they have nothing else in common with apples. It isn't the sign 3 either: 3, the Persian ۳, the Roman III and the word "three" are only different names for the same number.
So what do all groups of three share? Line them up and match them one to one: each dot with one square, each square with one ring, with nothing left over. Groups that can be matched like that have the same number. The philosopher Gottlob Frege turned this into an answer: a number is what all the groups that match one to one have in common. That answer doesn't end the question, though. Are numbers real things that exist whether we think of them or not? Ideas in our minds? Or a language people invented? Philosophers of mathematics still argue about it. This video goes with the What Is Three? lesson of Numbers Level 1 on Knaph.
This video shows depth 1 of What a number is.
Learn What a number isTranscript
- 0:00What is three?
- 0:04Three dots, three squares, three rings. The things are all different.
- 0:10And these are only names for three.
- 0:15What the groups share is that they match one to one.
- 0:22Frege said a number is what matching groups share.
- 0:27A real thing, an idea, or a language? Still argued.
- 0:31Three is what all threes share.