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>A Bongard Problem traditionally includes a dividing line, six images on the left side of the dividing line, and six images on the right side of the dividing line.
>Most important, there is some simple description fitting all the images on the left side (but none on the right) and a simple description fitting all the images on the right side (but none on the left).
So we can describe numbers with a pattern recognition test, place groups of n objects on the left and groups of objects with more or less than n objects on the right, this implies that the foundations of math are definied intuitively.
Same is true for the name "butterfly", every butterfly is unique and distinct, but we associate them all with the word until by pattern recognition we can tell what the word refers to.
This begs the question, what if we have a word that refers to all even numbers and 57? I could name even numbers forever, and exclude odd numbers besides 57 forever, but how would you ever know I'm referring to the even numbers and 57, and not just the even numbers?