Where do numbers come from? Are they “real”? Philosopher and mathematician Kit Fine asks these questions and more in an instructive lesson on the nature of numbers. Kit Fine explores the… Video Rating: 4 / 5

Not being a mathematician myself, I’ve always been bothered that a number
can, on the one hand, be used to represent a thing while, on the other
hand, it can be used to show a relationship. For example, in 2+2 = 4, the
“2” is a representation of a countable thing (2 apples + 2 apples).
However, in an equation like 10/5 = 2, the “2” defines the relationship
between the number 5 to the number 10 (5 goes into 10 two times). It seems
(to me) logically inconsistent to say 3 – 1 = 10/5, because the result on
either side of the equation is not the same “type” of 2. It’s akin to that
particle/wave duality in physics, where one measure represent a countable
thing (a particle), while another measures the relationship (wave).

I really wish I understood him better.. It is hard for me to conceptualize
what he is describing aren’t the Frege-Russel view and the Cantor view the
same?

Good lecture. Have you taken a step back to think about what numbers really

are?

http://bit.ly/1BGEuoA

It’s a wonderful thing to see Kit Fine on here.

Not being a mathematician myself, I’ve always been bothered that a number

can, on the one hand, be used to represent a thing while, on the other

hand, it can be used to show a relationship. For example, in 2+2 = 4, the

“2” is a representation of a countable thing (2 apples + 2 apples).

However, in an equation like 10/5 = 2, the “2” defines the relationship

between the number 5 to the number 10 (5 goes into 10 two times). It seems

(to me) logically inconsistent to say 3 – 1 = 10/5, because the result on

either side of the equation is not the same “type” of 2. It’s akin to that

particle/wave duality in physics, where one measure represent a countable

thing (a particle), while another measures the relationship (wave).

I really wish I understood him better.. It is hard for me to conceptualize

what he is describing aren’t the Frege-Russel view and the Cantor view the

same?

Nice job, now let’s do it with imaginary number sets. ;)

cantors theorem relates to this

sur les nombres.

Oh god, this is what I call underwhelming. Today’s philosophy is in a deep

rut.

2nd

First

What are numbers. It took him 13 minutes to answer. While it took me 4

seconds to count from 0 to 9