Comment author:Epictetus
23 February 2015 06:07:49AM
0 points
[-]

If you believe in applied math, what are the grounds for excluding "pure" math? Most of the time "pure" just means that the mathematician makes no explicit reference to real-world applications and that the theorems are formulated in an abstract setting. Abstraction usually just boils down to figuring out exactly which hypotheses are necessary to get the conclusion you want and then dispensing with the rest.

Let's take the theory of probability as an example. There's nothing in the general theory that contradicts everyday, real-world probability applications. Most of the time the general theory does little other than make precise our intuitive notions and avoid the paradoxes that plague a naive approach. This is an artifact of our insistence on logic. A thorough, logical examination of just about any piece of mathematics will quickly lead to the domain "pure" math.

Comment author:Epictetus
23 February 2015 04:22:00PM
1 point
[-]

There are beliefs that directly pay rent, and then there are beliefs that are logical consequences of rent-paying beliefs. The same basic principles that give you applied math will also lead to pure math. We can justify spending effort on pure math on the grounds that it may pay off in the future. However, our belief in pure math is tied to our belief in logic.

If you asked whether this can be applied to something like astrology, I'd ask whether astrology was a logical consequence of beliefs that do pay rent.

## Comments (245)

OldIf you believe in applied math, what are the grounds for excluding "pure" math? Most of the time "pure" just means that the mathematician makes no explicit reference to real-world applications and that the theorems are formulated in an abstract setting. Abstraction usually just boils down to figuring out exactly which hypotheses are necessary to get the conclusion you want and then dispensing with the rest.

Let's take the theory of probability as an example. There's nothing in the general theory that contradicts everyday, real-world probability applications. Most of the time the general theory does little other than make precise our intuitive notions and avoid the paradoxes that plague a naive approach. This is an artifact of our insistence on logic. A thorough, logical examination of just about any piece of mathematics will quickly lead to the domain "pure" math.

*0 points [-]I am not making the

statement"exclude pure math", I am posing thequestion"if pure math stays, what else stays?"Maybe post utopianism is an abstract idealisation that makes certain concepts precise.

There are beliefs that directly pay rent, and then there are beliefs that are logical consequences of rent-paying beliefs. The same basic principles that give you applied math will also lead to pure math. We can justify

spending efforton pure math on the grounds that it may pay off in the future. However, ourbeliefin pure math is tied to our belief in logic.If you asked whether this can be applied to something like astrology, I'd ask whether astrology was a logical consequence of beliefs that do pay rent.