how my philosophy homework turned into a rant

WARNING: The following is not very interesting.


Philosophy of Mathematics

Discuss: "Realism-in-truth-value leads to a normative philosophy of mathematics"

A normative philosophy of mathematics is one which prescribes how one should do mathematics.

A mathematician is a realist-in-truth-value iff he believes that forall statements phi about mathematics (phi \/ ~phi).

Such a mathematician is likely to believe in the following norm: the goal of a mathematician should be to determine whether phi or ~phi is the case for whatever phi they are working on. Thus realism in truth-value automatically leads to this norm.

How is such a mathematician to deal with the Continuum Hypothesis, given that both CH and ~CH are consistent with core mathematics? One possibility is to have method of deciding which one is true, e.g. intuition; but he may even simply acknowledge that we don't know and can never know which of phi or ~phi is the true one, while still maintaining that exactly one of them is true.

To such a mathematician, intuitionistic mathematics is overly restrictive, because to him, all proofs of ~~phi are actually proofs of phi. The structure of intuitionistic mathematics, however, may still be an interesting object of mathematical study; and as in all other areas of mathematics, our realist-in-truth-value will attempt to determine where phi or ~phi is the case for each question under investigation phi. And in this sense, he would be no different from intuitionists, who tend to do their meta-reasoning classically while keeping a straight face.

variants of Go

Variants of Go

I just went crazy with the Voronoi JavaScript (can't remember ever playing with this... the areas look like little skin cells). I really like Open Go, where stones are placed in a continuous space.

If you're a hardcore geek, try topological Go.

preventing arrogance?

Me - [fiddle solo]
J- Wow, that was great!
Me - Thanks.
J- And fiddle is such a hard instrument!

Freeze the scene.

In my paranoia about not being arrogant, I stop and wonder "what should I say?"

"- Yeah, you're right it is a hard instrument." (therefore I am good, therefore this is an arrogant remark)
or
"- Actually, playing fiddle's not that hard." (even more arrogant!)

My arrogance becomes thus unfalsifiable.