Without going through the details, I'll agree that I think this should follow.

Well.... I think saying its from the "Columbia math department" is a stretch. I've met peter woit a few times (he's a nice guy willing to listen to his "enemies") and i really don't think his opinion on string theory is THAT different from mine. I'm obv more willing to shrug off lack of SUSY at the LHC, but there remain very good arguments to study string theory.

And if you want to compare it to a religion, Witten is atleast the pope....and I don't think he's said anything other than "there is a lot of circumstantial evidence to think that string theory is a huge step forward...... but maybe not". Dont thnk religious people describe their religion in that way.

Also, String theory spin offs like SUSY, ADS/CFT, and very liberally 2D QFT, are mathematically interesting enough to where the mere fact that string theory provides a sandbox for the concepts to be explored means string theory isn't worthless.

Right. The idea that there is essentially only one successor function is that all such functions are isomorphic. That is, for any two such functions f and g on, respectively, the sets with distinguished elements (X, a) and (Y, b), there exists a bijection h : X -> Y such that h(a) = b, and such that h(f(x)) = g(h(x)). Similar comments apply to successor orders. I think we agree on that.

The successor function associated with the successor order 1 < 2 < 3 < ... is obviously 1 -> 2, 2 -> 3, ..., and vice versa. I claim that learning one is closely related to learning the other, and I still fail to either agree with or understand your comments such as:

"It’s my impression that Susskind and others are believing something for sociological and psychological reasons, something for which they have no rational, scientific argument. This behavior is not distinguishable from that of many of the intelligent designers, and if it becomes more widespread it ultimately threatens to do real damage to the public perception of science in general and theoretical physics in particular."

-Peter Woit

Amen.

The reason S(a) = b is not a successor function is because it violates the
"no top element" condition. What is S(z)? The alphabet is not isomorphic to the natural numbers. It's not enough for there to be a next thing sometimes, there must be a next thing all the time.

Similarly when we memorize digits (notation-dependence), what is S(9)? We want to say that S(9) = 10, but that takes us out of the realm of digits and ascribes a sort of numerical meaning to the symbols, which is beyond that which kids understand (at first). That is, for little kids learning to count, there comes a point at which they run out of numbers. For example, I have a friend whose child can count to ten, and when I ask him "What's next?" he just starts making gibberish sorts of noises (or he smiles and runs away).

So I'll requote myself:

The bolded is a FINITE string of sounds.

Okay, thanks. I understand that it's not the successor function if there's a top element.

My calculator behaves similarly if the numbers get large enough.

onety-one, onety-two, onety-three,..... Then eighty, nintey, tenty....

Don't you mean onety-ty?

Starting with just 0, set theory with power sets, we can get to the natural numbers ( and the integers, rational numbers ). If we want to sum series nicely and have algebraic completeness, surely R and C follow. If we want to understand symmetry and general algebraic structures, we would like groups, rings, fields, morphisms and we may as well include categories and quasi-categories.

Platonists should take a stance similar to Gödel's philosophy of mathematics and may as well go "the whole nine yards" by accepting all four levels of the Tegmarkian cosmos; anything mathematicians find out in mathematics is simply discovery and not a human construction. The Wignerian unreasonable effectiveness of mathematics in physics should then be clear.

What is not so clear seems to be whether other general concepts truly exist. Surely, truth, existence and the concept seem to truthfully exist as concepts; however, there's a vast distance between these and ethics, philosophy or theology.

I find peters behavior closer to that of the IDers...focusing on making convincing arguments to laymen rather than experts.

it is a linguistic problem. It is a method of describing and it only points to what you are referring to and never actually is the thing.

Does one exist? my first response is one what?

If anything exists it must be the zero, even if it is such a PITA in the threads in SMP. One, two, three etc can be some weird manner to look at the world. But zero, non-existence, has to be there for making the concept of existence meaningful.

In Zen I think its called non-duality. not one and not two