>>194
You can define "God" as anything you cant comprehend/sense. That way God is equivalent to Infinity/incompletness, which scientists care about.
Fine then, then we can talk about some "ineffable" stuff, especially if that "ineffable" stuff has consequences. Such kind of stuff usually appears once you keep reducing and reducing things until you can't reduce anymore, and yet it's too simple to be able to explain in terms of anything else, but still can be reasoned about.
Common sense meaning has nothing to do with math. It's limited to our senses.
How do you think you learn about math or recursion?
When it's done in local, controlled and well understood environment. For example, crate wont cause sound, if it's dropped from outer space into the Sun.
Of course. It's not like we don't build fairly exhaustive models given our observations in a variety of environments.
I cant understand them, because they are full of these cryptic "sets", together with mysterious "for all" and "there exist" wordings, buried under some ugly curly brace infix syntax, which isn't even context-free.
Heh, if you're going to avoid talking about real things because you have problems with the the language used (or problems with notions in foundations of mathematics), you'll lose more, because those real things actually have consequences. You don't refuse to talk in English, but English is provably inconsistent as far as what sentences it allows you construct.
Just like reciting Torah is a learned skill for a rabbi.
Except one lets me make accurate predictions and the other is just mythology.
Wait! What are "my theories"? I do happen to agree with prof. Norman Wildberger on his rational-trigonometry, but he happen to demonstrate that geometry can be done without referencing "Infinity".
I considered your subjective idealism as a hypothesis. Ultrafinitism as a hypothesis. Do you really think that a strong form of ultrafinitism (which posits some finite upper bound for naturals) doesn't have severe limiting consequences as far as what physical law can be? As I said before, there's no problem with assuming some hard limits, but this might contradict some current theories which are (mostly) experimentally verified (such as quantum mechanics or general realitivity).
Author just recites what had been said already by George Berkeley a few centuries ago?
Not really. In the story, a highly unexpected/unusual event happens and one of the possible hypotheses that were thrown around was that they might have been wrong about that countable infinity after all and a finite upper bound might exist. (Maybe it would disappoint you, but I can easily see a solution to their problem which does not lead to ultrafinitism, although this wasn't really discussed in the book, it was mostly left as an open problem/cliffhanger; of course, some form of ultrafinitism in the ontology could explain that event as well).
If Einstein's theory contains errors, then it could be a work of art.
But pretty much all scientific theories are wrong. Some are just less wrong than the other. The goal of science is to get as close as possible to the least wrong theory, possibly reaching a true one. (They are of course applicable within their context, so they are mostly correct within the right context, but for example, general realitivity is likely wrong (and incomplete) regarding what happens singularities (big bang, black holes, etc), while quantum mechanics is wrong at the large scale as it includes no theory of gravity.)
You should note, that I'm not an "ultrafinitist", I'm "subjective idealist". These terms are different, like "Atheist" vs "Agnostic"
I wonder why does everyone consider you an ultrafinitist then? How did you manage to acquire this reputation? Does that mean you're merely agnostic about the existence of an infinity of finite natural numbers? Or that you posit an upper bound?
Then there is nothing that will allow us to look "outside" the bound.
Not entirely sure I understand what you mean by this. Given some max constant k and some particular definition of computation, such an ultrafinitist computationalist ontology will have radically different predictions than a classically finitist computationalist ontology. It may seem to you that they are unobservable, but if an upper limit does exist, it will have severe consequeces about what physical law is/can be.
Some time ago Newtonian Physics was a "well-verified physical theory" and it definitely confirmed ability to devide space into "infinitesimals".
Newtonian physics is not wrong given the right context, it's just more wrong than general relativity. Newtonian physics is not an absolute physical law - it's a local emergent law, same as most other physical laws we know right now, but that doesn't mean that the goal of physics isn't to find the full, consistent law which explains all local physical phenomena within one coherent/consistent formula/function/structure. Given that law, you have all kinds of other laws which emerge from it which are locally true within some context. Taking Newtonian Physics as ontological primitive would be an error in our world as evidence says otherwise.
The good thing is that "non-trivial theories" are avoidable. http://en.wikipedia.org/wiki/Occam's_razor
I use it too. Do you know why Occam's razor is more likely to lead to true theories? It has to do with probability theory - the probability of something having multiple disjoint properties is lower than just having some of those properties, especially if those properties explain exactly the same phenomena - in which case, the other parts become superflous.
When I talked about non-trivial theories I didn't mean that they are higher in complexity. Actually they are much lower in complexity than the ultrafinitistic version. If you want to judge complexity more objectively, you could use some formalized version such as Kolmogorov complexity, but then you probably won't like it because it's not computable (although there are ways to define approximations).