What if science is wrong?

[esme]

There is no emotional investment in science, so it remains neutral and can adapt. There's tons of emotional investment in religion which provides resistance. Religion can, and will, change, but the change will be slower. Change will come about through new sects, or even new religions. Many people keep the religion of birth, but many also choose. Change comes about by people choosing the religion that best fits their beliefs, and those beliefs can change due to outside influences, including science.

 

Change in religions will be over generations, but change in science can be instantaneous with the publication of a paper, or Crick & Watson running into a pub.

 

I was going to add that the only thing that religion won't change on is the existence of god, and that since this was impossible to disprove it was no problem to religion. But since some religions don't even have a god this is somewhat debatable, I guess it is possible for an atheistic religion to evolve out of a theistic religion. Scientology?

Sounds reasonable.

 

Is Scientology a religion ?, I suppose they do believe in something so it could fit.

[esme]

Maybe I've misunderstood this, I didn't do much maths at degree level and what I did wasn't pure maths.

 

But this seems to imply that Cantors is only one characterisation and that you can look at infinities in other ways. And that if you do then different results occur.

Which I think is what I said earlier, it depends on how you look at it.

Well Cantors result seems to be the one that is being taught and is widely accepted, although there is still work being done in the area new scientist did an article on it that was quite interesting you may need a subscription to read the full article though.

 

I'd be very interested to see any alternative treatments of infinity though.

[HeadingNorth]

Well Cantors result seems to be the one that is being taught and is widely accepted

 

That's probably because it was proven to be true many decades ago.

[esme]

That's probably because it was proven to be true many decades ago.

Which was kinda the point I was making.

[Cyclone]

That's probably because it was proven to be true many decades ago.

 

I get the impression that it's true if you accept that it breaks certain mathematical rules and that other ways of looking at infinity are equally true if you switch which rules can be broken.

Maybe it's one of the most useful ways of looking at it though.

[Lucifer]

Last night I was watching something scientific. It got me thinking, what if the evidence we believe we have for scientific theories has been interpreted in a way to suit the scientists agenda or simply misinterpreted? Did we interpret things a particular way because it fit what we were looking for?

 

Now I'm pretty sure that the fact that I'm typing this on a computer is reason enough to believe scientists could be right about the majority of their work but, should I trust science just because things work?

 

Maybe believers in god are right. Perhaps we only discover how things work because god reveals the information to us in a way we understand. Hence why we will never truly understand some things.

 

If science is wrong, there could be problems of biblical proportions.

[HeadingNorth]

I get the impression that it's true if you accept that it breaks certain mathematical rules

 

Not at all. It's true if you follow mathematical rules.

[Cyclone]

No, it definitely requires that certain rules are broken, for example the infinite set +1 is identical to the infinite set, breaking basic mathematical rules.

[HeadingNorth]

No, it definitely requires that certain rules are broken, for example the infinite set +1 is identical to the infinite set, breaking basic mathematical rules.

 

 

The point about Cantor's proofs is that they demonstrate exactly why no mathematical rules are broken in coming to that conclusion.

[Cyclone]

Different characterizations can yield different results. For example, in the popular characterization of size chosen by Cantor, sometimes an infinite set A is larger (in that sense) than an infinite set B; while other characterizations[which?] may yield that an infinite set A is always the same size as an infinite set B.

 

For example, Cantor's characterization, while preserving the rule that sometimes one set is larger than another, breaks the rule that deleting an element makes the set smaller.

The Cantor characterization explicitly breaks at least this rule (and by implication the opposite).

 

Furthermore, some characterization may not "directly" break a rule, but it may not "directly" uphold it either, in the sense that whichever is the case depends upon a controversial axiom such as the axiom of choice or the continuum hypothesis. Thus there are three possibilities. Each characterization will break some rules, uphold some others, and may be indecisive about some others.

 

Which characterisation you use would seem to be dependent on what you are trying to achieve.

 

Finite, countable and uncountable sets

 

If the axiom of choice holds, the law of trichotomy holds for cardinality. Thus we can make the following definitions:

 

Any set X with cardinality less than that of the natural numbers, or | X | < | N |, is said to be a finite set.

Any set X that has the same cardinality as the set of the natural numbers, or | X | = | N | = ℵ0, is said to be a countably infinite set.

Any set X with cardinality greater than that of the natural numbers, or | X | > | N |, for example | R | = c > | N |, is said to be uncountable.

 

http://en.wikipedia.org/wiki/Axiom_of_choice