Actually, many mathematicians have, and sometimes if you invalidate a postulate it leads you down a whole road to new mathmatics, such as non-euclidian geometry. It turns out that if you invalidate Euclid's fifth(or was it fourth?) postulate that any two points determine only one line, and make the postulate read that two points detemine an infinite number of lines, you get a whole new field of gemetry leading to solutions to formerly insoluble problems. It also turns out that some of the resulting equations turn up in such unlikely places as quantum phsyics and fluid dynamics.
So the real thought here is that by limiting yourself to a set of postulates that are inviolable, you are cutting yourself off from learning things by eliminating them as possibilities. Of coures, in the real world, you have to impose some limits or you'd never accomplish anything. If Euclid had not made his postulates, we'd never even have had Euclidian geometry, let alone non-Euclidian.
To tie this back to our discussion on Athiesm vs Zealotry, It seems to me that they are just two sides of the same coin with different postulates. One side believes G-d must exist, and the other believes G-d must not exist. Based on these postulates, they get completely different world views. Now, the million dollar question is if either of them are really more "right" than the other or are they just different view based on different starting points, both equally valid based on the starting postulate?
Further, you have to add the complication that every individual has his own set of postulates about the world, so everyone to some degree is a zealot or an atheist about any point you want to raise, thus is spectrum of humanity. Now add in the complicating factor of everyone trying to convince others that his postulates are correct and you have the world--people willing to give in on points that aren't important to them because they will not affect their world view--and people who are inflexible on a postulate because to admit it's truth or falisity would mean that their whole world view would have to be revised--few people will allow this to happen because it means that everything they have ever believed in might again be suspect, because the supporting postulate has been destroyed.
On the other hand, some people believe in weird things. Should we not try to convince them of the folly of their postulates? It's a difficult question, isn't it? What's weird to you might not be wierd to others, and maybe it's only wierd because your postulates are completely incompatible with the other person's. But, if a postulate is demonstrably false, you can try to convince someone to change their belief in it. But what if the postulate is unprovable either way? Then you get into arguments about beliefs, and everyone is correct, based on their own beliefs. No side is stupider than another when it comes to unprovable beliefs, since they are both completely unprovable.
This is getting really long, so I'll wrap up this way. People have different beliefs. Some are provably wrong, others are not. Our job as a society is to make all the various postulates get along with each other so everyone can be as happy and free as possible, so we can all share the quest for life, liberty, and the pursuit of happiness.
Would like to hear more about this. Physicist, would you comment/can you confirm?
I not a QM physicist, and even if I played one on TV, noone would watch that stuff, but I do know a thing or two about fluid mechanics.
All laws relating to fluid dynamics that I know of derive from the 1st and 2nd LOTs and Newton's 2nd LOM (redundancy intentional), neither of which require any strange new geometrical idealogy, AFAIK.
I would be interested in hearing more about this, specifically with regards to fluid mechanics.
Thanks!
You were doing great unitl you got to the above
The only job anyone has to worry about is their own. Almost all the problems in this world are the result of individuals thinking they have some "higher" social objective then minding their own business which always ulimate means medling in other people's business.
Nobody needs to be "making" all the various postulates get along, because people do not have to "get along" in order to be decent, productive, or happy. Mostly, they just need to stay out of each other's way, that is, mind their own business.
Hank