The following post has nothing to do with Jack, James has said something slightly unrelated but interesting. Hopefully it'll mean something worthwhile comes from a thread Jack has started.
Sure. All of SR follows from two postulates (as formulated by Einstein), or even just the one about the laws of physics being the same in all inertial frames of reference (since those laws include Maxwell's equations, which predict the constancy of the speed of light).
I think you need to be careful here. The second postulate doesn't follow from the first alone, so if you want only SR and nothing might you might regard as related to it like Maxwell's equations. If you stipulate gauge theory in 3+1 dimensional space-times are consistent then you get Maxwell's equations and then you can infer the notion of Lorentz transformations, but this still doesn't allow you to drop the second postulate of SR as the implications aren't quite the same. Maxwell's equations are very nicely formulated in terms of space-time symmetries but you can't infer them.
Its arguable quite what you're assuming in such cases. You're obviously assuming a lot of mathematical work so you need to be clear in how you separate what is a physical assumption and what is mathematical.
Given some very very basic notions/postulations about physical symmetries you can infer the concepts of pretty much any area of physics. Space-time curvature and gauge fields can be formulated in
exactly the same way and much research
is based on little more than "I want my physics to have the following symmetry...."
Since everything follows from a single postulate, there's no possible room for logical inconsistency. A single postulate can't be logically inconsistent with itself..
Again, we need to be careful here. Given most people don't do any kind of logic theory (and I'm pretty much one of them but I know a few basic things via osmosis from other people who did) they regard a vast amount of logic to be 'taken as given'. The simplest example is the axiom of identity, p => p (to be said as 'p implies p'). Put in clearer language, a statement implies itself. Somewhat seemingly circular a statement implies that which is states. Yes it might seem to any non-mathematician as "That's fucking obvious!" but, contrary to the impression Jack has, mathematicians take great care in being very very careful and very very thorough. This lead to logic studying friends to end up chanting, when doing homework, things like "p implies p
implies p implies p", aka (p => p) => (p => p). p=>p is a statement and it implies itself, hence (p => p) => (p => p). Iteratively nest this till insane.
Anyway, back to my point. A statement and all its implications are only consistent if the statement is consistent else you suffer from
explosions. So can we think of a statement which is
not consistent with itself. Yes, we can take p to be the good old 'This statement is false'. If p=>p then it implies ¬p ('not p'). So p => ¬p.
Explosions abound. Conversely we can construct a self consistent closed axiomatic system via taking p as 'This statement is true'. Which it is, since it is, since it is, since it is,..... Repeat till insane.
Now you see why I'm not too fussed about not having done much logic!
