dextercioby said:
It's true.There is:the three laws imply everything at classical macroscopical level.
OK, derive the principle of conservation of energy from Newton's three laws of motion.
Not just conservation of kinetic energy, but of all forms, including the first law of thermodynamics.
Conservation of energy IS a fundamental proposition in Physics. It is not logically dependent on Newton's three laws for its truth.
So you see, there are other fundamental propositions upon which Physics rest, it's not just Newton's three laws.
BTW, "fundamental" is a rather nebulous word, especially when we're trying to grade it. Conservation of momentum is to me, just as fundamental as Newton's three laws. As I think I have shown, conservation of momentum is actually equivalent to the 2nd and third law of Newton. The major reason for splitting up the law into two in Newton's formulation is to
define the concept of a force as a rate of change of momentum. Force is no more fundamental than momentum, the former is just the first differential of the latter wrt time.
Let's leave analogies and collateral discussions to the phylosophers,okay??They have to make a living,right??
We ARE discussing the philosophy of science. You opened the door, remember ?
False is the conclusion,true is the hypothesis...I would advise you to read more.Science needs theory.Theory is logics and mathematically based.Axioms are a part of both...
A mathematical axiom is FUNDAMENTALLY DIFFERENT from a physical "axiom". A mathematical axiom can exist with totally *no* reference *whatsoever* to the "real world" of physical objects. A physical "axiom" or law or principle absolutely NEEDS to say something about something in the real world. Don't you see this very basic difference ?
True,however modern theoretical physics doesn't have the empirical basis anymore.
Of course it does ! Just because QM involves a lot of fancy mathematics doesn't mean the conclusions can stand unsupported by empirical verification. Why do you think so much money is spent building humongous particle accelerators and colliders, if not to verify the fruits of mathematical searching ?
Yet it's unanimously accepted,simply because it lack the only the only way of falsifying...
Even the most abstruse theory, like the ones that talk about superstrings and what not, are constructed to lend mathematical coherence to a greater model that CAN be verified in the real world. If a theory makes absolutely no predictions that can either directly, or through ramifications thereof, be falsified, then it is not a scientific theory and has no merit.
Really??Compare that to the fact:by definition,force is the time derivative of momentum.Is there any difference??
1st proposition : F = dp/dt
2nd proposition : 1 is a natural number.
The 1st proposition defines Force. It depends on the concept of momentum for its definition. However, forces can be measured by physical instruments, as can momentum, so they are both "real world entities". It is remotely possible that 50 years from now, an extremely subtle physical effect becomes apparent that changes this relationship. This would negate the proposition.
This is not so far fetched. If one were to look back to the 19th Century and question the validity of "F = ma = m(dv/dt)", one would be made a laughing stock. Of course, now we know that isn't correct, since mass alters with motion. Even though F = dp/dt is still correct at the moment, can you really rule out another paradigm shift in thought in the future ?
The 2nd proposition is Peano's first axiom. It relates two concepts : "1" and "natural number". Neither of these has any real meaning in the "real world". Although we can define the cardinality of a real world set using the naturals, the mathematical definition does not depend on the nature of the physical world for its veracity. The whole Universe can dissolve away tomorrow, leaving only one self aware particle and the particle can still cognize the successor of one, two, even though it cannot find anything to count using this new number.
Definitions are in a sense axioms...
You mean physics does not have "logical structure (...) built from the ground up"? What planet have you been living on??
Let's not assume airs here. Physics is much more bread and butter than mathematics, and is far more pragmatic. This need not be pragmatic in the sense of inventing new machines to do stuff, but can also be the pragmatism of needing to tie up observations of the physical world into a coherent theory. Mathematics can exist solely for the pleasure of an arbitrary game of the imagination.
Nope.It's irrefutable.If experiment falsfies the results of a theory,then its axioms were wrong.However,we can find a new theory...New axioms,new theorems,new sylogisms and this time confirmation of results...
You've just proved my point ! Your physical "axioms" are simply tentative truisms that can be falsified ! Mathematical axioms can NEVER be falsified. They can be undecidable in a theoretical framework (like the Axiom of Choice in ZF set theory) but cannot be proven "wrong", simply because they are by definition "right". Always and forever.
I'll get right on it. In the meantime, read more formal logic.
