Why Isn�t Edward P. Tryon A World-famous Physicist?

[oxmixmudd]

I don't think 'hypothesis' is the right correlation with a mathematical axiom. A hypothesis is derived from observation and then experiments are designed to test the hypothesis, which means it can be shown to be false. I think a better approximation to an axiom in the scientific realm would be something like the assumption that the behavior of the universe is discoverable through observation and experiment. Or that the universe itself is real and has existence independent of the mind.


Jim

[Truthseeker]

[little_monkey]

I don't think 'hypothesis' is the right correlation with a mathematical axiom. A hypothesis is derived from observation and then experiments are designed to test the hypothesis, which means it can be shown to be false. I think a better approximation to an axiom in the scientific realm would be something like the assumption that the behavior of the universe is discoverable through observation and experiment. Or that the universe itself is real and has existence independent of the mind.


Jim

An example of an hypothesis is: the speed of light is constant in all frames of reference. That cannot be proven, unless you're willing to test an infinite number of frames, ;-). So this hypothesis falls into the category of unprovable truths. But it is the corner stone of SR, which is the provable truth, that is, there are sufficient evidence to show that SR describes the real world.

So the structure is:

(1) The speed of light is constant in all frames of reference (Hypothesis) is the unprovable truth.
(2) SR (a theory based on 1) is the provable truth.

[oxmixmudd]

An example of an hypothesis is: the speed of light is constant in all frames of reference. That cannot be proven, unless you're willing to test an infinite number of frames, ;-). So this hypothesis falls into the category of unprovable truths. But it is the corner stone of SR, which is the provable truth, that is, there are sufficient evidence to show that SR describes the real world.

So the structure is:

(1) The speed of light is constant in all frames of reference (Hypothesis) is the unprovable truth.
(2) SR (a theory based on 1) is the provable truth.

It can't be proven true, but it can be shown to be false if there is a frame of reference wherein this cornerstone of SR fails.

In general, science doesn't prove things in the same sense as a logical or mathematical system of axioms and proofs - so to apply the concepts to science requires a certain logical extension to begin with. But even given that, if the hypothesis stands the test of time and becomes theory, it still is never 'proven' so I don't see the property of provability sufficient to make the correct mapping. However, since axioms form the foundation of a logical or mathematical system and are nether proven true OR false, then I'll stand by my original comment. The assumptions we make to do science map more appropriately to the axioms, not the things we attempt to 'prove' by experiment (hypothesis and theory).


Jim

[little_monkey]

It can't be proven true, but it can be shown to be false if there is a frame of reference wherein this cornerstone of SR fails.

That's the concept of falsifiability from Popper. And we do believe that science is subject to that test.

But nevertheless, in general, an assumption is taken to be true. If it produces a theory that is not in accordance with reality, then the first job is to check any cracks in the theory, if none is found, the next thing is to check the assumptions. This is what happened to the Galilean transformation laws: they were ok as long as the objects in consideration were moving at a speed very much lower than the speed of light. Once it was thought that the speed of light should be constant in every frame - from Maxwell's equations - then this hypothesis had to be amended by replacing the Galilean transformation with the Lorentz transformation laws.

In general, science doesn't prove things in the same sense as a logical or mathematical system of axioms and proofs - so to apply the concepts to science requires a certain logical extension to begin with. But even given that, if the hypothesis stands the test of time and becomes theory, it still is never 'proven' so I don't see the property of provability sufficient to make the correct mapping. However, since axioms form the foundation of a logical or mathematical system and are nether proven true OR false, then I'll stand by my original comment. The assumptions we make to do science map more appropriately to the axioms, not the things we attempt to 'prove' by experiment (hypothesis and theory).


Jim

That's true. In math you can map any set A with any set B. And mathematicians don't worry if a certain mapping produces a mathematical system that describes reality or not. Mathematicians worry about logical consistency. As its goal is to describe reality, science cannot afford the luxury of the mathematician. Both assumptions and theories in science are subject to Popper's falsifiability test.