Had we already abandoned falsifiability?

[Dmitry67]

That is positively wrong. A theory is falsifiable through its predictions and in no other way. The statement would be correct if it said but we do need to be able to in principle test any of its predictions.

Just as, if I am willing to sacrifice the blood, sweat, and billions of dollars, I can build a super-duper collider to test predictions of the standard model, I can also sacrifice my future by jumping into a black hole to verify the extension of GR into the interior of the event horizon. It is operationally meaningful to talk about what an astronaut might see if he crosses the event horizon of a black hole. We can describe how to go about choosing either to do this or not do this.

Yes, say there are 2 falsifiability principles: weak and strong.
Max is an adept of the weak principle while you insist on the strong principle

So we had finally reached the point why I had started this thread. Isn't it time to 'relax' the falsifiability?

Otherwise, you close the door for most of the superstring theories whith their branes, multiverse... you know, all that stuff...

I don't think we can reach TOE without making some sacrifices.

 

[Dmitry67]

P.S. I think there is more fundamental principle.

Mathematics started from the addition of the stones (natural numbers). The reversed operation, substraction, was not "closed", so people invented the negative numbers.

multiplication forced people to invent rational numbers, then irrational and transcendental numbers, then complex numbers.

In all cases we 'extend' or 'extrapolate' what we see here and what we can test to what we can't test.

You say, billion dollars, super puper colliders, what's about particles at Planks mass? You say that In principle you can build such collider, bigger then solar system? Does that claim have any physical sense?

Nobody plans to jump into a black hole. No articles are delayed until whe have the very first kamikaze astranaut. Instead, we extrapolate GR to what is inside the black hole. In the same way we did for the negative numbers. If it works outside - it works inside!

 

[jambaugh]

P.S. I think there is more fundamental principle.

Mathematics started from the addition of the stones (natural numbers). The reversed operation, substraction, was not "closed", so people invented the negative numbers.

multiplication forced people to invent rational numbers, then irrational and transcendental numbers, then complex numbers.

In all cases we 'extend' or 'extrapolate' what we see here and what we can test to what we can't test.

But this is mathematics. It is not extrapolation of what is or what happens but rather extension of constructs within our imagination. And we can likewise construct "number systems" which have non-associative addition or arbitrarily weird mathematical universes.

With regards to Mr. Tegmark's mathematical universe he is effectively returning to Platonism wile trying to incorporate a reified wave-function interp. of QM. We learned to move away from taking our mathematics too seriously back when distinct models of geometry sans the parallel postulate led us to understand that there were a whole multitude of geometries, each elegant and self consistent and thus we could not via pure deduction select one over the other as a description of nature. Math and science began diverging at that time. Math was understood to be "virtual" and knowledge about mathematical constructs must begin with undefined terms and axioms. Science contrawise developed as an epistemological discipline distinct from pure reason. As one cannot serve two masters the epistemology of empiricism prevails. Thus any assertions which cannot in principle be empirically falsified must either be, math, a model, or a religion.

You say, billion dollars, super puper colliders, what's about particles at Planks mass? You say that In principle you can build such collider, bigger then solar system? Does that claim have any physical sense?

Certainly. It would be a matter of engineering with known materials (as opposed to say building Larry Niven's ring world which required some super-metal). That and an immense amount of time and resources.

Nobody plans to jump into a black hole. No articles are delayed until whe have the very first kamikaze astranaut. Instead, we extrapolate GR to what is inside the black hole. In the same way we did for the negative numbers. If it works outside - it works inside!

Right. Speculative theories are valid as scientific theories provided they are operationally meaningful i.e. one can falsify their claims in principle. That means one can describe how any individual or group could with sufficient resources come to know the answer to the implicit question.

Without this restriction the door is open to the wackiest of "theories" and arguments e.g. "how much does God weigh?" and "How many angels can dance on the head of a pin". We've (or most of us) have moved beyond such speculation outside of science's empirical domain.

 

[Dmitry67]

Math and science began diverging at that time. Math was understood to be "virtual" and knowledge about mathematical constructs must begin with undefined terms and axioms. Science contrawise developed as an epistemological disciplinedistinct from pure reason.

So how do you imagine the axiomatisation of physics (one of the Hilberts problems)? Iagree with Max Tegrmark that it is pure mathematics. The TOE will look like as a number of equations (or may even only one equation).

Do you believe that physics can not be covered completely by the pure mathematics? That there are some specific 'physical' axioms?

But listen let say we have some TOE equations: M1, M2, MN. Now you say: there are additional physical axioms which are not covered by M1-Mn.

In that case there are 2 options: if we can express these axioms in the language of mathematics then we just add equations P1,P2... to our previous list, getting a pure mathematical system again!

An axiom is a 'pure physical' when... when it can not in principle be written in a form of a formula! It must be something really weird... like a turtle or an elephant... or something like about the consciousness...

Certainly. It would be a matter of engineering with known materials (as opposed to say building Larry Niven's ring world which required some super-metal). That and an immense amount of time and resources.

Then we had already relaxed in once. For the scientists of the 17,18,19 centuries falsiability was an immediate action item. You have doubts - go and do the damned experiment NOW. If you would say "you know, we can verify in principle that world outside out huble space is the same in principle we just need to wait few billion years to see the light of the more distant sources they would laugh!

Compare:
* I will send you a wire of 10'000USD
* In principle, I can send you a wire of 10'000USD

Do you feel the difference? :) 'In principle' has a NEGATIVE meaning: in principle we can do it but... What is a practicle meaning of saying 'in principle, I can jump into a black hole' or 'in principle, I can wait 10**18 years...'?

It is nothing more then a mantra: if you repeat it many times, you are starting to believe in it :)

Without this restriction the door is open to the wackiest of "theories" and arguments e.g. "how much does God weigh?" and "How many angels can dance on the head of a pin". We've (or most of us) have moved beyond such speculation outside of science's empirical domain.

So mutiple branes = "How many angels can dance on the head of a pin"? :)