List of requirements for new theories.

[SergUpstart]

Once on the air of the radio station "Echo of Moscow" in a program about science, which is led by mathematician Andrey Konyaev, I heard a list of requirements for new theories.
1. There should be no internal contradictions in the new theory.
2. The new theory should not contradict the data from experiments and observations.
3. A new theory should not contradict existing recognized scientific theories.
I have a question, why is item 3 on this list? It seems superfluous to me. After all, if a new theory contradicts an existing theory where the existing theory is confirmed by experiment or observations, then paragraph 2 is sufficient. And if a new theory contradicts the existing one in the field of predictions that have not been tested experimentally, then perhaps this should be a reason for further checks, and not for rejecting the new theory.

[Genady]

8 minutes ago, SergUpstart said:

Once on the air of the radio station "Echo of Moscow" in a program about science, which is led by mathematician Andrey Konyaev, I heard a list of requirements for new theories.
1. There should be no internal contradictions in the new theory.
2. The new theory should not contradict the data from experiments and observations.
3. A new theory should not contradict existing recognized scientific theories.
I have a question, why is item 3 on this list? It seems superfluous to me. After all, if a new theory contradicts an existing theory where the existing theory is confirmed by experiment or observations, then paragraph 2 is sufficient. And if a new theory contradicts the existing one in the field of predictions that have not been tested experimentally, then perhaps this should be a reason for further checks, and not for rejecting the new theory.

Didn't he elaborate on these points in the program?

[SergUpstart]

6 minutes ago, Genady said:

Didn't he elaborate on these points in the program?

No, he just announced the list.

[Genady]

1 minute ago, SergUpstart said:

No, he just announced the list.

Who knows then? Maybe he meant that a new theory has to be an extension of an existing recognized theory having it as an approximation / limiting case / subdomain / ...

[exchemist]

33 minutes ago, SergUpstart said:

Once on the air of the radio station "Echo of Moscow" in a program about science, which is led by mathematician Andrey Konyaev, I heard a list of requirements for new theories.
1. There should be no internal contradictions in the new theory.
2. The new theory should not contradict the data from experiments and observations.
3. A new theory should not contradict existing recognized scientific theories.
I have a question, why is item 3 on this list? It seems superfluous to me. After all, if a new theory contradicts an existing theory where the existing theory is confirmed by experiment or observations, then paragraph 2 is sufficient. And if a new theory contradicts the existing one in the field of predictions that have not been tested experimentally, then perhaps this should be a reason for further checks, and not for rejecting the new theory.

Item 3 looks to me not only unnecessary but actively wrong.

There is no reason why a new theory cannot contradict an existing one, so long as it (a) successfully accounts for all the observations that the old one deals with and either ( b ) accounts for something the old one cannot account for, or ( c) accounts for the same observations but in a  simpler and more insightful way.

An example of (b) would be the Rutherford-Bohr model of the atom contradicting the plum pudding model. An example of ( c) would be the heliocentric astronomical system contradicting the Ptolemaic one.  

Item 2 seems to be key: it is the ability to account for observations and predict new ones that is the test of validity.    

[swansont]

I agree that 3 is wrong.

QM actively contradicted classical physics, and relativity actively contradicted Galilean/Newtonian notions. It became apparent that these existing models were incomplete and/or had areas where they failed.

[studiot]

2 hours ago, SergUpstart said:

Once on the air of the radio station "Echo of Moscow" in a program about science, which is led by mathematician Andrey Konyaev, I heard a list of requirements for new theories

When was this broadcast please ?

I ask because we should perhaps be discussing the mathematical validity of all 3 of these requirements.

Set theory violates  both (1) and (2) on your list, and yet is said to underlie all of Mathematics.
Bifurcation theory contradicted existing theories of dynamics when it was broached in the 1960s, contradicting (3).

 

 

 

Edited January 23, 2022 by studiot

[SergUpstart]

1 hour ago, studiot said:

When was this broadcast please ?

last year

 

Paragraph 2 refers to experimental data and observational data, so this list applies to physics, not mathematics.

3 hours ago, exchemist said:

Item 3 looks to me not only unnecessary but actively wrong.

If we reformulate paragraph 3 as &Gennady said (Maybe he meant that a new theory has to be an extension of an existing recognized theory having it as an approximation / limiting case / subdomain / ...), then it will cease to be incorrect, but it will still not become necessary

Edited January 23, 2022 by SergUpstart

[Danijel Gorupec]

I also think that a point is missing - one that a theory should not be more complex than necessary.

[exchemist]

1 hour ago, SergUpstart said:

last year

 

Paragraph 2 refers to experimental data and observational data, so this list applies to physics, not mathematics.

If we reformulate paragraph 3 as &Gennady said (Maybe he meant that a new theory has to be an extension of an existing recognized theory having it as an approximation / limiting case / subdomain / ...), then it will cease to be incorrect, but it will still not become necessary

But it is not true that all new theories are mere extensions of older ones. There is no way to reconcile the plum pudding model of the atom with the Rutherford-Bohr one.  And it is a stretch, to say the least, to reconcile the Ptolemaic astronomical system with the heliocentric one. Sometimes the previous theory is thrown out completely. Another example would be the phlogiston theory of combustion. Or the cooling earth theory of mountain building.

I agree that, quite often, new theories can be seen to be related to earlier ones, as with Newtonian mechanics and relativity or QM, but there is no necessity for this to be so.   

 

Edited January 23, 2022 by exchemist

[Genady]

Requirements 1 and 2 are not absolute either.

For example, Newton's theory contradicted observations of perihelium of Mercury for centuries (requirement 2), but this was not enough to reject it.

GR has singularities which can be easily turned into mathematical contradictions (requirement 1), but they are considered being out of scope of the theory's applicability, not enough to reject the theory.

[studiot]

2 hours ago, SergUpstart said:

last year

 

Paragraph 2 refers to experimental data and observational data, so this list applies to physics, not mathematics.

 

Thank you for your answer.

This is true, but there is much commonality between Physics and Mathematics.
My particular example of bifurcation occurs in both purely  mathematical analysis and in observable practical examples in mechanical dynamics, which was part of Physics, last time I looked.

 

I really don't think any of those 3 conditions are always met because examples are not simple.

For instance until radioactivity was discovered experimentally, no existing theory either confirmed denied or predicted it.

Yet those existing theories were correct within the bounds of their applicability.

On the other hand, new theory, beyond any existing, led to the search for and final discovery of the Higgs boson.

You cannot simply take external conditions like your 1,2 & 3, and apply them irrespective of the particular conditions of the theory you wish to apply them to.

Conditions sometimes interact in a most unpredictable and unruly way.

[swansont]

1 hour ago, Genady said:

For example, Newton's theory contradicted observations of perihelium of Mercury for centuries (requirement 2), but this was not enough to reject it.

To be fair, that wasn’t measured until well after the model was proposed, so “contradicted” might not be the best description. It took some time to be sure that unknown masses in the solar system weren’t responsible, and that this was truly an anomaly. 

[beecee]

1 hour ago, Genady said:

Requirements 1 and 2 are not absolute either.

For example, Newton's theory contradicted observations of perihelium of Mercury for centuries (requirement 2), but this was not enough to reject it.

GR has singularities which can be easily turned into mathematical contradictions (requirement 1), but they are considered being out of scope of the theory's applicability, not enough to reject the theory.

 Newtonian gravity, simply was not accurate enough to pick up the perhelion shift of Mercury, as opposed to contradicting it. GR was far more accurate and subsequently picked it up. I don't see Newtonian gravity as wrong because of that...just less accurate, but certainly accurate enough to be used everyday in Earth based situations (other then perhaps gps satellites where to maintain accuracy, GR is invoked) and in all our space shots.

At least they are my versions of it.

Edited January 23, 2022 by beecee

[SergUpstart]

9 hours ago, studiot said:

but there is much commonality between Physics and Mathematics.

Of course there is, mathematics is the main tool for a physicist. We can say that physics is a mathematical modeling of nature. I know only one law of physics that is not written in the form of a formula, this is Newton's first law. In turn, the need to solve certain physical problems leads to the development of relevant branches of mathematics, such as differential integral calculus.

But there is also a significant difference, in physics the criterion of truth is an experiment, and in mathematics - a strict sequence of logical proofs.

[exchemist]

2 minutes ago, SergUpstart said:

Of course there is, mathematics is the main tool for a physicist. We can say that physics is a mathematical modeling of nature. I know only one law of physics that is not written in the form of a formula, this is Newton's first law. In turn, the need to solve certain physical problems leads to the development of relevant branches of mathematics, such as differential integral calculus.

But there is also a significant difference, in physics the criterion of truth is an experiment, and in mathematics - a strict sequence of logical proofs.

Agreed, except that I would say an "observation" rather than an "experiment", as it is more general: doing "experiments" in astrophysics is not easy. 

However I think it is instructive to keep in mind that, even in physics, one can only apply mathematics once one has developed conceptions of the quantities to be included in the modelling: energy, momentum, electric charge, velocity, or what have you . To do that, words are required. 

[Genady]

I don't see such a "list of requirements for new theory" serving any purpose in science.