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we say that they are competing because their logically contradictory if accept one of them we must reject the other.......to choose between them therefore we need to expand the scope of our observational generalization.

My question is what to do if we cannot have observational generalization.May be thought experiments.

Take for examples both heliocentric theory and geocentric theory matches with the data/observation but both conceptually contradictory theories...

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    One word, barycenter!
    – Hudjefa
    Jan 10 at 4:33
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    Empirically equivalent theories can be compared on so-called cognitive values, like unification, explanatory power, simplicity and coherence with broader context, see SEP. While this weeds out particularly poor candidates, those values are open to interpretation and several viable candidates may well remain. What to do then? There is nothing we can do other than wait for more observational evidence to become available. This is currently the case with major interpretations of quantum mechanics.
    – Conifold
    Jan 10 at 6:04
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    @Conifold, but there is no reason to think those cognitive values are indicators of truth. Jan 10 at 6:13
  • @DavidGudeman It is popular, albeit controversial, to think that there are such reasons, see IEP, for example. It is even more popular and less controversial that knowledge and understanding have added value compared to bare truth and cognitive values are linked to them.
    – Conifold
    Jan 10 at 6:55
  • A theory that can't be verified with data is a speculation. Wait for the facts. Two theories that can't be verified with data are... Nevermind.
    – Scott Rowe
    Jan 10 at 12:10

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  1. Your example presents two competing theories – the heliocentric and the geocentric – and astronomy at that time could not decide by observation which one is right.

    Why do we accept today the heliocentric theory?

    Because the heliocentric theory treats all the planets in the sun system according to the same principle of kinematics. While the sun, which is distinguished by its mass, holds the distinguished position in one of focal point of the planet orbits.

    Much later after Copernikus Newton discovered the law of gravity which even explains the dynamics observed by Kepler. A similar dynamical explanation could not be given by the geocentric theory.

    Hence today we prefer the theory with explains more than its rival.

  2. A different example from history is the explanation of light either as a wave (Huygens) or as particles (Newton). The case had to be left open until the 20th century, when it found a solution in quantum theory, a totally different paradigm.

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  • if we cannot have observational generalizations then what to do
    – quanity
    Jan 10 at 6:41
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    @quanity I pointed out for both examples: One had to keep the question open, until the case could be settled later by a more profound theory - Newton's theory of gravity resp. quantum mechanics.
    – Jo Wehler
    Jan 10 at 7:08
  • light is vector in Hilbert space so its neither particle nor wave
    – quanity
    Jan 10 at 7:40
  • @quanity Please give a reference for your last statement about light being a vector in Hilbert space. IMO it is not correct.
    – Jo Wehler
    Jan 10 at 7:52
  • observables are represented by operator and state is represented by vectors/wave function postulates of QM
    – quanity
    Jan 10 at 10:23

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