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I wrote this originally as a response to another question posed on Quora as to whether or not but I was wondering if someone could reexamine this and find any possible possible gaps in logic or knowledge.

I used it as an answer to a question about whether or not it was possible to create a complete scientific (i.e. empirical) model of physical reality that encapsulated an explanation of all physical phenomena.

The answer concludes that such a formulation would be impossible by contradiction.

Assume that there is a scientific model capable of explaining any physical phenomena. That would mean such a model would include any physical event at any given point in time. In other words, it would account for every physical event that has happened, is happening and will happen. The problem with this model is that when it comes time to empirically test it using experiment the model would already be able to predict the experiment that will occur and the results of that experiment which would make it an unfalsifiable hypothesis since any experiment would always assert the hypothesis' correctness. Of course if no experiment is performed then it is not empirically proven and therefore not a scienctific theory. That means that if there is a complete empirical model of physical reality it would have to be accepted as empirical even though it can never be tested empirically. A contradiction.

I feel like I may have reinvented the wheel here but working through this has definitely got my wheels turning. Can anyone find any holes in this or point out if this work has already been done by others?

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    i don't think a Theory of Everything (TOE) needs be like Laplace's TOE (sorta a "Clockwork Universe") where all we need to do is perform all of the summations to predict how every interaction occurs. a TOE can have, in its model, a random component just as QM does now.
    – robert bristow-johnson
    May 7, 2017 at 5:24
  • @robertbristow-johnson that's true but it is still possible to use an experiment to determine if an event is probabilistic along with those probabilities and if the probabilities predicted by a hypothetical TOE are confirmed by experiment that same TOE would predict the experiment and its outcomes a priori leading to the same contradictions mentioned earlier.
    – Mike
    May 7, 2017 at 5:27
  • no, it is not possible to predict exactly how an experiment will turn out if the experiment is set up to falsify (or not) a model or theory that itself has a random component. it does not obviate a falsifiable claim.
    – robert bristow-johnson
    May 7, 2017 at 5:31
  • @robertbristow-johnson that's what I'm trying to work out. If there is a scientific TOE that can predict any physical phenomena, or the exact probabilities that any phenomena would occur, that would mean it would be able to predict any outcome of any experiment intended to falsify it thus rendering the initial hypothesis to confirm a TOE unfalsifiable. Even if you include the probabilistic component that same TOE would predict those probabilities and hence the probability of the outcomes and hence would always assert its correctness and remain unfalsifiable.
    – Mike
    May 7, 2017 at 5:37
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    No theory can be validated empirically in the sense required by your argument, so it is moot. Scientific theories are hypothetical and experiments either confirm or infirm their consequences. Experiments presumably will always agree with TOE (as is the case with QM so far) but that is exactly what will empirically confirm it, not make it unconfirmable. It is not required that some experiment actually contradict a theory, only that such a contradiction be possible, and "master kernel" is compatible with that.
    – Conifold
    May 8, 2017 at 18:31

4 Answers 4

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Hawking said that he gave up on toe due to Godel's incompleteness thm. Godel showed that there will always be a sentence whose truth is undecidable within its own system.

so your approach to the proof of impossibility of toe cannot be in the right direction in the first place.

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  • Thanks for bringing the Hawking's position to my attention, I wasn't aware of it. How do you conclude that because Hawking used Godel's incompleteness theorem to come to his conclusion invalidates mine? Godel proved his conclusions via contradiction, i.e. any system of math that asserts itself as a consistent and complete set of truths must be simultaneously consistent and inconsistent which is a contradiction and therefore impossible. How do you gather that differs from what was stated above?
    – Mike
    May 8, 2017 at 6:13
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Your argument begs the conclusion. You cannot state that the hypothesis can never be false because the model proves it can never be false until you accept the model. Given that model is the thing under test, you have no reason to assume its proofs are true.

The more interesting issue is the challenge of developing meaningful empirical experiments. At some point, as with all science, you're going to have to declare that the evidence you gathered is empirically sufficient to "prove" the model is correct. Designing an experiment to test something which does a good job of predicting what experiments you are going to want to run is a bit disconcerting.

The issues with Godel are also fascinating, but they only apply if you have a system which can mathematically prove its own correctness. If you are not relying on mathematical correctness, and instead are only relying on empirical validation, you can sidestep his issues.

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Your proof contains a few unwarranted assumptions.

  1. As Mr.Johnson correctly points out, your very first assumption (there is a scientific model capable of explaining any physical phenomena) is unwarranted. Laplace's Demon asserts that, if he knows the momentum and position of each and every particle in the universe, he can predict the past and the future as if they are unfolding presently, with his unbound computation capacity.

Heisenberg, however, showed that the Demon cannot do so since the knowledge of momentum and position simultaneously is unattainable.

  1. You regard falsifiability as the criterion for scientificity, which is again unwarranted. The current consensus among philosophers of science is that a scientific theory cannot be reduced to testable statements. The Duhem-Quine thesis is the accepted view.
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    1) The uncertainty principle posits that the universe is indeterministic but it does not preclude that the probability of events can be scientifically validated through experiment which is the goal of QM and therefore makes a complete probabilistic map of the universe throughout time possible. 2) Do you have a source that falsifiability is not necessary for a hypothesis? And wouldn't a ToE be a refutation of Duhem-Quine? A validated ToE would mean that physics is complete making it impossible for a hypothesis to remain perpetually valid since no change can be made to any accepted physics.
    – Mike
    May 8, 2017 at 18:14
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    With pilot wave theory it is possible to know both position and momentum of a particle at the same time.
    – Xaqron
    May 8, 2017 at 21:04
  • to Mike, 2) Popper is way of favor in the US. just google any d-h thesis to get info.
    – Nanhee Byrnes PhD
    May 8, 2017 at 21:44
  • to Mike, 2) Popper is out of favor: check out Carnap's criticism of Popper. just google any d-h thesis to get the info.1) i thought qm theorists fight among themselves what probability should mean (e.g., the inherent structure of the world, partial ignorance..). help us understand what you mean by toe.
    – Nanhee Byrnes PhD
    May 8, 2017 at 21:50
  • so i just checked out the pwt, and i realize it is a theory type based on the hidden variable assumption. I am sure this type of theories is pretty much repudiated by experiments in qm.
    – Nanhee Byrnes PhD
    May 8, 2017 at 22:07
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I have a problem with the below statement in your argument:

"The problem with this model is that when it comes time to empirically test it using experiment the model would already be able to predict the experiment that will occur and the results of that experiment which would make it an unfalsifiable hypothesis since any experiment would always assert the hypothesis' correctness."

First, recall that a falsifiable theory doesn't mean that an experiment can be designed whose outcome goes against the theory. Rather, it means that a criteria can be given which, when met via the outcome of an experiment, can lead to a contradiction to the theory. For example, if I am testing the model of classical gravitation on earth via dropping apples, I am dropping apples with the criterion in mind that if one floats up, I now have a piece of evidence which falsifies the model.

However, you seem to be asking for something else when you say "falsifiable". You are asking if an experiment can be designed whose outcome shows the theory to be false. Rather, what you should be asking is, "What is the criterion which would lead me to believe a given TOE is false?"

Here's one criterion: Suppose the model predicts that a particular experiment will happen and the outcome of that experiment, but in reality it does not happen. Then the model hypothesis was falsified by observation.

If the TOE model is actually the "correct" model of reality, it'll just keep correctly predicting the outcomes of experiments, just like any other theory. Therefore, there can be an empirically supported TOE.

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