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In the early 1800’s it was found that the observed orbit of Uranus deviated from the theoretical predictions (based on Newton’s theory of gravity and a seven planet model of the solar system). Instead of rejecting Newton’s theory on the basis that it gave the wrong predictions, it was hypothesized that the auxiliary premise that there are seven planets is false and that there is another—hitherto unobserved—planet outside the orbit of Uranus. Was this an ad hoc hypothesis?

For what I understand, this was not an ad hoc hypothesis since it the existence of another planet was indeed testable which contradicts the criterion of an ad-hoc hypothesis, namely that introducing an ad-hoc hypothesis does not intreoduce any new testable consequences. Am I correct?

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It was not an ad-hoc hypothesis. Instead, searching and detecting a further planet - Neptune - was a brilliant confirmation of Newton's theory of gravitation.

In the beginning of 20th century most of the precession of mercury could be explained by Newton's theory of gravitation. But all attempts failed to explain also the rest. I do not know whether ad-hoc explanations have been suggested. Nevertheless, when finishing the General Theory of Relativity Einstein derives the full precession from a preliminary version of his theory. That's another brilliant example that a theory explains many facts, which have not been used as input to develop the theory.

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    It is not so simple. Leverrier and Adams's estimates for mass and orbital radius of Neptune were vastly off, so the predicted position in the sky might have been correct only by coincidence theoriginal1701.hubpages.com/hub/… After Neptune Leverrier attempted the same trick with Mercury's anomalous precession, predicting planet Vulcan, which never materialized. But Seeliger's 1906 hypothesis of flat ring around the sun succeeded at explaining it, and was accepted by many until Einstein gave an alternative explanation mathpages.com/rr/s8-10/8-10.htm – Conifold Aug 24 '15 at 23:46
  • @Conifold These are two interesting historical sources shedding some light on the people behind. I think the sources do not change my answer. But I made a slight edit concerning the chronological order. As stated by the second source, chapter 8.6 of the textbook Weinberg, Steven: Gravitation and Cosmology. 1972 follows Einstein's way of calculation the precession. – Jo Wehler Aug 26 '15 at 4:27
  • I am willing to entertain an idea that ad-hocness may depend on whether it becomes a pattern with a theory. Vulcan, then Newcomb's zodiacal cloud, then his correction to the inverse square law, then Seeliger. On its own each one is fine, but as a pattern... Unlike others, Einstein and Poincare didn't buy into it, they felt that the problem was fundamental. Still, Seeliger's ring could materialize after all. Also, an ad-hoc hypothesis may turn out to be true. Cosmological constant seems like a candidate. If ad-hoc is taken as "supported by a single discrepancy" Neptune was that. – Conifold Aug 26 '15 at 18:41
  • @Conifold I agree with you concerning the cosmological constant. Its status is in doubt. A bit sloppy: If it's Einstein, who invents an ad-hoc explanation, then he possibly hits at a fundamental addition :-) – Jo Wehler Aug 26 '15 at 18:42
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You have to understand that there's a huge difference between a theory and a model. A theory can never be disproved, so its either the universal law for gravitation that would be disproved, either your theoretical models trying to describe our solar system. Obviously, it could also be an experimental problem: either a technical one, either a bad interpretation of what people saw in the sky. Let me explain why.

A theory is basically a world-view: a metaphysical framework, defining primitive concepts (like space, time, mass, force) and how they are related (the second law), in order to interpret the laws of nature and how they function. The goal of a theory is not at all to describe an explicit "realization" of the laws of nature. For example, Newtonian mechanics takes as primitives concepts such as (absolute) space, time, mass, and force. From them, it is able to define inertial frames, third law, and second law. What is the (non trivial) link between this abstract world-view and the real world we experience?

Before explaining that it is the goal of models to do such a link, notice that the second law F = ma really is a constraint on how the primitive concepts are related. That is, given the data of the force knowing the mass, one is able to compute the acceleration. Reciprocally, given the data of the acceleration and knowing the mass, one is able to compute the force required on an object of mass m in order to fulfill such dynamics.

Keeping that in mind, a model is nothing else than to make explicit two of the third primitives involved in the second law, and to compute the third one from the theory (here the second law). If the theory is a good explanation of the world, then it would give a correct prediction for such model. Point is, you don't know yet if the model you proposed is realized in nature, or how to link it with real life. Now, the power of classical mechanics comes from the fact that there exists a universal model for gravity: its simple, can be easily justified (by mean of rotational invariance and energy invariance related to Galilean invariance) and it is the same for all physical objects. Quite an achievement!

The thing to remember, still, is that when one is trying to predict phenomenon of the real world (that is, instantiation of these laws if one believes the latter are really good description of the world), one has to produce such a model. Yet, it is always possible to complexify these models, at such points that all phenomenon you're going to see in real life are effectively described by your theory.

Now, it is also really easy to produce a model that cannot be realized in nature: the model where F is some exponential of exponential of exponential of ... of exponential of time, with mass 1. Try to see it and confirm it, good luck. Does this mean that the theory is shitty? Not at all. It means that your model is shitty, quite a difference. Reciprocally, it is really easy to find real life experiments that are hard to link with known models. You will have hard time predicting how a spring behaves with the universal model of gravity applied to all particles composing the spring. Is the universal model of gravity shitty then? Well, no, it's just not complete enough to describe everything. The theory being able to produce easy phenomenological models, like the one of a spring, it is actually even strengthened by the failure of the universal model of gravity to predict the motion of a spring.

To conclude, let me just add that you shouldn't believe the bullshit of Popper and his liberals/marxists followers: they are materialists people who don't understand that it is never trivial to link the physical world with abstractions like theories and models.

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