'Correlation Does Not Prove Causation'

A few people have told me that before, but now I get it.

My physics textbook says, "If our model is a good approximation to the real world, our prediction will be a good approximation to what will actually happen."

This is a false assumption because though your model fits the data you've collected, you have no reason to think that it actually does so, in that way. It's like assuming that your outcome could only possibly be caused by one thing, then your model must be that cause. Even if the data continues to seemingly corroborate your model, all you've proved is that the model hasn't changed, not that your model is the correct one. Your model could very well be Ptolemaic.

It's like you're given a set of data points, and instead of looking for the function of those data points, you connect them in what seems the most obvious pattern to you. Then you extrapolate that pattern without regard for the cause of your data points. And if ever your model should fail to predict the data points, then you simply alter the model to now fit both patterns, rather than looking for the cause of the difference. Replace the term 'you' with 'theoretical physicist' and you get the mess of quantum mechanics today.

A mathematical model may certainly be internally valid, in a deductive sense, and indeed may accurately reflect the data. But where does this model come from; how does it fit the data; why did you pick it as opposed to any other model that also fits the data? It is these relationships between the cause of an event and the event that needs to be identified, and then from there you can make a simplified model.