My point was that trying to express epicycles in the new terminology is not possible.
But it is! You simply specify the position as a function of time and you’ve done it! The reason why that seems so strange isn’t because modern physics has erased our ability to add circles together, it’s because we no longer have epicycles as a fundamental object in our model of the world.
So if you want the copernican revolution to be a paradigm shift, the idea needs to be extended a bit. I think the best way is to redefine paradigm shift as a change in the language that we describe the world in. If we used to model planets in terms of epicycles, and now we model them in terms of ellipses, that’s a change of language, even though ellipses can be expressed as sums of epicycles, and vice versa.
In fact, in every case of inexpressibility that we know of, it’s been because one of the ways of thinking about the world didn’t give correct predictions. We have yet to find two ways of thinking about the world that let you get different experimental results if you plan the experiment two different ways. In these cases, the paradigm shift included the falsification of a key claim.
Rather, I think it would be surprising for a discipline independent of empirical facts to have paradigm shifts
I don’t think it’s necessarily true (for example, you can imagine an abstract game having a revolution in how people thought about what it was doing), but it seems reasonable for math, depending on how you define “math.” I think people are just giving you a hard time because you’re trying to make this general definitional argument (generally not worth the effort) on pretty shaky ground.
Thanks, that’s quite clear. Should I reference abandonment of fundamental objects as the major feature of a paradigm shift?
In fact, in every case of inexpressibility that we know of, it’s been because one of the ways of thinking about the world didn’t give correct predictions.
Yes, every successful paradigm shift. Proponents of failed paradigm shifts are usually called cranks. :)
My position is that the repeated pattern of false fundamental objects suggest that we should give up on the idea of fundamental objects, and simply try to make more accurate predictions without asserting anything else about the “accuracy” of our models.
Predictions about the world are only possible to the extent the world controls the predictions, to the extent considerations you use to come up with the predictions correspond to the state of the world. So it’s not possible to make useful predictions based on considerations that don’t correspond to reality, or conversely if you manage to make useful predictions, there must be something in your considerations that corresponds to the world. See Searching for Bayes-Structure.
Isn’t “makes accurate predictions” synonymous with “corresponds to reality in some way” ? If there was absolutely no correspondence between your model and reality, you wouldn’t be able to judge how accurate your predictions were. In order to make such a judgement, you need to compare your predictions to the actual outcome. By doing so, you are establishing a correspondence between your model and reality.
But it is! You simply specify the position as a function of time and you’ve done it! The reason why that seems so strange isn’t because modern physics has erased our ability to add circles together, it’s because we no longer have epicycles as a fundamental object in our model of the world.
So if you want the copernican revolution to be a paradigm shift, the idea needs to be extended a bit. I think the best way is to redefine paradigm shift as a change in the language that we describe the world in. If we used to model planets in terms of epicycles, and now we model them in terms of ellipses, that’s a change of language, even though ellipses can be expressed as sums of epicycles, and vice versa.
In fact, in every case of inexpressibility that we know of, it’s been because one of the ways of thinking about the world didn’t give correct predictions. We have yet to find two ways of thinking about the world that let you get different experimental results if you plan the experiment two different ways. In these cases, the paradigm shift included the falsification of a key claim.
I don’t think it’s necessarily true (for example, you can imagine an abstract game having a revolution in how people thought about what it was doing), but it seems reasonable for math, depending on how you define “math.” I think people are just giving you a hard time because you’re trying to make this general definitional argument (generally not worth the effort) on pretty shaky ground.
Thanks, that’s quite clear. Should I reference abandonment of fundamental objects as the major feature of a paradigm shift?
Yes, every successful paradigm shift. Proponents of failed paradigm shifts are usually called cranks. :)
My position is that the repeated pattern of false fundamental objects suggest that we should give up on the idea of fundamental objects, and simply try to make more accurate predictions without asserting anything else about the “accuracy” of our models.
How can you make accurate predictions while at the same time discarding the notion of accuracy ?
I have no reason to expect that our models correspond to reality in any meaningful way, but I still think that useful predictions are possible.
Predictions about the world are only possible to the extent the world controls the predictions, to the extent considerations you use to come up with the predictions correspond to the state of the world. So it’s not possible to make useful predictions based on considerations that don’t correspond to reality, or conversely if you manage to make useful predictions, there must be something in your considerations that corresponds to the world. See Searching for Bayes-Structure.
Isn’t “makes accurate predictions” synonymous with “corresponds to reality in some way” ? If there was absolutely no correspondence between your model and reality, you wouldn’t be able to judge how accurate your predictions were. In order to make such a judgement, you need to compare your predictions to the actual outcome. By doing so, you are establishing a correspondence between your model and reality.