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How do I describe the difference between a theory that is purely descriptive in nature, vs one that is predictive? I.e. the former gives a rigorous description of the physical state of a system, while the latter will give expressions for the laws which govern the evolution of the system (thus the former can in principle be deduced from the latter).

A simple example is the following pair:

  1. A purely geometric description of the shape of islands on Earth (via fractal geometry or whatever you like), which is agnostic to the generating process of those islands which it is describing

  2. A geological theory that predicts the manifestation of islands on Earth (from which the description offered in (1) could in principle be recovered). This works the other way around; the generating process is fully described, while the outcome is emergent from that process.

I'm not well-versed enough in philosophy to know how to eloquently describe this difference. It seems like it may be a contrast between ontology and (something)?

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    Fawcett and Downs give a much more detailed classification of theories than just descriptive/predictive. I also think that your definition of "predictive" is too narrow, predictions may have nothing to do with evolution and time. For example, chemistry predicts certain spectral properties for light emitted or reflected by certain compounds, but there is no evolution involved. – Conifold Apr 15 at 19:34
  • @Conifold Sure. We are going to get into semantics now, but even your example is really about evolution of some system. That is, for any spectral signature, you depend on quantum models which predict by what means, and with what energies, a system will transition from one state to another. Or, for the reflection case, predict the photon interaction (I can write the incident wave as such, express the compound as such, and then compute the fields during an interaction). – Anonymous Apr 15 at 19:45
  • Such reinterpretations are not always possible (think of thermodynamics) or helpful. Predictions can be structural, from describing a system in terms of primitives to its global properties, for example. – Conifold Apr 15 at 19:49
  • Hi Anonymous, welcome to Phil.SE! I've edited the titles to perhaps provide better answers. An adjustment to the body of the question is required accordingly, but to not mess with your question too much I'll leave it to you. You can always revert back the change if you want. – Yechiam Weiss Apr 20 at 10:25
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Maybe this is the kind of thing you are looking for:

In Machine learning, we discern between discriminative and generative models. The difference is:

Take a true generative process P

  • a discriminative model is a function that tells us whether an example was likely generated by this process P (is this stock going up, or down? Is this XRay image generated by a cancerous patient or a healthy one? Is this land or water? ...)
  • a generative model can often also tell us this, but more importantly it is a (possibly approximate) model of P, so it can be used to create new examples (create training examples for cancer xrays, create art looking like it came from author, create new continent shapes starting from different initial conditions, ...)

Note how the discriminative model also predicts something, but does so in a different way from the generative model.

Mathematical proofs can be constructive or non-constructive:

  • non-constructive means you prove the existence of some mathematical object
  • constructive means the proof actually contains instructions for how to construct such an object
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