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Do you know if 'impossible' properties exist when viewing it from a Platonic realism viewpoint? An example of an 'impossible' property might be something like "being faster than the speed of light" which could never be instantiated because it would break the laws of physics. Does that property still exist (according to Platonic realism) even though nothing could be faster than the speed of light?

I have heard that there are no uninstantiated properties (https://en.wikipedia.org/wiki/Instantiation_principle) so does this mean that the property of "being faster than the speed of light" does not exist because it cannot be instantiated?

Thanks

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    There is a version of platonist realism developed by Meinong that allows nonexistent, physically impossible, like perpetuum mobile, or even logically impossible objects, like square circles, see SEP, Nonexistent Objects and Impossible Worlds. Those can then have impossible properties without violating the instantiation principle.
    – Conifold
    Aug 13 at 17:52

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Physically impossible forms certainly exist from the point of view of Platonic Realism. Classic examples are perfect circles and triangles on an infinite Euclidean plane. No actual circle or triangle drawn on a sheet of paper can be perfect. The lines are of non-zero width. They wobble. The paper at the microcopic level is a tangle of fibres that is far from flat, and very far from infinite. A perfect circle is physically impossible to instantiate, but exists in the Platonic realm.

So we have three levels:

  • Substance - like paper and pencil lead;

  • Particulars - the shapes into which some actual substance is arranged, like an approximately flat sheet, or an approximate circle;

  • Forms - mathematically idealised circles and planes - the shapes that real-world pencil-and-paper circles are representing or approximating.

Philosophical positions on which of these are 'real' can (oversimplifying grossly) be roughly classified as:

  • Nominalism - only the substance is real. Everything else is in the mind. Circles and planes and even sheets of paper are all mental categories our brains invent to try to split the world up into manageable chunks. They don't exist in objective reality.

  • Immanent Realism - substance and particulars exist, but forms do not. We can take the set of all approximately flat sheets of paper, the set of all approximate circles, as being real, since they actually exist in the world. But physical impossibilities like the perfect circle and the infinite Euclidean plane do not actually exist. They're false inventions of our brains. (This is the position the Instantiation Principle belongs to.)

  • Platonic Realism - all three levels exist, independently of human minds. Orbits approached elliptical and stars and planets approached spherical long before humans came along to invent those ideas.

There is no problem at all in Platonic Realism with physically impossible properties being real things. I'm not so sure about logically impossible things. Personally, I think they should also be acceptable, at least as forms you can only approximate but never actually reach. (For example, the concept of 'actual infinity' was invented as the ideal point to which ever more distant points approached/approximated, even though from Euclid's original point of view the idea is logically impossible - it is the 'end' of the endless.) But I'm not sure Plato himself would have agreed! The reality and logical consistency of 'actual infinity' has long been a controversial subject.

As a final sidenote, it's probably worth mentioning that things moving faster than light isn't actually physically impossible, depending on what you mean by 'things'. For example, if a moth circles a candle flame at just under the speed of light, its shadow on the surrounding circular wall a hundred times further away travels at just under a hundred times the speed of light. If a giant pair of scissors closes, the point at which the blades intersect can move faster than light. The speed at which the wave peaks travel when light passes through a refractive medium (called the phase velocity) is generally faster than light.

According to the rules of physics as we currently understand them, you can't get matter ('substance') to move faster than light (measured locally in an inertial frame - definitions get a bit messier in rotating frames of reference, curved space, or an expanding universe), but 'particulars' and 'forms' like shadows, boundaries, and intersection points are not so limited.

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