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I have confronted a philosophical problem related to the definition of the "property of an object."

What I believe is:

The capability of an object (the capability to desire) is the property of an object. However, the action that stems from such capability, or the action itself (the action of desiring) cannot be the property of an object.

For instance, let's look at the example of a quail:

The ability to fly is the property of a quail.

However, the action of flying cannot be the property of a quail.

Can the action of an object be the property of an object? Consequently, can the action of an object be the property of a certain state of an object? Or is the action the state of an object itself?

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    Those are pretty rare objects that can desire and act. Are you talking about agents or something similar? And while being capable of acting in some way can be a property the action itself is not, see SEP Properties.
    – Conifold
    Mar 27 '20 at 3:47
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    – J D
    Mar 28 '20 at 11:11
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What you're talking about, I think, is the distinction between a categorical property and an instantiation of that property. The category 'quail' has the property 'can fly,' because flying is something that all quail can do. But the quality 'is flying' is something that refers to a specific moment in time for a specific member of the category, and may be true of false.

In bullet points:

  • The proposition "Quails can fly" is always true, because 'can fly' is a property of the category 'quail'
  • The proposition "A quail is flying" may be true or false, depending on context

Keep your mental eye on the distinction between categorical universals and the idiosyncratic dispositions of individual members of a category. "All men are mortal" means that (as a universal principle) all men die; it does not say anything at all about whether you and I (idiosyncratically) are dead.

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I would argue that there is at least one case where the actual performance of an action characterizes something more than the ability to perform the action.

For example, any piece of space debris has the ability to orbit a larger celestial body, but only the ones that do so are satellites.

I guess whether or not the performance of an action can be considered a 'property' of something is still up in the air, but I find it significant that the distinction between 'satellite' and 'not a satellite' is whether or not it's orbiting instead of whether or not it's able to orbit. If 'property' is meant to be synonymous to 'characteristic' - or something that characterizes something else - then this might be relevant to the discussion.

Maybe to get around this (get it? like orbiting?) you could phrase the property of a satellite as a state of being in orbit as opposed to the action of orbiting. Personally, I find that to be just a semantical trick and not a very definitive answer to the OP's question, but it might satisfy some people.

I admit that there are probably not many examples of this kind of case... but I think it's still worth considering!

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It's a bit like asking if the velocity of a point can be the property of the point itself. For the velocity to exist other points are required. It's a relational property, and so is the action of the quail. It can't have desire if there is nothing to be desired for. Other quails live in the neighborhood (or at least, let's imagine). To get closer or further away (if the desire is negative), there is quail space around them needed. The quails can move through this space and they can do this accordingly to their desire. The bigger the desire the faster they will try to get there (or move away from it). So their relationship to other quails can be expressed as their movement through space. They move through this space with a speed, or in the case of an action, more space is needed. The action can be seen as the measure of their desire. All ( or a part) of space is needed to express this desire. So the action is a property of the quails. But is is situation dependent, and as such a relational property (as are all desires).

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