Specifically, I like the notion of mental shape because shapes have specific properties, and our properties or abilities 'fit' with what I've described as environmental gradients — Pantagruel

In the ecological or enactive approach to psychology, perception is a recognition of environmental affordances - https://en.wikipedia.org/wiki/Affordance

:up:
I think this concept fits well with the approach of embodied or embedded cognition as well.

What exactly does Searle say about intentionality and background abilities?

John Searle talks about intentionality rising to the level of background abilities. In other words, your mind steers at the level of its expertise (which is a function of experience and skill). A beginning skier focuses on 'shifting weight onto the downhill ski' in each corner, while an expert skier just 'picks a path' down a slope. — Pantagruel

The example is Searle's, from the book Rediscovery of Mind.

stick can be used to bash over the head, or it can be used as a lever to roll a giant rock down a hill. Or it can be used to scratch symbols in the sand. The same basic physical form can have radically different functionalities. Therefore radically different abilities. So even if beings have the same physical form, they can have radically different 'shapes' with respect to their environments. And hence different properties as reflections of their 'shapes.' Which are different abilities.

If as a result of a purely mental operation otherwise identical physical things can acquire different properties, then these properties are instantiations of the mental. And if these properties enhance survival then they result in progressive physical modifications. So the 'shape' of the mind in the world is a product of its own mental operations (in a physical context) and not merely a physical product. — Pantagruel

I think it is misleading, and therefore incorrect to call this immaterial property "shape". What you describe is that the same physical object can be used for a multitude of purposes. Hence the same "shape", the shape which the object has, can have different functions. "Function" is determined by purpose which is dependent on a goal. So "function" is determined in relation to the goal. It is incorrect to say that the function of a thing is a property of the thing, because it is really a feature of the thing's relation to the goal. So we cannot correctly call it a property or "shape" of the thing.

pecifically, I like the notion of mental shape because shapes have specific properties, and our properties or abilities 'fit' with what I've described as environmental gradients. — Pantagruel

The problem with this perspective is that our capacities always extend beyond our properties. This you describe in the op when you say that the same physical object can be used in multiple ways. "Property", if could by applied to usage, would refer to the current usage, and cannot go beyond that, as it is incorrect to say that something has a property which is not currently existing. But if a creature produces a new intention, has a new goal, then the same physical object might be be used in a new way, and this may become a new property (if property could be applied to usage). But as I explained above, the capacity of the object to be used in all sorts of different ways is not a property of the object itself, because it does not exist within the object, as it is dependent on the mind which views the object with intent toward a goal.

The problem with this perspective is that our capacities always extend beyond our properties. — Metaphysician Undercover

Exactly. As Descartes says, "the will is much wider in its range and compass than the understanding." And yet not everyone discovers a bashing stick can be a lever.

But for the person using the stick, whatever functional effects that stick confers de facto become properties of that person in the context of the world. If someone attacks me, and I have access to a stick, it is a property of mine that I will bash him over the head. Just like it is a property of glass that it will shatter when struck. It's called a dispositional property.

If you use "properties" in that way, referring to the function of a thing, then you must respect that functions which the object does not currently have, though the object has the capacity to be used that way if approached by the right mind, are not actually properties of the thing, because it is not being used that way. Otherwise the thing has all sorts of different properties at the very same time, in violation of the law of non-contradiction.

Do you have a page reference please?

If you use "properties" in that way, referring to the function of a thing, then you must respect that functions which the object does not currently have, though the object has the capacity to be used that way if approached by the right mind, are not actually properties of the thing, because it is not being used that way. Otherwise the thing has all sorts of different properties at the very same time, in violation of the law of non-contradiction. — Metaphysician Undercover

True. And as I suggested, different people with the same physical capacities can nevertheless have very different abilities. Will and understanding are definitely factors. The properties of a conscious entity are much more complex than those of a material object.

↪Pantagruel Do you have a page reference please? — Daemon

Of course. The example I cited is from page 195 of the original MIT press hardcover.

Consciousness is a state of being. It cannot be quantified. It is.

A given individual Mind has its own set of experiences, which cannot be quantified.

Forget about trying to quantify life. It is what it is and it's continuously changing.

Consciousness is a state of being. It cannot be quantified. It is. — MondoR

If I have a new experience, then my state of being is different subsequent to that experience and prior. It seems reasonable to view this as an additive change. One doesn't have to quantify absolutely to recognize a relative difference.

It seems reasonable to view this as an additive change. — Pantagruel

Experience is a strange little breast. Experience does create change (a creative action), but is it additive? I would say it is transformative.

Experience is a strange little breast. Experience does create change (a creative action), but is it additive? I would say it is transformative. — MondoR

Interestingly, you used the term creative. I think creation implies novelty, hence something being added.

Yes, I would liken it to molding a piece of clay into a new shape.

A perfect example. And a sphere has the property of rolling which a lump of clay does not have. So this is an additional property (reduced surface friction).

The first precept against killing, since all life is sacred. And all living things partake of Buddha nature. — Pantagruel

This is a Mahayana/Vajrayrana view. Other Buddhist schools would point out that by killing, one accrues "bad karma" for oneself. A Buddhist might also argue that killing is wrong because it doesn't solve the problem of suffering, even though one engages in kiling for the purpose of solving the problem of suffering.