How I'm viewing the Incorporeal Trait Description
First paragraph regards how an incorporeal creature or object moves.
"An incorporeal creature or object has no physical form. It can pass through solid objects, including walls. When inside an object, an incorporeal creature can’t perceive, attack, or interact with anything outside the object, and if it starts its turn in an object, it is slowed 1. Corporeal creatures can pass through an incorporeal creature, but they can’t end their movement in its space."
Second paragraph regards how a incorporeal creature or object interacts with checks.
"An incorporeal creature can’t attempt Strength-based checks against physical creatures or objects -only against incorporeal ones- unless those objects have the ghost touch property rune. Likewise, a corporeal creature can’t attempt Strength-based checks against incorporeal creatures or objects."
Third paragraph regards a incorporeal creature or objects immunizes, resistances, and weaknesses.
"Incorporeal creatures usually have immunity to effects or conditions that require a physical body, like disease, poison, and precision damage. They usually have resistance against all damage (except force damage and damage from Strikes with the ghost touch property rune), with double the resistance against non-magical damage."
Now if their intent is to allow all check types to inflict damage in all cases of incorporeal vs corporeal then adding this to the end of both sentences in the second paragraph should work.
End of first sentence "...or the check is to inflict damage."
End of second sentence "...unless the check is to inflict damage."
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Someone gave an example of a bolder falling on to a incorporeal creature and it would do damage. Well although their is no example in the core rule book for how to deal with damage from a falling object. What we do have is damage from traps. Lets look at three traps Slamming Door, Spear Launcher, and Scythe Blades all on Pg.523
All three are mechanical traps so they do non-magical damage.
The slamming door effect is "3d8 bludgeoning damage to anyone beneath or adjacent to the slab when it drops" Before damage is done all being effected by this trap roll a reflex save its a dexterity check so incorporeal creatures roll this check because they can roll the check they can take damage from this trap. But because it takes an athletics check (a strength-based check) to lift the slab a incorporeal creature would not be able to move the slab once its fallen.
The spear launcher effect is "The trap shoots a spear, making a Strike against the creature or object on the floor tile. This strike action the spear trap does is ranged so it dexterity-based so it can make the strike against a incorporeal creature or object thus possible causing non-magical damage to them.
Scythe blades effect is "Both blades swing down, each one Striking all creatures under the ceiling grooves." This strike action the scythe blades do is a melee so its strength-based so no check is made against the incorporeal creature or object.
And yes I know an incorporeal creature would not be able to activate traps in most cases. I'm using them as example for if a incorporeal creature or object where it be hit will damage that's from a source that's not form a creature (or player character).
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How I would completely rewrite the second paragraph to make it more clear.
Incorporeal creatures can make checks that use their strength modifier against incorporeal creatures and objects. If an incorporeal creature attempts a check that uses their Strength modifier against corporeal creatures or objects and the result is a success or critical success they get a failure instead unless those objects have the ghost touch property rune. Likewise, if a corporeal creature attempts a check that uses their strength modifier against incorporeal creatures or objects and the result is a success or critical success they get a failure instead.
And again same as before if all check types are suppose to do damage in all cases of incorporeal vs corporeal then adding this to the end of second and third sentences in the second paragraph should work.
End of second sentence "...or the check is to inflict damage."
End of third sentence "...unless the check is to inflict damage."
Why do I use "a check that uses their strength modifier" instead of keeping "Strength-based checks".
I did it so people reading it understand it's the modifier being used in the check that matters not the check itself. In case they have some feat or trait that allows them to use a different modifier then strength for a check that usually uses strength. As for instance with the finesse trait.
Why change from "can't" to "if they preform check and succeed or critical success they fail".
To me I find it very stupid to imply in your rules that an action is impossible to attempt. To me its saying, before you preform a check using strength against a incorporeal creature or object your GM must tell the player no your can't roll that check do something else. I find this stupid, no check should be impossible to roll, instead a impossible checks should have you roll against the appropriate DC but getting a success or critical success always results in a failure. This leaves open the possibility of getting a critical failure.
Also the GM telling the play to do something else stops the player from making a mistake in the game world thus preventing the player and character seeing their check do nothing (in most cases).