Generally it’s not obvious when there’s something invisible in your line of sight. That’s kinda the point of invisibility.
I think the issue is that Invisibility is encompassing two separate concepts: When someone
can't see you (ie: the Invisibility spell), and when someone
doesn't see you (ie: hidden).
In both cases, the person is unable to see you, but the reasons for that are different. In one, the light isn't reflecting off of you for the person's eyes to see. In the other, the person just isn't looking in the right place, or you've painted yourself to look like a wall and blend in with the background, or you cover yourself in mud to avoid the IR senses of the alien, or whatever.
The conditions that allow the person to see you are thus different based on the source and method of Invisibility, even though they both have the same practical effect — the person doesn't see you — and thus are listed as the same condition.
Fine, a special sense then. My point is, invisibility is definitionally the inability to see something with normal vision, even when it’s right in front of you.
"the inability to see something with normal vision" — Yes
"even when it’s right in front of you." — No
And going back to the original text, as posted by Treantmonk, but leaving out his edit:
With the hide action, you try to conceal yourself. To do so, you must succeed on a DC 15 Dexterity (Stealth) check while you're Heavily Obscured or behind Three-Quarters Cover or Total Cover, and you must be out of any enemy's line of sight; if you can see a creature, you can discern whether it can see you.
On a successful check, you have the Invisible condition. Make note of your check's total, which is the DC for a creature to find you with a Wisdom (Perception) check. The condition ends on you immediately after any of the following occurs: you make a sound louder than a whisper, an enemy finds you, you make an attack roll, or you cast a spell with a Verbal component.
Note that without Treantmonk's edit, there's a bit more flexibility in the meaning.
- You lose the condition after an enemy finds you.
- Your Stealth check's total is the DC for a creature to find you with a Wisdom (Perception) check.
Note that finding you does not include the requirement that it be done using a Wisdom (Perception) check, only that finding you with a Wisdom (Perception) check must beat the DC of your Dexterity (Stealth) check.
So that leaves open the option that you can be found by means other than a Wisdom (Perception) check, which should include standing out in the open where you're easily seen. Another method might include using a spell like Scrying.
The only real question is the interaction with the spell See Invisible. If I'm hidden and standing behind you, and you cast See Invisible, do you know that I'm there if you're still looking away from me?