I don't think it works like that. Consider that you can make a doughnut from the plane in two ways; make a horizontal cylinder and bend it round, or make a vertical cylinder and bend it round.
So I make a horizontal cylinder, but standing at the back of flat Pac-world, and the 'corners are now left and right middle facing me. Now I bend the cylinder around, and the corners are on the inside of the hole facing away from me. Or I can do the same thing with the vertical cylinder. So is the hole N-S or E-W? Or to put it another way, one pair of edges forms the inner ring around the hole, and the other pair goes through the hole. But which is which? — unenlightened
Btw, that Feyerabend quote in your profile recall the pleasure I've had reading that book. Maybe time for another reread. :smirk: — 180 Proof
Or I'm not expressing what I mean intelligibly. — 180 Proof
I am skeptical of holes being a typographic feature, however, given the ability to represent a donut on a plane without a hole in a topologically identical manner. — Moliere
I would consider objects to exist "on their own" otherwise they wouldn't exist. — Benkei
A torus in 3D is not topologically equivalent to a rectangle — SophistiCat
In any case, finding one way to fail to detect a hole as a topological feature does not establish your general thesis, which I take to be that a hole cannot be conceptualized solely as a property of the entity that encompasses it — SophistiCat
The question is not whether you can conceptualize holes that way, but whether you must, as a matter of principle. — SophistiCat
Likely this is a naive materialist response, but for the example in the OP, the word "hole" identifies a collection of physical objects occupying a particular space. What are the objects? Air molecules, dust, perhaps the odd bird that happens to fly by, etc. So this particular "hole" has mass and occupies a reasonably well defined space. To my naive way of thinking that's sufficient to say that it exists.
What about if this hole is on an airless asteroid in outer space - in a vacuum? There's no air. But there are still countless atomic and subatomic particles flying through, not to mention the quantum foam and energy fields that permeate even the deepest vacuum in space.
So I have no problem saying that holes exists. Not sure about shadows, tho. Will have to think about that some more. — EricH
Hi, could either of you expound? Or provide a link to an appropriate SEP article? I don't think I'm familiar with this yet. — Benkei
Honestly I find myself becoming more and more a naive realist, but being surprised at what that really entails... — Moliere
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