The essay appears to mix two different meanings of "hole".
Holes are a topological property of the slice of cheese. It's not scale invariant, as we're talking about holes on a human visible scale, not microscopic holes. The actual number is not fixed and may depend on the person doing the measuring.
I therefore don't see the need for "perforated", much less shape-predicates like "singly-perforated", "doubly-perforated" and "triply-perforated."
> For ‘hole’ read ‘bottle;’ for ‘hole-lining’ also read ‘bottle.’
Topologically speaking, a bottle doesn't have a hole, so this uses a different definition.
I think your definition still leaves the essence of the discussion in the same place: do topological properties "exist"? That's how I tend to blanket-interpret this debate; it's whether one is wiling to define existence to include things that aren't material.
Yeah but then neither does the cheese right? There’s no actual unity to objects, even solid objects, just parts interacting circumstantially, and any part can be subdivided into more parts interacting circumstantially.
The unity of the block of cheese is circumstantial, but nonetheless we define a piece of cheese defined on the presence of actual matter. The article goes to some trouble to devise a definition of holes that's also based on matter rather than its absence. But only a strict materialist would feel the need to do that, assuming they didn't want to outright deny existence to holes.
An old joke that I was thinking about recently: Two local government consultants - tasked with seeing if it'd be financially beneficial to dig a new tunnel so that cars don't have to drive up and down a mountain - dig two small holes on opposite sides of the mountain then stand at either end.
The punchline, which I can't remember, is something about the two holes being, according to the two consultants, an MVP of a tunnel: "Just stand at either end of it."
When the British government invited commercial proposals for the digging of the Channel Tunnel between England and France, one man submitted a bid for only £10,000. “How can you possibly dig under the English Channel for only £10,000?” asked the project manager.
“It’s simple,” replied the low bidder. “My partner takes a spade, goes to France and starts digging. I take another spade and start digging from England. We’ll both keep digging until we meet in the middle.”
“Hm, I see. But what happens if, through a miscalculation, you two do not meet?”
“That’s even better for you!” replied the bidder enthusiastically. “In that case you will have two tunnels!”
This is a debate between grammarians, not logicians. Just because "hole" and "object" are both nouns doesn't mean they belong to the same logical category.
The essay appears to mix two different meanings of "hole".
Holes are a topological property of the slice of cheese. It's not scale invariant, as we're talking about holes on a human visible scale, not microscopic holes. The actual number is not fixed and may depend on the person doing the measuring.
I therefore don't see the need for "perforated", much less shape-predicates like "singly-perforated", "doubly-perforated" and "triply-perforated."
> For ‘hole’ read ‘bottle;’ for ‘hole-lining’ also read ‘bottle.’
Topologically speaking, a bottle doesn't have a hole, so this uses a different definition.
I think your definition still leaves the essence of the discussion in the same place: do topological properties "exist"? That's how I tend to blanket-interpret this debate; it's whether one is wiling to define existence to include things that aren't material.
Yeah but then neither does the cheese right? There’s no actual unity to objects, even solid objects, just parts interacting circumstantially, and any part can be subdivided into more parts interacting circumstantially.
The unity of the block of cheese is circumstantial, but nonetheless we define a piece of cheese defined on the presence of actual matter. The article goes to some trouble to devise a definition of holes that's also based on matter rather than its absence. But only a strict materialist would feel the need to do that, assuming they didn't want to outright deny existence to holes.
Topological properties exist to the same degree that the number 2 exists, which Argle and Blargle blithely accept.
I still object to how the exchange mixes two different concepts of "hole".
An old joke that I was thinking about recently: Two local government consultants - tasked with seeing if it'd be financially beneficial to dig a new tunnel so that cars don't have to drive up and down a mountain - dig two small holes on opposite sides of the mountain then stand at either end.
The punchline, which I can't remember, is something about the two holes being, according to the two consultants, an MVP of a tunnel: "Just stand at either end of it."
I don't know that one, but here's a superficially similar joke from somewhere among http://miresperanto.com/humuro.htm :
When the British government invited commercial proposals for the digging of the Channel Tunnel between England and France, one man submitted a bid for only £10,000. “How can you possibly dig under the English Channel for only £10,000?” asked the project manager.
“It’s simple,” replied the low bidder. “My partner takes a spade, goes to France and starts digging. I take another spade and start digging from England. We’ll both keep digging until we meet in the middle.”
“Hm, I see. But what happens if, through a miscalculation, you two do not meet?”
“That’s even better for you!” replied the bidder enthusiastically. “In that case you will have two tunnels!”
A perfect joke, really.
This is a debate between grammarians, not logicians. Just because "hole" and "object" are both nouns doesn't mean they belong to the same logical category.
Eh. Grammar, logic, it's all just trivium stuff, unrelated to the sciences proper.
I thought at first that this would be Holes[0], a novel by Louis Sachar.
[0]: https://en.wikipedia.org/wiki/Holes_(novel)
Ie, “Magic Realism for Kids”. It’s an excellent book (as is everything else Louis Sachar wrote).
Holes might not really exist, but hollers definitely do, because that's where my papaw lived.