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> it makes not difference whether he bumps into a tree because you decided Exactly. It makes no difference for him that you want to see a proof of individual t

> it makes not difference whether he bumps into a tree because you decided Exactly. It makes no difference for him that you want to see a proof of individual trees' objective existence - because he already knows this for a fact! That's what that pesky objective reality does, sometimes forcing knowledge about itself upon us, whether we like it or not, or whether we would prefer some other "proof." The proof is in the pudding, as they say. > Mathematics is not that. Sure it is. One who knows about numbers knows more about the objective reality than those who don't. One who knows about Lie groups knows even more. > you gain knowledge about the name of my dog. No discovery involved That's not quite true: I discover that you have a dog (as long as you did not "invent" it). > Nothing about them on their own is related to three. It does, if you look at it from the right angle. There's a different thing at play here. While the number of legs could be easily matched with the corresponding number of apples, by itself this correspondence does not necessarily make any particular number stand out (although in some cases, like, say, in the case of a non-wobbly stool, a triangle, or the number of eyes and hands, it would - simply because there are many pairs of eyes, etc.); what's also at play here is different ways to look at numbers, which includes seeing them not only as "cardinals" (which is what you are still limiting yourself to) but also as "ordinals": the number 1 "stands out" as the smallest ordinal (greater than "nothing"), the number 2 is what follows it, etc. It is all these aspects combined that form the true content of the notion of the number.

danbruc 3y ago
It makes no difference for him that you want to see a proof of individual trees' objective existence - because he already knows this for a fact! You are missing my point here. The blind guys knows he bumped into something, so something exists. He could just say he bumped into a part of the universe, he is not forced to say he bumped into a forest or a tree. He could even consider himself part of the universe and say one part of the universe bumped into another part of the universe, just as one part of you bumps into another part of you when you clap your hands. The consequence of that is that there are no distinct objects to count, it is just one really complex object, the universe, interacting with itself. Sure it is. One who knows about numbers knows more about the objective reality than those who don't. One who knows about Lie groups knows even more. No, that is a kind of map territory thing. You can have knowledge of mathematics but mathematics is not knowledge. You can have knowledge of my dos's name but my dog's name is not knowledge. It does, if you look at it from the right angle. Switching from the cardinals to the ordinals will not really make a difference, you are glossing over a lot of heavy lifting. I have to repeat myself, the non-wobbly stool is not related to three, it is the set of its legs that is related to three. On to get there, you have to single out parts of the stool and combine the parts into a set and the take about the cardinality of it. There are a lot of steps and concepts on that way which makes it at least very non-obvious how the number three was always there and is not just the result of that process. I am open to an example how I would find the ordinals in nature, I am not sure it will be any easier than with the cardinals. Non of the trees in the forest is the first one, you will have to impose an order an them. Maybe something with time, sunrises or days, they are at least already ordered.
- Koshkin 3y ago
  > You are missing my point here. Not at all! Talk about losing the trees for the forest... Even the blind guy knows, viscerally, that what he is hugging is not the "entire universe," or that stepping off a cliff would result in a dramatic experience; that a sighted person (and a philosopher) can see "a bigger picture" does not change the facts; indeed, a focus on "a bigger picture" can be deceiving (think of quantum vs. classical mechanics). > my dog's name is not knowledge We are going in circles. Mathematics is not just "names." > the non-wobbly stool is not related to three It is. You have a class of non-wobbly stools with a matching number of legs. You have a class of girls with a matching number of eyes that boys like more than others. Examples abound. > how I would find the ordinals in nature The early bird may get the worm, but it's the second mouse who gets the cheese. See also https://byjus.com/maths/ordinal-numbers/ https://byjus.com/maths/ordinal-numbers/
  - danbruc 3y ago
    The blind guy is of curse not hugging the entire universe but a part of it. Where there trees before humans existed? No. It took our minds to look at the universe and say »Hey, it would be really helpful for talking about the universe if we would consider those wooden pieces of the universe that are roughly cylindrical and have the green stuff attached on the top individual things and give them a name, maybe something like tree.« We could have decided otherwise, never invented the concept of a tree and always just talk about forests. The subdivision of the universe into objects, at least on the macroscopic level, is not intrinsic to universe, it is an invention of the human mind. Also the non-wobbly stool is just that, one non-wobbly stool. [1] It again takes your mind to divide it up into components, including the legs, collect the legs back into a set and count them. Take a monocrystalline non-wobbly stool, it is just a weirdly shaped single crystal, nothing indicates that one should consider three specific areas of it as legs. Look, I am not arguing that it makes no sense for humans to think of this thing as a stool with three legs, but if you want to argue that numbers exist in nature independent of humans, then you have to keep human concepts out of the argument. Because we see the stool as a distinct part of the universe with three subcomponents that we can group together in a set to count them, does not mean that there was a stool or legs or a set of legs or a set of cardinality three before a human mind had a look at the situation. You have to argue that objects are not a human invention, that cutting a forest up into trees instead of considering it one whole thing makes sense in absence of humans. If you have that, you have to argue that collecting objects into sets makes sense in the absence of humans. And then finally you can argue that the cardinality of those sets is not an human invention but was discovered. [1] Or maybe not even that, maybe just a specifically shaped part of the universe.

danbruc 3y ago

It makes no difference for him that you want to see a proof of individual trees' objective existence - because he already knows this for a fact! You are missing my point here. The blind guys knows he bumped into something, so something exists. He could just say he bumped into a part of the universe, he is not forced to say he bumped into a forest or a tree. He could even consider himself part of the universe and say one part of the universe bumped into another part of the universe, just as one part of you bumps into another part of you when you clap your hands. The consequence of that is that there are no distinct objects to count, it is just one really complex object, the universe, interacting with itself. Sure it is. One who knows about numbers knows more about the objective reality than those who don't. One who knows about Lie groups knows even more. No, that is a kind of map territory thing. You can have knowledge of mathematics but mathematics is not knowledge. You can have knowledge of my dos's name but my dog's name is not knowledge. It does, if you look at it from the right angle. Switching from the cardinals to the ordinals will not really make a difference, you are glossing over a lot of heavy lifting. I have to repeat myself, the non-wobbly stool is not related to three, it is the set of its legs that is related to three. On to get there, you have to single out parts of the stool and combine the parts into a set and the take about the cardinality of it. There are a lot of steps and concepts on that way which makes it at least very non-obvious how the number three was always there and is not just the result of that process. I am open to an example how I would find the ordinals in nature, I am not sure it will be any easier than with the cardinals. Non of the trees in the forest is the first one, you will have to impose an order an them. Maybe something with time, sunrises or days, they are at least already ordered.

Koshkin 3y ago
> You are missing my point here. Not at all! Talk about losing the trees for the forest... Even the blind guy knows, viscerally, that what he is hugging is not the "entire universe," or that stepping off a cliff would result in a dramatic experience; that a sighted person (and a philosopher) can see "a bigger picture" does not change the facts; indeed, a focus on "a bigger picture" can be deceiving (think of quantum vs. classical mechanics). > my dog's name is not knowledge We are going in circles. Mathematics is not just "names." > the non-wobbly stool is not related to three It is. You have a class of non-wobbly stools with a matching number of legs. You have a class of girls with a matching number of eyes that boys like more than others. Examples abound. > how I would find the ordinals in nature The early bird may get the worm, but it's the second mouse who gets the cheese. See also https://byjus.com/maths/ordinal-numbers/ https://byjus.com/maths/ordinal-numbers/
- danbruc 3y ago
  The blind guy is of curse not hugging the entire universe but a part of it. Where there trees before humans existed? No. It took our minds to look at the universe and say »Hey, it would be really helpful for talking about the universe if we would consider those wooden pieces of the universe that are roughly cylindrical and have the green stuff attached on the top individual things and give them a name, maybe something like tree.« We could have decided otherwise, never invented the concept of a tree and always just talk about forests. The subdivision of the universe into objects, at least on the macroscopic level, is not intrinsic to universe, it is an invention of the human mind. Also the non-wobbly stool is just that, one non-wobbly stool. [1] It again takes your mind to divide it up into components, including the legs, collect the legs back into a set and count them. Take a monocrystalline non-wobbly stool, it is just a weirdly shaped single crystal, nothing indicates that one should consider three specific areas of it as legs. Look, I am not arguing that it makes no sense for humans to think of this thing as a stool with three legs, but if you want to argue that numbers exist in nature independent of humans, then you have to keep human concepts out of the argument. Because we see the stool as a distinct part of the universe with three subcomponents that we can group together in a set to count them, does not mean that there was a stool or legs or a set of legs or a set of cardinality three before a human mind had a look at the situation. You have to argue that objects are not a human invention, that cutting a forest up into trees instead of considering it one whole thing makes sense in absence of humans. If you have that, you have to argue that collecting objects into sets makes sense in the absence of humans. And then finally you can argue that the cardinality of those sets is not an human invention but was discovered. [1] Or maybe not even that, maybe just a specifically shaped part of the universe.