4 ms·

> What does it mean for three horses and three apples to exist? You tell us. You seem perfectly comfortable speaking of a multiplicity of instances. (Personal

> What does it mean for three horses and three apples to exist? You tell us. You seem perfectly comfortable speaking of a multiplicity of instances. (Personally, I would begin the discussion with substantial form. I can speak of many triangles that instantiate the same triangularity which allows me to assert the same properties of triangularity of them all. And yet triangularity is not to be identified with any particular triangle.)

Koshkin 4y ago
This is a valuable point. Our thinking is too much tied to the language. Of course when we say that the abstract triangle exists we mean that what exists is the property of triangularity. Properties (of things) do exist, whether we like it or not. Just like the number 3, say, also exists - in the form of “threeness” property (of a collection of objects). There is not much more to be said here, except maybe that most, if not all, properties manifest themselves in, or indeed are, relations between things, and also that they are not arbitrary products of the mind, being impressed into us by the objective reality - and how can something be impressed into us that is not itself part of reality, i.e. does not exist in the most obvious sense of the word.
- TuringTest 4y ago
  > they are not arbitrary products of the mind, being impressed into us by the objective reality - and how can something be impressed into us that is not itself part of reality, i.e. does not exist in the most obvious sense of the word. They are not arbitrary products of the mind, for the reasons you explain; but they are products of the mind. The property of NP-completeness didn't exist until we invented algorithms and analysed their time complexity, though many problems do posses that property; and in the same way the property of triangularity didn't exist until Greeks started imagining geometry in terms of idealized regions of space, defined in terms of simple relations between points without size. (And then, the triangularity property changed a lot when people started questioning the parallel postulate and discovered non-euclidean geometry). It is not necessary that an entity exists for it to form impressions in the mind, it is enough that the mind can imagine it from actual existing perceptual elements, and our imagination fills in the details. Is it truly needed for a monster to exist under the bed for it to impress our juvenile minds?
  - Koshkin 4y ago
    > they are products of the mind Well, a fighter jet, too, is a product of the mind. > triangularity didn't exist until Tell this to triangular molecules. > a monster This says more about people than it does about the reality (though even fears and phantasms can indeed be rooted in reality).
    - TuringTest 4y ago
      > Well, a fighter jet, too, is a product of the mind. I'd say there's a difference between having a physical, tangible fighter jet in front of you, with all the connections between its molecules in a configuration that allows it to fly, and having "the property of being a fighter jet" in front of you. > Tell this to triangular molecules. Do they have "a triangular" in them? https://www.smbc-comics.com/comic/real-2 https://www.smbc-comics.com/comic/real-2 > This says more about people than it does about the reality Right, and having people believe that properties exist as an entity outside of the mind says more about people than it does about the reality.
  - archi42 4y ago
    > The property of NP-completeness didn't exist until we invented algorithms and analysed their time complexity [...] Now that is a bolt statement to make with such certainty :) Imagine it's 1822 and you're a salesmen, travelling from town to town to sell your wares. Of course you want to save on time and distance travelled, so you'd like to pick the shortes route that covers all towns on your list. Now how complicated can that be? I'd dare to say the probem you're facing was already NP-complete back then, you just didn't know if you're too stupid (no, you're not!) or if it was in fact impossible without trying every possible route (yes). In other words: When inventing a new predicate (e.g. is_np_complete) in non-temporal, binary logic, that predicate is always true or false (or undecided :)) for a given input. You essentially say that the predicate only exists once it has been created, but I say it has merely been given a name to reference it. I'd like to present a logical argument why I am right beyond a doubt, but this might be undecidable; at least I'm stuck thinking about it, much like the imaginative you from 1822 (my problem is that I don't know if it's possible to enumerate all possible predicates [that map each possible input to every possible output {true, false, undecidable}] - if it is I think I can make a sound argument). And very much like that fictive person should probably just start travelling on a good enough route, I should also get back to work ;) Maybe you can come up with a formal proof why a predicate can only exist once it has been formalized for the first time? //edit: some clarification to show that this is a friendly discussion :)

Koshkin 4y ago

This is a valuable point. Our thinking is too much tied to the language. Of course when we say that the abstract triangle exists we mean that what exists is the property of triangularity. Properties (of things) do exist, whether we like it or not. Just like the number 3, say, also exists - in the form of “threeness” property (of a collection of objects). There is not much more to be said here, except maybe that most, if not all, properties manifest themselves in, or indeed are, relations between things, and also that they are not arbitrary products of the mind, being impressed into us by the objective reality - and how can something be impressed into us that is not itself part of reality, i.e. does not exist in the most obvious sense of the word.

TuringTest 4y ago
> they are not arbitrary products of the mind, being impressed into us by the objective reality - and how can something be impressed into us that is not itself part of reality, i.e. does not exist in the most obvious sense of the word. They are not arbitrary products of the mind, for the reasons you explain; but they are products of the mind. The property of NP-completeness didn't exist until we invented algorithms and analysed their time complexity, though many problems do posses that property; and in the same way the property of triangularity didn't exist until Greeks started imagining geometry in terms of idealized regions of space, defined in terms of simple relations between points without size. (And then, the triangularity property changed a lot when people started questioning the parallel postulate and discovered non-euclidean geometry). It is not necessary that an entity exists for it to form impressions in the mind, it is enough that the mind can imagine it from actual existing perceptual elements, and our imagination fills in the details. Is it truly needed for a monster to exist under the bed for it to impress our juvenile minds?
- Koshkin 4y ago
  > they are products of the mind Well, a fighter jet, too, is a product of the mind. > triangularity didn't exist until Tell this to triangular molecules. > a monster This says more about people than it does about the reality (though even fears and phantasms can indeed be rooted in reality).
  - TuringTest 4y ago
    > Well, a fighter jet, too, is a product of the mind. I'd say there's a difference between having a physical, tangible fighter jet in front of you, with all the connections between its molecules in a configuration that allows it to fly, and having "the property of being a fighter jet" in front of you. > Tell this to triangular molecules. Do they have "a triangular" in them? https://www.smbc-comics.com/comic/real-2 https://www.smbc-comics.com/comic/real-2 > This says more about people than it does about the reality Right, and having people believe that properties exist as an entity outside of the mind says more about people than it does about the reality.
- archi42 4y ago
  > The property of NP-completeness didn't exist until we invented algorithms and analysed their time complexity [...] Now that is a bolt statement to make with such certainty :) Imagine it's 1822 and you're a salesmen, travelling from town to town to sell your wares. Of course you want to save on time and distance travelled, so you'd like to pick the shortes route that covers all towns on your list. Now how complicated can that be? I'd dare to say the probem you're facing was already NP-complete back then, you just didn't know if you're too stupid (no, you're not!) or if it was in fact impossible without trying every possible route (yes). In other words: When inventing a new predicate (e.g. is_np_complete) in non-temporal, binary logic, that predicate is always true or false (or undecided :)) for a given input. You essentially say that the predicate only exists once it has been created, but I say it has merely been given a name to reference it. I'd like to present a logical argument why I am right beyond a doubt, but this might be undecidable; at least I'm stuck thinking about it, much like the imaginative you from 1822 (my problem is that I don't know if it's possible to enumerate all possible predicates [that map each possible input to every possible output {true, false, undecidable}] - if it is I think I can make a sound argument). And very much like that fictive person should probably just start travelling on a good enough route, I should also get back to work ;) Maybe you can come up with a formal proof why a predicate can only exist once it has been formalized for the first time? //edit: some clarification to show that this is a friendly discussion :)