• Tristan L
    89
    Good point. "HarryPotterhood" it is then.
  • Tristan L
    89
    You seem to think ideas exist in the ether, and that they are not tied to a consciousness ground, and not subject to evolutionary principles.Pop

    Yes, of course, just as numbers, functions, sets, properties, relationships, and all the other abstract things exist in the ‘above-heavenly world (hyperuranion)’ – which is just another way of saying that they don’t exist in space or time (but not outside them, either, for outsideness is a spatial notion) – and aren’t tied to awareness or evolution or anything conrete for that matter, be it physical, mindly, spatial, or temporal. However, instances of abstract entities of ideas, such as my thought about the fact that all ideas are timeless, are often: concrete, subject to change and evolution, and in need of a physical and/or mental substrate.

    You seem to be arguing that cave men could have flown to the moon?Pop

    Not at all, for what does the one have to do with the other?

    Really? What substrate do your ideas exist on?Pop

    What you call “Tristan’s ideas” are actually mental instances of ideas, and these exist in my consciousness.

    Human ideas exist on a substrate of human consciousness.They are shared via a collective consciousness know as culture. Human ideas and human consciousness evolved together - inextricably linked - ideas are an expression of human consciousness!Pop

    If you replace the word “ideas” with the phrase “instances of ideas”, I’ll agree with you.

    For an idea to exist it must exist somewhere – [...]Pop

    Actually no, just as numbers don’t have to exist anywhere in order to exist. Indeed, what just exists (abstractly) has a purer shape of existence and is at least as real as what exists somewhere (and therefore concretely).

    [...] – If "they just exist", where do they just exist?Pop

    The question is wrong, in a similar in way in which the question “What color is the electron?” is wrong – they’re both based on false premises and thereby meaningless. I think that you think too concretely.
  • Tristan L
    89
    Why is it certain that all existing things will be discovered?Luke

    All the ideas that my algoritm may discover, it will discover.

    I don't understand what "possibilities are defined in terms of their belonging ideas" means, or how it follows that "ideas must always be actual as well".Luke

    Let EID be an arbitrary idea that someone has found. Since someone has found EID, it must always have been actually possible that someone could someday find EID. So the possibility Poss(EID) that someone might someday come up with EID must have always actually existed. But Poss(EID) is actually defined in terms of EID – it’s the possibility of finding EID after all –, and so, there is an actual, essential, fixed bond between EID and Poss(EID). Hence, EID must also have always actually existed.

    You previously defined an "understander" as "the person or group of people who reads/read every finite-length string put out by the string-outputter". Do you know of anyone who has such perfect knowledge? You seem to be talking about a theoretically ideal "person or group", not an actual "person or group".Luke

    Firstly, I never meant my algorithm to be used in practice, so scientists, artists, mathematicians, and philosophers don’t have to worry that they’ll be out of work soon. The existence of my algorithm and its ability in principle to find all ideas finitely expressible in the Modern English speech is what counts.

    Secondly, even if the understander isn’t perfect, he’ll still deterministically find a great many ideas which you claim to be have to be made creatively. However, bear in mind that any real-life shortcoming of the understander is also a shortcoming of other traditional idea-finders, so there’s nothing that a creative person can do which my algorithm can’t do (although the algorithm needs a very long time). But yep, my understander is idealized nonetheless, though certainly not all-knowing or anything of the like at all.

    Perhaps, but your algorithm could take thousands or millions of years to output many of the symbol-strings, by which time Modern English (2020) will most likely have evolved or died.Luke

    it requires someone with perfect knowledge of Modern English to understand each and every idea. This is all fanciful.Luke

    You are arguing that all ideas pre-exist, are discoverable, and will be output by your algorithm. But you think that the practical issue of being able to discover them in the output of your algorithm is beside the point?Luke

    The point is to show that any idea can in principle be found deterministically, so practical issues are indeed beside the point. But even so, my algorithm with the idealized understander will find every idea finitely expressible in Modern English, and even with an imperfect understander, it’ll find a great many ideas that are supposedly invented. Mind you also that any imperfection of the understander is also an imperfection of creative people and their recipients, so creative folks cannot find anything which my algorithm can’t find.

    Your arguing against my point is like someone arguing against a determinist that there is no Laplace's demon in real life – he brings up a practical issue which is beside the point (not that I’m a determinist; I just used this as an illustration).


    Moreover, I did away with all the practical issues by using the formal, Turing-complete programming speech PASCAL instead of Modern English, so what do you say to that?


    Your algorithm will supposedly spit out every possible combination of symbols. This is virtually irrelevant to the supposed pre-existence of ideas. Your algorithm doesn't just output representations of ideas; it outputs mostly junk. This is hardly an algorithmic way of discovering ideas.Luke

    What do you mean by “virtually irrelevant”?

    My algorithm finds each possible finitely expressible idea after a finite time. It works without flaw. That it’s very inefficient because of all the junk is of no relevance, except if your goal is to make creative folks jobless rather that prove a point about the nature of ideas.

    Your algorithm will also take infinitely long to output all possible combinations of symbolsLuke

    At what point does your program stop outputting?Luke
    It won’t ever stop. Bear in mind that the there-is-quantifier ∃ doesn’t commute with the for-all-quantifier ∀, so the proposition that there is a time at which the algorithm has output all finite strings is strictly stronger than the proposition that for each finite string, there is a time at which the algorithm will have output that string. As a matter of fact, the former is untrue while the latter is true. I’ve only ever claimed the latter.

    The point is that nobody is omniscient, including any actual "understander".Luke

    Just like the Pascal Compiler doesn’t know every possible PASCAL-program, yet can still compile any and every source-code that obeys PASCAL-syntax as well as check it for syntax-compliance before that.

    Yes, because your program wouldn't be able to recreate those books in either of our lifetimes.Luke

    I’m not talking about that practical issue. I’m asking you whether there’s any inherent difference between Rowling’s HP books and my algorithm’s HP books.

    The algorithm wouldn't be able to write its own program if you hadn't first invented the algorithm.Luke

    But my program will also find any similar program that you write independently of you, and likewise, your hypothetical program will find my program.

    Is there a program that has perfect knowledge of Modern English?Luke

    So do you at least accept that all programs already exist?

    Unlike the output of your algorithm, I don't have to disregard a whole bunch of meaningless junk when dealing with the natural numbers. I can simply find any number I want whenever I want.Luke

    What’s the problem with disregarding junk other than that it gobbles up a lot of time? The process of separating the wheat from the chaff is straightforward and well-defined. In the case of the compiler, there’s even no issue whatsoever.

    I don't need to; you've already conceded that "There are certainly not-finitely-expressible-ideas".Luke
    Yep, you do, for though I’m quite certain that there are such ideas, that doesn’t mean that any of them have been discovered. In fact, although I think that some unsayable ideas have been discovered (which by definition only the respective discoverer and hypothetical thoughtcasters can know about), I believe that no only infinitely expressible ideas have ever been discovered. Anyways, they’re not of much practical weight, and they’re likely not what you had in mind when talking about ideas. The Mona Lisa, the toaster, the Van-de-Graaf hight-voltage generator, and all other ideas in science, technology, art, mathematics, and philosophy are finitely expressible anyhow.

    Your argument is that if your argument is true, then why shouldn't your argument be true? That's not much of an argument.Luke

    No, that is untrue. This argument of mine runs thus: The algorithm-argument shows that all finitely expressible ideas must fore-exist. This includes all practially relevant ideas. Hence, why shouldn’t the same be true for only infinitely expressible ideas and unsayable ones (which aren’t of much scientific, mathematical, artistic, literary, or technological interest anyhow)?

    It is your claim that your algorithm will output every idea. If some ideas cannot be output by your algorithm, e.g., because they are "not-finitely-expressible" or because they are "totally unsayable", then your algorithm cannot output every idea and therefore your claim is false.Luke

    It is in fact your claim about mine which is false. I never claimed that my algorithm can output all ideas. Rather, I have claimed that all finitiely ideas will come out of my algorithm. If you focus only on the other ideas, of which you can, by definition, not give me an example, that would already be a great retreat on your part.
  • jgill
    787
    . . . mathematicians, and philosophers don’t have to worry that they’ll be out of work soonTristan L

    :cool:
  • Janus
    9.3k
    Let EID be an arbitrary idea that someone has found. Since someone has found EID, it must always have been actually possible that someone could someday find EID.Tristan L

    Is this right? What if what is actually possible ( as distinguished form what is merely logically possible) changes in subtle ways that we have no way of knowing about? I mean if the world is not deterministic, then this could be, no?
  • Pop
    238
    A consciousness has to create the ideas, otherwise what is the substrate that they exist on?
    — Pop

    They don’t need any substrate at all; they just exist.
    — Tristan L

    Really? What substrate do your ideas exist on?
    Pop
    — Pop

    What you call “Tristan’s ideas” are actually mental instances of ideas, and these exist in my consciousness.— Tristan L

    Exactly.Tristan's mental instances of ideas are grounded in Tristan's consciousness, and nowhere else.If they were not they could not exist. Where did they exist before there was Tristan, or 10,000 years ago? - Nowhere!

    Only nothing can exist on its own. Everything else exists relative to something - including ideas.

    So your assertion for ideas :"They don’t need any substrate at all; they just exist." is incorrect, as they cannot exist on their own - only nothing can exist on its own!

    Numbers and abstract concepts exist relative to human consciousness.They are expressions of human consciousness. They are inextricably linked, and evolve together. Before there were people they did not exist!
    When Human consciousness was little different to primate consciousness, they did not exist - there was no substrate for them to exist on!
  • Luke
    1k
    Let EID be an arbitrary idea that someone has found. Since someone has found EID, it must always have been actually possible that someone could someday find EID.Tristan L

    ...or invent EID.

    So the possibility Poss(EID) that someone might someday come up with EID must have always actually existed. But Poss(EID) is actually defined in terms of EID – it’s the possibility of finding EID after all –, and so, there is an actual, essential, fixed bond between EID and Poss(EID). Hence, EID must also have always actually existed.Tristan L

    The possibility of coming up with the idea might have always existed. But that does not mean that the idea has always existed; someone needs to come up with it first. The possibility of coming up with the idea is not equivalent to actually coming up with the idea. Your attempted collapse of the distinction between possible and actual here is fatalistic.

    Firstly, I never meant my algorithm to be used in practice, so scientists, artists, mathematicians, and philosophers don’t have to worry that they’ll be out of work soon. The existence of my algorithm and its ability in principle to find all ideas finitely expressible in the Modern English speech is what counts.

    Secondly, even if the understander isn’t perfect, he’ll still deterministically find a great many ideas which you claim to be have to be made creatively. However, bear in mind that any real-life shortcoming of the understander is also a shortcoming of other traditional idea-finders, so there’s nothing that a creative person can do which my algorithm can’t do (although the algorithm needs a very long time). But yep, my understander is idealized nonetheless, though certainly not all-knowing or anything of the like at all.
    Tristan L

    You may recall I initially asked what algorithm exists that can help us to discover every idea that supposedly pre-exists. I find it questionable whether your algorithm actually helps us to discover any pre-existing ideas - particularly those which have not yet been discovered. Your algorithm produces only every possible combination of "the printable ASCII-characters". In our talk of ideas, I presume we are talking about useful ideas or ideas of some sort of value or interest to humanity. This is why I question your "understander" and their ability to detect ideas amidst junk strings of symbols, particularly ideas that nobody has previously known.

    Perhaps your algorithm might eventually output a representation of every idea that humankind will ever come up with (together with 99.99% junk), but I doubt that it would actually help in finding any of them. This is not to say that those ideas all exist now, either, since I am speaking hypothetically from a perspective at the end of humankind's existence. Anyhow and ultimately, I don't see that this helps to resolve the question of whether ideas are invented or discovered.
  • Tristan L
    89
    I broadly agree with you.

    Creativity is simply the ability to discover previously undisocvered solutions to problems.Magnus Anderson

    Or ideas generally, not necessarily solutions to problems, I think. Yes, that’s true.

    How you're going to discover such solutions is completely irrelevant. In other words, you can use a deterministic process but you can also use a random process. It does not matter.Magnus Anderson

    Actually, I think that it does matter. If the discovery-process is deterministic, the concrete instance of the solution exists from the start, although it only becomes “seeable” at the time that it manifests in a direct shape. Therefore, this is only creation in the broad sense, not in the strict sense. For example, the concrete software solutions that my algorithm will find already exist now, although not in a recognizable shape, so they can’t yet be used right now. They only become usable once the algorithm actually finds them, and that is the moment at which they are created (in the not-strict way). By contrast, if the concrete instance of the solution is found by a not-deterministic process, that instance is created in the strict sense. For instance, if I replace my deterministic program with a monkey banging on a keyboard (with the understander, including compiler, staying in place, of course), then the software solutions are created at about the time that the monkey writes them, and they’re created in the strict sense.

    [Pfhorrest said:] “I hold that there really isn't a clear distinction between invention and discovery of ideas[...]”

    I disagree with the bolded.

    I will repeat what Luke said.

    "Discovery" implies that the thing that is discovered existed before discovery whereas "invention" implies that the thing that is invented did not exist before.
    Magnus Anderson

    Yes, I also think that.

    If you are talking about the set of all possible ideas, these can't be invented, since they already exist; they can only be discovered.

    But that's because we're talking about the set of all possible ideas. The set contains all ideas that are possible -- there is absolutely no room for new ideas. If we're talking about the set of all actual ideas, however, one can introduce new ideas to it so as long it does not contain all possible ideas. An actual idea, that one that either existed within someone's brain at some point in time or did not, can be invented, provided there was no brain within which it existed previously.
    Magnus Anderson

    That is also what I think if what you call “possible idea” is what I call “idea” and what you call “actual idea” is what I call “concrete mental instance of an idea”. In any case, though, I think (though I’m not sure) that your position is not too far from mine.

    An actual idea [...] can be invented, provided there was no brain within which it existed previously.Magnus Anderson

    I agree with you if you mean the following: A mental instance of an idea in Alice’s mind has been invented by Alice, unless it was first invented by Bob’s mind, in which case Alice’s mind only discovers that instance of the idea.

    However, I’d like to add that two minds can create different mental instances of one and the same idea. This is what we call “independently coming up with the same idea”.
  • Tristan L
    89
    Exactly.Tristan's mental instances of ideas are grounded in Tristan's consciousness, and nowhere else.If they were not they could not exist. Where did they exist before there was Tristan, or 10,000 years ago? - Nowhere!Pop

    The mental instances were indeed nowhere and didn’t even exist at all, but the ideas of which they are instances have always existed.

    Only nothing can exist on its own. Everything else exists relative to something - including ideas.

    So your assertion for ideas :"They don’t need any substrate at all; they just exist." is incorrect, as they cannot exist on their own - only nothing can exist on its own!
    Pop

    You have still not given any justification of this assumption. Moreover, while I also think that everything, including ideas and the other abstract objects, needs something to explain its existence, that something isn’t any individual mind, but likely the all-encompassing godly Hyge (Nous, Mind) and ultimately Oneness, the or-principle (first principle) which gives each abstract entity its wist (essence).

    Numbers and abstract concepts exist relative to human consciousness.They are expressions of human consciousness. They are inextricably linked, and evolve together. Before there were people they did not exist!
    When Human consciousness was little different to primate consciousness, they did not exist - there was no substrate for them to exist on!
    Pop
    That claim is showably false. Let’s look at three Triassic cynodonts who want to equally share two burrows between them so that each cynodont has the same number of cynodonts living together with it. It won’t work, for the number 3 is eternally undividable by the number 2. This shows that numbers and facts about them have always existed. Likewise, seven before-human primates wouln’t have been able to equally share 15 fruits, for 15 isn’t divisible by 7 – then as now.

    The same goes for abstract concepts: the possibility of finding ... but I’m repeating myself:

    Let EID be an arbitrary idea [e.g. abstract concept] that someone has found. Since someone has found EID, it must always have been actually possible that someone could someday find EID. So the possibility Poss(EID) that someone might someday come up with EID must have always actually existed. But Poss(EID) is actually defined in terms of EID – it’s the possibility of finding EID after all –, and so, there is an actual, essential, fixed bond between EID and Poss(EID). Hence, EID must also have always actually existed.Tristan L
  • Tristan L
    89
    Actually, what is actually possible can change, but only in one direction: possibilites can at most get fewer with time. That is so because it is a logical fact that for every proposition Þ and all time-points t1, t2, t3 with t1 ≤ t2 ≤ t3: if it’s actually possible at t2 that Þ is true at t3, then it’s actually possible at t1 that it’s actually possible at t2 that Þ is true at t3, so (since if something may be possible, then it is possible) it’s actually possible at t1 that Þ is true at t3.

    Why is something possible if it may be possible? Well, if something may be possible, then there is a chance that it will be possible, in which case there is a chance that it will happen.

    So, what I say still stands: What is actually possible now has always been actually possible. For instance, it is actually possible (and even actual) in the year 2020 CE that Janus and Tristan discuss the nature of ideas in the year 2020 CE, and it has always been actually possible, e.g. in the year 2009 CE, that Janus and Tristan would discuss the nature of ideas in the year 2020 CE.
  • Tristan L
    89
    The possibility of coming up with the idea might have always existed.Luke

    ... and has therefore always existed, for what may be possible is possible. See my answer to @Janus.

    But that does not mean that the idea has always existed; someone needs to come up with it first. The possibility of coming up with the idea is not equivalent to actually coming up with the idea. Your attempted collapse of the distinction between possible and actual here is fatalistic.Luke

    You seem to still not understand what I’m saying and therefore ascribe claims to me which are not mine, hindering you from actually talking about my true points. It’s the other way round to what you claim it to be, for it is I who very clearly distinguishes between abstract ideas and their concrete instances, while you seem to still fail to make that crucial distinction.

    The idea EID itself is essentially linked to the possibility Poss(EID) of finding that idea. However, a particular mental instance eid(Alice) of the idea has to be invented, created. So far, so good? But since Poss(EID) has always actually existed, so has EID (not eid(Alice) mind you).

    Also, you’re just repeating your not-backed-up claim that “someone needs to come up with it [the idea] first”.

    In our talk of ideas, I presume we are talking about useful ideas or ideas of some sort of value or interest to humanity.Luke

    All of which are finitely expressible (save for ones restricted to e.g. private gasty (spiritual) experiences).

    You may recall I initially asked what algorithm exists that can help us to discover every idea that supposedly pre-exists. I find it questionable whether your algorithm actually helps us to discover any pre-existing ideas - particularly those which have not yet been discovered. Your algorithm produces only every possible combination of "the printable ASCII-characters". In our talk of ideas, I presume we are talking about useful ideas or ideas of some sort of value or interest to humanity. This is why I question your "understander" and their ability to detect ideas amidst junk strings of symbols, particularly ideas that nobody has previously known.Luke

    I trust that you can distinguish junk from the Harry Potter books without any knowledge about HP before, right? Well, the understander does the same thing.

    Perhaps your algorithm might eventually output a representation of every idea that humankind will ever come up with (together with 99.99% junk), but I doubt that it would actually help in finding any of them.Luke

    You seem to contradict yourself. On the one hand, you rightly say that my algorithm will in the end find every idea that humans will ever express, but on the other hand, you (falsely) claim that it supposedly won’t help finding them. Which one do you choose?

    This is not to say that those ideas all exist now, either, since I am speaking hypothetically from a perspective at the end of humankind's existence. Anyhow and ultimately, I don't see that this helps to resolve the question of whether ideas are invented or discovered.Luke

    Since it is already fixed and fore-determined now that the algorithm will find the ideas, they must exist now.
  • Luke
    1k
    The idea EID itself is essentially linked to the possibility Poss(EID) of finding that idea.Tristan L

    In your previous post you indicated that "Poss(EID)" refers to the possibility of coming up with the idea. Now you are indicating that "Poss(EID)" refers to the possibility of finding the idea. I don't know why you even talk of possibilities since it your position that all ideas already exist. Why beat around the bush with talk of the possibilities of finding or coming up with ideas?

    I trust that you can distinguish junk from the Harry Potter books without any knowledge about HP before, right? Well, the understander does the same thing.Tristan L

    No, not necessarily, and I'm sure I could think up better examples, such as a 12th century person being unable to recognise the idea of a computer algorithm, etc. Your understander wouldn't be able to recognise other futuristic ideas by analogy.

    You seem to contradict yourself. On the one hand, you rightly say that my algorithm will in the end find every idea that humans will ever express, but on the other hand, you (falsely) claim that it supposedly won’t help finding them. Which one do you choose?Tristan L

    I didn't say your algorithm would find them; I said it might eventually output a representation of every idea. What I meant was, even if we assume that your algorithm does output every idea (by brute force), it still doesn't help us to find those ideas. It would probably be easier for someone to invent the idea themself than to wade through the mountainous pile of junk produced by your algorithm, and this is even assuming that your algorithm has - at the relevant time - output the idea that might have otherwise been invented, since your algorithm could take an infinite amount of time to produce all the ideas.

    Since it is already fixed and fore-determined now that the algorithm will find the ideas, they must exist now.Tristan L

    That's my point: it doesn't find ideas. It just endelssly spits out combinations of symbols, which is irrelevant to the question of whether ideas are invented or discovered.
  • Luke
    1k
    Have you found a new logical law which says that the implication-operator is commutative? Please do tell! I have shown that if discovering an idea is possible, then the idea must fore-exist. Yet you claim the conclusion of that argument to be an assumption. You do know the difference between assuming and showing, don’t you? Could you please be clearer make your point less confused?Tristan L

    To come back to this, one could equally say that if inventing an idea is possible, then the idea must not fore-exist. It should be obvious that this doesn't prove anything about whether ideas are invented or discovered.
  • Magnus Anderson
    355
    Hi @Tristan L,

    If the discovery-process is deterministic, the concrete instance of the solution exists from the start, although it only becomes “seeable” at the time that it manifests in a direct shape. Therefore, this is only creation in the broad sense, not in the strict sense. For example, the concrete software solutions that my algorithm will find already exist now, although not in a recognizable shape, so they can’t yet be used right now. They only become usable once the algorithm actually finds them, and that is the moment at which they are created (in the not-strict way).

    If the discovery-process is deterministic, the discovered solution will necessarily be a solution that existed in a number of spaces long before it was discovered. Two of those spaces are:

    1) the space of all possible solutions to all possible problems that can be discovered by following an existing algorithm (this is the space you're referring to)

    2) the space of all possible solutions to all possible problems (this is where even solutions that were discovered through a random process existed long before they were discovered)

    However, the discovered solution does not necessarily exist in the space of all possible solutions to all possible problems hitherto actualized (by humans, other living beings or machines.) And it is this space that ultimately matters.

    One can very easily write a computer program that outputs every possible 32-bit 1920x1080 bitmap. The moment someone does so is the moment the first space (the one you're referring to) becomes filled with EVERY possible painting. If creativity is measured in relation to that set, that would make every subsequent painter an uncreative painter (even if they came up with a painting that depicts something of value that wasn't previously visually depicted.)

    That is also what I think if what you call “possible idea” is what I call “idea” and what you call “actual idea” is what I call “concrete mental instance of an idea”.

    I'd say so.

    There is the set of everything someone can think of (possible ideas) and the set of everything people thought of (actual ideas.)

    I agree with you if you mean the following: A mental instance of an idea in Alice’s mind has been invented by Alice, unless it was first invented by Bob’s mind, in which case Alice’s mind only discovers that instance of the idea.

    I wouldn't say that Alice discovered it. I would say she reinvented it.
  • jgill
    787
    On the one hand, you rightly say that my algorithm will in the end find every idea that humans will ever expressTristan L

    How do you define "the end"? :chin:
  • Tristan L
    89
    I wouldn't say that Alice discovered it. I would say she reinvented it.Magnus Anderson

    You’re right, of course. I must’ve gotten something mixed up. I wanted to say that if Alice finds the idea based on Bob’s coming-up, then she only discovers the mental instance created by Bob (as well as the idea itself, which is always only discovered). But if she finds the idea independently of Bob, she “reinvents” it, that is, she invents another mental instance of it, thereby rediscovering the idea itself.
  • Tristan L
    89
    My proof also works when starting from the assumption that ideas can be invented (in my text that you quoted, I should have used a neutral word, like “come up”, instead of “discover”): If inventing an idea EID is possible, then that possibility Poss(invent EID) must have always existed. Since Poss(invent EID) is essentially linked to EID, it follows that EID must also have always existed. Hence, if it is possible to invent an idea, then the idea must have always existed, and can therefore not be invented. Now apply Clavius's Law (consequentia mirabilis).
  • Pfhorrest
    3.1k
    I just want to chime in here that my view on creativity and the invention/discovery of ideas in no way hinges on the kind of platonism that Tristan is on about. I think that even on a nominalist account, whatever it means to say that an abstract thing like an idea (say for example, a number) "exists" now, that "existed" in the same way before anyone first thought about it, even if in a strict philosophical sense it's wrong to say that numbers "exist" at all.

    I don't think even a nominalist would say that anyone invented the square root of 2, or irrational numbers generally, in a way that is distinguishable from discovery; even a nominalist would say that we discovered that whatever number it is that measures the diagonal of a 1x1 square, that number is not expressible as a ratio of any two natural numbers. Nobody made that up; it was figured out, and it was always the case long before anybody figured it out. Even if there aren't reified abstract objects beyond space and time that are "the irrational numbers" to make that the case.

    Similarly, there is some natural number that is so large that nobody has counted up to it yet, but that doesn't mean that that number "doesn't exist" yet, in whatever sense numbers can be said to "exist" at all.

    Likewise with all ideas, on my account. Just because nobody has thought them up yet, doesn't mean they don't "exist", in whatever sense at all it could be said that any ideas "exist" in the first place. My account is neutral toward what that kind of "existence" is; my only claim (on this matter) is that someone thinking of an idea doesn't change the status of its existence.
  • Luke
    1k
    Hence, if it is possible to invent an idea, then the idea must have always existed, and can therefore not be invented.Tristan L

    If it is possible to invent an idea, then it is impossible to invent an idea? Hmm.

    Since Poss(invent EID) is essentially linked to EID, it follows that EID must also have always existed.Tristan L

    It does not follow. That is your assumption. What does "essentially linked" mean?
  • Pop
    238
    Only nothing can exist on its own. Everything else exists relative to something - including ideas.

    So your assertion for ideas :"They don’t need any substrate at all; they just exist." is incorrect, as they cannot exist on their own - only nothing can exist on its own!
    — Pop

    You have still not given any justification of this assumption. Moreover, while I also think that everything, including ideas and the other abstract objects, needs something to explain its existence, that something isn’t any individual mind, but likely the all-encompassing godly Hyge (Nous, Mind) and ultimately Oneness, the or-principle (first principle) which gives each abstract entity its wist (essence).
    Tristan L

    There is a vast difference in what can exist in mind and what can exist in the real world.

    Basic relational theory states that something can exist only in relation to something else.

    Thanks for the chat, and good luck.
  • RussellA
    18
    . The square was a square (and many other things, too) before the observer saw it, so it must have been sharing in the idea of squareness (th.i. (that is) the Shape / Form / Idea of Squareness) before the obsever saw it. Hence, squareness itself must also have existed before the observer saw the shape.Tristan L

    I am quite certain that abstract entities broadly and possibilities in particular do in fact “lie around” in some abstract “space”.Tristan L

    This shows that all the ideas must be abstract and uncreated,Tristan L
  • RussellA
    18
    If the observer discovers the idea of squareness in the external world rather than in their own minds, this means that the observer has also discovered the external world.
    This raises the question of how we know that there is an external world.
    Three theories are Idealism, Indirect Realism and Realism.
    As for Idealism, as there is no external world, we can only discover ideas in our minds, ie, invent them.
    As for Indirect Realism, as what we perceive is only a representation of what is in the world, this means that we discover ideas in our representation of the external world and not in the external world, ie, invent them.
    As for Direct Realism, where we have a direct awareness of the external world and objects in the external world have the properties that they appear to us to have, there remains the problem as to how we can ever know whether we are experiencing an illusion or not.
    In summary, the idea of squareness being discoverable in the external world is up against Idealism, Indirect Realism and the problem of illusion in Direct Realism.
  • Tristan L
    89
    In your previous post you indicated that "Poss(EID)" refers to the possibility of coming up with the idea. Now you are indicating that "Poss(EID)" refers to the possibility of finding the idea. I don't know why you even talk of possibilities since it your position that all ideas already exist. Why beat around the bush with talk of the possibilities of finding or coming up with ideas?Luke

    I mean to use the words “come up” and “find” in a neutral way, that is, as over-terms for “invent” and “discover”. Note that in German, the word “erfinden” means to invent, so “find” doesn’t imply discovery. By the way, it’s interesting to note that the German word hints at the right intuition that invention of instances of ideas involves the discovery (finding in the strict sense) of ideas themselves.

    No, not necessarily,Luke

    I don’t quite understand; you could understand the Harry Potter books on their own, but not when you read a book of junk before or after them?

    such as a 12th century person being unable to recognise the idea of a computer algorithm, etc. Your understander wouldn't be able to recognise other futuristic ideas by analogy.Luke

    Actually, the twelfth century person would be able to recognize the idea of a computer algorithm, for among the texts that my program outputs, there is a detailed account of all technological development from the twelfth yearhundred till 2020, so the middle-ager only needs to read through that account. My program will also output a text telling in perfect detail all conversations that ever happened from the dawn of Man to the fifteenth yearthousand and beyond, including, for example, all talk that happened in Plato’s Academy about his unwritten Doctrine of Principles, all conversations between computer pioneers and scientists and their before-comers, and all conversations that lead up to futuristic ideas.

    I didn't say your algorithm would find them; I said it might eventually output a representation of every idea.Luke

    What’s the difference? To find an idea is to get/make a representation of it, except in the case of the seldom achievement of hygely (noetic) knowledge of the Shapes, which also doesn’t involve any invention whatsoever (indeed, it’s as least inventional as possible afaik).

    What I meant was, even if we assume that your algorithm does output every idea (by brute force), it still doesn't help us to find those ideas. It would probably be easier for someone to invent the idea themself than to wade through the mountainous pile of junk produced by your algorithm, and this is even assuming that your algorithm has - at the relevant time - output the idea that might have otherwise been invented, [...]Luke

    My algorithm is not there to be put into actual practice anymore than quantum field theory is meant to be used to predict car accidents. It’s existence and principle abilities, rather than its practical usefulness, are what count.

    since your algorithm could take an infinite amount of time to produce all the ideas.Luke
    Bear in mind that the there-is-quantifier ∃ doesn’t commute with the for-all-quantifier ∀, so the proposition that there is a time at which the algorithm has output all finite strings is strictly stronger than the proposition that for each finite string, there is a time at which the algorithm will have output that string. As a matter of fact, the former is untrue while the latter is true. I’ve only ever claimed the latter.Tristan L



    That's my point: it doesn't find ideas. It just endelssly spits out combinations of symbols, which is irrelevant to the question of whether ideas are invented or discovered.Luke

    No, for since the understander is part of the whole algorithm (as opposed to just its string-finding part), it does actually find ideas.
  • Tristan L
    89
    It means that for every finitely expressible idea EID, there’s a time-point t(EID) finitely far into the future such that my algorithm has found EID by the time t(EID).
  • Tristan L
    89
    It does not follow. That is your assumption. What does "essentially linked" mean?Luke

    Why do you first say that it supposedly doesn’t follow, but then ask what it even means? How can you judge a my statement without knowing what it even means?

    That Poss(EID) and EID are essentially linked means that the wist (essence) of one involves the other, in this case the wist of Poss(EID). Poss(EID) is defined in terms of EID, so that (namely its wist) which makes Poss(EID) what it is has to do with EID. Hence, there’s a wistly link tying Poss(EID) to EID.
  • Tristan L
    89
    Basic relational theory states that something can exist only in relation to something else.Pop

    Did I say otherwise?



    I still cannot make out coherent arguments in your posts, and you also don’t give justifications for your claims.

    You’re welcome and good luck with that kind of philosophizing.
  • Tristan L
    89
    Abstract entities, including (Platonish) Shapes (Forms, Ideas), do not exist in the mind or the external physical spacetimely realm. Rather, they exist in an abstract world which lays the ground for both the mindly and the physical. The self can have direct, inwitly (intuitive) knowledge of those Shapes and the other abstract things through its hyge (nous).

    You raise good points about whether the external world exists, but why do you say “we”? Just as I don’t know whether the external world exists independently of me or is just invented by my mind, I also don’t know whether your mind exists independently of me or is just my mind’s invention.
  • RussellA
    18
    Abstract entities, including (Platonish) Shapes (Forms, Ideas), do not exist in the mind or the external physical spacetimely realm. Rather, they exist in an abstract world which lays the ground for both the mindly and the physical.Tristan L

    Thinking about the quote on abstract entities, how can abstract entities exist but neither in the mind nor the world external to the mind ?
    Because, if there was absolute nothingness, neither mind nor world external to the mind, there would be nothing for an abstract entity to be expressed in, and in absolute nothing nothing can exist.
    Therefore, abstract entities need their existence to either the mind, the world external to the mind, or both,
    Unless, however, there is a god that exists outside of both the mind and the world external to the mind, and it is in the mind of god that abstract entities exist.

    I agree , I should have written "I". But it was more of a "royal we", as, at the back of my mind, I suppose that I believe that the external world exists, although I can never prove it, in which case I sense that my uncertainty about the existence of the external world is also shared by another person's uncertainty about the existence of the external world.
  • Tristan L
    89
    Thinking about the quote on abstract entities, how can abstract entities exist but neither in the mind nor the world external to the mind ?RussellA

    Well, that’s the definition of abstractness, see e.g. the third section of the SEP's entry on abstract things

    if there was absolute nothingness, neither mind nor world external to the mind,RussellA

    That assumes that everything must be either in the mind or the external world.

    Because, if there was absolute nothingness, neither mind nor world external to the mind, there would be nothing for an abstract entity to be expressed in, and in absolute nothing nothing can exist.
    Therefore, abstract entities need their existence to either the mind, the world external to the mind, or both,
    RussellA

    Here, you assume that abstract objects must be expressed in something. However, that isn’t the case as far as I can tell. For example, if all yellow objects are destroyed and all thoughts about yellowness are no more, the Shape of Yellowness would still exist. In fact, it must exist even in that case, for then, the (hypothetical) very fact that there are no yellow things and no thoughts about yellowness needs yellowness itself to even make sense.

    Unless, however, there is a god that exists outside of both the mind and the world external to the mind, and it is in the mind of god that abstract entities exist.RussellA
    That is likely the godly Hyge (Nous), the first emanation of Oneness.



    While the abstract things don’t need any mind (except perhaps for the godly Hyge), every mind needs abstract things. Why? Well, to be a mind is to instantiate the Shape of Mindhood, and the latter is an abstract entity.

    Likewise, everything physical needs the Shape of Physicalness.

    I agree , I should have written "I". But it was more of a "royal we", as, at the back of my mind, I suppose that I believe that the external world exists, although I can never prove it, in which case I sense that my uncertainty about the existence of the external world is also shared by another person's uncertainty about the existence of the external world.RussellA

    That’s also what I think, except that it is your (RussellA’s) mind’s existence of which I’m unsure, not that of mine (Tristan’s) :wink:.
  • RussellA
    18
    For example, if all yellow objects are destroyed and all thoughts about yellowness are no more, the Shape of Yellowness would still exist.Tristan L

    The SEP article "Abstract Objects" notes that there need not be one single "correct" way of explaining the abstract/concrete distinction.
    A version of Frege's account is what Stanford calls the Way of Negation, where an object is abstract if and only if it is both non-mental and non-physical.
    An alternative to the Way of Negation is the Way of Abstraction, where an object is abstract if it is (or might be) the referent of an abstract idea, ie, an idea formed by an abstraction.
    For example, the abstract idea of yellowness could be invented by considering several yellow objects and finding what feature they had in common

    In summary, I know that I can invent abstract ideas such as yellowness in my mind by observing the physical world, but I know that I can never discover whether or not yellowness is a non-physical and non-mental abstract idea. Following Occam's Razor in choosing the simplest explanation, I can therefore ignore non-physical and non-mental abstract ideas, because even if they exist I don't need them.
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