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. — RussellA

When I say “abstract”, I mean not physical, not mindly, not spatial, not temporal, and onefold (simple).

For example, the abstract idea of yellowness could be invented by considering several yellow objects and finding what feature they had in common — RussellA

That doesn’t work, for no group of objects only share a single feature. For example, any group of yellow objects is also a group of things, of seeable things, and of colored things. How could you abstract yellowness instead of thinghood, seableness, or coloredness from the group?

In summary, I know that I can invent abstract ideas such as yellowness in my mind by observing the physical world, — RussellA

We’ve just seen that this can’t be done, and there are other reasons, see below and my earlier comments.

but I know that I can never discover whether or not yellowness is a non-physical and non-mental abstract idea. — RussellA

Actually, you can even show that: Every physical yellow thing and every thought of yellowness is what it is in douth (virtue) of instantiating Yellowness itself. Hence, the latter must be abstract. Also, how can a property, such as yellowness, not be abstract? By the way, yellowness itself isn’t a yellow entity, I think, for abstract things don’t have color afaik.

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. — RussellA

You can’t Occam’s Razor to things that must necessarily exist. For evey abstract idea EID, if EID did not exist, then at least that (supposed) very fact (that EID doesn’t exist) would exist. But that fact is defined in terms of EID and thus is wistlily (essentially) linked to it. Therefore, if EID didn’t exist, then that fact couldn’t exist either, leading to a contradiction. Hence, EID must exist after all.

Also, that there are no abstract ideas means that abstract ideahood has no instances, again leading to a contradiction if the not-existence of abstract ideas is assumed.

You do very much need abstract ideas. As we’ve just seen, if they exist, you need Abstract Ideahood itself, and if they don’t exist, you also need Abstract Ideahood itself. Moreover, you can be sure of the existence of your mind. But to be a mind is to instantiate the Shape of Mindhood. Without Mindhood itself, your mind wouldn’t be a mind – it would make no sense to regard it as a mind. You need mindhood even more if you assume the existence of other minds, for what is is that they all share which justifies us in calling them minds?

I think that I have convincingly shown now and before that abstract ideas must exist. That’s why I can be sure of their realness and existence; after all, I can prove that with logic. On the other hand, I cannot prove that a physical external world or minds other than my own exist. Because of that, I’m much surer that abstract ideas exist and are fully real than that the external physical world or other minds or even both exist.

Furthermore, you can directly “see” abstract entities with your "mind’s eye", unlike physical objects and others’ minds and thoughts.

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

Now apply Clavius's Law (consequentia mirabilis). — Tristan L

For example, any group of yellow objects is also a group of things, of seeable things, and of colored things. How could you abstract yellowness instead of thinghood, seableness, or coloredness from the group? — Tristan L

I agree that an object may have several features. Given a set of objects each having several properties, I could define a particular object as being yellow, ie, having yellowness, if it emits a wavelength of between 570 and 590 nm, regardless of what other properties it had.

The observer abstracts what is beneficial to themselves and ignores what isn't. A bee abstracts the colours and scents in a flower indicative of nectar whilst ignoring the number of petals which isn't. The bee could have evolved to abstract the number of petals in a flower if it were of some benefit.Though a study by the University of Queensland has shown that bees can count up to a certain number in order to communicate between themselves using the "waggle dance", showing that animals can abstract when of some evolutionary advantage.

I agree that an object may have several features. Given a set of objects each having several properties, I could define a particular object as being yellow, ie, having yellowness, if it emits a wavelength of between 570 and 590 nm, regardless of what other properties it had. — RussellA

Yes, and that property simply exists, as do the other abtract things which it’s closely linked with, like wavelengthhood, lighthood, nanometrehood, 570, and 590.

The observer abstracts what is beneficial to themselves and ignores what isn't. — RussellA

Exactly; the fact about what’s good for you contains additional info which isn’t contained in the group of objects which you abstract a concept (the mindly image of an abstract idea) from. The fact about what’s good for you is arguably more basic than the concept you abstract, for the latter is created based on the former. But the fact involves the idea of which the concept is an image, so the idea must be more fundamental that the creation of the concept as well.

A bee abstracts the colours and scents in a flower indicative of nectar whilst ignoring the number of petals which isn't. — RussellA

Yes, and the very existence of this fact depends on the existence of colorhood, smellhood, and numberhood, for it involves these things. How could it be the case that being able to abstract color and scent is beneficial to bees without colorhood and scenthood themselves?

Though a study by the University of Queensland has shown that bees can count up to a certain number in order to communicate between themselves using the "waggle dance", showing that animals can abstract when of some evolutionary advantage. — RussellA

What I’ve said before also applies here. Furthermore, the bees deal with the same numbers as we do. The “bee-numbers” don’t obey any different laws to “human-numbers”, do they? If bees and humans had invented their numbers, they should be able to craft them as they wish, yet they obviously can’t do so. The reason is that both the human mind and the bee mind “see” the selfsame numbers, and in discovering them, each invents a mental image thereof.

And of course: Wonderful and amazing little creatures!

I don't know if someone already posted it, but this seems relevant:

https://youtu.be/sfXn_ecH5Rw

As a songwriter, accident plays an enormous role, and as a musician jamming is the main means of creating opportunities for accidents. This is a semi-guided search of configuration space, where you stop when you find something aesthetically pleasing and hopefully original-sounding (parameters of the metric we're optimising). But sometimes a riff, baseline, melody, chord sequence or drum beat just seems to occur to me. My feeling is that this is a similar kind of search, just in a highly discontinuous way. Sometimes a new starting position is seeded well before it's explored.

The similarity between creativity and numerical optimisation is a subject I'm extremely interested in. Obviously I'm a tad late to join in, but I'm encouraged to see that others think similarly. I raised this on a writing forum once. It was a very unpopular opinion haha!

:up:

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

Now apply Clavius's Law (consequentia mirabilis). — Tristan L

I think this requires much further justification to avoid your clear contradiction. Does Clavius' Law save you from all contradictions?

The matter seems fairly simple to me:

I doubt that anybody is arguing against the existence of possibilities (i.e. non-substantive, non-Platonist possibilties, as attempted to clarify earlier). I have certainly not been arguing against the mere possibility of invention. What I take issue with is the suggestion or assertion that all of those possibilities have (already) been actualised.

Unless your algorithm has completed producing every possible combination of characters, then those alleged invention ideas (possibilities) have not yet been actualised and do not yet have any substantive existence. Until your algorithm produces a new idea (and someone finds it), then that idea/invention remains only possible and not actual.

As a Platonist, you probably take the view that there is no distinction between possible and actual existence of those ideas. However, this precludes the possibility of human invention from the outset: If all ideas already exist (substantively), then nobody can actualise them.

Does Clavius' Law save you from all contradictions? — Luke

Clavius' Law says that "if (not-P implies P) then P".

In this case P is it is impossible to invent an idea.

So:

If
(it is not impossible to invent an idea implies it is impossible to invent an idea)
then
it is impossible to invent an idea

If (it is not impossible to invent an idea implies it is impossible to invent an idea) — Pfhorrest

Does it? I don't think so. How is this implied?

:up:

Yes, I agree with you. So there are quite a few folks who think like that!

I don't know if someone already posted it, but this seems relevant:

https://youtu.be/sfXn_ecH5Rw — Kenosha Kid

This video is really great and very relevant. (I’ve already given it a like. Please also do so!) I’ve done the same thing for texts: Here, you can find the source-code of a PASCAL-program written by me, called “AllEndlyStrings”, which outputs each finite-length text written in the alphabet of 2 times 26-bookstaffs (upper- and lowercase), 10-digits, spaces, and the main punctuation marks, after a finite (endly) time. This includes, among so much more, Pherecydes’ lost work, the Iliad, Plato’s dialogues, the Eddas, Twelfth Night, the whole text and music score of Richard Wagner’s monumental The Ring of the Nibelung (including Winterstürme wichen dem Wonnemond and the well-known Ride of the Valkyries), a proof of the Feichtinger-Conjecture, and a text detailing all human dialogues that ever happened from the dawn of Man till today. Together with a person or group of people who understand(s) English, this program makes up a system which will find every finitely expressible idea after a finite time without any need for creativity. Btw., whether an how can I upload the belonging executable .exe file to this forum?

I'm encouraged to see that others think similarly. — Kenosha Kid

I’m also happy that others think that way.

I raised this on a writing forum once. It was a very unpopular opinion haha! — Kenosha Kid

Could you please tell me the forum and the discussion? I’d like to add my two cents there, including my program. I don’t get how it could be an unpopular opinion. I’ll give proofs that it is true, and hopefully, it’ll become more popular then. Even if it’s old, I wouldn’t mind that.

:up: (an over-thumbs-up, th.i. a meta-thumbs-up)

:up:

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. — Tristan L

Unless your algorithm can discover ideas via actual practice, then it adds nothing to the argument that ideas are discovered rather than invented. In principle, your algorithm can discover whatever ideas are possible. Likewise, in principle, a person (i.e. an inventor of ideas) can invent whatever ideas are possible.

You appear to assume that any given idea is expressible in the ASCII characters that your algorithm produces. An inventor of ideas must likewise be able to express an (invented) idea using the same characters.

What your algorithm does is simply produce or actualise every possible combination of characters. Therefore - along with an enormous bunch of junk - your algorithm actualises all possibilities. More specifically, your algorithm produces all possible expressions. Since we are assuming that all ideas are expressible within the ASCII characters, and since your algorithm produces all possible expressions, then all ideas will find their expression somewhere in the output of your algorithm. Therefore, there is little difference between the output of your algorithm and all possibilities (i.e. whatever ideas are possible). Your algorithm actualises the expression of all possibilities (and much other junk) by outputting all possible expressions.

However, not every string of characters is an idea. Whether or not all possibilities are actualised (and putting aside the practical issues of doing so), what this overlooks is that ideas - in the sense we are discussing - have some usefulness or interest to humanity. The important part is finding the useful or interesting ideas within the range of possibilities. All of the possibilities already exist whether your algorithm actualises them or not, but the possibilities are not the ideas.

Any example of an idea that you will give is one that humanity has found to be useful or interesting. Deciding what counts as an interesting or useful idea is easily done for all past ideas which have already been found to be so. How does your algorithm decide which as-yet undiscovered or uninvented ideas will be useful and/or interesting for humanity? That is, how does your algorithm decide which expressions are ideas and which are not?

All possibilities exist whether ideas are discovered or invented. It begs the question to assume that the existence of all possibilities (or all possible expressions) implies the pre-existence of all ideas.

However, not every string of characters is an idea. — Luke

This is irrelevant. Every text -- and Tristan limited his purview to texts -- is a string of characters. That is, by searching the entire space of strings of characters, one searches the entire space of texts.

However, not every string of characters is an idea.
— Luke

This is irrelevant. — Kenosha Kid

It's completely relevant; we're discussing ideas.

Every text -- and Tristan limited his purview to texts -- is a string of characters. That is, by searching the entire space of strings of characters, one searches the entire space of texts. — Kenosha Kid

What do you mean by "text"? Where did Tristan limit his purview to texts?

What do you mean by "text"? Where did Tristan limit his purview to texts? — Luke

In a post you responded to, even quoted, but apparently didn't bother to read. I disagree btw with the notion that ideas pre-exist their discovery, but Tristan has defined his terms robustly. You can lead a horse to water...

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. — Tristan L

In the context of creativity, which this must be, my issue is that this is a philosopher's idea of "idea" being conflated with a creative person's idea of "idea". You are free to define your terms as you see fit, of course, but when I "have an idea" in a creative context, it is not some abstract thing, nor is it the output of a creative act.

I think Pfhorrest's description of it as a configuration space is accurate. Your algorithm and that used in the link I posted above is a brute force, unguided trawl through this configuration space, where each dimension is an independently variable (if not uncorrelated) parameter of creative exploration. (In music, tempo could be one, key another, verse melody, verse first harmony, verse second harmony, etc.) There is no means of assessing the success of the search.

When I have an idea for a song, say, it will typically be a bassline, or melody, or an interesting harmony for a section of the song, or maybe the theme of a lyric. This does not pin down the song, but rather it significantly reduces the number and/or range of those parameters. I.e. instead of searching the entire configuration space, I am searching a highly constrained subspace.

But most importantly, an idea comes with its own rough measure of success. If I am to explore an idea, I will have some means of assessing whether the execution, after further refinement, fell short of, met, or exceeded whatever quality made the idea attractive. So an idea, in a creative sense, means to me a highly guided, highly constrained search through a configuration subspace.

Computer algorithms are very good at the searching, but they need to be told what success looks like, something entirely absent from the infinite monkeys approach, and something difficult to conceive a computer figuring out by itself. Generally I think ideas are results of prior searches and some exact solutions (a great song I heard) whose vicinity could be explored with some translation. (What does Stand By Me sound like in a minor key? for instance.)

I think this requires much further justification to avoid your clear contradiction. Does Clavius' Law save you from all contradictions? — Luke

My contradiction? Your contradiction! I have shown that your assumption that ideas can be invented lets its own negation follow and thereby beats itself. Pfhorrest has already explained Clavius’ Law to you. I honestly ask: Do you understand the basic logical structure of my arguments?

What I take issue with is the suggestion or assertion that all of those possibilities have (already) been actualised. — Luke

An assertion that no one but you has made, so by taking issue with it, you’re attacking a straw-man.

To repeat the gist of my argument pertaining to that again: The mere existence from the start of the possibility that Alice could find (remember that I use both “find” and “come up with” neutrally as over-terms for both “invent” and “discover”) an idea EID means that EID itself must actually exist from the start. However, it doesn’t mean that any mental or physical instance (what you might call “actualization”) of EID has to exist from the start. Such an instance has to be created, invented, made.

Unless your algorithm has completed producing every possible combination of characters, then those alleged invention ideas (possibilities) have not yet been actualised and do not yet have any substantive existence. — Luke

Yep, of course they do! The fact that Alice thinks about EID exists only from the first moment at which it is certain that Alice would think about EID, but the fact that Alice might think about EID always actually exists. Regarding my algorithm, it is completely deterministic, and so any idea that it finds is found without any creativity. This shows that creativity is not needed when coming up with ideas.

Until your algorithm produces a new idea (and someone finds it), — Luke

That someone is already part of the algorithm, for he is the understander. Recall that my algorithm = my program + understander.

Until your algorithm produces a new idea (and someone finds it), then that idea/invention remains only possible and not actual. — Luke

The possibiliy itself, th.i. the fact that the idea might be come up with, is actual from the start. The finding of the idea, on the other hand, only comes into actual existence once it is foredetermined that the idea will be found, which is the case from the point at which my algorithm is started. My possibility-argument uses the former truth, namely the actual existence of the might-fact, and my algorithm-argument uses the latter truth, namely that from the time at which my algorithm is started, for every finitely expressible idea EID, the fact that EID will be found exists.

As a Platonist, you probably take the view that there is no distinction between possible and actual existence of those ideas. However, this precludes the possibility of human invention from the outset: If all ideas already exist (substantively), then nobody can actualise them. — Luke

Again a great example that you haven’t gotten basic points that I’ve said over and over again, and that even now, you misunderstand my position. Making reference to ’s remark, drinking is needed for living, and likewise, understanding the other’s position is needed to keep a philosophical talk meaningful and working. But of course, to drink or not to drink is each one’s own decision...

The gist of my position is this: Ideas are abstract things, and as such, they have eternal, absolute and pure being. In particular, they cannot be invented or otherwise created, for their existence isn’t time-bound. However, like many abstract entities, ideas have concrete mental and physical instances. Since these exist in time, they can be invented or otherwise created. What we call “actualization” of an idea is the instantiation of that idea, th.i. the making of a mental of physical instance of it. For example, the number 3 is eternal, but the thought I’m having about the number 3 right now is temporal, concrete, and mental. Furthermore, it is my creation, since I could have thought about something else, but freely chose to think about 3. In turn, don’t conflate this with the state-of-affairs that Tristan thinks about 3 on 18/09/2020, which is abstract and eternal, just as every state-of-affairs of the shape “Tristan thinks about n on 18/09/2020$”. Note that some of these states-of-affairs hold and others don’t, and by bringing about the holding of one of them, I create mental information. This concrete info is what we call “instance”.

Remark: I don’t use all terms here in the way I should use them. For instance, the talk of instances is metaphorically powerful but unaccurate in the end, and I use the word “fact” differently here from my right usage. In my philosophical theory, these issues are addressed and the terms used in the right way, but of course, this thread is hardly the place to discuss this not-so-small theory.

First things first: Do you now see that the following part

0. If ideas can be invented, then they cannot be invented. (premise)
1. If it’s not the case that ideas cannot be invented, then ideas cannot be invented. (from (0.) by Double Negation)
2. Ideas cannot be invented. (from (1.) by Clavius’ Law / consequentia mirabilis)

of my argument is logically valid?

If yes, then let’s check the truth of the primise (0.). I’ve shown it e.g. here:

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. — Tristan L

In risk of repeating myself, you can substitute “invent” (or “discover”, but that’s unrelevant here) for “find”/”come up with”.

Unless your algorithm can discover ideas via actual practice, then it adds nothing to the argument that ideas are discovered rather than invented. — Luke

But it can discover them through actual practice, at least as much as quantum field theory can in actual practice be used to describe cell division. However, just as describing cell division with QFT is extremely difficult, complex, cumbersome, and resource-intensive, so is finding ideas with my algorithm. (Note, however, that some simple ideas will be discovered by my algorithm in reasonable time.) This is what is meant by “impractical”. Another good example is Karl Fritiof Sundman’s solution of almost all instances of the general three-body-probem, which, though exact, would likely need more years when used in astronomy than there are particles in the observable universe. In fact, applying Sundman’s solution would take much more time than using my algorithm to find LOTR, for instance.

You appear to assume that any given idea is expressible in the ASCII characters that your algorithm produces. An inventor of ideas must likewise be able to express an (invented) idea using the same characters. — Luke

I do not make that assumption, as I’ve already said. However, any idea of any practical significance can be expressed in the ASCII-characters: all novels, all movies, all technological inventions, all theories, all pictures, and all pieces of music. In fact, they can even be expressed in nothing but 1’s and 0’s. For example, this talk that we’re having right now is represented by a long string of 1’s and 0’s. Only unspeakable ideas, like ones related to personal mystical and gasty experiences, cannot be expressed in ASCII, but these are hardly what most folks (including you, judging from your right claim that ideas should be somehow useful) have in mind when they talk about ideas. Also, my possibility-argument even applies to these unsayable ideas. And what about only endlessly expressible ideas? I strongly doubt that any such ideas have ever been found, for our brains are finite, and our minds use our brains as reckoning-machines. And the possibility-argument, as well as the independent-finding-argument, apply also to them anyway.

What your algorithm does is simply produce or actualise every possible combination of characters. — Luke

...and map each such string to the corresponding idea. Don’t forget the understander!

Therefore - along with an [...] all possible expressions. — Luke

Thus showing that the space of all possibilites is actual.

However, not every string of characters is an idea. — Luke

Even more: no string of characteres is an idea (actually, it technically is an idea, but usually not the same as the idea which it represents); rather, it represents, stands for, an idea.
However, conversely, as I’ve explained above, every idea of practical relevance can be expressed/represented/stood for by a finite string of symbols. The very history of all brain states of all humans that have ever lived can be expressed by a (albeit very long) finite string of symbols over a finite alphabet and therefore ultimately a number. (Here, I recall that guy Pythagoras’ doctrine that all is Number. Just a little food for thought...)

So...

Whether or not all possibilities are actualised — Luke

No worries, rest assured that all useful possibilites are really actualized.

what this overlooks is that ideas - in the sense we are discussing - have some usefulness or interest to humanity. The important part is finding the useful or interesting ideas within the range of possibilities. — Luke

True, except for the “overlooks”-part (see below).

Any example of an idea that you will give is one that humanity has found to be useful or interesting. Deciding what counts as an interesting or useful idea is easily done for all past ideas which have already been found to be so. How does your algorithm decide which as-yet undiscovered or uninvented ideas will be useful and/or interesting for humanity? That is, how does your algorithm decide which expressions are ideas and which are not? — Luke

With the help of its understander, of course. He will read all the texts, and once he finds a meaningful one whose content is useful, he’ll recognize it as such. For example, just as I recognized that the descriptions of the high-voltage VdG-generator which I read online mean a useful idea (and a very interesting one at that), the understander will see that a description of the VDGG output by the program refers to a useful and interesting idea.

All of the possibilities already exist whether your algorithm actualises them or not, — Luke

Of course they do; that’s my point! The deterministic nature of the algorithm just drives it home.

but the possibilities are not the ideas. — Luke

How often are you going to reiterate this point which I’ve been agreeing with all along?

All possibilities exist whether ideas are discovered or invented. — Luke

True (namely that each of idea-discoverableness and idea-inventability lets existence of all possibilities follow). At the same time, the existence of all possibilities is incompatible with the inventableness of ideas. What does that mean? That ideas cannot be invented.

It begs the question to assume that the existence of all possibilities (or all possible expressions) implies the pre-existence of all ideas. — Luke

No, it doesn’t, for the possibilities are essentially defined in terms of the ideas, so if the possibilities exist, so must the ideas.

I disagree btw with the notion that ideas pre-exist their discovery — Kenosha Kid

If ideas exist after their discovery, but they can’t be created, then they must also exist before the discovery. Otherwise, the discovery would actually be an act of creation.

In the context of creativity, which this must be, my issue is that this is a philosopher's idea of "idea" being conflated with a creative person's idea of "idea". You are free to define your terms as you see fit, of course, but when I "have an idea" in a creative context, it is not some abstract thing, nor is it the output of a creative act. — Kenosha Kid

You’ve got a point, so from now on, let’s try to use “widea” (from the Or-Indo-European root “*weid-” (“to see”), which “idea” and “eidos” are drawn from) for the philosophical and especially the Platonish concept and “idea” for the artistic one.

I think that when you say “I’ve got an idea”, you mean a mental and thereby concrete instance of an abstract widea. This instance is what the artist calls “idea”. However, I think that the idea, unlike the widea, actually is the output of a creative act, which at the same time is an act of discovery of a widea – unless that discovery is deterministic, in which case the idea exists from the start, but only becomes directly seeable later on. Take two dice for example. Alice throws her die and gets a 5. The number 5 itself is abstract and eternal, as is the state-of-affairs that Alice’s throw would lead to a five. However, the piece of information corresponding to the making-true (“actualization”) of that state-of-affairs is created by Alice’s throw. Now if Bob throws his die and also gets a 5, then his piece of info, what we call his “instance”, is different from Alice’s, although both involve one and the same abstract entity 5. By contrast, if he puts his die on the table with “5” on the upper face on account of Alice’s die showing a “5”, then his instance is basically the same as Alice’s, and his activity doesn’t make any new info. Rather, it only copies existing info.

I think Pfhorrest's description of it as a configuration space is accurate. — Kenosha Kid

As do I. The possibilities in the space are real, abstract entities, as are the wideas to which they are linked. I don’t understand why Pfhorrest and you unneededly seem to back down from full-fledged platonism, though. This is one point where I likely agree with Luke; he seems to understand Pfhorrest’s position as platonist, and I don’t see any way in which Pfhorrest cannot be interpreted as such.

There is no means of assessing the success of the search. — Kenosha Kid

In the case of my algorithm (= my program + understander), there is, namely the understander.

So an idea, in a creative sense, means to me a highly guided, highly constrained search through a configuration subspace. — Kenosha Kid

According to this definition, the widea also fore-exists, for just as the original possibility-space just exists, so does the space of all possible searches through it. However, instantiating one such possible search by free will creates mental information, and in this way, the process is creative. But again, we can make an algorithm which brute-forces all possible searches (and thus conducts a brute-force meta-search), another one which brute-forces all possible over-searches (meta-searches), and so on to infinity (and beyond?).

Computer algorithms are very good at the searching, but they need to be told what success looks like, something entirely absent from the infinite monkeys approach, and something difficult to conceive a computer figuring out by itself. — Kenosha Kid

Yes, and that’s what the understander is there for. The crucial point is that the understander only needs to have the mindly ability to understand, but no creativeness whatsoever. For example, if you take the role of the understander, you’ll get the same feelings, emotions, and thoughts when you hear "Winterstürme" and "Du bist der Lenz" regardless of whether the information stems from Wagner’s mind or from my deterministic program AllEndlyStrings.

On the whole, I like your and Pfhorrest’s ideas, but
1. I don’t see why you unneededly hold back from platonism,
and
2. I think that there is a clearly definable discovery-aspect and a clearly definable creative aspect to finding ideas.

My contradiction? Your contradiction! I have shown that your assumption that ideas can be invented lets its own negation follow and thereby beats itself. — Tristan L

Your supposed argument assumes the conclusion. I asked you earlier what "essentially linked" meant in your argument: "Since Poss(invent EID) is essentially linked to EID, it follows that EID must also have always existed". I didn't ask you this because I didn't understand it; I asked you this because I was trying to get you to see that it's problematic.

Your position is that ideas do (pre-)exist and people discover them. My position is that ideas do not (pre-)exist and people invent them. Your argument can't be that if it is possible to invent an idea then that idea must have always existed! That's the position you're meant to be arguing for, not simply assuming. I obviously don't agree that if it is possible to invent an idea then the idea must have always existed. That's absurd. It is entirely your own assumption (i.e. "essentially linked") that leads you to the contradiction that if it is possible to invent an idea then it is not possible to invent an idea.

Pfhorrest has already explained Clavius’ Law to you. I honestly ask: Do you understand the basic logical structure of my arguments? — Tristan L

Pfhorrest gave the following explanation:

If
(it is possible to invent an idea implies it is impossible to invent an idea)
then
it is impossible to invent an idea

Again, I do not agree to the bracketed statement, which is based on your own assumption. Therefore, I don't agree to the rest/whole.

Yep, of course they do! The fact that Alice thinks about EID exists only from the first moment at which it is certain that Alice would think about EID, but the fact that Alice might think about EID always actually exists. Regarding my algorithm, it is completely deterministic, and so any idea that it finds is found without any creativity. This shows that creativity is not needed when coming up with ideas. — Tristan L

I don't see how an idea exists before anybody thinks of it. I agree that "the fact that Alice might think about EID always actually exists". because what Alice might do or think is whatever it is possible to do or think. But that doesn't mean that she has actually thought of it, or that the idea already exists before she has actually thought of it. Let's not conflate possible ideas with actual ideas.

That someone is already part of the algorithm, for he is the understander. Recall that my algorithm = my program + understander. — Tristan L

Your "understander" seems to do a lot of the heavy lifting for your algorithm argument. They will have a lot of reading/sifting to do. How do they decide which string of symbols represents a new idea? Do they require any specialised knowledge or do they learn it as they go?

The gist of my position is this: Ideas are abstract things, and as such, they have eternal, absolute and pure being. In particular, they cannot be invented or otherwise created, for their existence isn’t time-bound. However, like many abstract entities, ideas have concrete mental and physical instances. Since these exist in time, they can be invented or otherwise created. — Tristan L

Ideas both can and cannot be invented? That's very confusing.

What we call “actualization” of an idea is the instantiation of that idea, th.i. the making of a mental of physical instance of it. For example, the number 3 is eternal, but the thought I’m having about the number 3 right now is temporal, concrete, and mental. — Tristan L

Is the thought of the number 3 the same as the idea of the number 3? When you think about the number 3, you consider this an instance of inventing the idea of the number 3?

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. — Tristan L

I agree that when someone has found/invented an idea then it was possible for them to do so.

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

Why must the idea have always actually existed? It was always possible to come up with the idea, but that doesn't mean the idea always existed prior to someone coming up with it. It is always possible that I could break my leg, but that doesn't mean that my leg was always broken prior to my breaking it. Please spell out the part of your argument re: the "fixed bond" or "essential link" between EID and Poss(EID).

However, any idea of any practical significance can be expressed in the ASCII-characters: all novels, all movies, all technological inventions, all theories, all pictures, and all pieces of music. In fact, they can even be expressed in nothing but 1’s and 0’s. For example, this talk that we’re having right now is represented by a long string of 1’s and 0’s. — Tristan L

Is a long string of 1's and 0's something that your "understander" understands?

Thus showing that the space of all possibilites is actual. — Tristan L

I agree. But Poss(EID) is not EID.

With the help of its understander, of course. He will read all the texts, and once he finds a meaningful one whose content is useful, he’ll recognize it as such. For example, just as I recognized that the descriptions of the high-voltage VdG-generator which I read online mean a useful idea (and a very interesting one at that), the understander will see that a description of the VDGG output by the program refers to a useful and interesting idea. — Tristan L

Isn't it possible that an understander could overlook an idea and judge it as a random string of meaningless symbols? How does the understander decide what is an idea and what isn't?

How often are you going to reiterate this point which I’ve been agreeing with all along? — Tristan L

But you don't really agree, because you keep repeating:

...the possibilities are essentially defined in terms of the ideas, so if the possibilities exist, so must the ideas. — Tristan L

That is, you make no (or only an artificial) distinction between the existence of possible ideas and the existence of actual ideas.

If ideas exist after their discovery, but they can’t be created — Tristan L

The creative idea is created. It is information: coordinates in configuration space. When I vary those coordinates, I am trying a new idea (a new vector).

This instance is what the artist calls “idea”. However, I think that the idea, unlike the widea, actually is the output of a creative act, which at the same time is an act of discovery of a widea – unless that discovery is deterministic, in which case the idea exists from the start, but only becomes directly seeable later on. — Tristan L

That is not how it seems to me. The output of the creative act is a piece of art, or a piece of a piece, or a draft. I can read it and know how it reads or hear it and know how it sounds, etc. The idea might be: how would it sound if, instead of everyone singing the same thing, half the people sing the fifth note up in the scale? Et voila: rudimentary harmony us invented. But you still need to evaluate a cost function -- you near to hear the thing and measure it against expectations -- to know if the idea was good and, if so, if you've nailed it. This is the extra thing that ideas have above the bland coordinates that a brute force, unguided trawl through the space of possible ideas must have to be creative.

As the OP says, this expectation must be derived from experience, even if the parameters of the idea are derived from genius. In the case of fifths, perhaps someone heard the effect of someone trying and failing to sing along, with that failure sometimes producing a nice effect. This provides both a narrowed search and a measure of success.

. I don’t understand why Pfhorrest and you unneededly seem to back down from full-fledged platonism, though. — Tristan L

I think that both of us are distinguishing between an act of creativity and systematic permutations of coordinates. I'm not sure the question of the ontological status of those coordinates is particularly relevant. They correspond to arrangements that could be made, be it if sounds, words, colours, etc. They don't strike me as any more or less compelling a case for idealism than anything else, making it a separable discussion.

It's analogous to the distinction between going on holiday to Florence and the coordinates of, say, the peak of the Duomo. I am saying that a molecule of oxygen that eventually drifts from Tokyo to Florence has not gone on holiday, because it is not a guided trip with intent and expectation. And you are asking whether the position that the peak of the Duomo occupies is real and eternal.

I'm not sure the question of the ontological status of those coordinates is particularly relevant. — Kenosha Kid

Yes, this is my stance on the ongoing argument in this thread. My view on creativity is not anti-platonic, it’s just platonism-agnostic: it doesn’t matter whether platonism is true or not.

My point in the OP was that an algorithm like this AllEndlyStrings does not count as a creative process even though it will eventually come up with every product of a creative process; BUT that adding randomness to that (making it non-deterministic), or even making the search process completely random jumps around the configuration space, doesn’t help at all, its still just as non-creative. What matters is the details of the algorithm, how it identifies new (undiscovered) possibilities in relation to old possibilities. That relationship between the known and unknown is reality what I’m getting at.

A lot of creative works of our age would seem completely off the wall (“random”) uninteresting nonsense to people from a thousand years ago, because they lack the context of all the intervening works.

. . . mathematicians, and philosophers don’t have to worry that they’ll be out of work soon — Tristan L

Well, philosophers have to worry about getting INTO work as soon as possible. Not many positions as resident philosopher at Walmart or General Ford.

Why must the idea have always actually existed? It was always possible to come up with the idea, but that doesn't mean the idea always existed prior to someone coming up with it. It is always possible that I could break my leg, but that doesn't mean that my leg was always broken prior to my breaking it. — Luke

However, it does mean that the state-of-affairs and the proposition that you would break your leg has always existed, as has its negation. Take e.g. the proposition B that you break your leg tomorrow (on 21/09/2020). That proposition is as of yet (today, on 20/09/2020) neither true nor false (at least for argument’s sake; whether the universe is deterministic or not is a different matter), but it will be either true or false after-tomorrow (on 22/09/2020) (and then stay so for ever after). Now I already hope today, on 20/09/2020, that B will be false on 22/09/2020. So B has the property today that I hope it to become false after-tomorrow. So B must already exist today. Indeed, how could I possibly hope anything about something not-existent? Also, the proposition that you break your leg yesterday (on 19/09/2020) is false today (on 20/09/2020) (I hope), yet to be false, it must exist in the first place. The only thing that would come into existence should B become true (which I strongly hope not to happen) would be a piece of information, which is what we might call “the breaking of your leg on 21/09/2020”. If B becomes false, then the opposite piece of info, which might be called “the not-breaking of your leg on 21/09/2020”, comes into being. Information and propositions are not the same thing. The proposition B is defined in terms of, among other things, your leg, as is the proposition MAYBE(B) that you may break your leg tomorrow. Therefore, since the former exists today and the latter not only exists today, but is (unluckily) even true today, your leg must also exist today.

It’s exactly analogous with the finding of ideas.

Let's not conflate possible ideas with actual ideas. — Luke

Indeed we shouldn’t conflate things, but that’s just what you’re doing here:

Ideas both can and cannot be invented? That's very confusing. — Luke

You’re mixing abstract ideas (called “wideas” henceforth) up with concrete instances thereof.

Is the thought of the number 3 the same as the idea of the number 3? — Luke

Of course not! That’s just what I say in the paragraph to which you’ve given the above answer. A thought of the numbers 3 is (in a way) a mental and therefore concrete instance of the widea of threehood.

When you think about the number 3, you consider this an instance of inventing the idea of the number 3? — Luke

No. When I choose to think about 3 today (on 20/09/2020), I bring about the truth of the proposition that I think about 3 on 20/09/2020. The piece of info which I thus create is not that impressive, though. To discover 3 by myself is to bring about the truth of the much more impressive proposition that I think about 3 at some time in my life (and thereby create and invent the belonging impressive piece of information). This proposition has already been true since at least my early childhood, and I don’t really know what brought about my first thought about 3. Maybe I brought it about with my own free will, in which case I’d really be an independent discoverer of 3, or perhaps my parents did, or maybe knowledge of numbers is “hardwired” into my (and others’) mind(s) so deeply that the proposition that I would think of 3 at some point was always true by the nature (wist) of my mind.

Your supposed argument assumes the conclusion. — Luke

Not without reason did I ask you whether

quote="Tristan L;453377"]you now see that the following part [...] of my argument is logically valid[/quote]

(the boldface is new). The crucial part of my argument is obviously not this trivial application of Clavius’ Law, but my proof that if wideas can be invented, then they cannot be invented. I clarified the point with Clavius’ Law only because you said:

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

That’s as if you had said, “It’s impossible to invent an idea? Hmm.”, for (A => NOT A) is logically equivalent to (NOT A). However, even after I mentioned Clavius’ Law, you seem to still think that (A => NOT A) is a contradiction, as seen here:

I think this requires much further justification to avoid your clear contradiction. Does Clavius' Law save you from all contradictions? — Luke

My statement that if it’s possible to invent a widea, then it’s impossible to invent one, which I have shown to be true btw, is logically equivalent to the statement that it’s impossible to invent a widea. Hence, your claim that this my statement is a contradiction is logically equivalent to the claim that wideas can be invented, a claim for which you have yet to give a justification.

I asked you earlier what "essentially linked" meant in your argument — Luke

Right, you did here:

What does "essentially linked" mean? — Luke

and I have also given you an answer:

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

I didn't ask you this because I didn't understand it — Luke

I didn’t ask you whether you understand this point; I asked you whether you understand the point about Clavius’ Law.

I asked you this because I was trying to get you to see that it's problematic. — Luke

In what way is this problematic?

Take the (false) proposition that 3 is an even number, for example. This proposition, by its very essence (wist), involves the number 3, so if this proposition exists (which it obviously does as we’re thinking and talking about it right now, and as only existing things can have properties, like falsehood), then 3 must exist, too (which it obviously does, of course).

Your position is that ideas do (pre-)exist and people discover them. My position is that ideas do not (pre-)exist and people invent them. Your argument can't be that if it is possible to invent an idea then that idea must have always existed! That's the position you're meant to be arguing for, not simply assuming. — Luke

Well, as I said above, that isn’t my argument, but rather only a trivial application of Clavius’ Law which I wouldn’t even have bothered with hadn’t it been for your belief that the conclusion (widea-inventability => widea-notinventability) of my real argument is a contradiction. This real argument does show, conclude, that if it is possible to invent a widea, then that widea must have always existed.

Your argument can't be that if it is possible to invent an idea then that idea must have always existed! That's the position you're meant to be arguing for, not simply assuming. — Luke

My argument shows, rather than assumes, that if a widea can be invented, then it must have always existed.

I obviously don't agree that if it is possible to invent an idea then the idea must have always existed. That's absurd. — Luke

It is indeed absurd to assume that wideas can be invented. However, to assume (which I btw. don’t do; rather, I show it) that if it is possible to invent a widea then the widea must have always existed is logically equivalent to assuming that wideas cannot be invented. How is that absurd?

It is entirely your own assumption (i.e. "essentially linked") — Luke

How is this my assumption? Poss(EID) is defined in terms of EID. How could there not be a wistly (essential) link?

It is entirely your own assumption (i.e. "essentially linked") that leads you to the contradiction that if it is possible to invent an idea then it is not possible to invent an idea. — Luke

You seemingly still fail to see the simple logical fact that (A => NOT A) is not a contradiction, but rather logically equivalent to (NOT A), for every proposition A. How is it my assumption that Poss(EID) and EID are essentially linked when the former is directly defined in terms of the latter?

Again, I do not agree to the bracketed statement — Luke

You’ve made that evidently clear, meaning that you don’t think that this (trivial) part of my argument is sound, yet...

Therefore, I don't agree to the rest/whole. — Luke

...you have to concede that this trivial part of my argument is valid.

the bracketed statement, which is based on your own assumption. — Luke

That’s not the case, as I’ve explained.

Please spell out the part of your argument re: the "fixed bond" or "essential link" between EID and Poss(EID). — Luke

I’ve already spellt it out above, but I’ll do it again: The possibility is defined in terms of the widea, so it couldn’t be what it is without the widea any more than B could be what it is without your leg (or the widea of breaking).

I agree. But Poss(EID) is not EID. — Luke

In turn, I agree with that. In fact, there are many other possibilities beside Poss(EID) (the possibility that a thinking living thing would come up with EID) that do the job just as well, such as Poss(EID, human) (the possibility that a human being would come up with EID) and Poss(EID, Andromedan) (the possibility that a being from the Andromeda galaxy would come up with EID). Since each of these is different from all the others, at most one could be identical to EID, yet they all do the job equally well.

That is, you make no (or only an artificial) distinction between the existence of possible ideas and the existence of actual ideas. — Luke

I certainly do make real and substantial distinction between wideas and associated possibilities, for as I’ve explained above, there are several essentially different possibilities associated with the same widea EID which are all essentially linked to the widea (and to other things, too, e.g. Poss(EID, Alice) to Alice and Poss(EID, Bob) to Bob) and so do their job equally well. On the other hand, the existence of the possibilites is indeed equivalent to the existence of the wideas because the former are defined in terms of the latter.

Your "understander" seems to do a lot of the heavy lifting for your algorithm argument. — Luke

The understander neither needs nor uses any creativity at all. That’s the whole point. How is that heavy lifting?

How do they decide which string of symbols represents a new idea? — Luke

By knowing English syntax and semantics; by knowing the English meaning-mapping (the function which sends each meaningful English expression to what it means, e.g. the word “six” to the number 6); just like you can check that the LOTR-books are meaningful and understand them without creativity.

Do they require any specialised knowledge or do they learn it as they go? — Luke

The only knowledge the which the understander has at the start is knowledge of the English meaning-mapping and perhaps some very basic stuff like fundamental logical laws. By mapping strings to the abstract things that they mean (e.g. the expression “e^ix = cos x + i sin x”, Euler’s Formula, to the deep law about complex numbers, the exponential function, and trigonometric functions), he can, of course, learn, and then apply that knowledge later on in the text. (After each text, he can even forget all the new stuff he learned, because for any texts T1 and T2, there’s a further text made up of T1 followed by T2.) For example, he can use his knowledge of basic logic to check whether a text is a valid proof. He’ll thus find the proof of, say, the Feichtinger-Conjecture by just reading and understanding and thinking logically, but without any creative thinking.

Is a long string of 1's and 0's something that your "understander" understands? — Luke

Yes, because for any string of 1's and 0's, there’s a text containing that string along with a before-going English explanation and/or description of how to interpret that string, e.g. containing a definition of the mp4-format and the png-format.

Isn't it possible that an understander could overlook an idea and judge it as a random string of meaningless symbols? — Luke

Nope, in the same way that no English-speaker can mistake this forum discussion for a meaningless string of symbols.

How does the understander decide what is an idea and what isn't? — Luke

By knowing the English meaning-mapping, just as a compiler can judge whether a text is a valid compilable source-code or just a meaningless string. Tell me, in what way is your creativity needed for you to understand the LOTR-books? And more weightily, in what way is Tolkien’s creativity needed for you to understand the LOTR-books?

I don't see how an idea exists before anybody thinks of it. I agree that "the fact that Alice might think about EID always actually exists". because what Alice might do or think is whatever it is possible to do or think. But that doesn't mean that she has actually thought of it, or that the idea already exists before she has actually thought of it. Let's not conflate possible ideas with actual ideas. — Luke

It may be that you call actual abstract wideas “possible ideas”, and actual concrete mental instances of wideas “actual ideas”. It might also be that you call not-yet-existing pieces of information about wideas “possible ideas”. In such a case, you’d be talking past my point all the time. (More on this in my next comment.)

The following are just some thoughts of mine, and I’m not dogmatic about them at all.

I think that when the platonist talks with another person about the existence of wideas, he (used gender-neutrally) doesn’t try to prove the existence of wideas. Indeed, it is self-evident that wideas must exist, for if any widea W did not exist, then that very (supposed) fact NOTEXIST(W) would at least exist, but NOTEXIST(W) is defined in terms of W, so W must exist after all. Another way to see it is this: NOTEXIST(W) is the state-of-affairs that W-hood doesn’t have an instance, so NOTEXIST(W) needs at least W-hood. But the widea of W is the thing which underlies W, W-hood, W-hood-hood, aso. to infinity and beyond, so the widea of W must exist after all. Furthermore, the proposition that no ideas exist is the proposition that wideahood has no instances. So this proposition needs at least one widea, namely wideahood, if it is to be what it is. Hence, it defeats itself and is thus false.

So what is the platonist trying to do? I’d say that he’s trying to show the other guy the wideas. He isn’t trying to show him that they exist, mind you; he’s trying to show him the wideas themselves. He isn’t trying to help him get propositional knowledge (knowledge-that, German Wissen-dass), but rather knowledge by acquaintance (knowledge-of, German Kennen). You see, wideas are so fundamental that just as the Laws of Self-Identity (each thing is the selfsame as itself) and Self-Implication (each proposition follows from itself), we might not be very aware of them. Similarly, the self is so close to itself that self-knowledge is perhaps the most marvellous of all knowledge. It’s a bit like it’s easier to see your hands and feet that your own belly, which in turn is easier to see than the top of your own chest, because these things get progressively closer to your eyes!

At least regarding platonism of the kind I hold, when someone who espouses such platonism talks about wideas as ideal prototypes or as floating around in the above-heavenly world, they’re just trying to help the more concrete-minded become aware of the wideas by using concreter terms. But these terms are just metaphors, and even wrong ones in the end, leading to things like the Third Man Argument. Then, when the against-platonist seems to argue against platonism, what’s really happening is that he still isn’t consciously aware of the wideas and in particular wideahood and thus can’t even so much as negate platonism; rather, he misunderstands the platonist as claiming the existence of concrete-like objects whose existence really is dubious, such as a perfect chair hovering above the sky. In other words, he thinks that the platonist says that there exists an object which has chairhood in a perfect and ideal way (th.i. that 1 has chairhood perfectly, or 2 has chairhood perfectly, or Mt. Everest has chairhood perfectly, or ...), without being consciously aware of chairhood. But the platonist actually has that very Widea of Chairhood itself in mind, a fully abstract thing of which the against-platonist only has underconscious awareness.

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). — Tristan L

Your argument boils down to the claim that since the possibility of inventing an idea has always existed, then the idea has always existed. That is, if inventing a thing is possible then that thing is (and has always been) actual. That's your absurd assumption.

Clavius' Law can only be applied if "the idea must have always existed" follows from "it is possible to invent an idea". It doesn't follow. You tried to smuggle it in via your "essential link" between the possible and actual existence of an idea, on the basis that they both relate to the same idea.