I hold that there really isn't a clear distinction between invention and discovery of ideas... — Pfhorrest

That this language of "discovery" doesn't make a lot of sense (where were they sitting, waiting to be discovered?) goes to my point that in the context of abstract ideas there isn't any difference between "invention" and "discovery". I am not saying that there is no invention, only discovery. I'm saying that neither of those, in senses distinguishable from each other, really works as applied to abstract ideas. In that context, they are the same thing, indistinguishable; we equally make and find ideas, kinda both, kinda neither. — Pfhorrest

No, I’m saying that in the case of abstract objects like ideas, it makes no sense to differentiate invention from discovery. — Pfhorrest

Your talk about planets and gold is missing the point: there is a difference there, in concrete cases. But not in abstract ones. — Pfhorrest

What similar algorithm exists in order for us to "discover" the supposedly pre-existing ideas of the Mona Lisa or the toaster?
— Luke

Trivially, one could mechanically iterate through every possible series of brush strokes on the canvas (more clearly illustrated if we think of a digital image and iterate through every possible series of pixels) and eventually get the Mona Lisa. Likewise one could iterate through every possible arrangement of atoms and eventually get a toaster. Or instead one could randomly throw together brush strokes or atoms until eventually one got the thing in question — like the infinite monkeys with typewriters producing the complete works of Shakespeare. — Pfhorrest

I hold that there really isn't a clear distinction between invention and discovery of ideas: there is a figurative space of all possible ideas, what in mathematics is called a configuration space or phase space, and any idea that anyone might "invent", any act of abstract "creation" (prior to the act of realizing the idea in some concrete medium), is really just the identification of some idea in that space of possibilities. — Pfhorrest

In relating already known ideas to each other across a space of previously unexplored ideas, new works can give further context and significance to existing ones and draw context and significance from them, and it is that process of connection and contextualization, not mere nondeterministic randomness, that constitutes creativity. — Pfhorrest

Perhaps the difference between "discovery" and "invention" in these terms could be viewed as whether the space of possibilities exists completely - awaiting to be discovered - or whether the invention of new ideas help to create and open up new spaces of possibilities. — Luke

Was the steam engine invented or discovered? Or penicillin? — Janus

When I write a poem, am I inventing or discovering it? I would say inventing because that is different than, say, calling to mind a poem I have previously memorized, which would be an act of discovery of or finding something already there, however complete or incomplete it might be. — Janus

Of course I am not suggesting that invention is an act of creation ex nihilo, but it is, I would say in any context, the bringing of some novel form and content into the world, something that had not previously existed. Since discovery is not bringing anything new into the world, either in the physical world or the world of ideas, but rather of revealing something pre-existent, I continue to think the distinction between discovery and invention is a valid and useful one. — Janus

What about fictional concepts/characters? Surely they are invented and not discovered? — Luke

find it odd to speak of the "invention" or "discovery" of abstract ideas (only). I had assumed - with respect to creativity - that you weren't just talking about the ideas, but also the realisation of those ideas. — Luke

This sounds more concrete than abstract. — Luke

Perhaps the difference between "discovery" and "invention" in these terms could be viewed as whether the space of possibilities exists completely - awaiting to be discovered - or whether the invention of new ideas help to create and open up new spaces of possibilities. — Luke

I'm unfamiliar with the explicit idea that creativity is a result of "nondeterministic randomness". Perhaps creativity could be viewed in contrast to following the same deterministic pattern that went before. — Luke

Anyway, I broadly agree that creativity is a "process of connection and contextualization". — Luke

I'm not seeing how creating anything new could add to or, the obverse possibility, subtract from, either of these "spaces of possibility". I would rather say these spaces of possibility subsist than "exist"; they are not actual, but "sleep" inherently, in logic and physicality respectively. — Janus

OK, so the valid distinction then seems to be that possibilities are discovered and (novel) actualities are invented. I — Janus

Eh, except the ephemeral "existence" of possibilities makes calling it "discovery" about them kinda wonky too. That's why I think "invention" and "discovery" merge in that regime, and it's not clearly one nor the other but in some ways both or neither. — Pfhorrest

It would be possible in principle to set out on a deterministic process of mechanically identifying every possible idea — Pfhorrest

I don't accept that; someone needs to come up with those ideas. — Luke

What similar algorithm exists in order for us to "discover" the supposedly pre-existing ideas of the Mona Lisa or the toaster? — Luke

Computers can do pattern recognition. They can even (mostly) do bad pattern recognition: I asked Google Lens to identify a bush the other day and it told me it was a "plantation", then I asked it to identify a flower and it told me it was "marine life". — Pfhorrest

I don't accept that; someone needs to come up with those ideas.
— Luke

We have already shown at length that this claim is indeed false. — Tristan L

I must have missed it. — Luke

Can you quote where this was "shown at length"? — Luke

It would be possible in principle to set out on a deterministic process of mechanically identifying every possible idea — Pfhorrest

Surely every possibility is already possible, right? There is some (infinite) set of things that are possible, and by discovering that something is possible, we don't thereby become the cause of its possibility; it was already a possibility, we just found it among that infinite set of possibilities. — Pfhorrest

What similar algorithm exists in order for us to "discover" the supposedly pre-existing ideas of the Mona Lisa or the toaster? — Luke

Trivially, one could mechanically iterate through every possible series of brush strokes on the canvas (more clearly illustrated if we think of a digital image and iterate through every possible series of pixels) and eventually get the Mona Lisa. Likewise one could iterate through every possible arrangement of atoms and eventually get a toaster. Or instead one could randomly throw together brush strokes or atoms until eventually one got the thing in question — like the infinite monkeys with typewriters producing the complete works of Shakespeare. — Pfhorrest

Indeed, all ideas already exist, only waiting for minds to discover them. Here’s a proof: It’s certainly possible for two individuals, say, Alice and Bob, to come up with the same idea EID independently of each other (this happened e.g. with Newton and Leibniz independently discovering calculus). But what gives us the right to say that they have both come up with the same idea? Well, if Alice and Bob had independently invented EID, then Alice’s EID would be different from Bob’s EID, and there would be no basis whatsoever on which we could rightly say that Alice and Bob came up with the same idea EID. Therefore, Alice and Bob must have independently discovered one and the same idea EID, which is an abstract entity which always was and always will be and whose existence is independent of Alice and Bob.

It is only on ground of both Pfhorrest and I having independently discovered the idea that ideas are abstract and cannot be made and how to show this, that it is meaningful and true that we both came up with the same idea. Like that, we can use the theory that ideas are eternal and uncreated to prove that very same theory :wink:. — Tristan L

Another proof uses possibilities, which Pfhorrest already mentioned. It runs thus: For every idea EID that anyone can come up with, the possibility that someone can come up with EID must have always existed. But since this possibility is essentially tied to EID itseld, EID must also always have existed. I used a very similar argument with the same idea some years ago on another forum to show that coming into existence and going out of existence are illusions. — Tristan L

It would be possible in principle to set out on a deterministic process of mechanically identifying every possible idea — Pfhorrest

For example like this: Write a program that systematically outputs all possible finite-length strings of letters: a, b, c, ..., z, aa, ab, ..., az, ba, bb, bc, ..., bz, ..., ..., aaa, aab, aac, ... . For every idea EID expressible in finitely many symbols (including relativity theory, quantum mechanics, Plato’s Theory of Shapes, his unwritten Theory of Principles, the plot, theme and ideas of Hamlet, to name just a few), this program will output a description of EID after a finite amount of time. Does that mean that the mind is unneeded for finding new ideas? Certainly not, for the program doesn’t understand the meaning of the symbol-strings which it outputs. What you still need is a person (or group of people) who reads every string output by the program. The system made up of program and person (or group of people) will find every finitely describable idea after a finite time in a fully deterministic, uncreative way, independently of all other folks who might come up with the same ideas in the more traditional (and efficient) way. This shows that all the ideas must be abstract and uncreated, and it is the nail in the coffin of any claim that ideas are invented rather than discovered. It also shows that while the mind is totally needed and indispensible when finding new ideas, its creative faculty is not needed in the least; rather, what is needed is the mind’s ability to understand, to “see” ideas, and to map symbol-strings to ideas. — Tristan L

We have already given concrete examples of such algorithms. The Mona Lisa is made up of finitely many atoms; hence, my algorithm will spit out a complete description of the Mona Lisa after a finite time. The same goes for the toaster – the algorithm will spit out a complete and accurate description of the toaster after a finite time. This description is then read by the reading person in a finite time, whose mind is thus directed to “look at” the abstract idea of the toaster. No invention needed whatsoever. — Tristan L

This presupposes that all ideas already exist in their entirety prior to being discovered. — creativesoul

Another proof uses possibilities, which Pfhorrest already mentioned. It runs thus: For every idea EID that anyone can come up with, the possibility that someone can come up with EID must have always existed. But since this possibility is essentially tied to EID itseld, EID must also always have existed. — Tristan L

When I write a poem, am I inventing or discovering it? I would say inventing because that is different than, say, calling to mind a poem I have previously memorized, which would be an act of discovery of or finding something already there, however complete or incomplete it might be. — Janus

Would you please actually read what Pfhorrest and I have written and then reply to each point? — Tristan L

• On what ground can we say that Alice and Bob have independently come up with the same idea?
  
• How can ideas be created when my algorithm deterministically spits them out?
  
• You seemed to imply that one could not algorithmically find the Mona Lisa or the toaster as one can find natural numbers, but Pfhorrest and I have shown you otherwise. What do you say to that?

On what ground can we say that Alice and Bob have independently come up with the same idea? — Tristan L

How can ideas be created when my algorithm deterministically spits them out?
You seemed to imply that one could not algorithmically find the Mona Lisa or the toaster as one can find natural numbers, but Pfhorrest and I have shown you otherwise. What do you say to that? — Tristan L

They each came up with the same idea independently. Isn’t that what you’ve told us? What other ground do you need? — Luke

They each came up with the same idea independently. Isn’t that what you’ve told us? What other ground do you need? — Luke

I asked what algorithm exists. Such an algorithm does not exist. — Luke

{
* Copyright (c) 2020 Tristan L. All rights reserved.
* }

program AllEndlyStrings (input, output);

  const
  FIRSTASCII = 32;
  LASTASCII = 126;

  type
  tRefChainlink = ^tChainlink;
  tChainlink = record
                 c : integer;
                 next : tRefChainlink
               end;
  
  var
  charstr : tRefChainlink;
  HowManyTextsNext : longint;
  z : tRefChainlink;
  seekfurther : boolean;
  textnumber : int64;
  
  procedure writecharstr ( incharstr : tRefChainlink );
  
    var
    t : tRefChainlink;
    seekfurther : boolean;
  
  begin
    t := incharstr^.next;
    while t <> nil do
    begin
      write ( chr(t^.c) );
      t := t^.next
    end
  end;

begin
  writeln ( 'Copyright (c) 2020 Tristan L. All rights reserved.' );
  writeln();
  new ( charstr );
  charstr^.c := -1;
  charstr^.next := nil;
  HowManyTextsNext := 1;
  textnumber := 0;
  while 0 = 0 do
  begin
    while HowManyTextsNext > 0 do
    begin
      HowManyTextsNext := HowManyTextsNext - 1;
      z := charstr;
      if z^.next = nil then
        seekfurther := false
      else
        if z^.next^.c < LASTASCII then
          seekfurther := false
        else
          seekfurther := true;
      while seekfurther do
      begin
        z^.next^.c := FIRSTASCII;
        z := z^.next;
	    if z^.next = nil then
          seekfurther := false
        else
          if z^.next^.c < LASTASCII then
            seekfurther := false
          else
            seekfurther := true
	  end;
	  if z^.next <> nil then
	    z^.next^.c := z^.next^.c + 1
	  else
	  begin
	    new ( z^.next );
	    z^.next^.c := FIRSTASCII;
	    z^.next^.next := nil
	  end;
	  writeln ( 'Please read and understand the following text #', textnumber, ' if it is meaningful:' );
      writecharstr ( charstr );
      writeln();
      writeln();
      textnumber := textnumber + 1
    end;
    write ( 'How many texts do you want to read next?' );
    readln ( HowManyTextsNext );
    writeln();
  end
 end. { AllEndlyStrings }

What about fictional concepts/characters? Surely they are invented and not discovered? — Luke

Separate concrete instances of ideas are not the same as each other, only the ideas themselves are the same. But it is only the instances that are clearly made or invented, not the ideas themselves. — Pfhorrest

Actually, that is not true, for such an algorithm does very much exist. Here is a working implementation in PASCAL which I have written: — Tristan L