Your argument is similar in spirit to the claim that all, even infinite sets can have single element selected from to form a new set (so called "axiom of choice"). I.e. you equate the mere possibility of existence with a proof of existence (it's not a slur, there are a lot of mathematicians who do just that).
I don't see the reason to think that coincidentally arrived at ideas mean that ideas are discovered. We use the same framework, with the same rules. It's not unlikely that we'll create same ideas, because we use all the same rules, but the framework is so vast... it has so many rule combinations it's mind-boggling how would you think all ideas already exist in this framework.
More practically, we call an action a "discovery" when we (unbeknownst to us) faced the consequences of the phenomenon being discovered, but didn't know why we were facing them. An astronomer who finds a "new" star was ever so slightly influenced by that star's light, gravity etc. A marine biologist who discovers a new deep-water fish was ever so slightly affected by that fish through a complicated chain linking many different species through biosphere.
An artist drawing a new painting isn't discovering it in the same sense. She isn't interested in how an existing painting was connected to the consequences of her life or the lives of the whole human species. By selecting of all possible ways the paint can be laid down on canvas her particular way of doing that she creates something genuinely new, or as new as it can possibly be. It's counterproductive to label this activity "discovery" because then we lose an important distinction between the nature of the work of an astronomer and that of a painter (or a mathematician).
There are sculptors who'd jokingly say that they "discover" the statue in a stone slab. But they do so in a sarcastic kind of way, really (well, artists are weird and will make a lot of nonsense claims just to trigger non-artistic audience). But, deep down, nobody believes that they are searching and finding good images, melodies or novels. I cannot really imagine a mechanism through which I'd discover the answer writing to you. It's a lot easier to explain what i wrote by saying that I meant to write it.
I don't see the reason to think that coincidentally arrived at ideas mean that ideas are discovered. We use the same framework, with the same rules. It's not unlikely that we'll create same ideas, because we use all the same rules, but the framework is so vast... it has so many rule combinations it's mind-boggling how would you think all ideas already exist in this framework.
More practically, we call an action a "discovery" when we (unbeknownst to us) faced the consequences of the phenomenon being discovered, but didn't know why we were facing them. An astronomer who finds a "new" star was ever so slightly influenced by that star's light, gravity etc. A marine biologist who discovers a new deep-water fish was ever so slightly affected by that fish through a complicated chain linking many different species through biosphere.
An artist drawing a new painting isn't discovering it in the same sense. She isn't interested in how an existing painting was connected to the consequences of her life or the lives of the whole human species. By selecting of all possible ways the paint can be laid down on canvas her particular way of doing that she creates something genuinely new, or as new as it can possibly be. It's counterproductive to label this activity "discovery" because then we lose an important distinction between the nature of the work of an astronomer and that of a painter (or a mathematician).
There are sculptors who'd jokingly say that they "discover" the statue in a stone slab. But they do so in a sarcastic kind of way, really (well, artists are weird and will make a lot of nonsense claims just to trigger non-artistic audience). But, deep down, nobody believes that they are searching and finding good images, melodies or novels. I cannot really imagine a mechanism through which I'd discover the answer writing to you. It's a lot easier to explain what i wrote by saying that I meant to write it.