This is actually a trivial question and I'm just being mischievous.
It turns on the shades of meaning of both "idea" and "exist."
Mathematically, a concept exists whether anyone has happened upon it or not. (A meaningless attempt at a concept is not a concept).
When first thought about by an actual brain of any kind, a concept acquires its first glimmer of existence as in the real world.
I will attempt to provide an answer by recalling a fascinating lecture given by Professor Enrico Bellone. In a letter dated May 7th, 1952, addressed to his friend Maurice Solovine, Einstein shared a drawing that summarized his ideas on the subject. The drawing features a horizontal line labeled E, which represents immediate experiences or the empirical basis, and a vertical line labeled A, which represents the axioms underlying theories. Einstein argued that there is no logical process that allows us to derive axioms from experiences; instead, it requires an intuitive, extralogical, and psychological leap. Once we have intuited the axioms, we can deduce special statements S1, S2... by assuming their truthfulness and then comparing them with experience. According to Einstein, the crucial level lies in the axioms, and therefore there is no distinction between science and philosophy, but rather a single set of concepts. He also maintained that the theoretical principles of scientific theories are fictional, and any attempt to deduce ideas and laws from elementary experiences is doomed to fail. So, what is science according to Albert Einstein? Einstein believed that all the games are played at the top of the drawing, where we jump from one idea to another, from one theory to another, and where we model nature because we have categories of ideas that are fairly standard. In this context, Einstein praised the great philosophers he admired.
Alessandro Rizzo
You managed to post an interesting response to this, kudos!
I'm aware of Einstein's general approach and I think some scientists are missing his advice on the hard topics of today like consciousness.
Thanks again,
KS
Dear Karl Sipfle
The best questions that man can ask are the simplest and most profound ones, like in this case, that implicitly carry an answer. My compliments to you. As Einstein argued, ideas are often intuitive and not derivable from elementary experiences, and therefore it might be more fruitful to focus on intuition and understanding rather than searching for an exact answer to this question.
Regards,
Alessandro
The autonomous existence of ideas is a rather old story and Plato already placed them in the hyperuranium in his work Phaedrus in 370 BC.
I think that asking this question again today makes sense above all by placing it in the semantic sphere, as you rightly say, therefore first questioning the meaning we want to attribute to the words "idea", "concept" and "exist". Having agreed on their meaning, I think it is easy to answer the question.
Mathematically speaking, whether an 'idea' exists before it can be 'had', relates to the question of whether mathematical concepts exist a priori, leaving them to be 'discovered', or whether the mind must piece them together, leaving them to be 'invented'.
For those interested in the distinction 'invention' and 'discovery' in this context, Jacques Hadamard has published interesting views to this matter in his booklet "The Psychology of Invention in the Mathematical Field" (1954).
Thanks Karl Sipfle for this non-trivial question.
Hi Pieter van de Griend
But there is a case of "proving [or knowing] that a solution exists," without knowing the solution. There, it has not been pieced together.
Similarly, "does the set of all primes exist?" The answer is "Yes." Mathematical existence requires only consistency with the system.
Even one of many specific solutions exist, even if never discovered. What does not exist is knowledge of it.
Further, a given solution thought to exist does not if it is untrue, even before being proven so. That proof also already exists.
I think you would point out that some concepts are what we might call dreamed up to taste, such as a new object type defined as that for which every instance exhibits some arbitrary list of properties. That would be a construction of a (capricious) mind.
All good?
K
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