Could the same be said about just about everything?
Like Music. Is a Song just a combination of notes, beats, intervals, voice etc. waiting to be discovered? Or is it something that a musician invents in her brain through talent, experience, practice and trail and error.
Or for that matter, a startup idea? A product/service that would bring immense value to its consumers, but it is not there yet, waiting to be discovered.
I guess philosophers must have dwelled on such questions before.
I think I get your point and I‘m open to ideas which drive home your point in a more precise way. However, the main difference between concerning ourselves with whether or not mathematical objects exists vs music or start-up ideas is their place in building a foundation for understanding reality. Science has been a productive program for understanding reality. It happens to be underpinned by math. And as a result, we have encountered some pretty interesting relationships between what the math tells us and what we observe. For instance, neutrinos and black holes were known to exist mathematically before they were ever observed and measured “in reality”. It’s not clear to me that music and start-up ideas hold up to math when it comes to being a tool for understanding or describing our reality, or perception the rig. Math is somehow fundamental to many successful enterprises which seek to describe and explain reality. Therefore, it becomes the point of focus of much philosophical inquiry when seeking to understand reality. Hence the foundational question, do mathematical objects exist? And not, does music or blockchain kittens exist?
Yes, they do, in an abstract sense. Existence in math means a very different thing from existence in physics. There are mathematical objects that exist, and those that cannot and do not exist. Someone posted a SEP entry earlier, which is a good start on this topic.
>the main difference between concerning ourselves with whether or not mathematical objects exists vs music
There is no 'vs', because there is no difference. Music is math, any song or sound is a mathematical object. A physical waveform that you hear can be encoded digitally in numbers: ones and zeros. So any given wav/flac file is just a bunch of numbers that give rise to the qualitative experience of sound, when interpreted in a certain way.
For example, a digital waveform consists of samples, each sample takes 16 bits to encode. Sampling rate of 44.1kHz is 44,100 samples per second. So you have 16 bits per sample x 44100 samples per second per channel x 2 channels x 300 seconds = 2^423,360,000 possible permutations of a 5-minute audio file without compression, which is a number with over 127 million digits. A little percentage of these permutations would count as music (even if your tastes are really diversified), most of it would just be noise. But all these possible 5-minute audio files include not only every song and every performance that existed or will exist. They also include every possible sound recording: songs that will not be written, Paul Graham saying that he hates HN, Paul Graham saying that he loves me and the rest of the file is silence, you and me discussing this topic with Plato for 5 minutes, etc, etc. The data exists and can be discovered and listened to, even though some of these examples are obviously not physically possible (i.e. Plato is dead).
So all music already exists mathematically, and it can be a useful mindset that your job is to discover it. A lot of musicians see it that way, Tessa Violet, for example:
https://youtu.be/QzBoGVToWEo?t=342
You can try to answer a simpler question: does the number 3 exist? If you define 3 as "the obvious common feature shared by three cows, three pencils, and three stars in the sky," then the question becomes "does this common feature exist?" and the answer, then, is, well, of course, yes, it does - because it's obviously there!
Think of it this way: Anyone can invent a new song, and no matter how derivative or lacking in artistic merit, they can still claim to have composed a new piece of music.(La-la-la-laaa. There, I just did it! Short but sweet.)
But you cannot just "invent" a new proof to the Pythagorean theorem. Any proof that a^2 + b^2 = c^2 will have to clear the hurdle of being demonstrably "true."
Like Music. Is a Song just a combination of notes, beats, intervals, voice etc. waiting to be discovered? Or is it something that a musician invents in her brain through talent, experience, practice and trail and error.
Or for that matter, a startup idea? A product/service that would bring immense value to its consumers, but it is not there yet, waiting to be discovered.
I guess philosophers must have dwelled on such questions before.