Applicability of Maths to the Universe

[Belacqua]

That said, let me share with you how I intuit numbers like 2. Based on how I currently see things, there is no number 2 floating out there in the Platonic sense and serving as some form of cause for the concept of 2 in our minds. For me, number 2 strictly exists in our minds, as a way to "visualize" a certain quantity of identical things. The quantity is out there in a "vague" sense, but it is not decipherable as "2" without a mind to see separateness and "identicalness" of the objects of interest. What would be the biggest challenge to this view?

This is all very difficult for me. As so often on this forum, I find myself in the role not of advocating a position but of wanting others to hold back from a position about which they may have too much confidence. I can't say any more than Popper, and his ideas have been worked out in far more detail than I'm aware of, I'm sure. 

One thing to ponder: numbers which no human has ever thought of yet. Imagine, for example, a very large prime number which no one has discovered. It has never appeared in the mind of any person. If numbers depend for their existence on appearing in minds, then this number doesn't exist. But even so, it may be more proper to say that it does exist, but hasn't been discovered yet. If it does exist, but has never been thought, then "where" is it?

But I put the "where" in scare quotes because of our bad habit of thinking of existence in spatial terms. It is begging the question if we say that anything which exists must exist in a location, with extension. This is our habit, especially in modern times, but I'm not sure it's always true. It would probably be better to ask HOW it exists, if it does so without location or extension. 

It may be that while numbers are the inventions of people, they exist not only as their appearance in individual minds. They are somehow commonly held, and exist even if no one is currently thinking them. 

The example Popper uses is about symphonies, which are also World Three objects in his system, like numbers. Imagine Beethoven's 5th symphony. The symphony itself is not identical with its score or its CD. Those are recordings made of it, but are not the symphony itself. It somehow continues to exist whether anyone is hearing it or not. 

I have used the example of Sherlock Holmes, a character everyone knows. Holmes was made up by a person's mind, but is no longer dependent on any individual mind. It may well be that at any given moment, no one in the world is imagining him. Yet he still somehow exists. And though he doesn't exist materially, and can't be the object of scientific studies, it is still possible to make statements about him which are correct or incorrect. And it is possible to distinguish between the "real" Sherlock Holmes ("real" in what way?) and a parody or "re-boot." 

And god knows that no one here wants to talk about theology, but all of this has been discussed for millennia. It is only recent and naive people who assume that the Christian God has a location, physical extension, material existence, etc. As a non-material thingy, it is not the subject of science, but is still said to exist in a way that material things do not.