#### Ostronomos

##### Well-Known Member

I find it interesting where people will draw the line between discovered math and invented math. For you, it is calculus. For @sayak83 it seems to be partial differential equations (which are used extensively in quantum mechanics).

I see both as extensions of language that we use to model things we are interested in. But I have very serious doubts about the 'existence' of these systems outside of our minds.

I thought this would be an opportune time to point out that your serious doubts are due to the false belief in materialism. The fact that you are reading these words is proof that language is an object of a very different kind to matter. Welcome to the matrix, Neo. If we open our hearts and minds beyond the world of space and time then we may begin to see what is possible.

Fascinating.For example, you mention the natural numbers as 'God given' (following Kronecker). But take a look at Graham's number: Graham's number - Wikipedia

If we suppose that the observable universe is one trillionth of the 'real universe' and that ours in only one of 10^10^10^10 possible universes (far more than string theory postulates), and if we imagine each of these universes lasting 100 trillion years, and if we count the number of Plank units (plank volume times Plank time) for each of these universe, then the number of possible rearrangements of all of these Plank units throughout all of the possible universes is far, far, far smaller than Graham's number.

Our mind IS reality in mental form. You are creating a false dichotomy between mind and reality. I and a few other cosmologist have pointed this out numerous times.Given that, in what possible sense does Graham's number 'actually exist'?

As far as I can see, it *only* exists in our minds as a construct in a formal system. anything outside of that is excluded by its size.

*Mind = Reality = Language.*Once understood, this is strikingly obvious to even a casual observer.

This argument is flawed for a number of reasons because even the imaginary numbers existMy conclusion is that even the natural numbers cannot ALL exist. Only a very small part of that collection can 'really exist'.

*as a mathematical language in the mind.*

For those of you who may not have made the connection;

**existence can be placed on paper as language.**

Even here you are hinting at a mathematical reality, yet fail to see the obvious.The same can be said for the real numbers, differential equations, etc.

So, in answer to @vulcanlogician and @sayak83, I think we *invent* formal systems to mimic what we see. We are then amazed that those formal systems continue to mimic what we see. But those actual formal systems go far, far beyond what is testable. They have 'objects' that are simply too large to actually exist in any conception of a multiverse. But these systems are extensions of our ability to have language. We *invent* the ways to describe things. We choose systems that are flexible in their ability to describe. And that vast, vast majority of what those formal systems have has *nothing* to do with anything physical even in the remotest extension we can imagine.

So, no, I am not surprised that occasionally our patterns of thought show up in how we look at the universe around us.