Actual Infinities

[I_am_not_mafia]

Humans invented the symbols. They did not invent the correlation that exists between what those symbols represent - which are abstract objects - and the operations of nature.

Agreed. But the correlations and operations between what those symbols represent is not Maths. Maths and logic are languages used to represent those correlations. They are more suited to describe some applications than others.

That nature can be described as a mathematical structure may say just as much about the world and the nature of abstract entities as it does about our ability to engage it via mental processes.

If you think this then please explain specifically how this can be so.

The thing is that we could use a wholly different language to describe nature. And in fact we do. Natural language for example. When we discover something new about the world we then have to find the most efficient and effective way to describe it. The language does not come first. And sometimes we find that the language we do come up with does not scale or is limited in ways that we did not fully appreciate. For example, how the artificial intelligentsia tried to explain intelligence in terms of logic.

Stephen Wolfram came up with his own kind of Maths to describe emergent phenomena and complex processes for example. It is still not clear whether this is the most useful way to describe these Mathematical processes.

They can look very similar to what happens when biological structures grow (e.g. L-systems), but this is an entirely different phenomenon that has occurred for entirely different reasons. So a biologist may need to use a different language because Wolfram's abstractions leave out important details. In the same way I can provide three different rules for emulating flocking behaviour in birds but that does not mean to say that birds themselves use those very same rules or that a neuroscientist would find them useful.

Ultimately all these languages are useful because it often becomes too cumbersome to describe the constituent ingredients of the universe in terms of energy flows, thermodynamic gradients and entropy. We choose the most appropriate language to abstract the features that we are interested in at the time.