[JohnStrangeII]

This is a rather interesting article. I'm a Platonist. From what we know today, real numbers cannot exist in a finite space, but they seem to exist mathematically. The same can be said about many other mathematical structures, including those that can only be characterized adequately (categorically) in higher-order logic.

It's also worth noting that physical and mathematical existence are based on completely different criteria. For non-constructionists mathematical objects exist once they are not demonstrably contradictory (although the absence of contradictions often cannot be proved in an absolute sense). In contrast to this, for physicists an object exists once it can be measured, where measurement is ultimately tied to sensual experience. There are also theoretical entities in physics that cannot be directly measured, but their existence is usually downplayed, they're not supposed to "really" exist but only as theory-dependent entities. In any case,the two "kinds of existence" are very different from each other.

[TheOtherHobbes]

The perception of numbers exists mathematically. Likewise for more abstract structures.

You cannot show me threeness. You can show three things and tell me to generalise, and if you keep generalising you'll end up with a consistent-ish framework of sorts for your observations that can be applied to certain other physical experiences.

But fundamentally this is an exploration of the consequences of psychological processes - like perceptual grouping, and inductive relationship inference - not observations of external phenomena.

It doesn't seem that way, but there is no external authority you can appeal to which will state definitively that when mathematicians all agree on something their experience of "true" is absolutely and objectively correct, and not a distorted and limited artefact of human cognition.

[JohnStrangeII]

This kind of sensualism was often defended in the debate, but it has problems, too. I think the history of mathematics makes the position implausible.

For a long time, up until recently, mathematics was way ahead of the applications of mathematics to physics. In Ancient Greece there was a general consensus that infinity and real numbers do not exist. But then some people found out that the side of a triangle must sometimes be a real number. However, you cannot ever measure SQRT(2) precisely. Whatever number you extract from the physical world is only a rough finite approximation. You need to represent the number in a different way and solve the problem algebraically. Many scientists in Ancient Greece rejected this idea vigorously. Still, real numbers are very useful for describing the physical world, so useful that we couldn't possibly do without them today.

Imaginary numbers are another example. They were ridiculed as abstract nonsense when they were described for the first time and widely conceived to have no physical reality or application at all. Despite all that, they play a vital role in modern physics.

There are many more examples like that. To cut a long story short, at least until recently mathematics was always ahead of physics (now they seem to go more in tandem). This fact makes the idea very implausible that mathematical structures are merely useful abstractions from the physical world we invented to describe it. It simply doesn't describe what happened in mathematics. And I find the idea that mathematicians just came up with arbitrary imaginations equally implausible.

> no external authority you can appeal to which will state definitively that when mathematicians all agree on something their experience of "true" is absolutely and objectively correct, and not a distorted and limited artefact of human cognition

That is true for everything, it's just a radical skeptic position. Nevertheless, mathematics has the highest standards of rigor for proofs among all disciplines.

[dfischer]

Quite an astute observation. I’ve been thinking about this quite heavily recently. It has odd occult references too in the sense of “nothing creates something.”

That which is measured, exists.

No measurement itself, as in of itself as a thing, is a thing that exists. You can measure 3cm but “3” and “cm” don’t exist. Virtual values assigned by consensus. All axioms are agreements. Truth or existence itself is convergent and resembles certainty only in the majority agreeing to it.

Imagination allows nothingness (imaginary things) to be measured.

Imagine any unit, give it a “rule” and now it can be measured!

Pretty interesting bridge between the “imaginary” and the “real.”

There’s so much nuance on what existence is, and isn’t, or even not is nor isn’t is depending on if you subscribe to classical logic based on what we currently describe as mostly Aristolian or if you use many-valued logics which are making a come back yet rooted in the Vedas...

I find this extremely profound and it’s one of my top focal areas of study right now.

It’s also related to my observation of disagreement, chaos, and behavior of the human animal. It seems the zeitgeist of the egregore lacks the ability to adjust perspective and see truth depending on the “rule/roles being played” (all disciplines are games/acting in a way).

Tons to unpack.