[techno_modus]

> David Hilbert famously argued that infinity cannot exist in physical reality.

This statement reduces the problem to the definitions of "existence" and "physical reality" which of course may have quite different interpretations. For example, the existence of particles (with finite mass and finite coordinates which can be "touched") and the existence of waves are rather different notions.

[jamesrcole]

It seems to me that something can only have existence for us if it can have a transitive causal influence upon us, and surely both particles and waves exist in that same sense.

[whatshisface]

If by existence you also mean, "something that continues to exist upon closer inspection," then neither particles nor waves exist, you can always design an experiment to refract something around a corner and meausre individual quanta of it when it gets to the detector.

[simonh]

The comment gave a meaning of existence: "...if it can have a transitive causal influence upon us", so there is no need to imagine up straw ones.

[gowld]

The comment defined existence, but didn't define it. The followup commenter was clarifying that proving the is something that exists isn't a proof that a particular claimed thing exists.

[jamesrcole]

"it" is something being referenced - some details in the territory being marked out by the map. The map, and this act, provide no evidence that something exists. The only real basis is if you have evidence there's some details, of the nature claimed by your map, that can have some sort of transitive causal influence upon us.

[whatshisface]

Zeus and Sherlock Holmes could both be argued to have had transitive causal influences upon us - so in order to make that statement make sense there must be some other implied constraints on what is considered to "exist."

[simonh]

The fictional character Sherlock Holmes certainly exists.

[jamesrcole]

It all depends on what you mean when you say "The fictional character Sherlock Holmes". I believe that thoughts, memories and knowledge "about Sherlock Holmes" exist and are physical details, as are Sherlock Holmes books, etc. And that there's no other reality to "Sherlock Holmes", above and beyond these things.

But really, this discussion is too large to satisfactorily deal with here.

[jamesrcole]

> Zeus and Sherlock Holmes could both be argued to have had transitive causal influences upon us

There's some philosophers who'd argue that, but I think the arguments are pretty weak.

[openfuture]

Then this is easy, we are discussing the concept infinity, hence it is having a causal influence on our actions and so by your definition it exists.

[jamesrcole]

It's not that easy. It comes down to what "the concept of infinity" means. Does Santa Claus exist because the concept of Santa Claus exists? (See my other comments in this subthread for my view of this.)

[openfuture]

I would say he does. Santa Clause has a causal influence on the world. The image that we ascribe to 'him' (the concept) is different from the reality of it's influence but that is true for most things..

We characterize all sorts of things in all sorts of ways, trying to model the reality we perceive, but actually those models are also reality and they are not the same as the thing being modelled.

From this standpoint everything fictional exists but whether there is an 'infinite' amount of it is a super annoying question that just keeps going in circles so I don't really care so much what the answer is.

But if it's infinite then there is a god, right? :^)

[jamesrcole]

> From this standpoint everything fictional exists

No they don't. The mental representations exist, the thought processes exist. That doesn't mean the fictional entities exist above and beyond those.

[subroutine]

What aspect of waves as they exist in our universe is infinite?

[whatshisface]

If waves are continuous then they are over the real numbers, and there are an infinite number of reals between any two points.

[subroutine]

This is specifically addressed in the article - this is a function how our maths represent phenomena:

"Physicists have found it convenient to use the concept as a mathematical idealization where infinity occurs as a limit of large numbers, even though in physical reality there is no infinity of anything. An example is the Fourier series: while mathematically an infinite number of terms are needed to give an exact representation of the function representing an arbitrary waveform, this does not in fact mean that there are infinite physical frequencies occurring in the real physical system."