The paradox exists because of our choice of models, and would not exist in other models if different choices had been made.

In other words, as michaelfeathers said, "the map is not the territory."

Technically, then, there are no fields either - claiming that fields are real because the field model matches experiments better, commits the same mistake of taking the map as real, as when we said that particles are really there. As in Kantian noumena, we can't know the territory, we can just build more useful models.

Exactly. Thinking about it more. Imagine we came at it from the other direction. All we know are quantum phenomena and then we encounter this human-scale world. We would be amazed and stunned by things like billiard balls that behave only half like quanta.

I'm surprised this way of seeing the world isn't more wide spread. My opinion is that it should be among people who have a deep interest in science.

http://inwhy.net/quantum.jpg <- THEY EXISTS!

Yeah, I'm not sure why you got down-voted. In the 1890s people that everything was a wave but then phenomena like wave function collapse and the quantum Zeno paradox were hypothesized and observed. To combat this you can introduce mathematical tricks like delta functions but this more of a hack.

Perhaps, the biggest philosophical problem with waves are their integration requirements and the potential for such iterations to exceed cosmic speed limits. When the function is continuous a perturbation at one end must effect the other end.

He's downvoted because he doesn't seem to get what the entire discussion is about, which is on a higher level. Instead he is caught down in the "lesser models". Whenever you have a paradox, like wave-particle duality - but also the "French paradox" in nutrition, it's not because there really is a "paradox" in the universe, it's because the way you look at it is too limited, and if you find a better view you will see there is no paradox. That doesn't make the paradox-creating models untrue - in their context, but we have gone beyond them. That's the subject of the submitted link!

I think the down-vote happens, because he's argumenting too concrete for the question.

I don't know much about physics, but my take on this is:

First you model reality with waves and particles, then you see that particles can behave like waves and vice versa. The next step is to model reality with something different that can behave like a wave AND a particle and suddendly there is no paradoxon anymore.