...I have to jump in here, I just gotta.
> (1) No. Perfect circles (where each point is equidistant from a
> centre) cannot exist in this universe
...'course they can. Imagined objects have just as much claim to existence in the universe as objects we can interact with directly, no more, no less.
becuase this universe is
> *quantum*, not continuous.
...no, no, no, no, no. Tempting (very tempting) but no. The universe
qua universe is continuous. We FIND quanta because our construct is a
model. It's a very good model, it includes a great deal, but it is
still a model. Information gets left out, the more complex the
construct at any given level, the more information is left out in
...we cut away with occams razor and label the components. We're a sophisticated species and we've found ways to sharpen our blade so the pieces keep getting smaller, and smaller, and smaller - but they exist because we've been cutting, not because they're components.
The perfect circle is thus "Platonic",
> becuase real instances of it are but pale, imperfect shadows of the
> defined term "circle".
...throwing the baby out with the bathwater. Plato thought that ONLY the ideal existed and everything else was an imitation of it, making everything but conception, illusion. And while I think everything is illusion [real illusion, but illusion nonetheless] what you've done here is rejected a class of things [ideals] from a system of organization because that class of things was placed in a different category in another set of classification entirely.
> (2) The idea of circles exists via it's representations in
> matter/energy. These representations can only be understood by a
> being with the proper frame of reference.
...the statements can be meaningfully communicated between any beings using an agreed upon symbol set. That's why mathematics can claim to be a potential universal language - it divides the universe in mutually comprehensible, defined, well-ordered ways. ...whether or not the statements, once understood, have MEANING is another question entirely.
Thus, the "statement of
> truth" that is
> "A circle is a set of points equidistant from a common centre point"
> is embedded in a frame of reference -- as would be any other
> statement of truth about circles.
...yup. I think Hermits point is that the frame of reference is which that statement is embedded is communicable [through the vehicle of mathematics] to any conscious being. He thinks that makes is a true statement. [I think he's wrong]
...okay, I'm gonna stop there. Mostly I wanted to address that whole "universe as quantum" thing. Our construct is quantum, the manifold is continuous. Placing limits on the "universe" is always an error. [ :) ]