Can we imagine a perfect circle?

Question

Applied mathematicians often work with circles, but I'm guessing it's an abstraction that cannot save all the empirical data. Can we conceive of a perfect circle in our visual field -- as apparently they do not exist in nature?

Zombies in philosophy are imaginary creatures... Can we really imagine zombies? Daniel Dennett thinks those who accept the conceivability of zombies have failed to imagine them thoroughly enough

And Chalmers p153 says

it is arguable that one can modally imagine S when S involves an a priori contradiction. An example may be a case in which one imagines a geometric object with contradictory properties. In cases like this, one imagines a situation in something less than full detail... S is positively conceivable when it is coherently modally imaginable

So it seems being imaginary is usually a weaker state than being conceivable: we can imagine incoherent things perhaps like zombies, just not fully.

But with visible things appearing to us, that may not be the case. Because it also seems that we can conceive of perfect circles, but not imagine them -- not conceive of what it would be like to see a perfect circle.

If so, is that what makes a "circle" a phenomenological "essence" in Husserl's sense? i.e. is anything we can conceive of but not conceive of appearing to us an "essence"?

Answer 1

Chalmers does not mean ordinary visual imagination (our faculty to create representations which faintly resemble real visual sense impressions). Instead he means something like forming a concept, though only incompletely. I. e. not grasping all details, all internal relations of a concept – of which some may turn out to be incoherent.

Descartes famously gave the example of a chiliagon, a regular polygon with 1,000 sides. If we try to visually imagine a chiliagon the result, an imperfect round something, is indistinguishable from our attempts to visually imagine a circle.

So yes, we cannot create a perfect circle in our visual imagination.

But we can form the concept of a circle and the concept of a chiliagon. Those are surely distinct.

An example of an imagined incoherent concept, in Chalmers sense, would be a chiliagon with interior angles of 179°. This concept might feel reasonable for someone without geometric knowledge, and can be imagined, but is in reality self-contradicory. It cannot be conceived in all conceptual details, because then the internal relations would have to be correctly rationally grasped. Visual imagination is irrelevant – as we’ve seen there is not even a difference between our visual imagination of a chiliagon and a circle.

PS: You also ignore that Chalmers speaks of “modally imaginable”. This “modally” complicates everything and it would take more space to fully explain it. But that’s not necessary to point out your main misunderstanding.

Answer 2

A perfect circle can be imagined and visualized by a mathematician who is a geometer, and its definition can be precisely expressed by him or her mathematically.

That mathematical expression can be readily presented graphically as part of the definition and accepted as valid by other mathematicians, even though the graphic representation of it is imperfectly rendered.

A perfect circle cannot be realized in the world we inhabit because there is no infinitely precise manufacturing method which can produce one.