perfect circles (or triangles, etc.)

[Doge of Venice]

What is the significance of perfect circles not existing in nature? I am struggling to grasp concepts and universals in light of Lonergan's thought. Below is what's coming to mind as I work on this:

1. Plato imagines an actual world of forms--Aristotle/ St. Thomas/ Lonergan reject this.
2. Atheists say perfect circles only exist in the mind as concepts, and they charge God is a mere concept, too.
3. But a circle is a universally-acknowledged concept, so it is TRUE? does it speak to TRUTH? Since we identify God with the Truth, is it an instance of God and the intelligibility of His Creation?
4. Lonergan says the real is being, and being is what can be intelligently grasped and reasonably affirmed. Is a perfect circle real? Does it exist? Does reality consist of existents, or is that the significance of potentiality, formality, and actuality?
5. Lonergan says concepts are byproducts of knowledge, so knowledge of circles exists before we form the concept? We abstract this from the phantasm as in the Euclidean oversight of insight with the equilateral triangle and the two circles?
6. What of Aristotle's Ideas (of God)?
7. We can't actually imagine a circle because we can't imagine a line, correct? So first we know it, then we conceive it, but we can't imagine it?
8. An atheist tells me he wants "evidence" to affirm what is real. Does he think knowing consists in "taking a look?" When I tell him he knows circles without evidence, am I not showing that knowing is not "taking a look?" But he thinks conceptual knowledge is only real inside a human mind. Is he stuck on the "already out there now real" take on being?
9. Could we actually draw a circle in the sky, it's just that we don't have the instruments and our human eyes can't see it as perfect? By saying perfect circles don't exist in nature, are we just saying they don't occur accidentally, and that we can't create them as human beings?
10. In the field of structural engineering, the closer we get to true, geometric shape, the stronger a structure? We affirm the truth of the forms, then build as close to them as possible?

This is rambling, I know, and I think the answer may be short and cut through all my struggles. Perhaps the single question is: are perfect circles "real" since they can be intelligently grasped and rationally affirmed?

Thank you in advance.

[mounce.d]

Hi George, not sure I can help because those circles are crazy buggers!  You might notice how much you've addressed here just trying to answer what seems like a simple question.  One of my original ideas - `where are the straight lines in nature?'  We give semantic translation to math systems, and it's easy to show how rocks in a stream, or sheep in a field, are like numbers.  Let me know if you have any idea for where, in your typical low-tech environment, would man see examples of straight lines?  Rudy Rucker says they imply infinities, and that inspired me to ask the question once I had the answer.

Okay, enough for me.  When people start talking about circles, I like to use the Frasier circle illusion as an example of Lonergan's tripartite method.  That allows me to give my opinion that any reasonable description and explanation of reality always combines subject operations with object outcomes.  Or, on a lighter note, imagine one small circle inside another.  They are both composed of an infinited number of points, but isn't the bigger circle a bigger infinity?  Just thoughts, no help, sorry!

[Catherine B. King]

Hello George (and Doug):

I think most (or all) of us struggle(d) with your questions, which are the right ones to address--precisely because the eyes, so to speak, behind the answers we rest in profoundly affect every reflection we undertake, especially if our reflections have any direct philosophical meaning, as your questions do.  But It's no small thing to grasp; and from my experience, trying to understand these issues really "messes with your head" for a very long time before they can settle or, if they don't, I think we are not really authentic in our asking.

That being said, a circle (et al) is a circle because we have already understood something, and not merely looked at it or imagined it. Further, we have already understood something about what we see or imagine; so that when we look at a chalkboard, we are already resting in a bunch of understanding; but what we actually see is light on dark, marks on a board, etc. We bring our prior understanding to WHAT we see, and then can begin wondering and asking further questions for further understanding.

Further, when we "look inside" and "see" images of circles, we are "looking" or observing from some vantage point. That vantage point is not a part of the image, nor is it an "eye" or a "mind's eye," or if it is a mind's eye, we are speaking metaphorically. That "mind's eye" is in fact our intelligence on the move, or our questioning-to-insighting apparatus already in operation. The fact that you "automaticaly" recognize a circle when you see it only testifies to the fact that you have questioned that imperfect chalk/shape or image before, and now can bring up (resonate with) your prior understanding.

As an aside, our ability to bring up such meaning so quickly, and to supply imagery for it, is one of the reasons it's so easy to come to the (wrong) philosophical conclusion that seeing equates to understanding and seeing better equates to knowing.

I won't address the rest of your questions--but just to suggest you keep reading Insight and feeling (and recognizing) the internal shifts occurring because of it. Expect to feel confused--no initial confusion, no massive insights. the upshot is that knowing the real is not merely looking but is at the end of a process of questioning, insighting, reflective questioning and insighting, and judging.

You might want to peruse the chapters on knowing and then being--as in, the real is being. Also, look in the index for references to abstraction and how it enriches. Your questions will come clear with an understanding of Lonergan's differentiation of meaning as you go through the text. 

I hope this helps,

Catherine

Hi George, not sure I can help because those circles are crazy buggers!  You might notice how much you've addressed here just trying to answer what seems like a simple question.  One of my original ideas - `where are the straight lines in nature?'  We give semantic translation to math systems, and it's easy to show how rocks in a stream, or sheep in a field, are like numbers.  Let me know if you have any idea for where, in your typical low-tech environment, would man see examples of straight lines?  Rudy Rucker says they imply infinities, and that inspired me to ask the question once I had the answer.

Okay, enough for me.  When people start talking about circles, I like to use the Frasier circle illusion as an example of Lonergan's tripartite method.  That allows me to give my opinion that any reasonable description and explanation of reality always combines subject operations with object outcomes.  Or, on a lighter note, imagine one small circle inside another.  They are both composed of an infinited number of points, but isn't the bigger circle a bigger infinity?  Just thoughts, no help, sorry!

[Doge of Venice]

Thank you both for responding. Sorry for the delay in acknowledging your answers; I stopped looking after a week or so and thought I might get an automatic email or something when there was a reply.

I appreciate your thoughts, and will read and reflect on each of your answers.