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Is the world continuous ? Aristotle in his writings wrote that the world is continuous.

"And since every magnitude is divisible into magnitudes-for we have shown that it is impossible for anything continuous to be composed of indivisible parts, and every magnitude is continuous (Aristotle Physics VI)"

Are we now able to refute this claim?

I mean, is there a distance of length 2Pi actually ? I'm thinking here of the circle with radius of 1 meter, whose perimeter mathematically is 2Pi. If the smallest unit of length is Plank's distance 'h', then are we to assume that the circle is actually "pixelated" ? Could the smallest amount of matter be 'h', but we could still think of half of 'h' ?

Suppose that you answer that distance is discreet, in steps of 'h'. What about 'time' ? Does this also imply that we can not think of continuous time, because time is only a record of movement of objects?

Zeno's paradoxes in fact criticize both views of continuity and discreetness of time. Quote from http://cerebro.xu.edu/math/math147/02f/zeno/zenonotes.html

"Let us now step back and reconsider the four paradoxes and try to filter out Aristotle's perspective on the matter. In the Dichotomy and Achilles, Zeno argues that motion is impossible from the hypothesis that time is a continuous phenomenon. In the Arrow and the Stadium, he argues that motion is impossible from the hypothesis that time is a discrete phenomenon. Cobbling these together into one meta-argument gives us an even more powerful conclusion: regardless what your stand is on the nature of time, continuous or discrete, the conclusion is that motion is impossible. "

Finally, is our position on the continuity issue strictly because of Planks 'h' limit discovery, or are we able to arrive at it philosophically ?

Here's an argument on the impossibility of continuos distance (from the book "Quest for Omega", by G. Chaitin). Any irrational number, lets say 2Pi, contains infinitely many digits in its decimal expansion. That means that to store it in that form an infinitely large amount of space would be needed. The fact that it can be written concisely as "perimeter of circle of radius 1" means that an infinite amount of data can be compressed. Here "infinite" means any large number you want to pick. We are observing an amazing compression ratio, that looks unrealistic to expect. Chaitin uses a different irrational number that he constructs that illustrates the same issue more dramatically.

asked Oct 28 '12 at 18:21

rarden's gravatar image


edited Oct 29 '12 at 09:52

Greg%20Perkins's gravatar image

Greg Perkins ♦♦

"Cobbling these together into one meta-argument gives us an even more powerful conclusion: regardless what your stand is on the nature of time, continuous or discrete, the conclusion is that motion is impossible."

In other words (since we know that motion is possible), Zeno is wrong.

Aristotle's arguments, on the other hand, are compelling. Like all knowledge, the conclusions are contextual, but I'm not aware of any contexts yet discovered in which they don't hold (not counting fantasy worlds of "pure math", of course).

(Oct 30 '12 at 21:06) anthony anthony's gravatar image


"Even if, like Aristotle, you would rather believe your own senses than Zeno's deductions"

"What they say about the mathematical universe is even more important for us than what they say about the physical universe."

Clearly this is not the person you want to get an Objectivist view of reality from. :)

(Oct 30 '12 at 21:17) anthony anthony's gravatar image

This question pertains primarily to physics rather than to Objectivist philosophy, except for some basic epistemological issues raised by the question's methodology. Objectivism takes no position on purely physics issues; those are for the science of physics to resolve, following philosophically validated methodology.

This view may differ somewhat from some of Aristotle's views, but it must be remembered that all knowledge is contextual, and claims by Aristotle concerning continuity were valid within the context that was available in his era, and are still just as valid today in that same context. Quantum physics was not known in Aristotle's era, except perhaps in the speculative views of the philosopical atomists regarding discrete units of matter (if I understand ancient, pre-modern atomism correctly).

The question may also be confusing the Plank length with the Planck constant (h). Refer to the Wikipedia articles on "Planck length" and "Planck constant" for some apparently useful clarification, although I am not sufficiently versed in modern physics to comment on the accuracy of those Wikipedia discussions. I have certainly heard of matter and energy as existing in discrete quanta, but I have never heard of length as existing metaphysically in some kind of discrete quanta. The Wikipedia articles do not appear to confirm the applicability of quantum discreteness to length or distance, either. That issue, however, is physics, not philosophy. It's an issue to be decided by observations of reality, integrated into a comprehensive theory.

... is our position on the continuity issue strictly because of Planks 'h' limit discovery, or are we able to arrive at it philosophically ?

In addition to the apparent confusion of Planck constant and Planck length in this formulation, the answer to this question is: absolutely not; we cannot arrive at conclusions of physics philosophically. That is not the function of philosophy. Philosophy can address issues of basic methodology but cannot prejudge the results of applying a valid methodology to observations of reality.

The question ends with an argument apparently claiming that a distance of 2 x pi can't exist in reality, because there is no way to store all the digits in the value of the pi constant as expressed in the decimal number system, since the number of digits is endless (infinite). This argument represents methodological confusion between man's conceptual representations of magnitudes and the actual magnitudes as they exist in reality. Reality is not a product of man's consciousness (Kant notwithstanding). On the other hand, any physical existent such as the length of an actual object will become discrete (quantized) at the atomic level, simply because matter consists of atoms (which are comprised of still smaller, but ultimately discrete, quanta). As a mathematical abstraction, however, man can certainly conceive of a perfect circle (or perfect square), and can ascertain that the ratio of the circle's circumference (or the square's perimeter) to the circle's diameter (or the square's diagonal) is not a quantized magnitude, but a ratio that mathematically goes on without limit and without becoming repetitive, i.e., a mathematically "irrational number," not capable of being expressed as a ratio of two integers.

If physics asks us to scrap our concepts of existence, consciousness, and the relation between them, and start afresh with new concepts, physics is most likely overstepping its proper domain in so doing (or, more likely, reflecting anti-rational philosophy that preceded it), and encroaching into areas in which physics is unequipped to generalize. That domain -- the fundamental concepts on which all science depends -- requires philosophical formulation and validation before special sciences like physics can arise at all. If, however, a philosopher like Aristotle has allegedly overstepped the limits of philosophy, Objectivism is a philosophy that can identify and correct such a philosophical error.

answered Oct 29 '12 at 02:04

Ideas%20for%20Life's gravatar image

Ideas for Life ♦


Dr. Pat Corvini's lectures on "Achilles, the Tortoise, and the Objectivity of Mathematics" (MP3's available for a few dollars online) may be helpful on this front. She gives a great discussion of the fundamental difficulty with Zeno's Paradoxes, clearing a big stumbling block in the way of answering this question. Our concepts for space and time are continuous because that is what we face in our usual context -- but physically in terms of the ultimate constituents of reality, that is something for science to determine. The puzzles and paradoxes only seem to arise when people conflate our abstractions (continuous) with concrete existents.

(Oct 29 '12 at 10:11) Greg Perkins ♦♦ Greg%20Perkins's gravatar image

I listened to Dr. Pat Corvini's lectures, and it has now answered my question. Thank you for the tip, Greg, and here is a bitcookie for you #8635.

(Oct 31 '12 at 11:52) rarden rarden's gravatar image

Thanks for bitcookie #8635-fa

(Oct 31 '12 at 16:05) Greg Perkins ♦♦ Greg%20Perkins's gravatar image

I appreciate it! :^)

(Oct 31 '12 at 16:06) Greg Perkins ♦♦ Greg%20Perkins's gravatar image
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Asked: Oct 28 '12 at 18:21

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Last updated: Oct 31 '12 at 16:06