I’m unsure why, perhaps because of my strong interest in psychology, I find myself very intrigued by the workings of the mind. From where do our thoughts come? Why do we habitually sort and categorize? What assistance do we have to distinguish fact from fiction? How is our worldview generated? What role is played by our senses in the development of the mind? Does imagination, memory or repetition matter? How do we individually or collectively establish truth?
I recently read an article on thought that distinguished between “perceiving” and “conceiving.” To perceive is to see or become aware of something directly through the senses. To conceive is to form or originate something in the mind or to develop an understanding. Clearly, ideas come to us through both sources.
Simple numbers and geometry can help to concretize this difference. Imagine the number three. Do you see the numeral 3 or do you imagine three items? You can perceive the written numeral 3 and you can perceive three items; those can be taken in by the senses. You can also conceive the numeral 3 and the three items without actually seeing them. But the idea of “three” can only be conceived; we can’t really take in “three” with our senses. We can however, understand “three.” So perceiving is not necessary for understanding.
Another example can be had from simple geometrical shapes. Imagine a triangle, a three-sided figure. We can easily conceive what that looks like and can also perceive them in our environment. For example, a “Yield” sign is triangular. We can also easily perceive and conceive four and five sided figures. You could hardly open your eyes without seeing squares and rectangles. A famous government building in Washington, DC is a ready example of a five-sided figure, the pentagon. As the numbers of sides increases, the number of examples decreases. It becomes more difficult to perceive the larger polygons in our environment, but we still see them. The octagonal stop sign has eight sides. Decagons, ten-sided figures, are more difficult to perceive, but can be found. They are still quite easy to conceive. Just put more lines in the figure to close it.
What happens when the number of sides on the figures gets much larger? Can you perceive a figure with one hundred sides (a hectogon or centagon)? I can’t think of any example, but you might be able to draw one. But even if you can’t draw a hectogon, can you conceive it? Can you conceive a chiliagon with a thousand sides or a myriagon with ten thousand sides? I’m guessing you can! But you cannot perceive a chiliagon or myriagon. No matter how large or small you make the chiliagon, it differs from the area of its circumscribed circle by less than 0.0004%. We cannot perceive that difference and so will only see a circle, or an oval, if the sides vary in length. So again this tells us we are able to conceive things we cannot perceive. We are capable of knowing by conception what cannot be known by perception.
René Descartes (1596 – 1650) was a French philosopher, mathematician and writer who spent most of his life in the Dutch Republic. He uses the chiliagon as an example to demonstrate the difference between pure intellection and imagination. Descartes says that, when one thinks of a chiliagon, he "does not imagine the thousand sides or see them as if they were present" before him – as he does when one imagines a triangle, for example. The imagination constructs a "confused representation," which is no different from that which it constructs of a myriagon. However, the person does clearly understand what a chiliagon is, just as he understands what a triangle is, and he is able to distinguish it from a myriagon. Therefore, the intellect is not dependent on imagination, Descartes claims, as it is able to entertain clear and distinct ideas when imagination is unable to. (Meditation VI)
Other philosophers also reference the example of a chiliagon. A very early use is by Augustine of Hippo who argues that it does not follow from the fact that we cannot sense or perceive the attributes of God that we cannot know them. We are endowed at an intuitive level with certain understandings that we cannot justify rationally. Immanuel Kant does not actually use a chiliagon as his example, instead using a 96-sided figure, but he is responding to the same question raised by Descartes and compares the same concept to space and time. David Hume points out again that it is impossible for the eye to determine the angles of a chiliagon. Henri Poincare uses the chiliagon as evidence that "intuition is not necessarily founded on the evidence of the senses" because "we can not represent to ourselves a chiliagon, and yet we reason by intuition on polygons in general, which include the chiliagon as a particular case.” John Locke uses the chiliagon in his argument regarding the distinction between the thoughts of humans and beasts. Sensory experience, he says, is common to both, but only humans are capable of conceiving abstract thoughts.
So where does the chiliagon lead us? Without a doubt, our thinking is greatly influenced by what we perceive, by what we take in with our senses. Additionally, however, our knowledge is greatly expanded by what we can conceive, which takes us well beyond our powers of perception.
The mission of Heavyquestions.com is to provide thought provoking information and answers to your heavy questions.
Please contact us with your personal story, comment or concerns at
email@example.com or Click "Share Your Thoughts".
To Submit a question for us to answer, please click "Submit a Question".
Like us on Facebook + Follow us on Twitter + Thanks for visiting out site!