display all the ideas for this combination of texts
7 ideas
| 9790 | Geometry studies naturally occurring lines, but not as they occur in nature [Aristotle] |
| Full Idea: Geometry studies naturally occurring lines, but not as they occur in nature. | |
| From: Aristotle (Physics [c.337 BCE], 194a09) | |
| A reaction: What a splendid remark. If the only specimen you could find of a very rare animal was maimed, you wouldn't be particularly interested in the nature of its injury, but in the animal. |
| 22962 | Two is the least number, but there is no least magnitude, because it is always divisible [Aristotle] |
| Full Idea: The least number, without qualification, is the two. …but in magnitude there is no least number, for every line always gets divided. | |
| From: Aristotle (Physics [c.337 BCE], 220a27) | |
| A reaction: Showing the geometrical approach of the Greeks to number. Two is the last number because numbers are for counting, and picking out one thing is not counting. |
| 18090 | Without infinity time has limits, magnitudes are indivisible, and numbers come to an end [Aristotle] |
| Full Idea: If there is, unqualifiedly, no infinite, it is clear that many impossible things result. For there will be a beginning and an end of time, and magnitudes will not be divisible into magnitudes, and number will not be infinite. | |
| From: Aristotle (Physics [c.337 BCE], 206b09), quoted by David Bostock - Philosophy of Mathematics 1.8 | |
| A reaction: This is a commitment to infinite time, and uncountable real numbers, and infinite ordinals. Dedekind cuts are implied. Nice. |
| 22929 | Aristotle's infinity is a property of the counting process, that it has no natural limit [Aristotle, by Le Poidevin] |
| Full Idea: For Aristotle infinity is not so much a property of some set of objects - the numbers - as of the process of counting, namely of its not having a natural limit. This is 'potential' infinite | |
| From: report of Aristotle (Physics [c.337 BCE]) by Robin Le Poidevin - Travels in Four Dimensions 06 'Illusion' | |
| A reaction: I increasingly favour this view. Mathematicians have foisted fictional objects on us, such as real infinities, limits and zero, because it makes their job easier, but it makes discussion of the natural world very obscure. |
| 22930 | Lengths do not contain infinite parts; parts are created by acts of division [Aristotle, by Le Poidevin] |
| Full Idea: Aristotle says that a length does not already contain, waiting to be discovered, an infinite number of parts; such parts only come into existence once they are defined by an act of division. | |
| From: report of Aristotle (Physics [c.337 BCE]) by Robin Le Poidevin - Travels in Four Dimensions 07 'Two' | |
| A reaction: If that is true of infinite parts then it must also be true of finite parts. So a cake has no parts at all until it is cut. That could play merry hell with discussions of mereology. Wholes are ontologically prior to parts. |
| 18833 | A continuous line cannot be composed of indivisible points [Aristotle] |
| Full Idea: No continuum can be composed of indivisibles: e.g. a line cannot be composed of points, the line being continuous and the points indivisibles. | |
| From: Aristotle (Physics [c.337 BCE], 231a23), quoted by Ian Rumfitt - The Boundary Stones of Thought 7.4 | |
| A reaction: Rumfitt observes that ' the basic problem is to say what the ultimate parts of a continuum are, of they are not points'. Early modern philosophers had lots of proposals. |
| 9974 | Ten sheep and ten dogs are the same numerically, but it is not the same ten [Aristotle] |
| Full Idea: If there are ten sheep and ten dogs, the number is the same (because it does not differ by a numerical difference), but it is not the same ten (because the objects it is predicated of are different - dogs in one instance, horses in the other). | |
| From: Aristotle (Physics [c.337 BCE], 224a2-14) | |
| A reaction: Mega! Abstract objects are unique, and can't be 'added' to themselves. I think we need 'units' here, because 2+2 adds four units, so each 2 refers to something different. '2' must refer to something other than itself. |