| 13212 | Infinity is only potential, never actual [Aristotle] |
| Full Idea: Nothing is actually infinite. A thing is infinite only potentially. | |
| From: Aristotle (Coming-to-be and Passing-away (Gen/Corr) [c.335 BCE], 318a21) | |
| A reaction: Aristotle is the famous spokesman for this view, though it reappeared somewhat in early twentieth century discussions (e.g. Hilbert). I sympathise with this unfashionable view. Multiple infinites are good fun, but no one knows what they really are. |
| 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. |
| 9632 | Kant only accepts potential infinity, not actual infinity [Kant, by Brown,JR] |
| Full Idea: For Kant the only legitimate infinity is the so-called potential infinity, not the actual infinity. | |
| From: report of Immanuel Kant (Critique of Pure Reason [1781]) by James Robert Brown - Philosophy of Mathematics Ch.5 | |
| A reaction: This is part of what leads on the the Constructivist view of mathematics. There is a procedure for endlessly continuing, but no procedure for arriving. That seems to make good sense. |
| 15938 | Platonists ruin infinity, which is precisely a growing structure which is never completed [Dummett] |
| Full Idea: The platonist destroys the whole essence of infinity, which lies in the conception of a structure which is always in growth, precisely because the process of construction is never completed. | |
| From: Michael Dummett (Elements of Intuitionism [1977], p.57), quoted by Thomas J. McKay - Plural Predication | |
| A reaction: I don't warm to intuitionism, but I warm to this conception of infinity. Completed infinities are convenient reifications for mathematicians. |
| 15940 | The intuitionist endorses only the potential infinite [Lavine] |
| Full Idea: The intuitionist endorse the actual finite, but only the potential infinite. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VI.2) |