5 ideas
10855 | Actual infinities are not allowed in mathematics - only limits which may increase without bound [Gauss] |
Full Idea: I protest against the use of an infinite quantity as an actual entity; this is never allowed in mathematics. The infinite is only a manner of speaking, in which one properly speaks of limits ...which are permitted to increase without bound. | |
From: Carl Friedrich Gauss (Letter to Shumacher [1831]), quoted by Brian Clegg - Infinity: Quest to Think the Unthinkable Ch.7 |
16669 | Everything that exists is either a being, or some mode of a being [Malebranche] |
Full Idea: It is absolutely necessary that everything in the world be either a being or a mode [manière] of a being. | |
From: Nicolas Malebranche (The Search After Truth [1675], III.2.8.ii), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 13.4 |
4254 | Externalist accounts of knowledge do not require the traditional sort of justification [Kornblith] |
Full Idea: What is distinctive about externalist accounts of knowledge is that they do not require justification, at least in the traditional sense. | |
From: Hilary Kornblith (Internalism and Externalism: a History [2001], p.2) | |
A reaction: At least this gives animals the chance to know things, but I suspect that they never get beyond true beliefs. I'm sure humans have 'better' knowledge than animals. |
12726 | In a true cause we see a necessary connection [Malebranche] |
Full Idea: A true cause is one in which the mind perceives a necessary connection between the cause and its effect. | |
From: Nicolas Malebranche (The Search After Truth [1675], 1.649 (450)), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 5 | |
A reaction: Presumably Hume was ignorant of 'true' causes, since he says he never saw this connection. But then is the perception done by the mind, or by the senses? |
2594 | A true cause must involve a necessary connection between cause and effect [Malebranche] |
Full Idea: A true cause as I understand it is one such that the mind perceives a necessary connection between it and its effects. | |
From: Nicolas Malebranche (The Union of Body and Soul [1675], p.116) |