8 ideas
| 18844 | You would cripple mathematics if you denied Excluded Middle [Hilbert] |
| Full Idea: Taking the principle of Excluded Middle away from the mathematician would be the same, say, as prohibiting the astronomer from using the telescope or the boxer from using his fists. | |
| From: David Hilbert (The Foundations of Mathematics [1927], p.476), quoted by Ian Rumfitt - The Boundary Stones of Thought 9.4 | |
| A reaction: [p.476 in Van Heijenoort] |
| 3626 | Knowing the attributes is enough to reveal a substance [Descartes] |
| Full Idea: I have never thought that anything more is required to reveal a substance than its various attributes. | |
| From: René Descartes (Reply to Fifth Objections [1641], 360) |
| 3630 | Our thinking about external things doesn't disprove the existence of innate ideas [Descartes] |
| Full Idea: You can't prove that Praxiteles never made any statues on the grounds that he did not get from within himself the marble from which he sculpted them. | |
| From: René Descartes (Reply to Fifth Objections [1641], 362) |
| 3631 | A blind man may still contain the idea of colour [Descartes] |
| Full Idea: How do you know that there is no idea of colour in a man born blind? | |
| From: René Descartes (Reply to Fifth Objections [1641], 363) |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |
| 3639 | Necessary existence is a property which is uniquely part of God's essence [Descartes] |
| Full Idea: In the case of God necessary existence is in fact a property in the strictest sense of the term, since it applies to him alone and forms a part of his essence as it does of no other thing | |
| From: René Descartes (Reply to Fifth Objections [1641], 383) |
| 3640 | Possible existence is a perfection in the idea of a triangle [Descartes] |
| Full Idea: Possible existence is a perfection in the idea of a triangle, just as necessary existence is a perfection in the idea of God. | |
| From: René Descartes (Reply to Fifth Objections [1641], 383) |