6 ideas
| 23367 | Even pointing a finger should only be done for a reason [Epictetus] |
| Full Idea: Philosophy says it is not right even to stretch out a finger without some reason. | |
| From: Epictetus (fragments/reports [c.57], 15) | |
| A reaction: The key point here is that philosophy concerns action, an idea on which Epictetus is very keen. He rather despise theory. This idea perfectly sums up the concept of the wholly rational life (which no rational person would actually want to live!). |
| 11074 | 'It is true that this follows' means simply: this follows [Wittgenstein] |
| Full Idea: The proposition: "It is true that this follows from that" means simply: this follows from that. | |
| From: Ludwig Wittgenstein (Remarks on the Foundations of Mathematics [1938], p.38), quoted by Robert Hanna - Rationality and Logic 6 | |
| A reaction: Presumably this remark is simply expressing Wittgenstein's later agreement with the well-known view of Ramsey. Early Wittgenstein had endorsed a correspondence view of truth. |
| 6007 | If you know your father, but don't recognise your father veiled, you know and don't know the same person [Eubulides, by Dancy,R] |
| Full Idea: The 'undetected' or 'veiled' paradox of Eubulides says: if you know your father, and don't know the veiled person before you, but that person is your father, you both know and don't know the same person. | |
| From: report of Eubulides (fragments/reports [c.390 BCE]) by R.M. Dancy - Megarian School | |
| A reaction: Essentially an uninteresting equivocation on two senses of "know", but this paradox comes into its own when we try to give an account of how linguistic reference works. Frege's distinction of sense and reference tried to sort it out (Idea 4976). |
| 6006 | If you say truly that you are lying, you are lying [Eubulides, by Dancy,R] |
| Full Idea: The liar paradox of Eubulides says 'if you state that you are lying, and state the truth, then you are lying'. | |
| From: report of Eubulides (fragments/reports [c.390 BCE]) by R.M. Dancy - Megarian School | |
| A reaction: (also Cic. Acad. 2.95) Don't say it, then. These kind of paradoxes of self-reference eventually lead to Russell's 'barber' paradox and his Theory of Types. |
| 6008 | Removing one grain doesn't destroy a heap, so a heap can't be destroyed [Eubulides, by Dancy,R] |
| Full Idea: The 'sorites' paradox of Eubulides says: if you take one grain of sand from a heap (soros), what is left is still a heap; so no matter how many grains of sand you take one by one, the result is always a heap. | |
| From: report of Eubulides (fragments/reports [c.390 BCE]) by R.M. Dancy - Megarian School | |
| A reaction: (also Cic. Acad. 2.49) This is a very nice paradox, which goes to the heart of our bewilderment when we try to fully understand reality. It homes in on problems of identity, as best exemplified in the Ship of Theseus (Ideas 1212 + 1213). |
| 11073 | Two and one making three has the necessity of logical inference [Wittgenstein] |
| Full Idea: "But doesn't it follow with logical necessity that you get two when you add one to one, and three when you add one to two? and isn't this inexorability the same as that of logical inference? - Yes! it is the same. | |
| From: Ludwig Wittgenstein (Remarks on the Foundations of Mathematics [1938], p.38), quoted by Robert Hanna - Rationality and Logic 6 | |
| A reaction: This need not be a full commitment to logicism - only to the fact that the inferential procedures in mathematics are the same as those of logic. Mathematics could still have further non-logical ingredients. Indeed, I think it probably does. |