20 ideas
| 5896 | Speak the truth, for this alone deifies man [Pythagoras, by Porphyry] |
| Full Idea: Pythagoras advised above all things to speak the truth, for this alone deifies man. | |
| From: report of Pythagoras (reports [c.530 BCE]) by Porphyry - Life of Pythagoras §41 | |
| A reaction: Idea 4421 (of Nietzsche) stands in contrast to this. I am not quite sure why speaking the truth has such a high value. I am inclined to a minimalist view, which is just that philosophy is an attempt to speak the truth, as fishermen try to catch fish. |
| 3051 | Pythagoras discovered the numerical relation of sounds on a string [Pythagoras, by Diog. Laertius] |
| Full Idea: Pythagoras discovered the numerical relation of sounds on a string. | |
| From: report of Pythagoras (reports [c.530 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 08.1.11 |
| 21699 | Russell offered a paraphrase of definite description, to avoid the commitment to objects [Quine] |
| Full Idea: Russell's theory involved defining a term not by presenting a direct equivalent of it, but by 'paraphrasis', providing equivalents of the sentences. In this way, reference to fictitious objects can be simulated without our being committed to the objects. | |
| From: Willard Quine (Russell's Ontological Development [1966], p.75) | |
| A reaction: I hadn't quite grasped that the modern strategy of paraphrase tracks back to Russell - though it now looks obvious, thanks to Quine. Paraphrase is a beautiful way of sidestepping ontological problems. See Frege on the moons of Jupiter. |
| 17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
| Full Idea: There are many coherent stopping points in the hierarchy of increasingly strong mathematical systems, starting with strict finitism, and moving up through predicativism to the higher reaches of set theory. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], Intro) |
| 17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
| Full Idea: Roughly speaking, 'reflection principles' assert that anything true in V [the set hierarchy] falls short of characterising V in that it is true within some earlier level. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 2.1) |
| 17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
| Full Idea: There is at present no solid argument to the effect that a given statement is absolutely undecidable. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 5.3) |
| 7485 | For Pythagoreans 'one' is not a number, but the foundation of numbers [Pythagoras, by Watson] |
| Full Idea: For Pythagoreans, one, 1, is not a true number but the 'essence' of number, out of which the number system emerges. | |
| From: report of Pythagoras (reports [c.530 BCE], Ch.8) by Peter Watson - Ideas Ch.8 | |
| A reaction: I think this is right! Counting and numbers only arise once the concept of individuality and identity have arisen. Counting to one is no more than observing the law of identity. 'Two' is the big adventure. |
| 17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
| Full Idea: Some of the standard large cardinals (in order of increasing (logical) strength) are: inaccessible, Mahlo, weakly compact, indescribable, Erdös, measurable, strong, Wodin, supercompact, huge etc. (...and ineffable). | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) | |
| A reaction: [I don't understand how cardinals can have 'logical strength', but I pass it on anyway] |
| 17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
| Full Idea: To the extent that we are justified in accepting Peano Arithmetic we are justified in accepting its consistency, and so we know how to expand the axiom system so as to overcome the limitation [of Gödel's Second Theorem]. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.1) | |
| A reaction: Each expansion brings a limitation, but then you can expand again. |
| 17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
| Full Idea: The arithmetical instances of undecidability that arise at one stage of the hierarchy are settled at the next. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) |
| 21700 | Taking sentences as the unit of meaning makes useful paraphrasing possible [Quine] |
| Full Idea: The new freedom that Russell confers by paraphrasis (of definite descriptions) is our reward for recognising that the unit of communication is the sentence and not the word. | |
| From: Willard Quine (Russell's Ontological Development [1966], p.75) | |
| A reaction: Since many people hardly ever speak a properly formed sentence, I take propositions to be better candidates for this. However, I don't see how we can reject the compositional view (the meanings are assembled). |
| 21701 | Knowing a word is knowing the meanings of sentences which contain it [Quine] |
| Full Idea: We can say that knowing words is knowing how to work out the meanings of sentences containing them. Dictionary definitions are mere clauses in a recursive definition of the meanings of sentences. | |
| From: Willard Quine (Russell's Ontological Development [1966], p.76) | |
| A reaction: Do you have to recursively define all the sentences that might contain the word, before you can fully know the meaning of the word? He seems to credit Russell with the holistic view of sentences (though I think that starts with Frege). |
| 3053 | Pythagoras taught that virtue is harmony, and health, and universal good, and God [Pythagoras, by Diog. Laertius] |
| Full Idea: Pythagoras taught that virtue is harmony, and health, and universal good, and God. | |
| From: report of Pythagoras (reports [c.530 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 08.1.19 | |
| A reaction: I like the link with health, because I consider that a bridge over the supposed fact-value gap. Very Pythagorean to think that virtue is harmony. Plato liked that thought. |
| 5244 | For Pythagoreans, justice is simply treating all people the same [Pythagoras, by Aristotle] |
| Full Idea: Some even think that what is just is simple reciprocity, as the Pythagoreans maintained, because they defined justice simply as having done to one what one has done to another. | |
| From: report of Pythagoras (reports [c.530 BCE], 28) by Aristotle - Nicomachean Ethics 1132b22 | |
| A reaction: One wonders what Pythagoreans made of slavery. Aristotle argues that officials, for example, have superior rights. The Pythagorean idea makes fairness the central aspect of justice, and that must at least be partly right. |
| 553 | Pythagoreans think mathematical principles are the principles of all of nature [Pythagoras, by Aristotle] |
| Full Idea: The Pythagoreans thought that the principles of mathematical entities were the principles of all entities. | |
| From: report of Pythagoras (reports [c.530 BCE]) by Aristotle - Metaphysics 985b |
| 554 | Pythagoreans say things imitate numbers, but Plato says things participate in numbers [Pythagoras, by Aristotle] |
| Full Idea: Pythagoreans said that entities existed by imitation of the numbers, whereas Plato said that it was by participation. | |
| From: report of Pythagoras (reports [c.530 BCE]) by Aristotle - Metaphysics 987b |
| 375 | When musical harmony and rhythm were discovered, similar features were seen in bodily movement [Pythagoras, by Plato] |
| Full Idea: When our predecessors discovered musical scales, they also discovered similar features in bodily movement, which should also be measured numerically, and called 'tempos' and 'measures'. | |
| From: report of Pythagoras (reports [c.530 BCE]) by Plato - Philebus 17d |
| 638 | Pythagoreans define timeliness, justice and marriage in terms of numbers [Pythagoras, by Aristotle] |
| Full Idea: The Pythagoreans offered definitions of a limited range of things on the basis of numbers; examples are timeliness, justice and marriage. | |
| From: report of Pythagoras (reports [c.530 BCE]) by Aristotle - Metaphysics 1078b |
| 644 | For Pythagoreans the entire universe is made of numbers [Pythagoras, by Aristotle] |
| Full Idea: For Pythagoreans the entire universe is constructed of numbers. | |
| From: report of Pythagoras (reports [c.530 BCE]) by Aristotle - Metaphysics 1080b |
| 7467 | The modern idea of an immortal soul was largely created by Pythagoras [Pythagoras, by Watson] |
| Full Idea: The modern concept of the immortal soul is a Greek idea, which owes much to Pythagoras. | |
| From: report of Pythagoras (reports [c.530 BCE]) by Peter Watson - Ideas Ch.5 | |
| A reaction: You can see why it caught on - it is a very appealing idea. Watson connects the 'modern' view with the ideas of heaven and hell. Obviously the idea of an afterlife goes a long way back (judging from the contents of ancient graves). |