19 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 |
9616 | A set is a collection into a whole of distinct objects of our intuition or thought [Cantor] |
Full Idea: A set is any collection into a whole M of definite, distinct objects m ... of our intuition or thought. | |
From: George Cantor (The Theory of Transfinite Numbers [1897], p.85), quoted by James Robert Brown - Philosophy of Mathematics Ch.2 | |
A reaction: This is the original conception of a set, which hit trouble with Russell's Paradox. Cantor's original definition immediately invites thoughts about the status of vague objects. |
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. |
15896 | Cantor needed Power Set for the reals, but then couldn't count the new collections [Cantor, by Lavine] |
Full Idea: Cantor grafted the Power Set axiom onto his theory when he needed it to incorporate the real numbers, ...but his theory was supposed to be theory of collections that can be counted, but he didn't know how to count the new collections. | |
From: report of George Cantor (The Theory of Transfinite Numbers [1897]) by Shaughan Lavine - Understanding the Infinite I | |
A reaction: I take this to refer to the countability of the sets, rather than the members of the sets. Lavine notes that counting was Cantor's key principle, but he now had to abandon it. Zermelo came to the rescue. |
23651 | Universals are not objects of sense and cannot be imagined - but can be conceived [Reid] |
Full Idea: A universal is not an object of any sense, and therefore cannot be imagined; but it may be distinctly conceived. | |
From: Thomas Reid (Essays on Intellectual Powers 5: Abstraction [1785], 6) | |
A reaction: If you try to imagine whiteness, what size is it, and what substance embodies it? Neither are needed to think of whiteness, so Reid is right. A nice observation. |
23650 | Only individuals exist [Reid] |
Full Idea: Everything that really exists is an individual. | |
From: Thomas Reid (Essays on Intellectual Powers 5: Abstraction [1785], 6) | |
A reaction: Locke is the probable inspiration for this nominalist affirmation. Not sure how high temperature plasma, or the oceans of the world, fit into this. On the whole I agree with him. He is mainly rejecting abstract universals. |
23649 | No one thinks two sheets possess a single whiteness, but all agree they are both white [Reid] |
Full Idea: If we say that the whiteness of this sheet is the whiteness of another sheet, every man perceives this to be absurd; but when he says both sheets are white, this is true and perfectly understood. | |
From: Thomas Reid (Essays on Intellectual Powers 5: Abstraction [1785], 3) | |
A reaction: Well said. Only a philosopher could think the whiteness of one sheet is exactly the same entity as the whiteness of a different sheet. We seem to have brilliantly and correctly labelled them both as white, and then thought that one word implies one thing. |
11874 | Real identity admits of no degrees [Reid] |
Full Idea: Wherever identity is real, it admits of no degrees. | |
From: Thomas Reid (Essays on Intellectual Powers 5: Abstraction [1785]), quoted by David Wiggins - Sameness and Substance Renewed 6 epig | |
A reaction: Wiggins quotes this with strong approval. Personally I am inclined to think that identity may admit of no degrees in human thought, because that is the only way we can do it, but the world is full of uncertain identities, at every level. |
23652 | We must first conceive things before we can consider them [Reid] |
Full Idea: No man can consider a thing which he does not conceive. | |
From: Thomas Reid (Essays on Intellectual Powers 5: Abstraction [1785], 6) | |
A reaction: This seems to imply concepts, but we should not take this to be linguistic, since animals obviously consider things and make judgements. |
23648 | First we notice and name attributes ('abstracting'); then we notice that subjects share them ('generalising') [Reid] |
Full Idea: First we resolve or analyse a subject into its known attributes, and give a name to each attribute. Then we observe one or more attributes to be common to many subjects. The first philosophers call 'abstraction', and the second is 'generalising'. | |
From: Thomas Reid (Essays on Intellectual Powers 5: Abstraction [1785], 3) | |
A reaction: It is very unfashionable in analytic philosophy to view universals in this way, but it strikes me as obviously correct. There are not weird abstract entities awaiting a priori intuition. There are just features of the world to be observed and picked out. |
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). |