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 |
17879 | Axiomatising set theory makes it all relative [Skolem] |
Full Idea: Axiomatising set theory leads to a relativity of set-theoretic notions, and this relativity is inseparably bound up with every thoroughgoing axiomatisation. | |
From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.296) |
14212 | A consistent theory just needs one model; isomorphic versions will do too, and large domains provide those [Lewis] |
Full Idea: A consistent theory is, by definition, one satisfied by some model; an isomorphic image of a model satisfies the same theories as the original model; to provide the making of an isomorphic image of any given model, a domain need only be large enough. | |
From: David Lewis (Putnam's Paradox [1984], 'Why Model') | |
A reaction: This is laying out the ground for Putnam's model theory argument in favour of anti-realism. If you are chasing the one true model of reality, then formal model theory doesn't seem to offer much encouragement. |
17878 | If a 1st-order proposition is satisfied, it is satisfied in a denumerably infinite domain [Skolem] |
Full Idea: Löwenheim's theorem reads as follows: If a first-order proposition is satisfied in any domain at all, it is already satisfied in a denumerably infinite domain. | |
From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.293) |
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. |
17880 | Integers and induction are clear as foundations, but set-theory axioms certainly aren't [Skolem] |
Full Idea: The initial foundations should be immediately clear, natural and not open to question. This is satisfied by the notion of integer and by inductive inference, by it is not satisfied by the axioms of Zermelo, or anything else of that kind. | |
From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.299) | |
A reaction: This is a plea (endorsed by Almog) that the integers themselves should be taken as primitive and foundational. I would say that the idea of successor is more primitive than the integers. |
17881 | Mathematician want performable operations, not propositions about objects [Skolem] |
Full Idea: Most mathematicians want mathematics to deal, ultimately, with performable computing operations, and not to consist of formal propositions about objects called this or that. | |
From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.300) |
14213 | Anti-realists see the world as imaginary, or lacking joints, or beyond reference, or beyond truth [Lewis] |
Full Idea: Anti-realists say the only world is imaginary, or only has the parts or classes or relations we divide it into, or doubt that reference to the world is possible, or doubt that our interpretations can achieve truth. | |
From: David Lewis (Putnam's Paradox [1984], 'Why Anti-R') | |
A reaction: [compression of a paragraph on anti-realism] Lewis is a thoroughgoing realist. A nice example of the rhetorical device of ridiculing an opponent by suggesting that they don't even know what they themselves believe. |
14210 | A gerrymandered mereological sum can be a mess, but still have natural joints [Lewis] |
Full Idea: The mereological sum of the coffee in my cup, the ink in this sentence, a nearby sparrow, and my left shoe is a miscellaneous mess of an object, yet its boundaries are by no means unrelated to the joints of nature. | |
From: David Lewis (Putnam's Paradox [1984], 'What Might') | |
A reaction: In that case they do, but if there are no atoms at the root of physics then presumably their could also be thoroughly jointless assemblages, involving probability distributions etc. Even random scattered atoms seem rather short of joints. |
14215 | Causal theories of reference make errors in reference easy [Lewis] |
Full Idea: Whatever happens in special cases, causal theories usually make it easy to be wrong about the thing we refer to. | |
From: David Lewis (Putnam's Paradox [1984], 'What Is') | |
A reaction: I suppose the point of this is that there are no checks and balances to keep reference in focus, but just a requirement to keep connected to an increasingly attenuated causal chain. |
14209 | Descriptive theories remain part of the theory of reference (with seven mild modifications) [Lewis] |
Full Idea: Description theories of reference are supposed to have been well and truly refuted. I think not: ..it is still tenable with my seven points, and part of the truth of reference [7: rigidity, egocentric, tokens, causal, imperfect, indeterminate, families]. | |
From: David Lewis (Putnam's Paradox [1984], 'Glob Desc') | |
A reaction: (The bit at the end refers to his seven points, on p.59). He calls his basic proposal 'causal descriptivism', incorporating his seven slight modifications of traditional descriptivism about reference. |
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. |
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 |
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 |
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 |
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 |
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). |