16 ideas
| 1765 | Diogenes said avoidance of philosophy is the lack of a desire to live properly [Diogenes of Sin., by Diog. Laertius] |
| Full Idea: When a man said that he was not suited to philosophy, Diogenes said to him, 'Why then do you live, if you have no desire to live properly.' | |
| From: report of Diogenes (Sin) (reports [c.360 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 06.Di.6 | |
| A reaction: Meaning philosophy is already more practice than theory. |
| 17892 | For clear questions posed by reason, reason can also find clear answers [Gödel] |
| Full Idea: I uphold the belief that for clear questions posed by reason, reason can also find clear answers. | |
| From: Kurt Gödel (works [1930]), quoted by Peter Koellner - On the Question of Absolute Undecidability 1.5 | |
| A reaction: [written in 1961] This contradicts the implication normally taken from his much earlier Incompleteness Theorems. |
| 9188 | Gödel proved that first-order logic is complete, and second-order logic incomplete [Gödel, by Dummett] |
| Full Idea: Gödel proved the completeness of standard formalizations of first-order logic, including Frege's original one. However, an implication of his famous theorem on the incompleteness of arithmetic is that second-order logic is incomplete. | |
| From: report of Kurt Gödel (works [1930]) by Michael Dummett - The Philosophy of Mathematics 3.1 | |
| A reaction: This must mean that it is impossible to characterise arithmetic fully in terms of first-order logic. In which case we can only characterize the features of abstract reality in general if we employ an incomplete system. We're doomed. |
| 10620 | Originally truth was viewed with total suspicion, and only demonstrability was accepted [Gödel] |
| Full Idea: At that time (c.1930) a concept of objective mathematical truth as opposed to demonstrability was viewed with greatest suspicion and widely rejected as meaningless. | |
| From: Kurt Gödel (works [1930]), quoted by Peter Smith - Intro to Gödel's Theorems 28.2 | |
| A reaction: [quoted from a letter] This is the time of Ramsey's redundancy account, and before Tarski's famous paper of 1933. It is also the high point of Formalism, associated with Hilbert. |
| 17883 | Gödel's Theorems did not refute the claim that all good mathematical questions have answers [Gödel, by Koellner] |
| Full Idea: Gödel was quick to point out that his original incompleteness theorems did not produce instances of absolute undecidability and hence did not undermine Hilbert's conviction that for every precise mathematical question there is a discoverable answer. | |
| From: report of Kurt Gödel (works [1930]) by Peter Koellner - On the Question of Absolute Undecidability Intro | |
| A reaction: The normal simplistic view among philosophes is that Gödel did indeed decisively refute the optimistic claims of Hilbert. Roughly, whether Hilbert is right depends on which axioms of set theory you adopt. |
| 17885 | Gödel eventually hoped for a generalised completeness theorem leaving nothing undecidable [Gödel, by Koellner] |
| Full Idea: Eventually Gödel ...expressed the hope that there might be a generalised completeness theorem according to which there are no absolutely undecidable sentences. | |
| From: report of Kurt Gödel (works [1930]) by Peter Koellner - On the Question of Absolute Undecidability Intro | |
| A reaction: This comes as a bit of a shock to those who associate him with the inherent undecidability of reality. |
| 10614 | The real reason for Incompleteness in arithmetic is inability to define truth in a language [Gödel] |
| Full Idea: The concept of truth of sentences in a language cannot be defined in the language. This is the true reason for the existence of undecidable propositions in the formal systems containing arithmetic. | |
| From: Kurt Gödel (works [1930]), quoted by Peter Smith - Intro to Gödel's Theorems 21.6 | |
| A reaction: [from a letter by Gödel] So they key to Incompleteness is Tarski's observations about truth. Highly significant, as I take it. |
| 1762 | When someone denied motion, Diogenes got up and walked away [Diogenes of Sin., by Diog. Laertius] |
| Full Idea: Diogenes replied to one who asserted that there was no such thing as motion by getting up and walking away. | |
| From: report of Diogenes (Sin) (reports [c.360 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 06.Di.6 |
| 7813 | Cynicism was open to anyone, and needed neither education nor sophistication [Diogenes of Sin., by Grayling] |
| Full Idea: An advantage of Cynicism was that it was open to anyone who could grasp its simple teachings. Understanding it required neither education nor sophistication. | |
| From: report of Diogenes (Sin) (reports [c.360 BCE]) by A.C. Grayling - What is Good? Ch.3 | |
| A reaction: This was the source of the well-known opposition of Diogenes to Plato's Academy, and it makes him a key predecessor of the teachings of Jesus. Personally I think the really good life is difficult, and it needs education and careful rational thought. |
| 1763 | Diogenes said a plucked chicken fits Plato's definition of man [Diogenes of Sin., by Diog. Laertius] |
| Full Idea: Plato defined man as a two-footed featherless animal, so Diogenes plucked a cock and brought it into the school, and said, 'This is Plato's man'. | |
| From: report of Diogenes (Sin) (reports [c.360 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 06.Di.6 | |
| A reaction: You have to be very serious about your philosophy to enact your counterexamples, rather than just suggest them. Which university will actually reconstruct the Trolley Problem? |
| 5071 | The Cynics rejected what is conventional as irrational, and aimed to live by nature [Taylor,R on Diogenes of Sin.] |
| Full Idea: The Cynics were convinced of the purely conventional foundation of Athenian values, which meant they had no rational foundation at all. They therefore rejected them in favour of what is correct and worthwhile by nature. | |
| From: comment on Diogenes (Sin) (reports [c.360 BCE]) by Richard Taylor - Virtue Ethics: an Introduction Ch.8 | |
| A reaction: This shows how the Cynics are key players in the progress of the nomos-physis debate, which keeps resurfacing as relativism vs absolutism, cognitivism vs non-cognitivism, and even romanticism vs classicism. The trouble is, convention is natural! |
| 7812 | For peace of mind, you need self-government, indifference and independence [Diogenes of Sin.] |
| Full Idea: There are three essential conditions for peace of mind: autarchy, apathy and freedom. Autarchy is self-government and self-sufficiency; apathy is indifference to what the world can do to you; the freedom is from dependence and possessions. | |
| From: Diogenes (Sin) (reports [c.360 BCE]), quoted by A.C. Grayling - What is Good? Ch.3 | |
| A reaction: Quite good advice, but I don't see 'peace of mind' as the highest human ideal. The basic suggestion here is live alone and do nothing. Certainly don't get married, or have children, or try to achieve anything. |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
| From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
| A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |
| 1764 | Diogenes said he was a citizen of the world [Diogenes of Sin., by Diog. Laertius] |
| Full Idea: Diogenes said he was a citizen of no country, but of the world. | |
| From: report of Diogenes (Sin) (reports [c.360 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 06.Di.6 |
| 5968 | Diogenes masturbated in public, wishing he could get rid of hunger so easily [Diogenes of Sin., by Plutarch] |
| Full Idea: Chrysippus praises Diogenes for saying to bystanders as he masturbated in public, "Would that I could thus rub the hunger too out of my belly". | |
| From: report of Diogenes (Sin) (reports [c.360 BCE]) by Plutarch - 70: Stoic Self-contradictions 1044b | |
| A reaction: So it is not quite true that people only need corn and water. Diogenes' remark doesn't explain why he did it in public. Was it to defy local convention (as befits a citizen of the world), or was it to teach? |
| 1766 | Diogenes said that the most excellent thing among men was freedom of speech [Diogenes of Sin., by Diog. Laertius] |
| Full Idea: Diogenes said that the most excellent thing among men was freedom of speech. | |
| From: report of Diogenes (Sin) (reports [c.360 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 06.Di.6 |