15 ideas
| 21355 | The Pre-Socratics are not simple naturalists, because they do not always 'leave the gods out' [Leroi] |
| Full Idea: The problem with making naturalism the hallmark of Pre-Socratic thought ...is that they do not always 'leave the gods out'; the Divine can usually be found lurking somewhere is their cosmologies. | |
| From: Armand Marie LeRoi (The Lagoon: how Aristotle invented science [2014], 007) | |
| A reaction: An important observation. I've been guilty of this simplistic view. We tend to ignore the religious fragments, or we possess so little that we have no idea where religion figured in their accounts. |
| 20109 | Hegel inserted society and history between the God-world, man-nature, man-being binary pairs [Hegel, by Safranski] |
| Full Idea: Before Hegel, people thought in binary oppositions of God and the world, man and nature, man and being. After Hegel an intervening world of society and history was inserted between these pairs. | |
| From: report of Georg W.F.Hegel (Introduction to the Philosophy of History [1840]) by Rüdiger Safranski - Nietzsche: a philosophical biography 05 | |
| A reaction: This is what Popper later called 'World Three'. This might be seen as the start of what we islanders call 'continental' philosophy, which we have largely ignored. Analytic philosophy only discovered this through philosophy of language. |
| 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. |
| 23274 | World history has no room for happiness [Hegel] |
| Full Idea: World history is not the place for happiness. Periods of happiness are empty pages in history. | |
| From: Georg W.F.Hegel (Introduction to the Philosophy of History [1840], 3) | |
| A reaction: Clearly, Hegel thinks the progress of world history is much more important than happiness. This idea gives backing to those who don't care much about the casualties on either side in a major war. |
| 23275 | The state of nature is one of untamed brutality [Hegel] |
| Full Idea: The 'state of nature' is not an ideal condition, but a condition of injustice, of violence, of untamed natural drives, inhuman acts and emotions. | |
| From: Georg W.F.Hegel (Introduction to the Philosophy of History [1840], 3) | |
| A reaction: He agrees with Hobbes, and disagrees with Rousseau. Hobbes's solution is authoritarian monarchy, but Hegel's solution is the unified and focused state, in which freedom can be realised. |
| 23276 | The soul of the people is an organisation of its members which produces an essential unity [Hegel] |
| Full Idea: The soul [of the people] exists only insofar as it is an organisation of its members, which - by taking itself together in its simple unity - produce the soul. Thus the people is one individuality in its essence. | |
| From: Georg W.F.Hegel (Introduction to the Philosophy of History [1840], 3) | |
| A reaction: Hegel is seen (e.g. by Charles Taylor) as the ancestor of a rather attractive communitarianism, but I think Popper is more accurate in seeing him as the first stage of modern totalitarianism. The people seen as one individual terrifies me. |
| 23272 | The human race matters, and individuals have little importance [Hegel] |
| Full Idea: Individuals are of slight importance compared to the mass of the human race. | |
| From: Georg W.F.Hegel (Introduction to the Philosophy of History [1840], 3) | |
| A reaction: A perfect statement of the anti-liberal viewpoint. Hegel is complex, but this is the strand that leads to ridiculous totalitarianism, where the highest ideal is to die for the glory of your nation. Importance can only start from individuals. |
| 23273 | In a good state the goal of the citizens and of the whole state are united [Hegel] |
| Full Idea: A state is well constituted and internally strong if the private interest of the citizens is united in the universal goal of the state. | |
| From: Georg W.F.Hegel (Introduction to the Philosophy of History [1840], 3) | |
| A reaction: The obvious question is who decides on the goals, and what to do with the citizens who don't accept them. |
| 23271 | The goal of the world is Spirit's consciousness and enactment of freedom [Hegel] |
| Full Idea: The final goal of the world is Spirit's consciousness of its freedom, and hence also the actualisation of that very freedom. | |
| From: Georg W.F.Hegel (Introduction to the Philosophy of History [1840], 3) | |
| A reaction: I have the impression that this ridiculous idea has been very influential in modern French philosophy, since they all seem to be dreaming of some perfect freedom at the end of the rainbow. Freedom is good, but this gives it a bad name. |
| 23270 | We should all agree that there is reason in history [Hegel] |
| Full Idea: We ought to have the firm and unconquerable belief that there is reason in history. | |
| From: Georg W.F.Hegel (Introduction to the Philosophy of History [1840], 2) | |
| A reaction: This is a ridiculous but hugely influential idea, and I have no idea what makes Hegel believe it. It is the Stoic idea that nature is intrinsically rational, but extending it to human history is absurd. Human exceptionalism. Needs a dose of Darwin. |