21 ideas
| 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. |
| 13838 | A decent modern definition should always imply a semantics [Hacking] |
| Full Idea: Today we expect that anything worth calling a definition should imply a semantics. | |
| From: Ian Hacking (What is Logic? [1979], §10) | |
| A reaction: He compares this with Gentzen 1935, who was attempting purely syntactic definitions of the logical connectives. |
| 22094 | Subjective truth can only be sustained by repetition [Kierkegaard, by Carlisle] |
| Full Idea: If subjective truth is to be more than momentary, it has to be repeated continually. | |
| From: report of Søren Kierkegaard (Repetition [1843]) by Clare Carlisle - Kierkegaard: a guide for the perplexed 4 | |
| A reaction: This might apply to more traditional concepts of truth, if they are to be part of life, rather than remaining in books. |
| 13833 | 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking] |
| Full Idea: 'Dilution' (or 'Thinning') provides an essential contrast between deductive and inductive reasoning; for the introduction of new premises may spoil an inductive inference. | |
| From: Ian Hacking (What is Logic? [1979], §06.2) | |
| A reaction: That is, inductive logic (if there is such a thing) is clearly non-monotonic, whereas classical inductive logic is monotonic. |
| 13834 | Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' [Hacking] |
| Full Idea: If A |- B and B |- C, then A |- C. This generalises to: If Γ|-A,Θ and Γ,A |- Θ, then Γ |- Θ. Gentzen called this 'cut'. It is the transitivity of a deduction. | |
| From: Ian Hacking (What is Logic? [1979], §06.3) | |
| A reaction: I read the generalisation as 'If A can be either a premise or a conclusion, you can bypass it'. The first version is just transitivity (which by-passes the middle step). |
| 13835 | Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with [Hacking] |
| Full Idea: Only the cut rule can have a conclusion that is less complex than its premises. Hence when cut is not used, a derivation is quite literally constructive, building up from components. Any theorem obtained by cut can be obtained without it. | |
| From: Ian Hacking (What is Logic? [1979], §08) |
| 13845 | The various logics are abstractions made from terms like 'if...then' in English [Hacking] |
| Full Idea: I don't believe English is by nature classical or intuitionistic etc. These are abstractions made by logicians. Logicians attend to numerous different objects that might be served by 'If...then', like material conditional, strict or relevant implication. | |
| From: Ian Hacking (What is Logic? [1979], §15) | |
| A reaction: The idea that they are 'abstractions' is close to my heart. Abstractions from what? Surely 'if...then' has a standard character when employed in normal conversation? |
| 13840 | First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking] |
| Full Idea: First-order logic is the strongest complete compact theory with a Löwenheim-Skolem theorem. | |
| From: Ian Hacking (What is Logic? [1979], §13) |
| 13844 | A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking] |
| Full Idea: Henkin proved that there is no first-order treatment of branching quantifiers, which do not seem to involve any idea that is fundamentally different from ordinary quantification. | |
| From: Ian Hacking (What is Logic? [1979], §13) | |
| A reaction: See Hacking for an example of branching quantifiers. Hacking is impressed by this as a real limitation of the first-order logic which he generally favours. |
| 13842 | Second-order completeness seems to need intensional entities and possible worlds [Hacking] |
| Full Idea: Second-order logic has no chance of a completeness theorem unless one ventures into intensional entities and possible worlds. | |
| From: Ian Hacking (What is Logic? [1979], §13) |
| 13837 | With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking] |
| Full Idea: My doctrine is that the peculiarity of the logical constants resides precisely in that given a certain pure notion of truth and consequence, all the desirable semantic properties of the constants are determined by their syntactic properties. | |
| From: Ian Hacking (What is Logic? [1979], §09) | |
| A reaction: He opposes this to Peacocke 1976, who claims that the logical connectives are essentially semantic in character, concerned with the preservation of truth. |
| 13839 | Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking] |
| Full Idea: For some purposes the variables of first-order logic can be regarded as prepositions and place-holders that could in principle be dispensed with, say by a system of arrows indicating what places fall in the scope of which quantifier. | |
| From: Ian Hacking (What is Logic? [1979], §11) | |
| A reaction: I tend to think of variables as either pronouns, or as definite descriptions, or as temporary names, but not as prepositions. Must address this new idea... |
| 13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
| Full Idea: A Löwenheim-Skolem theorem holds for anything which, on my delineation, is a logic. | |
| From: Ian Hacking (What is Logic? [1979], §13) | |
| A reaction: I take this to be an unusually conservative view. Shapiro is the chap who can give you an alternative view of these things, or Boolos. |
| 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. |
| 22093 | Life is a repetition when what has been now becomes [Kierkegaard] |
| Full Idea: When one says that life is a repetition one affirms that existence which has been now becomes. | |
| From: Søren Kierkegaard (Repetition [1843], p.49), quoted by Clare Carlisle - Kierkegaard: a guide for the perplexed 4 | |
| A reaction: Not sure I understand this, but it seems very close to Nietzsche's Eternal Recurrence. |
| 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. |