14 ideas
| 8988 | Two marxist ideas have dominated in France: base and superstructure, and ideology [Scruton] |
| Full Idea: Two tenets of classical Marxism have played a decisive role in French culture during our century: the theory of base and superstructure, and the concept of ideology. | |
| From: Roger Scruton (Upon Nothing: Swansea lecture [1993], p.7) | |
| A reaction: It is striking how marxist attitudes permeate even the least political of French philosophical writings, to the point where you wonder if they are even aware of it any more. They largely have marxism and reaction, with liberalism passing them by. |
| 8987 | On the surface of deconstructive writing, technicalities float and then drift away [Scruton] |
| Full Idea: Deconstructive writing has a peculiar surface, in which technicalities float on the syntactic flood and vanish unexplained downstream. | |
| From: Roger Scruton (Upon Nothing: Swansea lecture [1993], p.2) | |
| A reaction: Not even the greatest fans of deconstruction can deny this, and Derrida more or less admits it. At first glance it certainly looks more like the ancient idea of rhetoric than it looks anything like dialectic. |
| 8992 | Deconstruction is the last spasm of romanticism, now become hopeless and destructive [Scruton] |
| Full Idea: The subversive patterns of thought in deconstruction are a last spasm of romanticism: one that has given up hope of an otherworldly redemption, and set out instead to destroy the illusions in which other still believe, the source of their power. | |
| From: Roger Scruton (Upon Nothing: Swansea lecture [1993], p.29) | |
| A reaction: It seems to be strongly connected with the failure of marxism in Europe, but it also seems to inherit all the values of the Dada movement. |
| 23445 | Naïve set theory says any formula defines a set, and coextensive sets are identical [Linnebo] |
| Full Idea: Naïve set theory is based on the principles that any formula defines a set, and that coextensive sets are identical. | |
| From: Øystein Linnebo (Philosophy of Mathematics [2017], 4.2) | |
| A reaction: The second principle is a standard axiom of ZFC. The first principle causes the trouble. |
| 23447 | In classical semantics singular terms refer, and quantifiers range over domains [Linnebo] |
| Full Idea: In classical semantics the function of singular terms is to refer, and that of quantifiers, to range over appropriate domains of entities. | |
| From: Øystein Linnebo (Philosophy of Mathematics [2017], 7.1) |
| 23443 | The axioms of group theory are not assertions, but a definition of a structure [Linnebo] |
| Full Idea: Considered in isolation, the axioms of group theory are not assertions but comprise an implicit definition of some abstract structure, | |
| From: Øystein Linnebo (Philosophy of Mathematics [2017], 3.5) | |
| A reaction: The traditional Euclidean approach is that axioms are plausible assertions with which to start. The present idea sums up the modern approach. In the modern version you can work backwards from a structure to a set of axioms. |
| 23444 | To investigate axiomatic theories, mathematics needs its own foundational axioms [Linnebo] |
| Full Idea: Mathematics investigates the deductive consequences of axiomatic theories, but it also needs its own foundational axioms in order to provide models for its various axiomatic theories. | |
| From: Øystein Linnebo (Philosophy of Mathematics [2017], 4.1) | |
| A reaction: This is a problem which faces the deductivist (if-then) approach. The deductive process needs its own grounds. |
| 13007 | Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz] |
| Full Idea: Archimedes gave a sort of definition of 'straight line' when he said it is the shortest line between two points. | |
| From: report of Archimedes (fragments/reports [c.240 BCE]) by Gottfried Leibniz - New Essays on Human Understanding 4.13 | |
| A reaction: Commentators observe that this reduces the purity of the original Euclidean axioms, because it involves distance and measurement, which are absent from the purest geometry. |
| 23446 | You can't prove consistency using a weaker theory, but you can use a consistent theory [Linnebo] |
| Full Idea: If the 2nd Incompleteness Theorem undermines Hilbert's attempt to use a weak theory to prove the consistency of a strong one, it is still possible to prove the consistency of one theory, assuming the consistency of another theory. | |
| From: Øystein Linnebo (Philosophy of Mathematics [2017], 4.6) | |
| A reaction: Note that this concerns consistency, not completeness. |
| 23448 | Mathematics is the study of all possible patterns, and is thus bound to describe the world [Linnebo] |
| Full Idea: Philosophical structuralism holds that mathematics is the study of abstract structures, or 'patterns'. If mathematics is the study of all possible patterns, then it is inevitable that the world is described by mathematics. | |
| From: Øystein Linnebo (Philosophy of Mathematics [2017], 11.1) | |
| A reaction: [He cites the physicist John Barrow (2010) for this] For me this is a major idea, because the concept of a pattern gives a link between the natural physical world and the abstract world of mathematics. No platonism is needed. |
| 23441 | Logical truth is true in all models, so mathematical objects can't be purely logical [Linnebo] |
| Full Idea: Modern logic requires that logical truths be true in all models, including ones devoid of any mathematical objects. It follows immediately that the existence of mathematical objects can never be a matter of logic alone. | |
| From: Øystein Linnebo (Philosophy of Mathematics [2017], 2) | |
| A reaction: Hm. Could there not be a complete set of models for a theory which all included mathematical objects? (I can't answer that). |
| 23442 | Game Formalism has no semantics, and Term Formalism reduces the semantics [Linnebo] |
| Full Idea: Game Formalism seeks to banish all semantics from mathematics, and Term Formalism seeks to reduce any such notions to purely syntactic ones. | |
| From: Øystein Linnebo (Philosophy of Mathematics [2017], 3.3) | |
| A reaction: This approach was stimulated by the need to justify the existence of the imaginary number i. Just say it is a letter! |
| 8989 | The benefits of social freedom outweigh the loneliness, doubt and alienation it brings [Scruton] |
| Full Idea: While the goods of freedom, such as rights, property, education and prosperity, can be obtained only at a price - the price of loneliness, doubt and alienation - it is a price worth paying. | |
| From: Roger Scruton (Upon Nothing: Swansea lecture [1993]) | |
| A reaction: A striking way for a liberal-conservative to confront the accusations of the marxists - by conceding a lot of their criticisms, but living with them. I still don't see why we shouldn't aspire to have both. |
| 8990 | So-called 'liberation' is the enemy of freedom, destroying the very structures that are needed [Scruton] |
| Full Idea: The promise of 'liberation' has always been the enemy of freedom - in 1968 as much as in 1789 and 1917. Its first desire, and its only policy, is to destroy the institutions and traditions (the 'structures') which make freedom durable. | |
| From: Roger Scruton (Upon Nothing: Swansea lecture [1993], p.9) | |
| A reaction: There is a dilemma, though, if your legal system is corrupt. Far too many political attitudes are formed because of high-profile spectacular cases, instead of looking at daily routines. The latter might make a corrupt legal system still worth saving. |