22 ideas
| 2922 | All intelligent Romans were Epicureans [Nietzsche] |
| Full Idea: Every mind of any account in the Roman Empire was an Epicurean. | |
| From: Friedrich Nietzsche (The Anti-Christ [1889], 58) |
| 10041 | Impredicative Definitions refer to the totality to which the object itself belongs [Gödel] |
| Full Idea: Impredicative Definitions are definitions of an object by reference to the totality to which the object itself (and perhaps also things definable only in terms of that object) belong. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], n 13) |
| 23520 | Truth has had to be fought for, and normal life must be sacrificed to achieve it [Nietzsche] |
| Full Idea: Truth has had to be fought for every step of the way, almost everything else dear to our hearts, on which our love and our trust in life depend, has had to be sacrificed to it. | |
| From: Friedrich Nietzsche (The Anti-Christ [1889], 50) | |
| A reaction: This, in one of his final works, seems to contradict every idea that Nietzsche is the high priest of relativism about truth. He (and Foucault) and interested in the social role of truth, but are not so daft as to reject its possibility. |
| 2914 | One must never ask whether truth is useful [Nietzsche] |
| Full Idea: One must never ask whether truth is useful. | |
| From: Friedrich Nietzsche (The Anti-Christ [1889], Fore) |
| 21716 | In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B] |
| Full Idea: In the superior realist and simple theory of types, the place of the axiom of reducibility is not taken by the axiom of classes, Zermelo's Aussonderungsaxiom. | |
| From: report of Kurt Gödel (Russell's Mathematical Logic [1944], p.140-1) by Bernard Linsky - Russell's Metaphysical Logic 6.1 n3 | |
| A reaction: This is Zermelo's Axiom of Separation, but that too is not an axiom of standard ZFC. |
| 10035 | Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel] |
| Full Idea: 'Mathematical Logic' is a precise and complete formulation of formal logic, and is both a section of mathematics covering classes, relations, symbols etc, and also a science prior to all others, with ideas and principles underlying all sciences. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], p.447) | |
| A reaction: He cites Leibniz as the ancestor. In this database it is referred to as 'theory of logic', as 'mathematical' seems to be simply misleading. The principles of the subject are standardly applied to mathematical themes. |
| 10042 | Reference to a totality need not refer to a conjunction of all its elements [Gödel] |
| Full Idea: One may, on good grounds, deny that reference to a totality necessarily implies reference to all single elements of it or, in other words, that 'all' means the same as an infinite logical conjunction. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], p.455) |
| 10038 | A logical system needs a syntactical survey of all possible expressions [Gödel] |
| Full Idea: In order to be sure that new expression can be translated into expressions not containing them, it is necessary to have a survey of all possible expressions, and this can be furnished only by syntactical considerations. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], p.448) | |
| A reaction: [compressed] |
| 10046 | The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel] |
| Full Idea: The generalized Continuum Hypothesis says that there exists no cardinal number between the power of any arbitrary set and the power of the set of its subsets. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], p.464) |
| 10039 | Some arithmetical problems require assumptions which transcend arithmetic [Gödel] |
| Full Idea: It has turned out that the solution of certain arithmetical problems requires the use of assumptions essentially transcending arithmetic. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], p.449) | |
| A reaction: A nice statement of the famous result, from the great man himself, in the plainest possible English. |
| 10043 | Mathematical objects are as essential as physical objects are for perception [Gödel] |
| Full Idea: Classes and concepts may be conceived of as real objects, ..and are as necessary to obtain a satisfactory system of mathematics as physical bodies are necessary for a satisfactory theory of our sense perceptions, with neither case being about 'data'. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], p.456) | |
| A reaction: Note that while he thinks real objects are essential for mathematics, be may not be claiming the same thing for our knowledge of logic. If logic contains no objects, then how could mathematics be reduced to it, as in logicism? |
| 10045 | Impredicative definitions are admitted into ordinary mathematics [Gödel] |
| Full Idea: Impredicative definitions are admitted into ordinary mathematics. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], p.464) | |
| A reaction: The issue is at what point in building an account of the foundations of mathematics (if there be such, see Putnam) these impure definitions should be ruled out. |
| 2921 | Philosophy grasps the limits of human reason, and values are beyond it [Nietzsche] |
| Full Idea: All the supreme problems of value are beyond human reason. To grasp the limits of human reason, only this is philosophy. | |
| From: Friedrich Nietzsche (The Anti-Christ [1889], 55) | |
| A reaction: The single most powerful idea in the writings of Nietzsche. Reason and truth are values. Why do we value philosophy? There is no escaping Nietzsche's question. |
| 20138 | Christianity is at war with the higher type of man, and excommunicates his basic instincts [Nietzsche] |
| Full Idea: Christianity has waged a war to the death against the higher type of man, it has excommunicated all the fundamental instincts of this type. | |
| From: Friedrich Nietzsche (The Anti-Christ [1889], 05) | |
| A reaction: It seems rather insulting to say that the finest and most dedicated altruism practised by the most admirable Christians is the expression of a 'lower' instinct. |
| 4375 | Evaluations are not disguised emotions; instead, emotion is a type of evaluation [Achtenberg] |
| Full Idea: The emotivist gets things backwards: evaluations are not disguised emotions; instead, emotions are types of evaluation. | |
| From: Deborah Achtenberg (Cognition of Value in Aristotle's Ethics [2002], 6.1) | |
| A reaction: A nice comment, though a bit optimistic. It is certainly a valuable corrective to emotivist to pin down the cognitive and evaluative aspects of emotion, rather than regarding them as 'raw' feelings. |
| 20375 | Virtues must be highly personal; if not, it is merely respect for a concept [Nietzsche] |
| Full Idea: A virtue has to be our invention, our most personal defence and necessity: in any other sense it is merely a danger. What does not condition our life harms it: a virtue merely from a feeling of respect for the concept 'virtue', as Kant desires it, is harm | |
| From: Friedrich Nietzsche (The Anti-Christ [1889], §11) | |
| A reaction: Presumably he sees virtue as the cutting edge of stiffling conventional morality. I'm a bit nervous about embracing highly personal virtues, partly because they might isolate me from my community. I ain't no übermensch. |
| 2915 | Each person should devise his own virtues and categorical imperative [Nietzsche] |
| Full Idea: Each one of us should devise his own virtue, his own categorical imperative. | |
| From: Friedrich Nietzsche (The Anti-Christ [1889], 11) |
| 2920 | A God who cures us of a head cold at the right moment is a total absurdity [Nietzsche] |
| Full Idea: A God who cures a headcold for us at the right moment is so absurd a God he would have to be abolished even if he existed. | |
| From: Friedrich Nietzsche (The Anti-Christ [1889], 52) |
| 2917 | Christianity is a revolt of things crawling on the ground against elevated things [Nietzsche] |
| Full Idea: Christianity is a revolt of everything which crawls along the ground against everything which is elevated. | |
| From: Friedrich Nietzsche (The Anti-Christ [1889], 43) |
| 2918 | The story in Genesis is the story of God's fear of science [Nietzsche] |
| Full Idea: Has the famous story which stands at the beginning of the Bible really been understood - the story of God's mortal terror of science? | |
| From: Friedrich Nietzsche (The Anti-Christ [1889], 48) |
| 2919 | 'Faith' means not wanting to know what is true [Nietzsche] |
| Full Idea: 'Faith' means not wanting to know what is true. | |
| From: Friedrich Nietzsche (The Anti-Christ [1889], 52) |
| 2916 | The great lie of immortality destroys rationality and natural instinct [Nietzsche] |
| Full Idea: The great lie of personal immortality destroys all rationality, all naturalness of instinct. | |
| From: Friedrich Nietzsche (The Anti-Christ [1889], 43) |