120 ideas
| 7170 | 'Wisdom' attempts to get beyond perspectives, making it hostile to life [Nietzsche] |
| 7167 | Words such as 'I' and 'do' and 'done to' are placed at the point where our ignorance begins [Nietzsche] |
| 7196 | Pessimism is laughable, because the world cannot be evaluated [Nietzsche] |
| 7137 | Is a 'philosopher' now impossible, because knowledge is too vast for an overview? [Nietzsche] |
| 7132 | Philosophers should create and fight for their concepts, not just clean and clarify them [Nietzsche] |
| 8721 | An 'impredicative' definition seems circular, because it uses the term being defined [Friend] |
| 8680 | Classical definitions attempt to refer, but intuitionist/constructivist definitions actually create objects [Friend] |
| 3678 | Reductio ad absurdum proves an idea by showing that its denial produces contradiction [Friend] |
| 8705 | Anti-realists see truth as our servant, and epistemically contrained [Friend] |
| 8713 | In classical/realist logic the connectives are defined by truth-tables [Friend] |
| 8708 | Double negation elimination is not valid in intuitionist logic [Friend] |
| 8694 | Free logic was developed for fictional or non-existent objects [Friend] |
| 8665 | A 'proper subset' of A contains only members of A, but not all of them [Friend] |
| 8672 | A 'powerset' is all the subsets of a set [Friend] |
| 8677 | Set theory makes a minimum ontological claim, that the empty set exists [Friend] |
| 8666 | Infinite sets correspond one-to-one with a subset [Friend] |
| 8682 | Major set theories differ in their axioms, and also over the additional axioms of choice and infinity [Friend] |
| 7188 | Logic tries to understand the world according to a man-made scheme [Nietzsche] |
| 7145 | Logic is not driven by truth, but desire for a simple single viewpoint [Nietzsche] |
| 7144 | Logic must falsely assume that identical cases exist [Nietzsche] |
| 8709 | The law of excluded middle is syntactic; it just says A or not-A, not whether they are true or false [Friend] |
| 8711 | Intuitionists read the universal quantifier as "we have a procedure for checking every..." [Friend] |
| 8675 | Paradoxes can be solved by talking more loosely of 'classes' instead of 'sets' [Friend] |
| 8674 | The Burali-Forti paradox asks whether the set of all ordinals is itself an ordinal [Friend] |
| 8667 | The 'integers' are the positive and negative natural numbers, plus zero [Friend] |
| 8668 | The 'rational' numbers are those representable as fractions [Friend] |
| 8670 | A number is 'irrational' if it cannot be represented as a fraction [Friend] |
| 8661 | The natural numbers are primitive, and the ordinals are up one level of abstraction [Friend] |
| 8664 | Cardinal numbers answer 'how many?', with the order being irrelevant [Friend] |
| 8671 | The 'real' numbers (rationals and irrationals combined) is the Continuum, which has no gaps [Friend] |
| 8663 | Raising omega to successive powers of omega reveal an infinity of infinities [Friend] |
| 8662 | The first limit ordinal is omega (greater, but without predecessor), and the second is twice-omega [Friend] |
| 8669 | Between any two rational numbers there is an infinite number of rational numbers [Friend] |
| 8676 | Is mathematics based on sets, types, categories, models or topology? [Friend] |
| 8678 | Most mathematical theories can be translated into the language of set theory [Friend] |
| 8701 | The number 8 in isolation from the other numbers is of no interest [Friend] |
| 8702 | In structuralism the number 8 is not quite the same in different structures, only equivalent [Friend] |
| 8699 | Are structures 'ante rem' (before reality), or are they 'in re' (grounded in physics)? [Friend] |
| 8696 | Structuralist says maths concerns concepts about base objects, not base objects themselves [Friend] |
| 8695 | Structuralism focuses on relations, predicates and functions, with objects being inessential [Friend] |
| 8700 | 'In re' structuralism says that the process of abstraction is pattern-spotting [Friend] |
| 8681 | The big problem for platonists is epistemic: how do we perceive, intuit, know or detect mathematical facts? [Friend] |
| 8712 | Mathematics should be treated as true whenever it is indispensable to our best physical theory [Friend] |
| 8716 | Formalism is unconstrained, so cannot indicate importance, or directions for research [Friend] |
| 8706 | Constructivism rejects too much mathematics [Friend] |
| 8707 | Intuitionists typically retain bivalence but reject the law of excluded middle [Friend] |
| 7153 | We can't be realists, because we don't know what being is [Nietzsche] |
| 7174 | Categories are not metaphysical truths, but inventions in the service of needs [Nietzsche] |
| 7175 | Philosophers find it particularly hard to shake off belief in necessary categories [Nietzsche] |
| 8704 | Structuralists call a mathematical 'object' simply a 'place in a structure' [Friend] |
| 7189 | Maybe there are only subjects, and 'objects' result from relations between subjects [Nietzsche] |
| 7207 | Counting needs unities, but that doesn't mean they exist; we borrowed it from the concept of 'I' [Nietzsche] |
| 7161 | The essence of a thing is only an opinion about the 'thing' [Nietzsche] |
| 7134 | Something can be irrefutable; that doesn't make it true [Nietzsche] |
| 7186 | There are no necessary truths, but something must be held to be true [Nietzsche] |
| 7154 | We can't use our own self to criticise our own capacity for knowledge! [Nietzsche] |
| 7146 | Belief in the body is better established than belief in the mind [Nietzsche] |
| 7156 | Sense perceptions contain values (useful, so pleasant) [Nietzsche] |
| 7181 | Pain shows the value of the damage, not what has been damaged [Nietzsche] |
| 7129 | Perception is unconscious, and we are only conscious of processed perceptions [Nietzsche] |
| 7149 | Comprehending everything is impossible, because it abolishes perspectives [Nietzsche] |
| 7169 | Is the perspectival part of the essence, or just a relation between beings? [Nietzsche] |
| 7182 | 'Perspectivism': the world has no meaning, but various interpretations give it countless meanings [Nietzsche] |
| 7183 | 'Subjectivity' is an interpretation, since subjects (and interpreters) are fictions [Nietzsche] |
| 7133 | There are different eyes, so different 'truths', so there is no truth [Nietzsche] |
| 7139 | Explanation is just showing the succession of things ever more clearly [Nietzsche] |
| 7131 | The intellect and senses are a simplifying apparatus [Nietzsche] |
| 5960 | When the soul is intelligent and harmonious, it is part of god and derives from god [Plutarch] |
| 7152 | With protoplasm ½+½=2, so the soul is not an indivisible monad [Nietzsche] |
| 7130 | Unity is not in the conscious 'I', but in the organism, which uses the self as a tool [Nietzsche] |
| 7155 | Consciousness exists to the extent that consciousness is useful [Nietzsche] |
| 7143 | Consciousness is a 'tool' - just as the stomach is a tool [Nietzsche] |
| 7157 | We think each thought causes the next, unaware of the hidden struggle beneath [Nietzsche] |
| 7148 | The 'I' is a conceptual synthesis, not the governor of our being [Nietzsche] |
| 7138 | The 'I' is a fiction used to make the world of becoming 'knowable' [Nietzsche] |
| 7135 | 'Freedom of will' is the feeling of having a dominating force [Nietzsche] |
| 8685 | Studying biology presumes the laws of chemistry, and it could never contradict them [Friend] |
| 7171 | Rationality is a scheme we cannot cast away [Nietzsche] |
| 8688 | Concepts can be presented extensionally (as objects) or intensionally (as a characterization) [Friend] |
| 7209 | There is no will; weakness of will is splitting of impulses, strong will is coordination under one impulse [Nietzsche] |
| 7194 | Experiencing a thing as beautiful is to experience it wrongly [Nietzsche] |
| 7136 | Morality is a system of values which accompanies a being's life [Nietzsche] |
| 7163 | Morality is merely interpretations, which are extra-moral in origin [Nietzsche] |
| 7147 | Values are innate and inherited [Nietzsche] |
| 7190 | Our values express an earlier era's conditions for survival and growth [Nietzsche] |
| 7201 | Knowledge, wisdom and goodness only have value relative to a goal [Nietzsche] |
| 7205 | Altruism is praised by the egoism of the weak, who want everyone to be looked after [Nietzsche] |
| 7141 | A living being is totally 'egoistic' [Nietzsche] |
| 7168 | Modest people express happiness as 'Not bad' [Nietzsche] |
| 7159 | The only happiness is happiness with illusion [Nietzsche] |
| 7197 | Pleasure needs dissatisfaction, boundaries and resistances [Nietzsche] |
| 7165 | Virtue is wasteful, as it reduces us all to being one another's nurse [Nietzsche] |
| 7193 | Virtue for everyone removes its charm of being exceptional and aristocratic [Nietzsche] |
| 7191 | What does not kill us makes us stronger [Nietzsche] |
| 7151 | Courage, compassion, insight, solitude are the virtues, with courtesy a necessary vice [Nietzsche] |
| 7185 | Replace the categorical imperative by the natural imperative [Nietzsche] |
| 7164 | Not feeling harnessed to a system of 'ends' is a wonderful feeling of freedom [Nietzsche] |
| 7198 | Nihilism results from measuring the world by our categories which are purely invented [Nietzsche] |
| 7150 | By developing herd virtues man fixes what has up to now been the 'unfixed animal' [Nietzsche] |
| 7177 | Virtues from outside are dangerous, and they should come from within [Nietzsche] |
| 7172 | Existence without meaning or goal or end, eternally recurring, is a terrible thought [Nietzsche] |
| 7166 | Man is above all a judging animal [Nietzsche] |
| 7204 | The upholding of the military state is needed to maintain the strong human type [Nietzsche] |
| 7173 | Rights arise out of contracts, which need a balance of power [Nietzsche] |
| 7176 | 'Purpose' is like the sun, where most heat is wasted, and a tiny part has 'purpose' [Nietzsche] |
| 7195 | If the world aimed at an end, it would have reached it by now [Nietzsche] |
| 7206 | Things are strong or weak, and do not behave regularly or according to rules or compulsions [Nietzsche] |
| 7140 | Chemical 'laws' are merely the establishment of power relations between weaker and stronger [Nietzsche] |
| 7142 | All motions and 'laws' are symptoms of inner events, traceable to the will to power [Nietzsche] |
| 7178 | The utility of an organ does not explain its origin, on the contrary! [Nietzsche] |
| 7179 | Survival might undermine an individual's value, or prevent its evolution [Nietzsche] |
| 7180 | Darwin overestimates the influence of 'external circumstances' [Nietzsche] |
| 7192 | Remove goodness and wisdom from our concept of God. Being the highest power is enough! [Nietzsche] |
| 7158 | Morality kills religion, because a Christian-moral God is unbelievable [Nietzsche] |
| 7199 | It is dishonest to invent a being containing our greatest values, thus ignoring why they exist and are valuable [Nietzsche] |
| 7162 | Morality can only be upheld by belief in God and a 'hereafter' [Nietzsche] |
| 7208 | Paganism is a form of thanking and affirming life? [Nietzsche] |
| 7160 | Christian belief is kept alive because it is soothing - the proof based on pleasure [Nietzsche] |
| 7203 | In heaven all the interesting men are missing [Nietzsche] |
| 7200 | A combination of great power and goodness would mean the disastrous abolition of evil [Nietzsche] |