127 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] |
10073 | There cannot be a set theory which is complete [Smith,P] |
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] |
10616 | Second-order arithmetic can prove new sentences of first-order [Smith,P] |
10075 | A 'partial function' maps only some elements to another set [Smith,P] |
10074 | A 'total function' maps every element to one element in another set [Smith,P] |
10612 | An argument is a 'fixed point' for a function if it is mapped back to itself [Smith,P] |
10076 | The 'range' of a function is the set of elements in the output set created by the function [Smith,P] |
10605 | Two functions are the same if they have the same extension [Smith,P] |
10615 | The Comprehension Schema says there is a property only had by things satisfying a condition [Smith,P] |
10595 | A 'theorem' of a theory is a sentence derived from the axioms using the proof system [Smith,P] |
10602 | A 'natural deduction system' has no axioms but many rules [Smith,P] |
10613 | No nice theory can define truth for its own language [Smith,P] |
10078 | An 'injective' ('one-to-one') function creates a distinct output element from each original [Smith,P] |
10077 | A 'surjective' ('onto') function creates every element of the output set [Smith,P] |
10079 | A 'bijective' function has one-to-one correspondence in both directions [Smith,P] |
10070 | If everything that a theory proves is true, then it is 'sound' [Smith,P] |
10086 | Soundness is true axioms and a truth-preserving proof system [Smith,P] |
10596 | A theory is 'sound' iff every theorem is true (usually from true axioms and truth-preservation) [Smith,P] |
10598 | A theory is 'negation complete' if it proves all sentences or their negation [Smith,P] |
10597 | 'Complete' applies both to whole logics, and to theories within them [Smith,P] |
10069 | A theory is 'negation complete' if one of its sentences or its negation can always be proved [Smith,P] |
10609 | Two routes to Incompleteness: semantics of sound/expressible, or syntax of consistency/proof [Smith,P] |
10080 | 'Effective' means simple, unintuitive, independent, controlled, dumb, and terminating [Smith,P] |
10087 | A theory is 'decidable' if all of its sentences could be mechanically proved [Smith,P] |
10088 | Any consistent, axiomatized, negation-complete formal theory is decidable [Smith,P] |
10081 | A set is 'enumerable' is all of its elements can result from a natural number function [Smith,P] |
10083 | A set is 'effectively enumerable' if a computer could eventually list every member [Smith,P] |
10084 | A finite set of finitely specifiable objects is always effectively enumerable (e.g. primes) [Smith,P] |
10085 | The set of ordered pairs of natural numbers <i,j> is effectively enumerable [Smith,P] |
10601 | The thorems of a nice arithmetic can be enumerated, but not the truths (so they're diffferent) [Smith,P] |
10600 | Being 'expressible' depends on language; being 'capture/represented' depends on axioms and proof system [Smith,P] |
10599 | For primes we write (x not= 1 ∧ ∀u∀v(u x v = x → (u = 1 ∨ v = 1))) [Smith,P] |
10610 | The reals contain the naturals, but the theory of reals doesn't contain the theory of naturals [Smith,P] |
10619 | The truths of arithmetic are just true equations and their universally quantified versions [Smith,P] |
10618 | All numbers are related to zero by the ancestral of the successor relation [Smith,P] |
10608 | The number of Fs is the 'successor' of the Gs if there is a single F that isn't G [Smith,P] |
10849 | Baby arithmetic covers addition and multiplication, but no general facts about numbers [Smith,P] |
10850 | Baby Arithmetic is complete, but not very expressive [Smith,P] |
10851 | Robinson Arithmetic 'Q' has basic axioms, quantifiers and first-order logic [Smith,P] |
10852 | Robinson Arithmetic (Q) is not negation complete [Smith,P] |
10068 | Natural numbers have zero, unique successors, unending, no circling back, and no strays [Smith,P] |
10603 | The logic of arithmetic must quantify over properties of numbers to handle induction [Smith,P] |
10848 | Multiplication only generates incompleteness if combined with addition and successor [Smith,P] |
10604 | Incompleteness results in arithmetic from combining addition and successor with multiplication [Smith,P] |
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] |
10617 | The 'ancestral' of a relation is a new relation which creates a long chain of the original relation [Smith,P] |
13795 | Properties only have identity in the context of their contraries [Elder] |
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] |
13798 | Maybe we should give up the statue [Elder] |
13797 | The loss of an essential property means the end of an existence [Elder] |
13794 | Essential properties by nature occur in clusters or packages [Elder] |
13796 | Essential properties are bound together, and would be lost together [Elder] |
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] |
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] |
7171 | Rationality is a scheme we cannot cast away [Nietzsche] |
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] |
7180 | Darwin overestimates the influence of 'external circumstances' [Nietzsche] |
7179 | Survival might undermine an individual's value, or prevent its evolution [Nietzsche] |
7178 | The utility of an organ does not explain its origin, on the contrary! [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] |