90 ideas
24084 | Seeing with other eyes is more egoism, but exploring other perspectives leads to objectivity [Nietzsche] |
18137 | Impredicative definitions are wrong, because they change the set that is being defined? [Bostock] |
24092 | I tell the truth, even if it is repulsive [Nietzsche] |
24114 | The pain in truth is when it destroys a belief [Nietzsche] |
24104 | We don't create logic, time and space! The mind obeys laws because they are true [Nietzsche] |
18122 | Classical interdefinitions of logical constants and quantifiers is impossible in intuitionism [Bostock] |
18114 | There is no single agreed structure for set theory [Bostock] |
18107 | A 'proper class' cannot be a member of anything [Bostock] |
18115 | We could add axioms to make sets either as small or as large as possible [Bostock] |
18139 | The Axiom of Choice relies on reference to sets that we are unable to describe [Bostock] |
18105 | Replacement enforces a 'limitation of size' test for the existence of sets [Bostock] |
18108 | First-order logic is not decidable: there is no test of whether any formula is valid [Bostock] |
18109 | The completeness of first-order logic implies its compactness [Bostock] |
18123 | Substitutional quantification is just standard if all objects in the domain have a name [Bostock] |
18120 | The Deduction Theorem is what licenses a system of natural deduction [Bostock] |
18125 | Berry's Paradox considers the meaning of 'The least number not named by this name' [Bostock] |
18101 | Each addition changes the ordinality but not the cardinality, prior to aleph-1 [Bostock] |
18100 | ω + 1 is a new ordinal, but its cardinality is unchanged [Bostock] |
18102 | A cardinal is the earliest ordinal that has that number of predecessors [Bostock] |
18106 | Aleph-1 is the first ordinal that exceeds aleph-0 [Bostock] |
18095 | Instead of by cuts or series convergence, real numbers could be defined by axioms [Bostock] |
18099 | The number of reals is the number of subsets of the natural numbers [Bostock] |
18093 | For Eudoxus cuts in rationals are unique, but not every cut makes a real number [Bostock] |
18110 | Infinitesimals are not actually contradictory, because they can be non-standard real numbers [Bostock] |
18156 | Modern axioms of geometry do not need the real numbers [Bostock] |
18097 | The Peano Axioms describe a unique structure [Bostock] |
18148 | Hume's Principle is a definition with existential claims, and won't explain numbers [Bostock] |
18145 | Many things will satisfy Hume's Principle, so there are many interpretations of it [Bostock] |
18149 | There are many criteria for the identity of numbers [Bostock] |
18143 | Frege makes numbers sets to solve the Caesar problem, but maybe Caesar is a set! [Bostock] |
18116 | Numbers can't be positions, if nothing decides what position a given number has [Bostock] |
18117 | Structuralism falsely assumes relations to other numbers are numbers' only properties [Bostock] |
18141 | Nominalism about mathematics is either reductionist, or fictionalist [Bostock] |
18157 | Nominalism as based on application of numbers is no good, because there are too many applications [Bostock] |
18150 | Actual measurement could never require the precision of the real numbers [Bostock] |
18158 | Ordinals are mainly used adjectively, as in 'the first', 'the second'... [Bostock] |
18127 | Simple type theory has 'levels', but ramified type theory has 'orders' [Bostock] |
18144 | Neo-logicists agree that HP introduces number, but also claim that it suffices for the job [Bostock] |
18147 | Neo-logicists meet the Caesar problem by saying Hume's Principle is unique to number [Bostock] |
18146 | If Hume's Principle is the whole story, that implies structuralism [Bostock] |
18129 | Many crucial logicist definitions are in fact impredicative [Bostock] |
18111 | Treating numbers as objects doesn't seem like logic, since arithmetic fixes their totality [Bostock] |
18159 | Higher cardinalities in sets are just fairy stories [Bostock] |
18155 | A fairy tale may give predictions, but only a true theory can give explanations [Bostock] |
18140 | The best version of conceptualism is predicativism [Bostock] |
18138 | Conceptualism fails to grasp mathematical properties, infinity, and objective truth values [Bostock] |
18131 | If abstracta only exist if they are expressible, there can only be denumerably many of them [Bostock] |
18134 | Predicativism makes theories of huge cardinals impossible [Bostock] |
18135 | If mathematics rests on science, predicativism may be the best approach [Bostock] |
18136 | If we can only think of what we can describe, predicativism may be implied [Bostock] |
18132 | The predicativity restriction makes a difference with the real numbers [Bostock] |
18133 | The usual definitions of identity and of natural numbers are impredicative [Bostock] |
24112 | To think about being we must have an opinion about what it is [Nietzsche] |
24089 | Essences are fictions needed for beings who represent things [Nietzsche] |
24115 | There is no proof that we forget things - only that we can't recall [Nietzsche] |
24090 | Our inclinations would not conflict if we were a unity; we imagine unity for our multiplicity [Nietzsche] |
24099 | We contain many minds, which fight for the 'I' of the mind [Nietzsche] |
24102 | Thoughts are signs (just as words are) [Nietzsche] |
24120 | Great orators lead their arguments, rather than following them [Nietzsche] |
18121 | In logic a proposition means the same when it is and when it is not asserted [Bostock] |
24097 | The pragmatics of language is more comprehensible than the meaning [Nietzsche] |
24108 | Actions are just a release of force. They seize on something, which becomes the purpose [Nietzsche] |
24105 | Drives make us feel non-feelings; Will is the effect of those feelings [Nietzsche] |
24117 | We need lower and higher drives, but they must be under firm control [Nietzsche] |
24113 | Our motives don't explain our actions [Nietzsche] |
24087 | People who miss beauty seek the sublime, where even the ugly shows its 'beauty' [Nietzsche] |
24091 | The sublimity of nature which dwarfs us was a human creation [Nietzsche] |
24093 | We can aspire to greatness by creating new functions for ourselves [Nietzsche] |
24121 | Greeks might see modern analysis of what is human as impious [Nietzsche] |
24107 | Once a drive controls the intellect, it rules, and sets the goals [Nietzsche] |
24085 | For absolute morality a goal for mankind is needed [Nietzsche] |
24101 | We always assign values, but we may not value those values [Nietzsche] |
24094 | Humans are vividly aware of short-term effects, and almost ignorant of the long-term ones [Nietzsche] |
24111 | Happiness is the active equilibrium of our drives [Nietzsche] |
24109 | Actual morality is more complicated and subtle than theory (which gets paralysed) [Nietzsche] |
24110 | Some things we would never do, even for the highest ideals [Nietzsche] |
24103 | You should not want too many virtues; one is enough [Nietzsche] |
7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
24106 | Talk of 'utility' presupposes that what is useful to people has been defined [Nietzsche] |
24086 | The goal is to settle human beings, like other animals, but humans are still changeable [Nietzsche] |
24123 | My eternal recurrence is opposed to feeling fragmented and imperfect [Nietzsche] |
24088 | See our present lives as eternal! Religions see it as fleeting, and aim at some different life [Nietzsche] |
24119 | The eternal return of wastefulness is a terrible thought [Nietzsche] |
24116 | Justice says people are not equal, and should become increasingly unequal [Nietzsche] |
24098 | Reasons that justify punishment can also justify the crime [Nietzsche] |
24118 | Do away with punishment. Counter-retribution is as bad as the crime [Nietzsche] |
24100 | If you don't want war, remove your borders; but you set up borders because you want war [Nietzsche] |
24095 | Our growth is too subtle to perceive, and long events are too slow for us to grasp [Nietzsche] |
24096 | Unlike time, space is subjective. Empty space was assumed, but it doesn't exist [Nietzsche] |
24122 | Life is forces conjoined by nutrition, to produce resistance, arrangement and value [Nietzsche] |