93 ideas
| 8013 | In the Reformation, morality became unconditional but irrational, individually autonomous, and secular [MacIntyre] |
| 8021 | The Levellers and the Diggers mark a turning point in the history of morality [MacIntyre] |
| 2056 | Philosophers are always switching direction to something more interesting [Plato] |
| 2086 | Understanding mainly involves knowing the elements, not their combinations [Plato] |
| 2083 | Either a syllable is its letters (making parts as knowable as whole) or it isn't (meaning it has no parts) [Plato] |
| 2082 | A rational account is essentially a weaving together of things with names [Plato] |
| 2052 | Eristic discussion is aggressive, but dialectic aims to help one's companions in discussion [Plato] |
| 15854 | A primary element has only a name, and no logos, but complexes have an account, by weaving the names [Plato] |
| 18137 | Impredicative definitions are wrong, because they change the set that is being defined? [Bostock] |
| 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] |
| 10216 | We master arithmetic by knowing all the numbers in our soul [Plato] |
| 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] |
| 2060 | There seem to be two sorts of change: alteration and motion [Plato] |
| 2084 | If a word has no parts and has a single identity, it turns out to be the same kind of thing as a letter [Plato] |
| 15844 | A sum is that from which nothing is lacking, which is a whole [Plato] |
| 15843 | The whole can't be the parts, because it would be all of the parts, which is the whole [Plato] |
| 2080 | Things are only knowable if a rational account (logos) is possible [Plato] |
| 16126 | Expertise is knowledge of the whole by means of the parts [Plato] |
| 2050 | It is impossible to believe something which is held to be false [Plato] |
| 2076 | How can a belief exist if its object doesn't exist? [Plato] |
| 2045 | Perception is infallible, suggesting that it is knowledge [Plato] |
| 2067 | Our senses could have been separate, but they converge on one mind [Plato] |
| 2068 | With what physical faculty do we perceive pairs of opposed abstract qualities? [Plato] |
| 2078 | You might mistake eleven for twelve in your senses, but not in your mind [Plato] |
| 2069 | Thought must grasp being itself before truth becomes possible [Plato] |
| 2089 | An inadequate rational account would still not justify knowledge [Plato] |
| 2085 | Parts and wholes are either equally knowable or equally unknowable [Plato] |
| 2091 | Without distinguishing marks, how do I know what my beliefs are about? [Plato] |
| 2087 | A rational account might be seeing an image of one's belief, like a reflection in a mirror [Plato] |
| 2090 | A rational account involves giving an image, or analysis, or giving a differentiating mark [Plato] |
| 2081 | Maybe primary elements can be named, but not receive a rational account [Plato] |
| 2088 | A rational account of a wagon would mean knowledge of its hundred parts [Plato] |
| 2047 | What evidence can be brought to show whether we are dreaming or not? [Plato] |
| 2053 | If you claim that all beliefs are true, that includes beliefs opposed to your own [Plato] |
| 2059 | How can a relativist form opinions about what will happen in the future? [Plato] |
| 2054 | Clearly some people are superior to others when it comes to medicine [Plato] |
| 8006 | When Aristotle speaks of soul he means something like personality [MacIntyre] |
| 18121 | In logic a proposition means the same when it is and when it is not asserted [Bostock] |
| 8002 | Sophists don't distinguish a person outside one social order from someone outside all order [MacIntyre] |
| 8012 | The value/fact logical gulf is misleading, because social facts involve values [MacIntyre] |
| 8005 | 'Happiness' is a bad translation of 'eudaimonia', which includes both behaving and faring well [MacIntyre] |
| 8001 | 'Dikaiosune' is justice, but also fairness and personal integrity [MacIntyre] |
| 8023 | My duties depend on my identity, which depends on my social relations [MacIntyre] |
| 8022 | I am naturally free if I am not tied to anyone by a contract [MacIntyre] |
| 8031 | Fans of natural rights or laws can't agree on what the actual rights or laws are [MacIntyre] |
| 2058 | God must be the epitome of goodness, and we can only approach a divine state by being as good as possible [Plato] |
| 8008 | The Bible is a story about God in which humans are incidental characters [MacIntyre] |
| 2057 | There must always be some force of evil ranged against good [Plato] |