71 ideas
| 2056 | Philosophers are always switching direction to something more interesting [Plato] |
| 24032 | Clever scholars can obscure things which are obvious even to peasants [Descartes] |
| 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] |
| 24033 | Most scholastic disputes concern words, where agreeing on meanings would settle them [Descartes] |
| 24024 | The secret of the method is to recognise which thing in a series is the simplest [Descartes] |
| 24018 | One truth leads us to another [Descartes] |
| 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] |
| 17749 | Post proved the consistency of propositional logic in 1921 [Walicki] |
| 17765 | Propositional language can only relate statements as the same or as different [Walicki] |
| 17764 | Boolean connectives are interpreted as functions on the set {1,0} [Walicki] |
| 17752 | The empty set is useful for defining sets by properties, when the members are not yet known [Walicki] |
| 17753 | The empty set avoids having to take special precautions in case members vanish [Walicki] |
| 17759 | Ordinals play the central role in set theory, providing the model of well-ordering [Walicki] |
| 17741 | To determine the patterns in logic, one must identify its 'building blocks' [Walicki] |
| 17747 | A 'model' of a theory specifies interpreting a language in a domain to make all theorems true [Walicki] |
| 17748 | The L-S Theorem says no theory (even of reals) says more than a natural number theory [Walicki] |
| 17763 | Axiomatic systems are purely syntactic, and do not presuppose any interpretation [Walicki] |
| 17761 | A compact axiomatisation makes it possible to understand a field as a whole [Walicki] |
| 17757 | Members of ordinals are ordinals, and also subsets of ordinals [Walicki] |
| 17758 | Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion [Walicki] |
| 17755 | Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals [Walicki] |
| 17756 | The union of finite ordinals is the first 'limit ordinal'; 2ω is the second... [Walicki] |
| 17760 | Two infinite ordinals can represent a single infinite cardinal [Walicki] |
| 24036 | I can only see the proportion of two to three if there is a common measure - their unity [Descartes] |
| 24035 | Unity is something shared by many things, so in that respect they are equals [Descartes] |
| 17762 | In non-Euclidean geometry, all Euclidean theorems are valid that avoid the fifth postulate [Walicki] |
| 17754 | Inductive proof depends on the choice of the ordering [Walicki] |
| 10216 | We master arithmetic by knowing all the numbers in our soul [Plato] |
| 24029 | Among the simples are the graspable negations, such as rest and instants [Descartes] |
| 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] |
| 17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
| 24030 | 3+4=7 is necessary because we cannot conceive of seven without including three and four [Descartes] |
| 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] |
| 24019 | If we accept mere probabilities as true we undermine our existing knowledge [Descartes] |
| 24020 | We all see intuitively that we exist, where intuition is attentive, clear and distinct rational understanding [Descartes] |
| 24031 | When Socrates doubts, he know he doubts, and that truth is possible [Descartes] |
| 24025 | Clear and distinct truths must be known all at once (unlike deductions) [Descartes] |
| 24022 | Our souls possess divine seeds of knowledge, which can bear spontaneous fruit [Descartes] |
| 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] |
| 2069 | Thought must grasp being itself before truth becomes possible [Plato] |
| 2078 | You might mistake eleven for twelve in your senses, but not in your mind [Plato] |
| 24034 | If someone had only seen the basic colours, they could deduce the others from resemblance [Descartes] |
| 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] |
| 24021 | The method starts with clear intuitions, followed by a process of deduction [Descartes] |
| 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] |
| 2054 | Clearly some people are superior to others when it comes to medicine [Plato] |
| 2059 | How can a relativist form opinions about what will happen in the future? [Plato] |
| 24027 | Nerves and movement originate in the brain, where imagination moves them [Descartes] |
| 24026 | Our four knowledge faculties are intelligence, imagination, the senses, and memory [Descartes] |
| 24028 | The force by which we know things is spiritual, and quite distinct from the body [Descartes] |
| 24023 | All the sciences searching for order and measure are related to mathematics [Descartes] |
| 2058 | God must be the epitome of goodness, and we can only approach a divine state by being as good as possible [Plato] |
| 2057 | There must always be some force of evil ranged against good [Plato] |