56 ideas
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] |
16877 | A 'constructive' (as opposed to 'analytic') definition creates a new sign [Frege] |
15854 | A primary element has only a name, and no logos, but complexes have an account, by weaving the names [Plato] |
11219 | Frege suggested that mathematics should only accept stipulative definitions [Frege, by Gupta] |
16878 | We must be clear about every premise and every law used in a proof [Frege] |
16867 | Logic not only proves things, but also reveals logical relations between them [Frege] |
16863 | Does some mathematical reasoning (such as mathematical induction) not belong to logic? [Frege] |
16862 | The closest subject to logic is mathematics, which does little apart from drawing inferences [Frege] |
21677 | How can the not-true fail to be false, or the not-false fail to be true? [Cicero] |
16865 | 'Theorems' are both proved, and used in proofs [Frege] |
16866 | Tracing inference backwards closes in on a small set of axioms and postulates [Frege] |
16868 | The essence of mathematics is the kernel of primitive truths on which it rests [Frege] |
16871 | A truth can be an axiom in one system and not in another [Frege] |
16870 | Axioms are truths which cannot be doubted, and for which no proof is needed [Frege] |
16869 | To create order in mathematics we need a full system, guided by patterns of inference [Frege] |
16864 | If principles are provable, they are theorems; if not, they are axioms [Frege] |
10216 | We master arithmetic by knowing all the numbers in our soul [Plato] |
2060 | There seem to be two sorts of change: alteration and motion [Plato] |
9388 | Every concept must have a sharp boundary; we cannot allow an indeterminate third case [Frege] |
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] |
16876 | We need definitions to cram retrievable sense into a signed receptacle [Frege] |
16875 | We use signs to mark receptacles for complex senses [Frege] |
16879 | A sign won't gain sense just from being used in sentences with familiar components [Frege] |
16873 | Thoughts are not subjective or psychological, because some thoughts are the same for us all [Frege] |
16872 | A thought is the sense expressed by a sentence, and is what we prove [Frege] |
16874 | The parts of a thought map onto the parts of a sentence [Frege] |
21667 | Oratory and philosophy are closely allied; orators borrow from philosophy, and ornament it [Cicero] |
21678 | If desire is not in our power then neither are choices, so we should not be praised or punished [Cicero] |
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] |