46 ideas
13786 | Wisdom is called 'beautiful', because it performs fine works [Plato] |
13780 | Good people are no different from wise ones [Plato] |
13778 | A dialectician is someone who knows how to ask and to answer questions [Plato] |
11223 | Definitions usually have a term, a 'definiendum' containing the term, and a defining 'definiens' [Gupta] |
11215 | Notable definitions have been of piety (Plato), God (Anselm), number (Frege), and truth (Tarski) [Gupta] |
11225 | A definition needs to apply to the same object across possible worlds [Gupta] |
11227 | The 'revision theory' says that definitions are rules for improving output [Gupta] |
11224 | Traditional definitions are general identities, which are sentential and reductive [Gupta] |
11226 | Traditional definitions need: same category, mention of the term, and conservativeness and eliminability [Gupta] |
11221 | A definition can be 'extensionally', 'intensionally' or 'sense' adequate [Gupta] |
11217 | Chemists aim at real definition of things; lexicographers aim at nominal definition of usage [Gupta] |
11216 | If definitions aim at different ideals, then defining essence is not a unitary activity [Gupta] |
11218 | Stipulative definition assigns meaning to a term, ignoring prior meanings [Gupta] |
11220 | Ostensive definitions look simple, but are complex and barely explicable [Gupta] |
13776 | Truths say of what is that it is, falsehoods say of what is that it is not [Plato] |
11222 | The ordered pair <x,y> is defined as the set {{x},{x,y}}, capturing function, not meaning [Gupta] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
13777 | A name is a sort of tool [Plato] |
13790 | A name-giver might misname something, then force other names to conform to it [Plato] |
13791 | Things must be known before they are named, so it can't be the names that give us knowledge [Plato] |
13789 | Anyone who knows a thing's name also knows the thing [Plato] |
8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
8764 | Categories are the best foundation for mathematics [Shapiro] |
8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
2063 | How can beauty have identity if it changes? [Plato] |
13775 | We only succeed in cutting if we use appropriate tools, not if we approach it randomly [Plato] |
13787 | Doesn't each thing have an essence, just as it has other qualities? [Plato] |
13774 | Things don't have every attribute, and essence isn't private, so each thing has an essence [Plato] |
13772 | Is the being or essence of each thing private to each person? [Plato] |
13788 | If we made a perfect duplicate of Cratylus, there would be two Cratyluses [Plato] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
13792 | There can't be any knowledge if things are constantly changing [Plato] |
13781 | Soul causes the body to live, and gives it power to breathe and to be revitalized [Plato] |
13785 | 'Arete' signifies lack of complexity and a free-flowing soul [Plato] |
13779 | The natural offspring of a lion is called a 'lion' (but what about the offspring of a king?) [Plato] |
13783 | Even the gods love play [Plato] |