59 ideas
501 | Reason is a more powerful persuader than gold [Democritus (attr)] |
10676 | The Axiom of Choice is a non-logical principle of set-theory [Hossack] |
10686 | The Axiom of Choice guarantees a one-one correspondence from sets to ordinals [Hossack] |
23623 | Predicativism says only predicated sets exist [Hossack] |
23624 | The iterative conception has to appropriate Replacement, to justify the ordinals [Hossack] |
23625 | Limitation of Size justifies Replacement, but then has to appropriate Power Set [Hossack] |
10687 | Maybe we reduce sets to ordinals, rather than the other way round [Hossack] |
10677 | Extensional mereology needs two definitions and two axioms [Hossack] |
23628 | The connective 'and' can have an order-sensitive meaning, as 'and then' [Hossack] |
23627 | 'Before' and 'after' are not two relations, but one relation with two orders [Hossack] |
10671 | Plural definite descriptions pick out the largest class of things that fit the description [Hossack] |
10666 | Plural reference will refer to complex facts without postulating complex things [Hossack] |
10669 | Plural reference is just an abbreviation when properties are distributive, but not otherwise [Hossack] |
10675 | A plural comprehension principle says there are some things one of which meets some condition [Hossack] |
10673 | Plural language can discuss without inconsistency things that are not members of themselves [Hossack] |
10680 | The theory of the transfinite needs the ordinal numbers [Hossack] |
10684 | I take the real numbers to be just lengths [Hossack] |
23626 | Transfinite ordinals are needed in proof theory, and for recursive functions and computability [Hossack] |
10674 | A plural language gives a single comprehensive induction axiom for arithmetic [Hossack] |
10681 | In arithmetic singularists need sets as the instantiator of numeric properties [Hossack] |
10685 | Set theory is the science of infinity [Hossack] |
23621 | Numbers are properties, not sets (because numbers are magnitudes) [Hossack] |
23622 | We can only mentally construct potential infinities, but maths needs actual infinities [Hossack] |
10668 | We are committed to a 'group' of children, if they are sitting in a circle [Hossack] |
10664 | Complex particulars are either masses, or composites, or sets [Hossack] |
10678 | The relation of composition is indispensable to the part-whole relation for individuals [Hossack] |
10665 | Leibniz's Law argues against atomism - water is wet, unlike water molecules [Hossack] |
10682 | The fusion of five rectangles can decompose into more than five parts that are rectangles [Hossack] |
19542 | It is nonsense that understanding does not involve knowledge; to understand, you must know [Dougherty/Rysiew] |
19543 | To grasp understanding, we should be more explicit about what needs to be known [Dougherty/Rysiew] |
19541 | Rather than knowledge, our epistemic aim may be mere true belief, or else understanding and wisdom [Dougherty/Rysiew] |
19540 | Don't confuse justified belief with justified believers [Dougherty/Rysiew] |
19539 | If knowledge is unanalysable, that makes justification more important [Dougherty/Rysiew] |
10663 | A thought can refer to many things, but only predicate a universal and affirm a state of affairs [Hossack] |
19538 | Entailment is modelled in formal semantics as set inclusion (where 'mammals' contains 'cats') [Dougherty/Rysiew] |
514 | Beauty is merely animal without intelligence [Democritus (attr)] |
525 | Behave well when alone, and feel shame in you own eyes [Democritus (attr)] |
502 | Good breeding in men means having a good character [Democritus (attr)] |
507 | Virtuous love consists of decorous desire for the beautiful [Democritus (attr)] |
521 | We should only choose pleasures which are concerned with the beautiful [Democritus (attr)] |
505 | Good and true are the same for everyone, but pleasures differ [Democritus (attr)] |
508 | Only accept beneficial pleasures [Democritus (attr)] |
520 | The great pleasures come from the contemplation of noble works [Democritus (attr)] |
522 | Moderation brings more pleasures, and so increases pleasure [Democritus (attr)] |
506 | Immoderate desire is the mark of a child, not an adult [Democritus (attr)] |
523 | It is as brave to master pleasure as to overcome the enemy [Democritus (attr)] |
503 | Virtue doesn't just avoid evil, but also doesn't desire it [Democritus (attr)] |
518 | A bad life is just a drawn-out death [Democritus (attr)] |
497 | Be virtuous from duty, not from fear [Democritus (attr)] |
499 | Repentance of shameful deeds is salvation [Democritus (attr)] |
524 | Virtue comes more from practice than from nature [Democritus (attr)] |
519 | One must avoid even speaking of evil deeds [Democritus (attr)] |
500 | The wrongdoer is more unfortunate than the person wronged [Democritus (attr)] |
1539 | The endless desire for money is a crueller slavery than poverty [Democritus (attr)] |
526 | Small appetite makes poverty equal to wealth [Democritus (attr)] |
511 | It is better to have one intelligent friend than many unintelligent [Democritus (attr)] |
498 | It is a great thing, when one is in adversity, to think of duty [Democritus (attr)] |
1541 | It is better to be poor in a democracy than be rich without freedom [Democritus (attr)] |
10683 | We could ignore space, and just talk of the shape of matter [Hossack] |