40 ideas
| 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] |
| 19284 | Asserting a necessity just expresses our inability to imagine it is false [Blackburn] |
| 14629 | If we are told the source of necessity, this seems to be a regress if the source is not already necessary [Blackburn] |
| 14529 | If something underlies a necessity, is that underlying thing necessary or contingent? [Blackburn, by Hale/Hoffmann,A] |
| 6451 | Visual sense data are an inner picture show which represents the world [Blackburn] |
| 2866 | A true belief might be based on a generally reliable process that failed on this occasion [Blackburn] |
| 10663 | A thought can refer to many things, but only predicate a universal and affirm a state of affairs [Hossack] |
| 23996 | Akrasia is intelligible in hindsight, when we revisit our previous emotions [Blackburn] |
| 11911 | Some philosophers always want more from morality; for others, nature is enough [Blackburn] |
| 2864 | The main objection to intuitionism in ethics is that intuition is a disguise for prejudice or emotion [Blackburn] |
| 2865 | Critics of prescriptivism observe that it is consistent to accept an ethical verdict but refuse to be bound by it [Blackburn] |
| 23223 | The word 'respect' ranges from mere non-interference to the highest levels of reverence [Blackburn] |
| 10683 | We could ignore space, and just talk of the shape of matter [Hossack] |
| 1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |