57 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] |
| 2730 | Because 'gold is malleable' is necessary does not mean that it is analytic [Audi,R] |
| 2715 | Beliefs are based on perception, memory, introspection or reason [Audi,R] |
| 2735 | Could you have a single belief on its own? [Audi,R] |
| 2736 | We can make certain of what we know, so knowing does not entail certainty [Audi,R] |
| 2722 | Sense-data theory is indirect realism, but phenomenalism is direct irrealism [Audi,R] |
| 2721 | If you gradually remove a book's sensory properties, what is left at the end? [Audi,R] |
| 2727 | Red and green being exclusive colours seems to be rationally graspable but not analytic [Audi,R] |
| 2728 | The concepts needed for a priori thought may come from experience [Audi,R] |
| 2716 | To see something as a field, I obviously need the concept of a field [Audi,R] |
| 2717 | How could I see a field and believe nothing regarding it? [Audi,R] |
| 2720 | Sense-data (and the rival 'adverbial' theory) are to explain illusions and hallucinations [Audi,R] |
| 2719 | Sense data imply representative realism, possibly only representing primary qualities [Audi,R] |
| 2718 | Perception is first simple, then objectual (with concepts) and then propositional [Audi,R] |
| 2729 | Virtually all rationalists assert that we can have knowledge of synthetic a priori truths [Audi,R] |
| 2741 | The principles of justification have to be a priori [Audi,R] |
| 2725 | To remember something is to know it [Audi,R] |
| 2724 | I might remember someone I can't recall or image, by recognising them on meeting [Audi,R] |
| 2731 | Justification is either unanchored (infinite or circular), or anchored (in knowledge or non-knowledge) [Audi,R] |
| 2739 | Internalism about justification implies that there is a right to believe something [Audi,R] |
| 2732 | Maths may be consistent with observations, but not coherent [Audi,R] |
| 2733 | It is very hard to show how much coherence is needed for justification [Audi,R] |
| 2734 | A consistent madman could have a very coherent belief system [Audi,R] |
| 2738 | Consistent accurate prediction looks like knowledge without justified belief [Audi,R] |
| 2740 | A reliability theory of knowledge seems to involve truth as correspondence [Audi,R] |
| 2737 | 'Reliable' is a very imprecise term, and may even mean 'justified' [Audi,R] |
| 2726 | We can be ignorant about ourselves, for example, our desires and motives [Audi,R] |
| 10663 | A thought can refer to many things, but only predicate a universal and affirm a state of affairs [Hossack] |
| 20064 | Actions are not mere effects of reasons, but are under their control [Audi,R] |
| 6005 | Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley] |
| 10683 | We could ignore space, and just talk of the shape of matter [Hossack] |