43 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] |
14329 | Some dispositional properties (such as mental ones) may have no categorical base [Price,HH] |
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] |
9032 | Before we can abstract from an instance of violet, we must first recognise it [Price,HH] |
9035 | If judgement of a characteristic is possible, that part of abstraction must be complete [Price,HH] |
9034 | There may be degrees of abstraction which allow recognition by signs, without full concepts [Price,HH] |
9036 | There is pre-verbal sign-based abstraction, as when ice actually looks cold [Price,HH] |
9037 | Intelligent behaviour, even in animals, has something abstract about it [Price,HH] |
9033 | Recognition must precede the acquisition of basic concepts, so it is the fundamental intellectual process [Price,HH] |
10663 | A thought can refer to many things, but only predicate a universal and affirm a state of affairs [Hossack] |
10645 | We reach concepts by clarification, or by definition, or by habitual experience [Price,HH] |
9030 | Abstractions can be interpreted dispositionally, as the ability to recognise or imagine an item [Price,HH] |
9029 | If ideas have to be images, then abstract ideas become a paradoxical problem [Price,HH] |
10644 | A 'felt familiarity' with universals is more primitive than abstraction [Price,HH] |
10646 | Our understanding of 'dog' or 'house' arises from a repeated experience of concomitances [Price,HH] |
9031 | The basic concepts of conceptual cognition are acquired by direct abstraction from instances [Price,HH] |
10683 | We could ignore space, and just talk of the shape of matter [Hossack] |
3029 | Stilpo said if Athena is a daughter of Zeus, then a statue is only the child of a sculptor, and so is not a god [Stilpo, by Diog. Laertius] |