38 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] |
7760 | Russell only uses descriptions attributively, and Strawson only referentially [Donnellan, by Lycan] |
5811 | A definite description can have a non-referential use [Donnellan] |
5812 | Definite descriptions are 'attributive' if they say something about x, and 'referential' if they pick x out [Donnellan] |
5814 | 'The x is F' only presumes that x exists; it does not actually entail the existence [Donnellan] |
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] |
10663 | A thought can refer to many things, but only predicate a universal and affirm a state of affairs [Hossack] |
10435 | A definite description 'the F' is referential if the speaker could thereby be referring to something not-F [Donnellan, by Sainsbury] |
10451 | Donnellan is unclear whether the referential-attributive distinction is semantic or pragmatic [Bach on Donnellan] |
5813 | A description can successfully refer, even if its application to the subject is not believed [Donnellan] |
5815 | Whether a definite description is referential or attributive depends on the speaker's intention [Donnellan] |
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] |