41 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] |
10663 | A thought can refer to many things, but only predicate a universal and affirm a state of affairs [Hossack] |
7404 | Nations are not obliged to help one-another, but are obliged not to harm one another [Grotius, by Tuck] |
7402 | Everyone has a right of self-preservation, and harming others is usually unjustifiable [Grotius, by Tuck] |
21938 | Democracy needs respect for individuality, but the 'community of friends' implies strict equality [Grotius] |
19845 | A person is free to renounce their state, as long as it is not a moment of crisis [Grotius, by Rousseau] |
22133 | Grotius and Pufendorf based natural law on real (rather than idealised) humanity [Grotius, by Ford,JD] |
7406 | A natural right of self-preservation is balanced by a natural law to avoid unnecessary harm [Grotius, by Tuck] |
7403 | Grotius ignored elaborate natural law theories, preferring a basic right of self-preservation [Grotius, by Tuck] |
23585 | It is permissible in a just cause to capture a place in neutral territory [Grotius] |
14586 | Physical causation consists in transference of conserved quantities [Dowe, by Mumford/Anjum] |
4787 | Causation interaction is an exchange of conserved quantities, such as mass, energy or charge [Dowe, by Psillos] |
4788 | Dowe commends the Conserved Quantity theory as it avoids mention of counterfactuals [Dowe, by Psillos] |
10683 | We could ignore space, and just talk of the shape of matter [Hossack] |
6892 | Moral principles have some validity without a God commanding obedience [Grotius, by Mautner] |