51 ideas
23728 | Analysis aims to express the full set of platitudes surrounding a given concept [Smith,M] |
18241 | Sufficient reason is implied by contradiction, of an insufficient possible which exists [Wolff, by Korsgaard] |
23744 | Defining a set of things by paradigms doesn't pin them down enough [Smith,M] |
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] |
23743 | Capturing all the common sense facts about rationality is almost impossible [Smith,M] |
23739 | Goals need desires, and so only desires can motivate us [Smith,M] |
23724 | A pure desire could be criticised if it were based on a false belief [Smith,M] |
23736 | A person can have a desire without feeling it [Smith,M] |
23723 | In the Humean account, desires are not true/false, or subject to any rational criticism [Smith,M] |
23735 | Subjects may be fallible about the desires which explain their actions [Smith,M] |
23738 | Humeans (unlike their opponents) say that desires and judgements can separate [Smith,M] |
23742 | If first- and second-order desires conflict, harmony does not require the second-order to win [Smith,M] |
23746 | Objective reasons to act might be the systematic desires of a fully rational person [Smith,M] |
23733 | Motivating reasons are psychological, while normative reasons are external [Smith,M] |
23740 | Humeans take maximising desire satisfaction as the normative reasons for actions [Smith,M] |
23745 | We cannot expect even fully rational people to converge on having the same desires for action [Smith,M] |
23731 | 'Externalists' say moral judgements are not reasons, and maybe not even motives [Smith,M] |
23732 | A person could make a moral judgement without being in any way motivated by it [Smith,M] |
23729 | Moral internalism says a judgement of rightness is thereby motivating [Smith,M] |
23730 | 'Rationalism' says the rightness of an action is a reason to perform it [Smith,M] |
23727 | Expressivists count attitudes as 'moral' if they concern features of things, rather than their mere existence [Smith,M] |
23741 | Is valuing something a matter of believing or a matter of desiring? [Smith,M] |
10683 | We could ignore space, and just talk of the shape of matter [Hossack] |
18242 | Confucius shows that ethics can rest on reason, rather than on revelation [Wolff, by Korsgaard] |