78 ideas
| 15801 | Many philosophers aim to understand metaphysics by studying ourselves [Chisholm] |
| 15802 | I use variables to show that each item remains the same entity throughout [Chisholm] |
| 8721 | An 'impredicative' definition seems circular, because it uses the term being defined [Friend] |
| 8680 | Classical definitions attempt to refer, but intuitionist/constructivist definitions actually create objects [Friend] |
| 3678 | Reductio ad absurdum proves an idea by showing that its denial produces contradiction [Friend] |
| 8705 | Anti-realists see truth as our servant, and epistemically contrained [Friend] |
| 8713 | In classical/realist logic the connectives are defined by truth-tables [Friend] |
| 8708 | Double negation elimination is not valid in intuitionist logic [Friend] |
| 8694 | Free logic was developed for fictional or non-existent objects [Friend] |
| 8665 | A 'proper subset' of A contains only members of A, but not all of them [Friend] |
| 8672 | A 'powerset' is all the subsets of a set [Friend] |
| 8677 | Set theory makes a minimum ontological claim, that the empty set exists [Friend] |
| 8666 | Infinite sets correspond one-to-one with a subset [Friend] |
| 8682 | Major set theories differ in their axioms, and also over the additional axioms of choice and infinity [Friend] |
| 8709 | The law of excluded middle is syntactic; it just says A or not-A, not whether they are true or false [Friend] |
| 21566 | 'Propositional functions' are ambiguous until the variable is given a value [Russell] |
| 8711 | Intuitionists read the universal quantifier as "we have a procedure for checking every..." [Friend] |
| 8675 | Paradoxes can be solved by talking more loosely of 'classes' instead of 'sets' [Friend] |
| 8674 | The Burali-Forti paradox asks whether the set of all ordinals is itself an ordinal [Friend] |
| 21567 | 'All judgements made by Epimenedes are true' needs the judgements to be of the same type [Russell] |
| 8667 | The 'integers' are the positive and negative natural numbers, plus zero [Friend] |
| 8668 | The 'rational' numbers are those representable as fractions [Friend] |
| 8670 | A number is 'irrational' if it cannot be represented as a fraction [Friend] |
| 8661 | The natural numbers are primitive, and the ordinals are up one level of abstraction [Friend] |
| 8664 | Cardinal numbers answer 'how many?', with the order being irrelevant [Friend] |
| 8671 | The 'real' numbers (rationals and irrationals combined) is the Continuum, which has no gaps [Friend] |
| 8663 | Raising omega to successive powers of omega reveal an infinity of infinities [Friend] |
| 8662 | The first limit ordinal is omega (greater, but without predecessor), and the second is twice-omega [Friend] |
| 8669 | Between any two rational numbers there is an infinite number of rational numbers [Friend] |
| 8676 | Is mathematics based on sets, types, categories, models or topology? [Friend] |
| 8678 | Most mathematical theories can be translated into the language of set theory [Friend] |
| 8701 | The number 8 in isolation from the other numbers is of no interest [Friend] |
| 8702 | In structuralism the number 8 is not quite the same in different structures, only equivalent [Friend] |
| 8699 | Are structures 'ante rem' (before reality), or are they 'in re' (grounded in physics)? [Friend] |
| 8696 | Structuralist says maths concerns concepts about base objects, not base objects themselves [Friend] |
| 8695 | Structuralism focuses on relations, predicates and functions, with objects being inessential [Friend] |
| 8700 | 'In re' structuralism says that the process of abstraction is pattern-spotting [Friend] |
| 8681 | The big problem for platonists is epistemic: how do we perceive, intuit, know or detect mathematical facts? [Friend] |
| 8712 | Mathematics should be treated as true whenever it is indispensable to our best physical theory [Friend] |
| 23457 | Type theory cannot identify features across levels (because such predicates break the rules) [Morris,M on Russell] |
| 21556 | Classes are defined by propositional functions, and functions are typed, with an axiom of reducibility [Russell, by Lackey] |
| 8716 | Formalism is unconstrained, so cannot indicate importance, or directions for research [Friend] |
| 8706 | Constructivism rejects too much mathematics [Friend] |
| 8707 | Intuitionists typically retain bivalence but reject the law of excluded middle [Friend] |
| 21568 | A one-variable function is only 'predicative' if it is one order above its arguments [Russell] |
| 15832 | Events are states of affairs that occur at certain places and times [Chisholm] |
| 15829 | The mark of a state of affairs is that it is capable of being accepted [Chisholm] |
| 15809 | A state of affairs pertains to a thing if it implies that it has some property [Chisholm] |
| 15828 | I propose that events and propositions are two types of states of affairs [Chisholm] |
| 15827 | Some properties, such as 'being a widow', can be seen as 'rooted outside the time they are had' [Chisholm] |
| 15830 | Some properties can never be had, like being a round square [Chisholm] |
| 15804 | If some dogs are brown, that entails the properties of 'being brown' and 'being canine' [Chisholm] |
| 8704 | Structuralists call a mathematical 'object' simply a 'place in a structure' [Friend] |
| 15810 | Maybe we can only individuate things by relating them to ourselves [Chisholm] |
| 15805 | Being the tallest man is an 'individual concept', but not a haecceity [Chisholm] |
| 15807 | A haecceity is a property had necessarily, and strictly confined to one entity [Chisholm] |
| 15814 | A peach is sweet and fuzzy, but it doesn't 'have' those qualities [Chisholm] |
| 12852 | If x is ever part of y, then y is necessarily such that x is part of y at any time that y exists [Chisholm, by Simons] |
| 15808 | A traditional individual essence includes all of a thing's necessary characteristics [Chisholm] |
| 12851 | Intermittence is seen in a toy fort, which is dismantled then rebuilt with the same bricks [Chisholm, by Simons] |
| 15806 | The property of being identical with me is an individual concept [Chisholm] |
| 15826 | There is 'loose' identity between things if their properties, or truths about them, might differ [Chisholm] |
| 15819 | Do sense-data have structure, location, weight, and constituting matter? [Chisholm] |
| 15816 | 'I feel depressed' is more like 'he runs slowly' than like 'he has a red book' [Chisholm] |
| 15817 | If we can say a man senses 'redly', why not also 'rectangularly'? [Chisholm] |
| 15818 | So called 'sense-data' are best seen as 'modifications' of the person experiencing them [Chisholm] |
| 15831 | Explanations have states of affairs as their objects [Chisholm] |
| 15811 | I am picked out uniquely by my individual essence, which is 'being identical with myself' [Chisholm] |
| 15815 | Sartre says the ego is 'opaque'; I prefer to say that it is 'transparent' [Chisholm] |
| 15813 | People use 'I' to refer to themselves, with the meaning of their own individual essence [Chisholm] |
| 15803 | Bad theories of the self see it as abstract, or as a bundle, or as a process [Chisholm] |
| 15821 | Determinism claims that every event has a sufficient causal pre-condition [Chisholm] |
| 8685 | Studying biology presumes the laws of chemistry, and it could never contradict them [Friend] |
| 8688 | Concepts can be presented extensionally (as objects) or intensionally (as a characterization) [Friend] |
| 15824 | There are mere omissions (through ignorance, perhaps), and people can 'commit an omission' [Chisholm] |
| 15822 | The concept of physical necessity is basic to both causation, and to the concept of nature [Chisholm] |
| 15823 | Some propose a distinct 'agent causation', as well as 'event causation' [Chisholm] |
| 15820 | A 'law of nature' is just something which is physically necessary [Chisholm] |