50 ideas
| 5515 | Imaginary cases are good for revealing our beliefs, rather than the truth [Parfit] |
| 19323 | 'Snow is white' depends on meaning; whether snow is white depends on snow [Etchemendy] |
| 19137 | We can get a substantive account of Tarski's truth by adding primitive 'true' to the object language [Etchemendy] |
| 15945 | Second-order set theory just adds a version of Replacement that quantifies over functions [Lavine] |
| 15914 | An 'upper bound' is the greatest member of a subset; there may be several of these, so there is a 'least' one [Lavine] |
| 15921 | Collections of things can't be too big, but collections by a rule seem unlimited in size [Lavine] |
| 15937 | Those who reject infinite collections also want to reject the Axiom of Choice [Lavine] |
| 15936 | The Power Set is just the collection of functions from one collection to another [Lavine] |
| 15899 | Replacement was immediately accepted, despite having very few implications [Lavine] |
| 15930 | Foundation says descending chains are of finite length, blocking circularity, or ungrounded sets [Lavine] |
| 15920 | Pure collections of things obey Choice, but collections defined by a rule may not [Lavine] |
| 15898 | The controversy was not about the Axiom of Choice, but about functions as arbitrary, or given by rules [Lavine] |
| 15919 | The 'logical' notion of class has some kind of definition or rule to characterise the class [Lavine] |
| 15900 | The iterative conception of set wasn't suggested until 1947 [Lavine] |
| 15931 | The iterative conception needs the Axiom of Infinity, to show how far we can iterate [Lavine] |
| 15932 | The iterative conception doesn't unify the axioms, and has had little impact on mathematical proofs [Lavine] |
| 15933 | Limitation of Size: if it's the same size as a set, it's a set; it uses Replacement [Lavine] |
| 15913 | A collection is 'well-ordered' if there is a least element, and all of its successors can be identified [Lavine] |
| 15926 | Second-order logic presupposes a set of relations already fixed by the first-order domain [Lavine] |
| 14181 | Validity is where either the situation or the interpretation blocks true premises and false conclusion [Etchemendy, by Read] |
| 14180 | Etchemendy says fix the situation and vary the interpretation, or fix interpretations with varying situations [Etchemendy, by Read] |
| 15934 | Mathematical proof by contradiction needs the law of excluded middle [Lavine] |
| 15907 | Mathematics is nowadays (thanks to set theory) regarded as the study of structure, not of quantity [Lavine] |
| 15942 | Every rational number, unlike every natural number, is divisible by some other number [Lavine] |
| 15922 | For the real numbers to form a set, we need the Continuum Hypothesis to be true [Lavine] |
| 18250 | Cauchy gave a necessary condition for the convergence of a sequence [Lavine] |
| 15904 | The two sides of the Cut are, roughly, the bounding commensurable ratios [Lavine] |
| 15912 | Counting results in well-ordering, and well-ordering makes counting possible [Lavine] |
| 15949 | The theory of infinity must rest on our inability to distinguish between very large sizes [Lavine] |
| 15947 | The infinite is extrapolation from the experience of indefinitely large size [Lavine] |
| 15940 | The intuitionist endorses only the potential infinite [Lavine] |
| 15909 | 'Aleph-0' is cardinality of the naturals, 'aleph-1' the next cardinal, 'aleph-ω' the ω-th cardinal [Lavine] |
| 15915 | Ordinals are basic to Cantor's transfinite, to count the sets [Lavine] |
| 15917 | Paradox: the class of all ordinals is well-ordered, so must have an ordinal as type - giving a bigger ordinal [Lavine] |
| 15918 | Paradox: there is no largest cardinal, but the class of everything seems to be the largest [Lavine] |
| 15929 | Set theory will found all of mathematics - except for the notion of proof [Lavine] |
| 15935 | Modern mathematics works up to isomorphism, and doesn't care what things 'really are' [Lavine] |
| 15928 | Intuitionism rejects set-theory to found mathematics [Lavine] |
| 5516 | Reduction can be by identity, or constitution, or elimination [Parfit, by PG] |
| 3539 | Personal identity is just causally related mental states [Parfit, by Maslin] |
| 5514 | Psychologists are interested in identity as a type of person, but philosophers study numerical identity [Parfit] |
| 1393 | One of my future selves will not necessarily be me [Parfit] |
| 5521 | If my brain-halves are transplanted into two bodies, I have continuity, and don't need identity [Parfit] |
| 5522 | Over a period of time what matters is not that 'I' persist, but that I have psychological continuity [Parfit] |
| 1392 | If we split like amoeba, we would be two people, neither of them being us [Parfit] |
| 5519 | It is fine to save two dying twins by merging parts of their bodies into one, and identity is irrelevant [Parfit] |
| 5520 | If two humans are merged surgically, the new identity is a purely verbal problem [Parfit] |
| 1391 | Concern for our own lives isn't the source of belief in identity, it is the result of it [Parfit] |
| 5518 | It doesn't matter whether I exist with half my components replaced (any more than an audio system) [Parfit] |
| 9762 | We should focus less on subjects of experience, and more on the experiences themselves [Parfit] |