74 ideas
| 15901 | Trying to represent curves, we study arbitrary functions, leading to the ordinals, which produces set theory [Cantor, by Lavine] |
| Full Idea: The notion of a function evolved gradually from wanting to see what curves can be represented as trigonometric series. The study of arbitrary functions led Cantor to the ordinal numbers, which led to set theory. | |
| From: report of George Cantor (works [1880]) by Shaughan Lavine - Understanding the Infinite I |
| 13444 | Cantor's Theorem: for any set x, its power set P(x) has more members than x [Cantor, by Hart,WD] |
| Full Idea: Cantor's Theorem says that for any set x, its power set P(x) has more members than x. | |
| From: report of George Cantor (works [1880]) by William D. Hart - The Evolution of Logic 1 |
| 18098 | Cantor proved that all sets have more subsets than they have members [Cantor, by Bostock] |
| Full Idea: Cantor's diagonalisation argument generalises to show that any set has more subsets than it has members. | |
| From: report of George Cantor (works [1880]) by David Bostock - Philosophy of Mathematics 4.5 | |
| A reaction: Thus three members will generate seven subsets. This means that 'there is no end to the series of cardinal numbers' (Bostock p.106). |
| 15505 | If a set is 'a many thought of as one', beginners should protest against singleton sets [Cantor, by Lewis] |
| Full Idea: Cantor taught that a set is 'a many, which can be thought of as one'. ...After a time the unfortunate beginner student is told that some classes - the singletons - have only a single member. Here is a just cause for student protest, if ever there was one. | |
| From: report of George Cantor (works [1880]) by David Lewis - Parts of Classes 2.1 | |
| A reaction: There is a parallel question, almost lost in the mists of time, of whether 'one' is a number. 'Zero' is obviously dubious, but if numbers are for counting, that needs units, so the unit is the precondition of counting, not part of it. |
| 10701 | Cantor showed that supposed contradictions in infinity were just a lack of clarity [Cantor, by Potter] |
| Full Idea: Cantor's theories exhibited the contradictions others had claimed to derive from the supposition of infinite sets as confusions resulting from the failure to mark the necessary distinctions with sufficient clarity. | |
| From: report of George Cantor (works [1880]) by Michael Potter - Set Theory and Its Philosophy Intro 1 |
| 10865 | The continuum is the powerset of the integers, which moves up a level [Cantor, by Clegg] |
| Full Idea: Cantor discovered that the continuum is the powerset of the integers. While adding or multiplying infinities didn't move up a level of complexity, multiplying a number by itself an infinite number of times did. | |
| From: report of George Cantor (works [1880]) by Brian Clegg - Infinity: Quest to Think the Unthinkable Ch.14 |
| 13016 | The Axiom of Union dates from 1899, and seems fairly obvious [Cantor, by Maddy] |
| Full Idea: Cantor first stated the Union Axiom in a letter to Dedekind in 1899. It is nearly too obvious to deserve comment from most commentators. Justifications usually rest on 'limitation of size' or on the 'iterative conception'. | |
| From: report of George Cantor (works [1880]) by Penelope Maddy - Believing the Axioms I §1.3 | |
| A reaction: Surely someone can think of some way to challenge it! An opportunity to become notorious, and get invited to conferences. |
| 14199 | Cantor's sets were just collections, but Dedekind's were containers [Cantor, by Oliver/Smiley] |
| Full Idea: Cantor's definition of a set was a collection of its members into a whole, but within a few years Dedekind had the idea of a set as a container, enclosing its members like a sack. | |
| From: report of George Cantor (works [1880]) by Oliver,A/Smiley,T - What are Sets and What are they For? Intro | |
| A reaction: As the article goes on to show, these two view don't seem significantly different until you start to ask about the status of the null set and of singletons. I intuitively vote for Dedekind. Set theory is the study of brackets. |
| 10082 | There are infinite sets that are not enumerable [Cantor, by Smith,P] |
| Full Idea: Cantor's Theorem (1874) says there are infinite sets that are not enumerable. This is proved by his 1891 'diagonal argument'. | |
| From: report of George Cantor (works [1880]) by Peter Smith - Intro to Gödel's Theorems 2.3 | |
| A reaction: [Smith summarises the diagonal argument] |
| 13483 | Cantor's Paradox: the power set of the universe must be bigger than the universe, yet a subset of it [Cantor, by Hart,WD] |
| Full Idea: The problem of Cantor's Paradox is that the power set of the universe has to be both bigger than the universe (by Cantor's theorem) and not bigger (since it is a subset of the universe). | |
| From: report of George Cantor (works [1880]) by William D. Hart - The Evolution of Logic 3 | |
| A reaction: Russell eliminates the 'universe' in his theory of types. I don't see why you can't just say that the members of the set are hypothetical rather than real, and that hypothetically the universe might contain more things than it does. |
| 8710 | The powerset of all the cardinal numbers is required to be greater than itself [Cantor, by Friend] |
| Full Idea: Cantor's Paradox says that the powerset of a set has a cardinal number strictly greater than the original set, but that means that the powerset of the set of all the cardinal numbers is greater than itself. | |
| From: report of George Cantor (works [1880]) by Michèle Friend - Introducing the Philosophy of Mathematics | |
| A reaction: Friend cites this with the Burali-Forti paradox and the Russell paradox as the best examples of the problems of set theory in the early twentieth century. Did this mean that sets misdescribe reality, or that we had constructed them wrongly? |
| 15910 | Cantor named the third realm between the finite and the Absolute the 'transfinite' [Cantor, by Lavine] |
| Full Idea: Cantor believed he had discovered that between the finite and the 'Absolute', which is 'incomprehensible to the human understanding', there is a third category, which he called 'the transfinite'. | |
| From: report of George Cantor (works [1880]) by Shaughan Lavine - Understanding the Infinite III.4 |
| 15905 | Cantor proved the points on a plane are in one-to-one correspondence to the points on a line [Cantor, by Lavine] |
| Full Idea: In 1878 Cantor published the unexpected result that one can put the points on a plane, or indeed any n-dimensional space, into one-to-one correspondence with the points on a line. | |
| From: report of George Cantor (works [1880]) by Shaughan Lavine - Understanding the Infinite III.1 |
| 9983 | Cantor took the ordinal numbers to be primary [Cantor, by Tait] |
| Full Idea: Cantor took the ordinal numbers to be primary: in his generalization of the cardinals and ordinals into the transfinite, it is the ordinals that he calls 'numbers'. | |
| From: report of George Cantor (works [1880]) by William W. Tait - Frege versus Cantor and Dedekind VI | |
| A reaction: [Tait says Dedekind also favours the ordinals] It is unclear how the matter might be settled. Humans cannot give the cardinality of large groups without counting up through the ordinals. A cardinal gets its meaning from its place in the ordinals? |
| 17798 | Cantor presented the totality of natural numbers as finite, not infinite [Cantor, by Mayberry] |
| Full Idea: Cantor taught us to regard the totality of natural numbers, which was formerly thought to be infinite, as really finite after all. | |
| From: report of George Cantor (works [1880]) by John Mayberry - What Required for Foundation for Maths? p.414-2 | |
| A reaction: I presume this is because they are (by definition) countable. |
| 9971 | Cantor introduced the distinction between cardinals and ordinals [Cantor, by Tait] |
| Full Idea: Cantor introduced the distinction between cardinal and ordinal numbers. | |
| From: report of George Cantor (works [1880]) by William W. Tait - Frege versus Cantor and Dedekind Intro | |
| A reaction: This seems remarkably late for what looks like a very significant clarification. The two concepts coincide in finite cases, but come apart in infinite cases (Tait p.58). |
| 9892 | Cantor showed that ordinals are more basic than cardinals [Cantor, by Dummett] |
| Full Idea: Cantor's work revealed that the notion of an ordinal number is more fundamental than that of a cardinal number. | |
| From: report of George Cantor (works [1880]) by Michael Dummett - Frege philosophy of mathematics Ch.23 | |
| A reaction: Dummett makes it sound like a proof, which I find hard to believe. Is the notion that I have 'more' sheep than you logically prior to how many sheep we have? If I have one more, that implies the next number, whatever that number may be. Hm. |
| 14136 | A cardinal is an abstraction, from the nature of a set's elements, and from their order [Cantor] |
| Full Idea: The cardinal number of M is the general idea which, by means of our active faculty of thought, is deduced from the collection M, by abstracting from the nature of its diverse elements and from the order in which they are given. | |
| From: George Cantor (works [1880]), quoted by Bertrand Russell - The Principles of Mathematics §284 | |
| A reaction: [Russell cites 'Math. Annalen, XLVI, §1'] See Fine 1998 on this. |
| 15906 | Cantor tried to prove points on a line matched naturals or reals - but nothing in between [Cantor, by Lavine] |
| Full Idea: Cantor said he could show that every infinite set of points on the line could be placed into one-to-one correspondence with either the natural numbers or the real numbers - with no intermediate possibilies (the Continuum hypothesis). His proof failed. | |
| From: report of George Cantor (works [1880]) by Shaughan Lavine - Understanding the Infinite III.1 |
| 11015 | Cantor's diagonal argument proved you can't list all decimal numbers between 0 and 1 [Cantor, by Read] |
| Full Idea: Cantor's diagonal argument showed that all the infinite decimals between 0 and 1 cannot be written down even in a single never-ending list. | |
| From: report of George Cantor (works [1880]) by Stephen Read - Thinking About Logic Ch.6 |
| 15903 | A real is associated with an infinite set of infinite Cauchy sequences of rationals [Cantor, by Lavine] |
| Full Idea: Cantor's theory of Cauchy sequences defines a real number to be associated with an infinite set of infinite sequences of rational numbers. | |
| From: report of George Cantor (works [1880]) by Shaughan Lavine - Understanding the Infinite II.6 | |
| A reaction: This sounds remarkably like the endless decimals we use when we try to write down an actual real number. |
| 18251 | Irrational numbers are the limits of Cauchy sequences of rational numbers [Cantor, by Lavine] |
| Full Idea: Cantor introduced irrationals to play the role of limits of Cauchy sequences of rational numbers. | |
| From: report of George Cantor (works [1880]) by Shaughan Lavine - Understanding the Infinite 4.2 |
| 15902 | Irrationals and the Dedekind Cut implied infinite classes, but they seemed to have logical difficulties [Cantor, by Lavine] |
| Full Idea: From the very nature of an irrational number, it seems necessary to understand the mathematical infinite thoroughly before an adequate theory of irrationals is possible. Infinite classes are obvious in the Dedekind Cut, but have logical difficulties | |
| From: report of George Cantor (works [1880]) by Shaughan Lavine - Understanding the Infinite II Intro | |
| A reaction: Almost the whole theory of analysis (calculus) rested on the irrationals, so a theory of the infinite was suddenly (in the 1870s) vital for mathematics. Cantor wasn't just being eccentric or mystical. |
| 15908 | It was Cantor's diagonal argument which revealed infinities greater than that of the real numbers [Cantor, by Lavine] |
| Full Idea: Cantor's 1891 diagonal argument revealed there are infinitely many infinite powers. Indeed, it showed more: it shows that given any set there is another of greater power. Hence there is an infinite power strictly greater than that of the set of the reals. | |
| From: report of George Cantor (works [1880]) by Shaughan Lavine - Understanding the Infinite III.2 |
| 13464 | Cantor proposes that there won't be a potential infinity if there is no actual infinity [Cantor, by Hart,WD] |
| Full Idea: What we might call 'Cantor's Thesis' is that there won't be a potential infinity of any sort unless there is an actual infinity of some sort. | |
| From: report of George Cantor (works [1880]) by William D. Hart - The Evolution of Logic 1 | |
| A reaction: This idea is nicely calculated to stop Aristotle in his tracks. |
| 10112 | The naturals won't map onto the reals, so there are different sizes of infinity [Cantor, by George/Velleman] |
| Full Idea: Cantor showed that the complete totality of natural numbers cannot be mapped 1-1 onto the complete totality of the real numbers - so there are different sizes of infinity. | |
| From: report of George Cantor (works [1880]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.4 |
| 8733 | The Continuum Hypothesis says there are no sets between the natural numbers and reals [Cantor, by Shapiro] |
| Full Idea: Cantor's 'continuum hypothesis' is the assertion that there are no infinite cardinalities strictly between the size of the natural numbers and the size of the real numbers. | |
| From: report of George Cantor (works [1880]) by Stewart Shapiro - Thinking About Mathematics 2.4 | |
| A reaction: The tricky question is whether this hypothesis can be proved. |
| 17889 | CH: An infinite set of reals corresponds 1-1 either to the naturals or to the reals [Cantor, by Koellner] |
| Full Idea: Cantor's Continuum Hypothesis (CH) says that for every infinite set X of reals there is either a one-to-one correspondence between X and the natural numbers, or between X and the real numbers. | |
| From: report of George Cantor (works [1880]) by Peter Koellner - On the Question of Absolute Undecidability 1.2 | |
| A reaction: Every single writer I read defines this differently, which drives me crazy, but is also helpfully illuminating. There is a moral there somewhere. |
| 13447 | Cantor: there is no size between naturals and reals, or between a set and its power set [Cantor, by Hart,WD] |
| Full Idea: Cantor conjectured that there is no size between those of the naturals and the reals - called the 'continuum hypothesis'. The generalized version says that for no infinite set A is there a set larger than A but smaller than P(A). | |
| From: report of George Cantor (works [1880]) by William D. Hart - The Evolution of Logic 1 | |
| A reaction: Thus there are gaps between infinite numbers, and the power set is the next size up from any infinity. Much discussion as ensued about whether these two can be proved. |
| 10883 | Cantor's Continuum Hypothesis says there is a gap between the natural and the real numbers [Cantor, by Horsten] |
| Full Idea: Cantor's Continuum Hypothesis states that there are no sets which are too large for there to be a one-to-one correspondence between the set and the natural numbers, but too small for there to exist a one-to-one correspondence with the real numbers. | |
| From: report of George Cantor (works [1880]) by Leon Horsten - Philosophy of Mathematics §5.1 |
| 13528 | Continuum Hypothesis: there are no sets between N and P(N) [Cantor, by Wolf,RS] |
| Full Idea: Cantor's conjecture (the Continuum Hypothesis) is that there are no sets between N and P(N). The 'generalized' version replaces N with an arbitrary infinite set. | |
| From: report of George Cantor (works [1880]) by Robert S. Wolf - A Tour through Mathematical Logic 2.2 | |
| A reaction: The initial impression is that there is a single gap in the numbers, like a hole in ozone layer, but the generalised version implies an infinity of gaps. How can there be gaps in the numbers? Weird. |
| 9555 | Continuum Hypothesis: no cardinal greater than aleph-null but less than cardinality of the continuum [Cantor, by Chihara] |
| Full Idea: Cantor's Continuum Hypothesis was that there is no cardinal number greater than aleph-null but less than the cardinality of the continuum. | |
| From: report of George Cantor (works [1880]) by Charles Chihara - A Structural Account of Mathematics 05.1 | |
| A reaction: I have no view on this (have you?), but the proposal that there are gaps in the number sequences has to excite all philosophers. |
| 18174 | Cantor extended ordinals into the transfinite, and they can thus measure infinite cardinalities [Cantor, by Maddy] |
| Full Idea: Cantor's second innovation was to extend the sequence of ordinal numbers into the transfinite, forming a handy scale for measuring infinite cardinalities. | |
| From: report of George Cantor (works [1880]) by Penelope Maddy - Naturalism in Mathematics I.1 | |
| A reaction: Struggling with this. The ordinals seem to locate the cardinals, but in what sense do they 'measure' them? |
| 15893 | Cantor's theory concerns collections which can be counted, using the ordinals [Cantor, by Lavine] |
| Full Idea: Cantor's set theory was not of collections in some familiar sense, but of collections that can be counted using the indexes - the finite and transfinite ordinal numbers. ..He treated infinite collections as if they were finite. | |
| From: report of George Cantor (works [1880]) by Shaughan Lavine - Understanding the Infinite I |
| 18173 | Cardinality strictly concerns one-one correspondence, to test infinite sameness of size [Cantor, by Maddy] |
| Full Idea: Cantor's first innovation was to treat cardinality as strictly a matter of one-to-one correspondence, so that the question of whether two infinite sets are or aren't of the same size suddenly makes sense. | |
| From: report of George Cantor (works [1880]) by Penelope Maddy - Naturalism in Mathematics I.1 | |
| A reaction: It makes sense, except that all sets which are infinite but countable can be put into one-to-one correspondence with one another. What's that all about, then? |
| 10232 | Property extensions outstrip objects, so shortage of objects caused the Caesar problem [Cantor, by Shapiro] |
| Full Idea: Cantor's theorem entails that there are more property extensions than objects. So there are not enough objects in any domain to serve as extensions for that domain. So Frege's view that numbers are objects led to the Caesar problem. | |
| From: report of George Cantor (works [1880]) by Stewart Shapiro - Philosophy of Mathematics 4.6 | |
| A reaction: So the possibility that Caesar might have to be a number arises because otherwise we are threatening to run out of numbers? Is that really the problem? |
| 18176 | Pure mathematics is pure set theory [Cantor] |
| Full Idea: Pure mathematics ...according to my conception is nothing other than pure set theory. | |
| From: George Cantor (works [1880], I.1), quoted by Penelope Maddy - Naturalism in Mathematics I.1 | |
| A reaction: [an unpublished paper of 1884] So right at the beginning of set theory this claim was being made, before it was axiomatised, and so on. Zermelo endorsed the view, and it flourished unchallenged until Benacerraf (1965). |
| 8631 | Cantor says that maths originates only by abstraction from objects [Cantor, by Frege] |
| Full Idea: Cantor calls mathematics an empirical science in so far as it begins with consideration of things in the external world; on his view, number originates only by abstraction from objects. | |
| From: report of George Cantor (works [1880]) by Gottlob Frege - Grundlagen der Arithmetik (Foundations) §21 | |
| A reaction: Frege utterly opposed this view, and he seems to have won the day, but I am rather thrilled to find the great Cantor endorsing my own intuitions on the subject. The difficulty is to explain 'abstraction'. |
| 20589 | Maybe a person's true self is their second-order desires [Tuckness/Wolf] |
| Full Idea: A second-order desire is a desire about what kind of desires you want to have. ....Some philosophers have argued that we should associate a person's second-order desires with her 'true self'. | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 2 'What is') | |
| A reaction: Presumably the buck stops at these second-order desires, though we might request an account of their origin. 'What sort of person do I want to be?' looks like a third-order question. I don't even want to be a saint. Self is nothing to do with desires? |
| 8715 | Infinities expand the bounds of the conceivable; we explore concepts to explore conceivability [Cantor, by Friend] |
| Full Idea: Cantor (in his exploration of infinities) pushed the bounds of conceivability further than anyone before him. To discover what is conceivable, we have to enquire into the concept. | |
| From: report of George Cantor (works [1880]) by Michèle Friend - Introducing the Philosophy of Mathematics 6.5 | |
| A reaction: This remark comes during a discussion of Husserl's phenomenology. Intuitionists challenge Cantor's claim, and restrict what is conceivable to what is provable. Does possibility depend on conceivability? |
| 13454 | Cantor says (vaguely) that we abstract numbers from equal sized sets [Hart,WD on Cantor] |
| Full Idea: Cantor thought that we abstract a number as something common to all and only those sets any one of which has as many members as any other. ...However one wants to see the logic of the inference. The irony is that set theory lays out this logic. | |
| From: comment on George Cantor (works [1880]) by William D. Hart - The Evolution of Logic 1 | |
| A reaction: The logic Hart has in mind is the notion of an equivalence relation between sets. This idea sums up the older and more modern concepts of abstraction, the first as psychological, the second as logical (or trying very hard to be!). Cf Idea 9145. |
| 6017 | Nomos is king [Pindar] |
| Full Idea: Nomos is king. | |
| From: Pindar (poems [c.478 BCE], S 169), quoted by Thomas Nagel - The Philosophical Culture | |
| A reaction: This seems to be the earliest recorded shot in the nomos-physis wars (the debate among sophists about moral relativism). It sounds as if it carries the full relativist burden - that all that matters is what has been locally decreed. |
| 20583 | If maximising pleasure needs measurement, so does fulfilling desires [Tuckness/Wolf] |
| Full Idea: Just as hedonists need a way to compare pleasures, so desire fulfilment theorists need a way to compare the fulfilment of desires. | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 1 'Is happiness') | |
| A reaction: A nice point. We picture desire fulfilment as just ticking it off when it is achieved, but if your desire is for a really nice house, the achievement of that can be pretty vague. |
| 20584 | Desire satisfaction as the ideal is confused, because we desire what we judge to be good [Tuckness/Wolf] |
| Full Idea: Critics of desire satisfaction theory argue that it gets things backward. We desire things because we already think they are good in some way. Desire theory puts it the other way round. | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 1 'Is happiness') | |
| A reaction: Not persuasive. It looks to me as if skiing is a spendid pastime, but I have no desire to do it. More exercise would even be a good for me, but I don't desire that either. Indeed, right now I desire more cake, which is very naughty. |
| 20598 | In a democracy, which 'people' are included in the decision process? [Tuckness/Wolf] |
| Full Idea: In any democratic state, who are 'the people' who get to rule themselves? That is, who gets to participate in the public decision process, and who is excluded? | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 5 'What is') | |
| A reaction: In the modern world this may be clear-cut when a democracy gets started, but people move around so much more that every democracy is faced with new types of residents. Then there is age, criminality, mental health... |
| 20614 | People often have greater attachment to ethnic or tribal groups than to the state [Tuckness/Wolf] |
| Full Idea: Some states have a number of different ethnic or tribal groups. Often these attachments are much stronger than the attachment people feel towards the state. | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 6 'Membership') | |
| A reaction: In Britain I fine people torn between attachments to the UK and to England or Wales or Scotland or NI. Attachments to football clubs are much stronger than most patriotism. Or attachment to a particular locality. Does it matter? |
| 20596 | For global justice, adopt rules without knowing which country you will inhabit [Tuckness/Wolf] |
| Full Idea: Imagine a new original position where we adopted rules for global justice without knowing which country we would inhabit. | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 4 'Cosmopolitan') | |
| A reaction: Nice question. North Korea!! Rawls says it is only within a nation, because there is a co-operative enterprise going on. That is, I presume, that the choosers involved are a 'people'. See Kant's 'Perpetual Peace' for an alternative. |
| 20593 | The veil of ignorance ensures both fairness and unanimity [Tuckness/Wolf] |
| Full Idea: The veil of ignorance ensures that the original position is fair, but it also guarantees that agreement will be unanimous (which would be impossible if each person insisted that justice should match her own conception). | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 4 'Original') | |
| A reaction: Not clear about this. If I choose very cautiously, but others choose very riskily, and they win, why I should I fall in with their unanimity? That can only be if we agree to be unanimous in backing the result. Like a democratic election? |
| 20608 | Unjust institutions may be seen as just; are they legitimate if just but seen as unjust? [Tuckness/Wolf] |
| Full Idea: Legitimacy and perceived legitimacy do not always go together: people can believe that their institutions are just, but they may be wrong. Is the reverse also possible? Can institutions be legitimate if people believe they are not? | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 5 'What are') | |
| A reaction: Nice thoughts. An institution cannot be just merely because it is seen that way (if someone gets away with rigging an election). If they are just but seen as unjust, I presume they are legitimate (which is objective), but disfunctional. |
| 20597 | If winning elections depends on wealth, we have plutocracy instead of democracy [Tuckness/Wolf] |
| Full Idea: If we let people's influence on election outcomes depend on their wealth, then we don't have a democracy any more. We have a plutocracy, where the people who have all the wealth have all the political power too. | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 5 'Intro') | |
| A reaction: [see Michael Walzer on 'complex equality'] This is startling true in the United States, but still somewhat true elsewhere. Being wealthy enough to control the media is the key in modern democracies. |
| 20606 | Epistemic theories defend democracy as more likely to produce the right answer [Tuckness/Wolf] |
| Full Idea: According to epistemic theories of democracy, democratic outcomes are justified because they are more likely to be true or right than the choice of the individual. | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 5 'Do the people') | |
| A reaction: Bear in mind Condorcet's proof that this claim is only correct if individuals have a better than 50% chance of being right, which may be so on obvious things, but is implausible for decisions like going to war. |
| 20600 | Which areas of public concern should be decided democratically, and which not? [Tuckness/Wolf] |
| Full Idea: Are there areas which are excluded from democratic decision making? Or should all issues of public concern be decided through a democratic process? | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 5 'What is') | |
| A reaction: Crucially, are we discussing direct democracy, or representative democracy? In Britain all major decisions are made by the cabinet. Our representatives appoint leaders, who then appoint the decision makers. Judiciary is non-democratic. |
| 20609 | If several losing groups would win if they combine, a runoff seems called for [Tuckness/Wolf] |
| Full Idea: It is possible that the people who supported several losing candidates might have joined forces and had a majority. For that reason, many countries have a runoff election. | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 5 'Does democracy') | |
| A reaction: The problem is that there is no rationale as to who stands in an election. If their views are evenly spread, the first result seems OK. If there are five left-wingers and one right-winger, a runoff seems to be produce a more just result. |
| 20605 | Rights as interests (unlike rights as autonomy) supports mandatory voting [Tuckness/Wolf] |
| Full Idea: If rights concern people's interests, that might support mandatory voting, but if rights rely on protecting autonomy that might oppose it. | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 5 'Interest') | |
| A reaction: I approach it from the other end, and am inclined to support mandatory voting, which suggests I am more concerned about interests than about autonomy. |
| 20599 | How should democratic votes be aggregated? Can some person's votes count for more? [Tuckness/Wolf] |
| Full Idea: A major question for democracy is how are the contributions of different people aggregated into a collective decision? Must votes have equal weight and consideration, or is it permissible for different people's votes to count differently? | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 5 'What is') | |
| A reaction: Mill hoped that wise and knowledgeable people would have a strong influence over the others, but we have recently moved into the post-truth era, where we are swamped by bogus facts. Does that strengthen the case for elite voting? |
| 20601 | Discussion before voting should be an essential part of democracy [Tuckness/Wolf] |
| Full Idea: According to advocates of deliberative democracy, people should have an opportunity to talk and reason with one another before votes are cast. | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 5 'Who gets') | |
| A reaction: This is now done on Facebook and Twitter, but no one thinks that is sufficient. We will never again persuade most people to actually meet up and discuss issues. |
| 20613 | We have obligations to our family, even though we didn't choose its members [Tuckness/Wolf] |
| Full Idea: Many of our most important obligations are things we did not consent to. If you think you have obligations to your family, did you choose to have them as family members? | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 6 'Gratitude') | |
| A reaction: A question that gets close to the heart of the communitarian ideal, I think. We choose to have children, and we bring them up, but even then we don't choose who our children are. |
| 20586 | Free speech does not include the right to shout 'Fire!' in a crowded theatre [Tuckness/Wolf] |
| Full Idea: Oliver Wendell Holmes (in 1919) noted that freedom of speech does not include the right to shout 'Fire!' in a crowded theatre. | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 1 'Conflict') | |
| A reaction: The point here is that such irresponsible free speech does not even require legislation, and there is probably already some law under which the perpetrator could be prosecuted. |
| 20587 | Most people want equality because they want a flourishing life [Tuckness/Wolf] |
| Full Idea: If we want equality so much, we find that it is often because they think of equality as a prerequisite for a certain kind of flourishing life. | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 1 'Happiness') | |
| A reaction: Most writers seem to agree that we don't want equality for its own sake. In what respects do we want to be equal? Why not equal in hair colour? Hence it looks as if equality drops out. I would aim to derive it from the social virtue of respect. |
| 20591 | If there is no suffering, wealth inequalities don't matter much [Tuckness/Wolf] |
| Full Idea: It is hard to get worked up over wealth inequalities if no one is suffering from them! | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 3 'Deprivation') | |
| A reaction: The more the poorer group resent the inequality, the more they suffer. When is resenting huge inequalities in wealth justified? It depends how the big wealth was obtained. |
| 20602 | Some rights are 'claims' that other people should act in a certain way [Tuckness/Wolf] |
| Full Idea: A 'claim right' is one in which the person asserting the right makes a claim on others to act or not act in a certain way. | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 5 'Claim') | |
| A reaction: There seems to be a crucial distinction between rights which entail obligations on some individual or institution, and those which don't. Contracts (including employment contracts) generate duties on the parties. |
| 20604 | Choice theory says protecting individual autonomy is basic (but needs to cover infants and animals) [Tuckness/Wolf] |
| Full Idea: Choice theorists hold that rights protect our rights to make autonomous judgements, because our basic right to autonomy must be protected, The theory has a problem with people unable to exercise autonomy (such as infants and animals). | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 5 'Interest') | |
| A reaction: The problem of infants and animals looks like a decisive objection to me. We obviously don't protect dangerous or hostile autonomous judgements, and it is not clear why protecting stupid autonomy should be basic. |
| 20603 | One theory (fairly utilitarian) says rights protect interests (but it needs to cover trivial interests) [Tuckness/Wolf] |
| Full Idea: Interest theorists hold that rights serve to protect people's important interests. This is closely allied with utilitarian values. The theory has difficulty accounting for relatively trivial interests (like owning a lemonade you bought). | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 5 'Interest') | |
| A reaction: This sounds more plausible than choice theory (Idea 20604). It is obvious that infants must have rights. The lemonade problem seems to demand some sort of rule utilitarianism. Sidgwick looks promising. Rights can also be moral claims. |
| 20607 | Having a right does not entail further rights needed to implement it [Tuckness/Wolf] |
| Full Idea: Possession of a right (such as self-defence) does not always imply that one has additional rights to whatever they need (such as a handgun) in order to exercise the first right. | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 5 'Is there') | |
| A reaction: The right to life entails a right to food (but not to a banquet), so it is a stronger right than self-defence. I have no obligation to let you defend yourself against me, but I may have an obligation to feed you if you are starving. (Distinction here?) |
| 20612 | If being subject to the law resembles a promise, we are morally obliged to obey it [Tuckness/Wolf] |
| Full Idea: One of the more common reasons people will give for having a moral obligation to obey the law is consent. ...It rests on the intuitively appealing idea of an analogy with a promise. | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 6 'Consent') | |
| A reaction: [They cite Locke and Jefferson] In Locke's case it has to be a 'tacit' promise, which is more realistic. In real life we have problems with people who 'said' they would do something. They are often accused of promising, when they didn't. |
| 20611 | If others must obey laws that we like, we must obey laws that they like? [Tuckness/Wolf] |
| Full Idea: If we expect others to obey the laws we think just, do we have an obligation to obey the laws that other people think just? | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 6 'What should') | |
| A reaction: Depends whether you have to be consistent about everything. I'm picky about which laws I obey, but I'm not going to tell you that, in case you get the same idea. Free riders. |
| 20610 | Instead of against natural law, we might assess unjust laws against the values of the culture [Tuckness/Wolf] |
| Full Idea: Do we need natural law theory in order to make sense of the idea that laws can be unjust? Perhaps not: we might consider whether laws are consistent with the values of the culture or society where they apply. | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 5 'Unjust') | |
| A reaction: So were the wicked laws passed by the Nazis consistent with 1930s German culture? Impossible to say. |
| 20617 | How should the punishment fit the crime (for stealing chickens?) [Tuckness/Wolf] |
| Full Idea: One criticism of the retributive theory of punishment is that it is hard to know how to fit the punishment to the crime. What punishment should correspond to stealing chickens? | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 7 'Rationales') | |
| A reaction: The ancient world was more keen on restitution for such crimes, which makes much better sense. Buy them some chickens, plus twenty percent. |
| 20615 | Just wars: resist aggression, done on just cause, proportionate, last resort, not futile, legal [Tuckness/Wolf] |
| Full Idea: Classical just war theory: resist aggression; just cause must be the real reason; must be proportionate; last resort; not futile; made by a nation's authority. | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 9 'Ius ad') | |
| A reaction: [My squashed summary of Tuckness and Wolf] A very helpful list, from Cicero, Augustine and Aquinas. So where is the sticking point for pacifists? Presumably it is never the last resort, and aggression should not answer aggression. |
| 20616 | During wars: proportional force, fair targets, fair weapons, safe prisoners, no reprisals [Tuckness/Wolf] |
| Full Idea: Classical just war theory during a war: force must be proportional; only legitimate targets; avoid prohibited weapons; safety for prisoners of war; no reprisals. | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 9 'In the conduct') | |
| A reaction: What of massacre if a besieged city refuses to surrender? It was commonplace, and sometimes the only way to achieve victory. What if the enemy breaks all the rules? Nice rules though. At the heart of civilisation. |
| 20620 | If minority views are accepted in debate, then religious views must be accepted [Tuckness/Wolf] |
| Full Idea: It is unfair to exclude religious arguments from the public square because they are not accepted by everyone, unless other views that are not accepted by everyone are also excluded. | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 9 'fairly') | |
| A reaction: Raises the obvious problems of a huge group in the grips of a fairly crazy view, and a tiny group (e.g. specialist scientists) in possession of a correct view. You can't just assess it on the size of the group. You can be wrong but reasonable. |
| 20619 | Is abortion the ending of a life, or a decision not to start one? [Tuckness/Wolf] |
| Full Idea: One group may consider abortion as a decision to end a life, while another may regard it as the decision not to start one. | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 8 'Hard I') | |
| A reaction: An early foetus is 'life', but is it 'a life'? Is a blade of grass 'a life'? Is a cell in a body 'a life'? |
| 10863 | Cantor proved that three dimensions have the same number of points as one dimension [Cantor, by Clegg] |
| Full Idea: Cantor proved that one-dimensional space has exactly the same number of points as does two dimensions, or our familiar three-dimensional space. | |
| From: report of George Cantor (works [1880]) by Brian Clegg - Infinity: Quest to Think the Unthinkable Ch.14 |
| 13465 | Only God is absolutely infinite [Cantor, by Hart,WD] |
| Full Idea: Cantor said that only God is absolutely infinite. | |
| From: report of George Cantor (works [1880]) by William D. Hart - The Evolution of Logic 1 | |
| A reaction: We are used to the austere 'God of the philosophers', but this gives us an even more austere 'God of the mathematicians'. |