72 ideas
| 5333 | Philosophy needs wisdom about who we are, as well as how we ought to be [Flanagan] |
| Full Idea: Any good philosophy will need to offer wisdom about who we are as well as about how we ought to be. | |
| From: Owen Flanagan (The Problem of the Soul [2002], p. 14) | |
| A reaction: This sop should be accepted gratefully by fans of bioethics, who seem inclined to think that describing 'how we are' is all that needs to be said. Maybe the key wisdom lies in the relationship between the 'is' and the 'ought' of human nature. |
| 5334 | We resist science partly because it can't provide ethical wisdom [Flanagan] |
| Full Idea: The inability of science to provide ethical wisdom is partly responsible for our resistance to the scientific image. | |
| From: Owen Flanagan (The Problem of the Soul [2002], p. 14) | |
| A reaction: This seems right. A.J. Ayer, for example, declared "I believe in science", and his account of ethics was vacuously nihilistic. A description of the mechanisms of moral life is not the same as ethical wisdom. |
| 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] |
| 4261 | The Lottery Paradox says each ticket is likely to lose, so there probably won't be a winner [Bonjour, by PG] |
| Full Idea: The Lottery Paradox says that for 100 tickets and one winner, each ticket has a .99 likelihood of defeat, so they are all likely to lose, so there is unlikely to be a winner. | |
| From: report of Laurence Bonjour (Externalist Theories of Empirical Knowledge [1980], §5) by PG - Db (ideas) | |
| A reaction: The problem seems to be viewing each ticket in isolation. If I buy two tickets, I increase my chances of winning. |
| 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'. |
| 4255 | Externalist theories of knowledge are one species of foundationalism [Bonjour] |
| Full Idea: Externalist theories of knowledge are one species of foundationalism. | |
| From: Laurence Bonjour (Externalist Theories of Empirical Knowledge [1980], Intro) | |
| A reaction: I don't see why there shouldn't be a phenomenalist, anti-realist version of externalism, which just has 'starting points' instead of a serious commitment to foundations. |
| 4257 | The big problem for foundationalism is to explain how basic beliefs are possible [Bonjour] |
| Full Idea: The fundamental question that must be answered by any acceptable version of foundationalism is: how are basic beliefs possible? | |
| From: Laurence Bonjour (Externalist Theories of Empirical Knowledge [1980], §I) | |
| A reaction: This question seems to be asking for a justification for basic beliefs, which smacks of 'Who made God?' Look, basic beliefs are just basic, right? |
| 4256 | The main argument for foundationalism is that all other theories involve a regress leading to scepticism [Bonjour] |
| Full Idea: The central argument for foundationalism is simply that all other possible outcomes of the regress of justifications lead inexorably to scepticism. | |
| From: Laurence Bonjour (Externalist Theories of Empirical Knowledge [1980], §I) | |
| A reaction: If you prefer coherence to foundations, you need the security of reason to assess the coherence (which seems to be an internal foundation!). |
| 4258 | Extreme externalism says no more justification is required than the truth of the belief [Bonjour] |
| Full Idea: The most extreme version of externalism would be one that held that the external condition required for justification is simply the truth of the belief in question. | |
| From: Laurence Bonjour (Externalist Theories of Empirical Knowledge [1980], §II) | |
| A reaction: The question is, why should we demand any more than this? The problem case is, traditionally, the lucky guess, but naturalist may say that these just don't occur with any regularity. We only get beliefs right because they are true. |
| 4259 | External reliability is not enough, if the internal state of the believer is known to be irrational [Bonjour] |
| Full Idea: External or objective reliability is not enough to offset subjective irrationality (such as unexplained clairvoyance). | |
| From: Laurence Bonjour (Externalist Theories of Empirical Knowledge [1980], §IV) | |
| A reaction: A good argument. Where do animals fit into this? If your clairvoyance kept working, in the end you might concede that you 'knew', even though you were baffled about how you managed it. |
| 4260 | Even if there is no obvious irrationality, it may be irrational to base knowledge entirely on external criteria [Bonjour] |
| Full Idea: It may be that where there are no positive grounds for a charge of irrationality, the acceptance of a belief with only external justification is still subjectively irrational in a sense that rules out its being epistemologically justified. | |
| From: Laurence Bonjour (Externalist Theories of Empirical Knowledge [1980], §IV) | |
| A reaction: A key objection. Surely rational behaviour requires a judgement to be made before a belief is accepted? If you are consistently clairvoyant, you must ask why. |
| 5340 | Explanation does not entail prediction [Flanagan] |
| Full Idea: Explanation does not entail prediction. | |
| From: Owen Flanagan (The Problem of the Soul [2002], p. 73n) | |
| A reaction: Presumably the inverse of this is also true, as we might be able to predict through pure induction, without knowing why something happened. We predict that smoking is likely to cause cancer. Complex things might be explicable but unpredictable. |
| 5346 | In the 17th century a collisionlike view of causation made mental causation implausible [Flanagan] |
| Full Idea: In the seventeenth century the dominant idea that causation is collisionlike made mental causation almost impossible to envision. | |
| From: Owen Flanagan (The Problem of the Soul [2002], p.136) | |
| A reaction: Interesting. This makes Descartes' interaction theory look rather bold, and Leibniz's and Malebranche's rejection of it understandable. Personally I still think of causation as collisionlike, except that the collisions are of very very tiny objects. |
| 5341 | Only you can have your subjective experiences because only you are hooked up to your nervous system [Flanagan] |
| Full Idea: It is easy to explain why certain brain events are uniquely experienced by you subjectively: only you are properly hooked up to your own nervous system to have your own experiences. | |
| From: Owen Flanagan (The Problem of the Soul [2002], p. 87) | |
| A reaction: This is in reply to Nagel's oft quoted claim that mind can only be understood as "what it is like to be" that mind. I agree with Flanagan, and it is nice illustration of how philosophers can confuse themselves with high-sounding questions. |
| 5351 | We only have a sense of our self as continuous, not as exactly the same [Flanagan] |
| Full Idea: We only have a sense of our self as continuous, but not as exactly the same. | |
| From: Owen Flanagan (The Problem of the Soul [2002], p.178) | |
| A reaction: Russell said this too, and it seems to me to be right. Personal identity is far too imprecise for me to assert that I remember my ten-year-old self as being identical to me now. Only physical objects like teddy bears can pass that test. |
| 5353 | The self is an abstraction which magnifies important aspects of autobiography [Flanagan] |
| Full Idea: The self is an abstraction from the story of a person's life that isolates and magnifies the experiences, traits and aspirations that are assigned importance. | |
| From: Owen Flanagan (The Problem of the Soul [2002], p.240) | |
| A reaction: Personally I am inclined to see personal identity as the central controller of brain activity, the aspect of the biological machine which keeps all the mental events focused on what matters, which is health, safety and happiness. |
| 5354 | We are not born with a self; we develop a self through living [Flanagan] |
| Full Idea: It is a bad mistake to think we are born with a self; the self develops, and acquiring it requires living in the world. | |
| From: Owen Flanagan (The Problem of the Soul [2002], p.260) | |
| A reaction: I think this is wrong. He is mistaking a complex cultural concept of the self as the subject for autobiography etc. for the basic biological self which even small animals must have if their brains are to serve any useful purpose in their lives. |
| 5349 | For Buddhists a fixed self is a morally dangerous illusion [Flanagan] |
| Full Idea: According to Buddhism, the idea of a permanent, constant self is an illusion, and a morally dangerous one. | |
| From: Owen Flanagan (The Problem of the Soul [2002], p.161) | |
| A reaction: We are familiar with the idea that it might be an illusion, but I am unconvinced by 'morally dangerous'. If you drop both free will and personal identity, I can't see any sort of focus for moral life left, but I am willing to be convinced. |
| 5338 | Normal free will claims control of what I do, but a stronger view claims control of thought and feeling [Flanagan] |
| Full Idea: The standard view of free will is that I have something like complete control over what I do. A stronger view (not widely held) is that I also have complete control over what I think and what I feel. | |
| From: Owen Flanagan (The Problem of the Soul [2002], p. 60n) | |
| A reaction: To claim free control of feelings looks optimistic, but it does look as if we can decide to think about something, such as a philosophical problem. Deciding what to say comes somewhere between thought and action. |
| 5344 | Free will is held to give us a whole list of desirable capacities for living [Flanagan] |
| Full Idea: Free will is said to give us self-control, self-expression, individuality, reasons-sensitivity, rational deliberation, rational accountability, moral accountability, the capacity to do otherwise, unpredictability, and political freedom. | |
| From: Owen Flanagan (The Problem of the Soul [2002], p.104) | |
| A reaction: Nice list. His obvious challenge is to either say we can live happily without some of these things, or else show how we can have them without 'free will'. Personally I agree with Flanagan that we meet the challenge. |
| 5332 | People believe they have free will that circumvents natural law, but only an incorporeal mind could do this [Flanagan] |
| Full Idea: Most people believe we have free will, and that this consists in the ability to circumvent natural law. The trouble is that the only device ever philosophically invented that can do this sort of job is an incorporeal soul or mind. | |
| From: Owen Flanagan (The Problem of the Soul [2002], Pref) | |
| A reaction: I think this is exactly right. We currently have a western world full of people who have rejected dualism, but still cling on to free will, because they think morality depends on it. I think morality depends on personal identity, but not on free will. |
| 5345 | We only think of ourselves as having free will because we first thought of God that way [Flanagan] |
| Full Idea: It is unimaginable to me that, despite the feeling that we control what we do, such a strong conception of ourselves as unmoved movers would have been added to our self-image unless we had first conceived of God along these lines. | |
| From: Owen Flanagan (The Problem of the Soul [2002], p.107) | |
| A reaction: I think this is right, though there are signs in fifth century Greece of contradictory evidence. The 'unmoved mover' seems unformulated before Plato's 'Laws' (idea 1423), but there is an implied belief in free will a hundred years earlier. |
| 5343 | People largely came to believe in dualism because it made human agents free [Flanagan] |
| Full Idea: I would say that that my consciousness doesn't seem either physical or non-physical, ..but the belief that the mind is non-physical partly took hold because that fits well with thinking of human agents as free. | |
| From: Owen Flanagan (The Problem of the Soul [2002], p.102) | |
| A reaction: I think this is right. I personally think there is no such thing as free will, and that belief in it has been the single greatest delusion amongst philosophers (and others) for the last two thousand years. Dualism has now gone, and free will is next. |
| 5347 | Behaviourism notoriously has nothing to say about mental causation [Flanagan] |
| Full Idea: Behaviourism was notorious in its heyday for having nothing to say about mental causation. | |
| From: Owen Flanagan (The Problem of the Soul [2002], p.141) | |
| A reaction: This is a bit unfair, as Ryle (idea 2622, following Spinoza, 4862) was one of the first to point out the paradox of 'double causation'. You have to be a mentalist to worry about mental causation, and eliminativists aren't bothered. |
| 5339 | Cars and bodies obey principles of causation, without us knowing any 'strict laws' about them [Flanagan] |
| Full Idea: Although everyone thinks cars and bodies obey the principles of causation, no one thinks it a deficiency that we don't know strict laws of automechanics or anatomy. | |
| From: Owen Flanagan (The Problem of the Soul [2002], p. 65) | |
| A reaction: This attacks Davidson's claim that there are no strict psycho-physical laws, and I agree with Flanagan. Huge dreams of free will and human dignity are being pinned on the flimsy point that we have no strict laws here. But brains are very complicated. |
| 5342 | Physicalism doesn't deny that the essence of an experience is more than its neural realiser [Flanagan] |
| Full Idea: One may be committed to the truth of physicalism without being committed to the claim that the essence of an experience is captured fully by a description of its neural realiser. | |
| From: Owen Flanagan (The Problem of the Soul [2002], p. 90) | |
| A reaction: This is a reply to the Leibniz Mill question (idea 2109) about what is missing from a materialist view. Flanagan's point is that just as the essence of a panorama is the view from the hill, so the essence of consciousness requires you to be that brain. |
| 5335 | Emotions are usually very apt, rather than being non-rational and fickle [Flanagan] |
| Full Idea: One can question the idea that emotions are non-rational, fickle and flighty; on the contrary, emotions normally seem to be very apt. | |
| From: Owen Flanagan (The Problem of the Soul [2002], p. 16) | |
| A reaction: This is the modern view of emotion which is emerging from neuroscience, which is greatly superior to traditional views, apart from Aristotle, who felt that wisdom and virtue arose precisely when emotions were apt for the situation. |
| 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. |
| 5348 | Intellectualism admires the 'principled actor', non-intellectualism admires the 'good character' [Flanagan] |
| Full Idea: There are two main pictures of the good person: there is the 'good character', and there is the 'principled actor'. ..The first picture is non-intellectualist, and the second is intellectualist. | |
| From: Owen Flanagan (The Problem of the Soul [2002], p.145) | |
| A reaction: The second ideal elevates the principle itself above the actor who carries it out. Presumably consistency is a virtue, so a good character will at least pay some attention to principles. A good magistrate comes out the same in both views. |
| 5355 | Cognitivists think morals are discovered by reason [Flanagan] |
| Full Idea: Cognitivists think morals are discovered by reason. | |
| From: Owen Flanagan (The Problem of the Soul [2002], p.301n) | |
| A reaction: I take cognitivism to be (strictly) the view that morals are knowable in principle. Our intellects might not be up to the task (and so we might have to ask the gods what is right). There is also the possibility that morals might be known by intuition. |
| 5336 | Ethics is the science of the conditions that lead to human flourishing [Flanagan] |
| Full Idea: Ethics is the normative science that studies the objective conditions that lead to flourishing of persons. | |
| From: Owen Flanagan (The Problem of the Soul [2002], p. 17) | |
| A reaction: This is a nice slogan for the virtue theory account of the nature of ethics. I think it is the view with which I agree. I am intrigued that he has smuggled the word 'science' in, which is a nice challenge to conventional views of science. |
| 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'. |
| 5350 | The Hindu doctrine of reincarnation only appeared in the eighth century CE [Flanagan] |
| Full Idea: The doctrine of a cycle of rebirths and reincarnations that are normally required before one achieve nirvana was only proposed in the eighth century CE, and then spread like wildfire among Hindus and, to a lesser extent, among Buddhists. | |
| From: Owen Flanagan (The Problem of the Soul [2002], p.166n) | |
| A reaction: Intriguing. Plato had proposed it in the fourth century BCE. Presumably Hindus had always been dualists, and then suddenly saw and exciting possibility that followed from it. The doctrine strikes me as (to put it mildly) implausible. |
| 5352 | The idea of the soul gets some support from the scientific belief in essential 'natural kinds' [Flanagan] |
| Full Idea: The idea of the soul could be easily trashed if science does not countenance essences, but science does countenance essences in the form of what are known as 'natural kinds' (such as water, salt and gold). | |
| From: Owen Flanagan (The Problem of the Soul [2002], p.181) | |
| A reaction: The existence of any essences at all does indeed make the existence of a soul naturally possible, but scientific natural kinds are usually postulated on a basis of chemical stability. Animals, for example, are no longer usually classified that way. |