86 ideas
| 23966 | The personal view can still be objective, so I call sciences 'impersonal', rather than objective [Goldie] |
| Full Idea: 'Objective' is misleading because it is possible to be, from a personal point of view, more or less objective; objectivity admits of degrees… I prefer to speak of sciences as 'impersonal', because the personal view is lost. | |
| From: Peter Goldie (The Emotions [2000], Intro) | |
| A reaction: This evidently relates to Perry's claim that the world contains additional indexical facts. I think I agree with this thought. Objectivity is a mode of subjectivity. Thermometers are not 'objective'. Physics is certainly impersonal. |
| 8877 | We can't attain a coherent system by lopping off any beliefs that won't fit [Sosa] |
| Full Idea: Coherence involves the logical, explanatory and probabilistic relations among one's beliefs, but it could not do to attain a tightly iterrelated system by lopping off whatever beliefs refuse to fit. | |
| From: Ernest Sosa (Beyond internal Foundations to external Virtues [2003], 6.4) | |
| A reaction: This is clearly right, so the coherentist has to distinguish between lopping off a belief because it is inconvenient (fundamentalists rejecting textual contradictions), and lopping it off because it is wrong (chemists rejecting phlogiston). |
| 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'. |
| 8884 | The phenomenal concept of an eleven-dot pattern does not include the concept of eleven [Sosa] |
| Full Idea: You could detect the absence of an eleven-dot pattern without having counted the dots, so your phenomenal concept of that array is not an arithmetical concept, and its content will not yield that its dots do indeed number eleven. | |
| From: Ernest Sosa (Beyond internal Foundations to external Virtues [2003], 7.3) | |
| A reaction: Sosa is discussing foundational epistemology, but this draws attention to the gulf that has to be leaped by structuralists. If eleven is not derived from the pattern, where does it come from? Presumably two eleven-dotters are needed, to map them. |
| 8878 | It is acceptable to say a supermarket door 'knows' someone is approaching [Sosa] |
| Full Idea: I am quite flexible on epistemic terminology, and am even willing to grant that a supermarket door can 'know' that someone is approaching. | |
| From: Ernest Sosa (Beyond internal Foundations to external Virtues [2003], 6.6) | |
| A reaction: I take this amazing admission to be a hallmark of externalism. Sosa must extend this to thermostats. So flowers know the sun has come out. This is knowledge without belief. Could the door ever be 'wrong'? |
| 8880 | In reducing arithmetic to self-evident logic, logicism is in sympathy with rationalism [Sosa] |
| Full Idea: In trying to reduce arithmetic to self-evident logical axioms, logicism is in sympathy with rationalism. | |
| From: Ernest Sosa (Beyond internal Foundations to external Virtues [2003], 6.7) | |
| A reaction: I have heard Frege called "the greatest of all rationalist philosophers". However, the apparent reduction of arithmetic to analytic truths played into the hands of logical positivists, who could then marginalise arithmetic. |
| 8881 | Most of our knowledge has insufficient sensory support [Sosa] |
| Full Idea: Almost nothing that one knows of history or geography or science has adequate sensory support, present or even recalled. | |
| From: Ernest Sosa (Beyond internal Foundations to external Virtues [2003], 6.7) | |
| A reaction: This seems a bit glib, and may be false. The main issue to which this refers is, of course, induction, which (almost by definition) is a supposedly empirical process which goes beyond the empirical evidence. |
| 8882 | Perception may involve thin indexical concepts, or thicker perceptual concepts [Sosa] |
| Full Idea: There is a difference between having just an indexical concept which one can apply to a perceptual characteristic (just saying 'this is thus'), and having a thicker perceptual concept of that characteristic. | |
| From: Ernest Sosa (Beyond internal Foundations to external Virtues [2003], 7.2) | |
| A reaction: Both of these, of course, would precede any categorial concepts that enabled one to identify the characteristic or the object. This is a ladder foundationalists must climb if they are to reach the cellar of basic beliefs. |
| 8883 | Do beliefs only become foundationally justified if we fully attend to features of our experience? [Sosa] |
| Full Idea: Are foundationally justified beliefs perhaps those that result from attending to our experience and to features of it or in it? | |
| From: Ernest Sosa (Beyond internal Foundations to external Virtues [2003], 7.3) | |
| A reaction: A promising suggestion. I do think our ideas acquire a different epistmological status once we have given them our full attention, though is that merely full consciousness, or full thoughtful evaluation? The latter I take to be what matters. Cf Idea 2414. |
| 8885 | Some features of a thought are known directly, but others must be inferred [Sosa] |
| Full Idea: Some intrinsic features of our thoughts are attributable to them directly, or foundationally, while others are attributable only based on counting or inference. | |
| From: Ernest Sosa (Beyond internal Foundations to external Virtues [2003], 7.5) | |
| A reaction: In practice the brain combines the two at a speed which makes the distinction impossible. I'll show you ten dot-patterns: you pick out the sixer. The foundationalist problem is that only those drained of meaning could be foundational. |
| 8876 | Much propositional knowledge cannot be formulated, as in recognising a face [Sosa] |
| Full Idea: Much of our propositional knowledge is not easily formulable, as when a witness looking at a police lineup may know what the culprit's face looks like. | |
| From: Ernest Sosa (Beyond internal Foundations to external Virtues [2003], 6.1) | |
| A reaction: This is actually a very helpful defence of foundationalism, because it shows that we will accept perceptual experiences as knowledge when they are not expressed as explicit propositions. Davidson (Idea 8801), for example, must deal with this difficulty. |
| 8879 | Fully comprehensive beliefs may not be knowledge [Sosa] |
| Full Idea: One's beliefs can be comprehensively coherent without amounting to knowledge. | |
| From: Ernest Sosa (Beyond internal Foundations to external Virtues [2003], 6.6) | |
| A reaction: Beliefs that are fully foundational or reliably sourced may also fail to be knowledge. I take it that any epistemological theory must be fallibilist (Idea 6898). Rational coherentism will clearly be sensitive to error. |
| 24005 | We know other's emotions by explanation, contagion, empathy, imagination, or sympathy [Goldie] |
| Full Idea: We know others' emotions by 1) understanding and explaining them, 2) emotional contagion, 3) empathy, 4) in-his-shoes imagining, and 5) sympathy. | |
| From: Peter Goldie (The Emotions [2000], 7 Intro) | |
| A reaction: He says these must be clearly distinguished, because they are often confused. In-his-shoes is 'me in their position', where empathy is how the position is just for them. The Simulationist approach likes these two. Sympathy need not share the feelings. |
| 24006 | Empathy and imagining don't ensure sympathy, and sympathy doesn't need them [Goldie] |
| Full Idea: Empathy and in-his-shoes imagining are not sufficient for sympathy. Nor are they necessary. You can even sympathise with another when these are impossible, with the sufferings of a whale or a dog, for example. | |
| From: Peter Goldie (The Emotions [2000], 7 'Sympathy') | |
| A reaction: Goldie is right that these distinct faculties are a blurred muddle in most of our accounts of dealing with other people. Empathy with a whale in not actually impossible, because we recognise their suffering, and we understand suffering. |
| 23978 | 'Having an emotion' differs from 'being emotional' [Goldie] |
| Full Idea: There is a contrast in commonsense psychology between 'being emotional' and 'having an emotion'. | |
| From: Peter Goldie (The Emotions [2000], 2 'Conclusion') | |
| A reaction: Is this just that being emotional is displaying the existing emotion? Though we say someone is 'being emotional' when the emotion seems to take control of their actions. |
| 23973 | Unlike moods, emotions have specific objects, though the difference is a matter of degree [Goldie] |
| Full Idea: Emotions have more specific objects than moods. The difference is a matter of degree, so emotions don't necessarily have a specific object, and moods are not necessarily undirected towards an object, or lacking in intentionality. | |
| From: Peter Goldie (The Emotions [2000], 2 'Intentionality') | |
| A reaction: Could you simultaneously have an emotion and a mood which were in conflict, such as joy and misery (singing the blues), or love and hate ('odi et amo')? Could one transition into the other, as the object became clear, or faded away? |
| 23974 | Emotional intentionality as belief and desire misses out the necessity of feelings [Goldie] |
| Full Idea: Many philosophers who discuss the intentionality of the emotions seek to capture the intentionality of the emotions in terms of beliefs, or beliefs and desires. I think this is a mistake, and runs the risk of leaving feelings out of emotional experience. | |
| From: Peter Goldie (The Emotions [2000], 2 'Intentionality') | |
| A reaction: [He gives a list, which includes Kenny and Davidson] I would have thought that desires, at least, necessarily involve feelings, and neuroscientists seem to find emotions everywhere, including as part of belief. Be more holistic? |
| 23972 | A long lasting and evolving emotion is still seen as a single emotion, such as love [Goldie] |
| Full Idea: In narratives the different elements of an emotion are conceived of as all being part of the same emotion, in spite of its complex, episodic and dynamic features. Verbs expressing emotions don not use continuous tenses, such as 'he is being in love'. | |
| From: Peter Goldie (The Emotions [2000], 2 'What') | |
| A reaction: Goldie is keen on seeing emotions as part of a life narrative. An intriguing problem for the metaphysics of identity. If someone's love for a person comes and goes, is it the same love each time? |
| 23992 | Some Aborigines have fifteen different words for types of fear [Goldie] |
| Full Idea: The Pintupi Aborigines of the Western Australian Desert have no less than fifteen words for different types of fear, including one for a sudden fear which leads one to stand up to see what caused it. | |
| From: Peter Goldie (The Emotions [2000], 4 'Evidence') | |
| A reaction: Reminiscent of the many Inuit words for snow, but this time it is about human experience, rather than the environment. We must assume they can distinguish the different types, so these gradations are real. |
| 23979 | Emotional responses can reveal to us our values, which might otherwise remain hidden [Goldie] |
| Full Idea: Our emotional responses can reveal to us what we value, and what we value might not be epistemically accessible to us if we did not have such responses. | |
| From: Peter Goldie (The Emotions [2000], 2 'Conclusion') | |
| A reaction: This obviously invites the question of whether the emotion reveals the value, or determines the value. I suspect it is more the latter, because it is hard to see what art (for example) could have for us if we had no emotional responses. |
| 23976 | If we have a 'feeling towards' an object, that gives the recognition a different content [Goldie] |
| Full Idea: The content of the recognition in 'feeling towards' is different from the content of the recognition where no emotion is involved. | |
| From: Peter Goldie (The Emotions [2000], 2 'Education') | |
| A reaction: ['Feeling toward' is Goldie's coinage, to capture the intentionality in felt emotion] Interesting, but not convinced. Maybe the emotion just follows fast after the mere recognition. When I recognise a friend in a crowd, that triggers a feeling. |
| 23977 | When actions are performed 'out of' emotion, they appear to be quite different [Goldie] |
| Full Idea: Consider striking a blow or seeking safety unemotionally. Now consider when you act out of emotion: angrily striking the blow, or fearfully running away. The phenomenology of such actions is fundamentally different in character. | |
| From: Peter Goldie (The Emotions [2000], 2 'Explanation') | |
| A reaction: True, I guess. This has the behaviourist's problem of Superactors and Superspartans, of pretended or suppressed anger or fear. There is a sliding scale from stone cold to frenzied emotion. |
| 23980 | It is best to see emotions holistically, as embedded in a person's life narrative [Goldie] |
| Full Idea: The best understanding of a person's emotions …will be holistic in its overall approach, seeing feelings as embedded in an emotion's narrative, as part of a person's life. | |
| From: Peter Goldie (The Emotions [2000], 3 Intro) | |
| A reaction: Sounds reasonable, but I didn't find it very helpful. When told that my Self or my life has a 'narrative' I don't learn much. The concept of narrative relies on selves and lives. Ditto for being told that emotions or language are 'holistic'. |
| 23982 | If emotions are 'towards' things, they can't be bodily feelings, which lack aboutness [Goldie] |
| Full Idea: If emotion has the world-directed intentionality of 'feeling towards' it follows that it is not bodily feeling, for bodily feelings lack the required 'direct' (as contrasted with 'borrowed') intentionality. | |
| From: Peter Goldie (The Emotions [2000], 3 'Towards') | |
| A reaction: This is a direct response to William James's view, and seems correct. It is a widely held view that emotions are usually 'about' something, and it is hard to see how getting red in the face could do that. |
| 23968 | If reasons are seen impersonally (as just causal), then feelings are an irrelevant extra [Goldie] |
| Full Idea: If someone thought that reasons can be characterised impersonally, say in terms of causal role …it is then glaringly obvious that feelings cannot be left out, so they have to be added on. Hence I introduce the idea of 'feeling towards'. | |
| From: Peter Goldie (The Emotions [2000], Intro) | |
| A reaction: [compressed] That is, he wants us to see feelings as intentional, active, motivating and causal, and not the marginal epiphenomena implied by an impersonal account. I think he is right. |
| 23969 | We have feelings of which we are hardly aware towards things in the world [Goldie] |
| Full Idea: One can be unreflectively emotionally engaged with the world, having feelings towards some object in the world, and yet at that moment not be reflectively aware of having those feelings. | |
| From: Peter Goldie (The Emotions [2000], Intro) | |
| A reaction: I'm thinking that we do not just await some 'object' to trigger a background feeling, because we always have feelings. They are the continuous shifting wallpaper of our mental dwellings - which we sometimes notice. |
| 23984 | An emotion needs episodes of feeling, but not continuously [Goldie] |
| Full Idea: I see no need to insist that feelings …must be present at all times whilst you are having an emotion, …but without at least episodes of feeling, of which you can be more or less aware, an experience would not be an emotional one. | |
| From: Peter Goldie (The Emotions [2000], 3 'Unreflective') | |
| A reaction: [He cites William James] An odd situation, but it is the same as many chronic illnesses. Presumably because of the actual episodes the person will be aware of the emotion as a background state of potential episodes. |
| 24001 | Moods can focus as emotions, and emotions can blur into moods [Goldie] |
| Full Idea: A mood can focus into an emotion, and an emotion can blur out of focus into the non-specificity of mood. | |
| From: Peter Goldie (The Emotions [2000], 6 'Mood') | |
| A reaction: I am struck by how the strong emotion of a vivid dream can remain as an inarticulate mood for the rest of the day. |
| 23970 | Emotions are not avocado pears, with a rigid core and changeable surface [Goldie] |
| Full Idea: In an evolutionary and cultural account of emotions, I resist the 'avocado pear' conception of emotions, that our emotional behaviour comprises an inner core of 'hard-wired' reaction, and an out element which is open to cultural influences. | |
| From: Peter Goldie (The Emotions [2000], Intro) | |
| A reaction: He is concerned with whether emotions can be educated, and defends the view that they can all be channelled or changed. In particular he rejects the idea that the stone consists of 'basic' emotions, which are untouchable. |
| 23985 | A basic emotion is the foundation of a hierarchy, such as anger for types of annoyance [Goldie] |
| Full Idea: The idea of basic emotions is that our concepts of emotions are hierarchically organised. For example, if anger is a basic emotion, then less basic species of anger might be annoyance, fury, rage, indignation, and so forth. | |
| From: Peter Goldie (The Emotions [2000], 4 'Evidence') | |
| A reaction: Most modern theorists seem to reject this idea. In a family of related emotions (each having a similar focal object), it is hard to see which one of them is basic, other than being the best known. Maybe the weakest one is basic? |
| 23986 | Early Chinese basic emotions: joy, anger, sadness, fear, love, disliking, and liking [Goldie] |
| Full Idea: The Chinese Li Chi encyclopaedia (1st century BCE) says there are seven 'feelings of men': joy, anger, sadness, fear, love, disliking, and liking. | |
| From: Peter Goldie (The Emotions [2000], 4 'Evidence') | |
| A reaction: [In J.Russell 1991] Love sounds like a stronger version of liking. If you are trying to train your feelings, it is helpful to have a basic list of them, even if the list is rather speculative. |
| 23991 | Cross-cultural studies of facial expressions suggests seven basic emotions [Goldie] |
| Full Idea: It has been suggested that there are seven 'basic' emotions, based on cross-cultural studies of facial expressions. | |
| From: Peter Goldie (The Emotions [2000], 4 'Evidence') | |
| A reaction: [Paul Ekman is cited] This makes the idea of universal basic emotions much more plausible. Goldie respects the research, but is cautious about inferences, mainly because digging deeper (such as interviews) makes it more complex. |
| 23967 | Some emotions are direct responses, and neither rational nor irrational [Goldie] |
| Full Idea: It is perfectly intelligible and entirely human to experience an emotion when seeing a low-flying bat, where we would not want to say that the experience was either rational or irrational. | |
| From: Peter Goldie (The Emotions [2000], Intro) | |
| A reaction: Goldie is attacking the common tendency of philosophers to over-intellectualise emotions. This example makes his point conclusively. |
| 23971 | Emotional thought is not rational, but it can be intelligible [Goldie] |
| Full Idea: Emotions are not based on syllogistic reasoning ….but the thoughts involved in an emotion can show it to be intelligible, intelligibility being a thinner notion than rationality. | |
| From: Peter Goldie (The Emotions [2000], 1 Intro) | |
| A reaction: A nice distinction. The emotion is the best explanation. Compare 'intuition' and 'sensible' behaviour as also intelligible. An obvious problem is that if a person runs amok because they have a brain tumour, that is intelligible, but in no way rational. |
| 23975 | Learning an evaluative property like 'dangerous' is also learning an emotion [Goldie] |
| Full Idea: The process of teaching a child how to identify things which are dangerous is typically one and the same process as teaching that child when fear is merited. ...'Dangerous' is an evaluative property, meriting a certain sort of response. | |
| From: Peter Goldie (The Emotions [2000], 2 'Education') | |
| A reaction: I like this, because it shows the unity between our inner life and our experience of the external world. Concepts and emotions are usually responses, rather than private initiatives. |
| 23983 | We call emotions 'passions' because they are not as controlled as we would like [Goldie] |
| Full Idea: In feeling towards things the imagination tends to 'run away with you', which is partly why the emotions are 'passions'; your thoughts and feelings are not always as much under your control as you would want them to be. | |
| From: Peter Goldie (The Emotions [2000], 3 'Towards') | |
| A reaction: This may have the chronology wrong. 'Passion' doesn't mean uncontrolled. I take it that 'passion' was an older word for 'emotion', and became attached to the older view of emotions as dangerous and corrupting. |
| 23999 | Emotional control is hard, but we are responsible for our emotions over long time periods [Goldie] |
| Full Idea: To some extent our emotions cannot be controlled. But to say that we are not responsible for our emotions is to ignore the possibility of educating them over time, so that, ideally, our responses come to be consonant with deliberated rational choices. | |
| From: Peter Goldie (The Emotions [2000], 4 'Education') | |
| A reaction: So people go on anger management courses, or talk through crises with councellors. This idea describes most people correctly, but some are in the grips of passions which seem impossible to control. |
| 23994 | Emotions are not easily changed, as new knowledge makes little difference, and akrasia is possible [Goldie] |
| Full Idea: Our emotional capabilities are not fully open to be developed. …First, they are to some extent cognitively impenetrable. Secondly, they can ground certain sorts of weakness of will, or akrasia. | |
| From: Peter Goldie (The Emotions [2000], 4 'Education') | |
| A reaction: Education makes us more receptive to evidence. We could probably rate emotions on a scale indicating how easy they are to change. Jealousy seems tenacious. Most fears respond quickly to clear evidence. |
| 23998 | Emotional control is less concerned with emotional incidents, and more with emotional tendencies [Goldie] |
| Full Idea: It is a mistake to speak as if emotional control is always a matter of controlling a token emotional response or action; …rather, it is like reshaping the channel along which future emotions can run. | |
| From: Peter Goldie (The Emotions [2000], 4 'Education') | |
| A reaction: Presumably wise parents direct habitual feelings, where less wise parents respond to outbursts. The very best parents therefore presumably achieve complete brainwashing, and eliminate all initiative. Er, perhaps I've misunderstood? |
| 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. |
| 23995 | Akrasia can be either overruling our deliberation, or failing to deliberate [Goldie] |
| Full Idea: I call it 'last ditch' akrasia when we deliberately decide to do something, and then don't do it, and 'impetuous' akrasia when we rush into doing something which, if we had deliberated, we would not have done. | |
| From: Peter Goldie (The Emotions [2000], 4 'Education') | |
| A reaction: I'm not convinced that his impetuous version counts as akrasia, which seems to be vice of people who deliberate. [But he cites Aristotle 1150b19-]. |
| 24000 | Justifying reasons say you were right; excusing reasons say your act was explicable [Goldie] |
| Full Idea: A justifying reason will show that what you did, all things considered, was the right thing to do; an excusing reason will not justify, but will give some excuse to explain why you did what you did. | |
| From: Peter Goldie (The Emotions [2000], 6 Intro) | |
| A reaction: There are also internal reasons before the event, and explicit reasons afterwards. A mistaken justification might still be an excuse. |
| 24003 | Character traits are both possession of and lack of dispositions [Goldie] |
| Full Idea: Most traits are dispositions of a relatively stable sort, but traits need not be dispositions. A trait can be a lack of disposition. | |
| From: Peter Goldie (The Emotions [2000], 6 'Traits') | |
| A reaction: Presumably only the lack relatively normal dispositions will count as traits. |
| 24002 | We over-estimate the role of character traits when explaining behaviour [Goldie] |
| Full Idea: We significantly overestimate the role of character traits in explaining and predicting people's action: the so-called Fundamental Attribution error. | |
| From: Peter Goldie (The Emotions [2000], 6 'Traits') | |
| A reaction: I think this point is incredibly important in daily life. 'When someone shows you who they are, believe them!' is a good thought. But we must distinguish the deeply revealing moment from the transient superficial one. |
| 24004 | Psychologists suggest we are muddled about traits, and maybe they should be abandoned [Goldie] |
| Full Idea: Empirical psychologists have suggested that our practice of trait ascription is systematically prone to error. Some philosophers have concluded that the whole business of trait ascription, and of virtue ethics, should be abandoned. | |
| From: Peter Goldie (The Emotions [2000], 6 'Traits') | |
| A reaction: [He cites Ross and Nisbet, and Gilbert Harman as a sceptic] I suspect the problem is that character traits are not precise enough for scientific assessment. How else are we going to describe a person? What else can we say at funerals? |
| 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 |
| 23993 | Our capabilities did not all evolve during the hunter gathering period [Goldie] |
| Full Idea: It is an unwarranted assumption that the only relevant evolutionary period in which our capabilities for emotions evolved is the period in which our ancestors were hunting and gathering. | |
| From: Peter Goldie (The Emotions [2000], 4 'Education') | |
| A reaction: Goldie says that the evolution of emotions could well extend to much earlier times. Presumably this also applies to other traits, notably those not obviously needed for hunting. Gathering needs long term planning. |
| 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'. |