47 ideas
| 23948 | Wisdom needs both thought and passion, with each reflecting on the other [Solomon] |
| Full Idea: Wisdom is a matter of living both thoughtfully and passionately, bringing understanding to bear on every passion and forcing every passion into the light of reflection. | |
| From: Robert C. Solomon (The Passions [1976], 3.4) | |
| A reaction: His main point is that passion is a key part of wisdom, and the idea that wisdom is cold and detached is quite false. Good point. At the very least, wise people must relate sympathetically to others. |
| 23942 | Philosophy is creating an intellectual conceptual structure for life [Solomon] |
| Full Idea: Philosophy is conceptual sculpture, the shaping and developing of the intellectual structures within which we live our lives. | |
| From: Robert C. Solomon (The Passions [1976], Intro.1) | |
| A reaction: Nice. I tend to see philosophy as conceptual analysis (though creating new concepts doesn't quite fit that), but the vision of creating a huge conceptual sculpture sounds good. I would call it a system. (See my book, 'Natural Ideas'!). |
| 23945 | Reason is actually passions, guided by perspicacious reflection [Solomon] |
| Full Idea: What is called 'reason' is the passions enlightened, 'illuminated' by reflection and supported by a perspicacious deliberation that the emotions in their urgency normally excluded. | |
| From: Robert C. Solomon (The Passions [1976], Intro.4) | |
| A reaction: To suggest that reason more or less is emotions strikes me as missing the point of 'perspicacious', which takes in facts outside our emotional world. We excitedly climb a cliff, then stop when we see the rocks are crumbling. |
| 10859 | A set is 'well-ordered' if every subset has a first element [Clegg] |
| Full Idea: For a set to be 'well-ordered' it is required that every subset of the set has a first element. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.13) |
| 10857 | Set theory made a closer study of infinity possible [Clegg] |
| Full Idea: Set theory made a closer study of infinity possible. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.13) |
| 10864 | Any set can always generate a larger set - its powerset, of subsets [Clegg] |
| Full Idea: The idea of the 'power set' means that it is always possible to generate a bigger one using only the elements of that set, namely the set of all its subsets. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.14) |
| 10872 | Extensionality: Two sets are equal if and only if they have the same elements [Clegg] |
| Full Idea: Axiom of Extension: Two sets are equal if and only if they have the same elements. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) |
| 10875 | Pairing: For any two sets there exists a set to which they both belong [Clegg] |
| Full Idea: Axiom of Pairing: For any two sets there exists a set to which they both belong. So you can make a set out of two other sets. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) |
| 10876 | Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg] |
| Full Idea: Axiom of Unions: For every collection of sets there exists a set that contains all the elements that belong to at least one of the sets in the collection. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) |
| 10878 | Infinity: There exists a set of the empty set and the successor of each element [Clegg] |
| Full Idea: Axiom of Infinity: There exists a set containing the empty set and the successor of each of its elements. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) | |
| A reaction: This is rather different from the other axioms because it contains the notion of 'successor', though that can be generated by an ordering procedure. |
| 10877 | Powers: All the subsets of a given set form their own new powerset [Clegg] |
| Full Idea: Axiom of Powers: For each set there exists a collection of sets that contains amongst its elements all the subsets of the given set. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) | |
| A reaction: Obviously this must include the whole of the base set (i.e. not just 'proper' subsets), otherwise the new set would just be a duplicate of the base set. |
| 10879 | Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg] |
| Full Idea: Axiom of Choice: For every set we can provide a mechanism for choosing one member of any non-empty subset of the set. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) | |
| A reaction: This axiom is unusual because it makes the bold claim that such a 'mechanism' can always be found. Cohen showed that this axiom is separate. The tricky bit is choosing from an infinite subset. |
| 10871 | Axiom of Existence: there exists at least one set [Clegg] |
| Full Idea: Axiom of Existence: there exists at least one set. This may be the empty set, but you need to start with something. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) |
| 10874 | Specification: a condition applied to a set will always produce a new set [Clegg] |
| Full Idea: Axiom of Specification: For every set and every condition, there corresponds a set whose elements are exactly the same as those elements of the original set for which the condition is true. So the concept 'number is even' produces a set from the integers. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) | |
| A reaction: What if the condition won't apply to the set? 'Number is even' presumably won't produce a set if it is applied to a set of non-numbers. |
| 10880 | Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg] |
| Full Idea: Three views of mathematics: 'pure' mathematics, where it doesn't matter if it could ever have any application; 'real' mathematics, where every concept must be physically grounded; and 'applied' mathematics, using the non-real if the results are real. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.17) | |
| A reaction: Very helpful. No one can deny the activities of 'pure' mathematics, but I think it is undeniable that the origins of the subject are 'real' (rather than platonic). We do economics by pretending there are concepts like the 'average family'. |
| 10860 | An ordinal number is defined by the set that comes before it [Clegg] |
| Full Idea: You can think of an ordinal number as being defined by the set that comes before it, so, in the non-negative integers, ordinal 5 is defined as {0, 1, 2, 3, 4}. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.13) |
| 10861 | Beyond infinity cardinals and ordinals can come apart [Clegg] |
| Full Idea: With ordinary finite numbers ordinals and cardinals are in effect the same, but beyond infinity it is possible for two sets to have the same cardinality but different ordinals. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.13) |
| 10854 | Transcendental numbers can't be fitted to finite equations [Clegg] |
| Full Idea: The 'transcendental numbers' are those irrationals that can't be fitted to a suitable finite equation, of which π is far and away the best known. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch. 6) |
| 10858 | By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg] |
| Full Idea: The realisation that brought 'i' into the toolkit of physicists and engineers was that you could extend the 'number line' into a new dimension, with an imaginary number axis at right angles to it. ...We now have a 'number plane'. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.12) |
| 10853 | Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg] |
| Full Idea: It is a chicken-and-egg problem, whether the lack of zero forced forced classical mathematicians to rely mostly on a geometric approach to mathematics, or the geometric approach made 0 a meaningless concept, but the two remain strongly tied together. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch. 6) |
| 10866 | Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg] |
| Full Idea: As far as Kronecker was concerned, Cantor had built a whole structure on the irrational numbers, and so that structure had no foundation at all. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) |
| 10869 | The Continuum Hypothesis is independent of the axioms of set theory [Clegg] |
| Full Idea: Paul Cohen showed that the Continuum Hypothesis is independent of the axioms of set theory. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) |
| 10862 | The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg] |
| Full Idea: The 'continuum hypothesis' says that aleph-one is the cardinality of the rational and irrational numbers. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.14) |
| 23957 | We often trust our intuitions as rational, despite their lack of reflection [Solomon] |
| Full Idea: We trust certain rational 'intuitions' in ourselves which dispense with reflection but seem to follow an indisputable logic. (note: it is thought ineffable because reflection is the paradigm of rationality. It is no less rational than reflection). | |
| From: Robert C. Solomon (The Passions [1976], 6.4) | |
| A reaction: [compressed] Solomon uses the example to support that emotion is part of rationality. Since this view of intuition is more or less mine (that intuition can be knowledge, when the justification is obscure), it seems to support his claim. |
| 23943 | Distinguishing reason from passion is based on an archaic 'faculty' theory [Solomon] |
| Full Idea: The distinction between reason and passion is based on an archaic 'faculty' psychology of the human soul. | |
| From: Robert C. Solomon (The Passions [1976], Intro.2) | |
| A reaction: I like faculties, for philosophical purposes, as explanatory tools to account for our metaphysical and conceptual framework, but this point is well made. The danger is that we impose sharp divisions, where reality is more complex. |
| 23952 | I say bodily chemistry and its sensations have nothing to do with emotions [Solomon] |
| Full Idea: I shall be making the claim (sujectively) that the chemistry of the body and the sensations caused by that chemistry have nothing to do with the emotions. | |
| From: Robert C. Solomon (The Passions [1976], 4.1) | |
| A reaction: Surely an unexpected stabbing pain causes fear? Isn't pain supposed to trigger appropriate emotions? That is not to say that emotions are a feature of body chemistry. |
| 23954 | Emotions are judgements about ourselves, and our place in the world [Solomon] |
| Full Idea: An emotion is a basic judgement about our Selves and our place in the world, the projection of the values and ideals, structures and mythologies | |
| From: Robert C. Solomon (The Passions [1976], 5.3) | |
| A reaction: Solomon's main theory. What about the Frege-Geach problem - that I feel emotions (and judgements) about fictions and remote events, in which my personal concerns and involvement are zero? Presumably these emotions are parasitic on his primary type? |
| 23960 | Emotions are defined by their objects [Solomon] |
| Full Idea: Direction, scope and focus set the stage, but the specific object is what defines the emotion. | |
| From: Robert C. Solomon (The Passions [1976], 7.3) | |
| A reaction: This is presumably the main distinction between an emotion and a mood. He emphasises that the objects are subjective, rather than factual. |
| 23961 | The heart of an emotion is its judgement of values and morality [Solomon] |
| Full Idea: The heart of every emotion is its value judgements, its appraisals of gain and loss, its indictment of offences and its praise of virtue, its often Manichean judgement of 'good' and 'evil'. | |
| From: Robert C. Solomon (The Passions [1976], 7.6) | |
| A reaction: He adds blame and excuse. Some of our strongest emotions can just be identifications, rather than judgements, as when we learn of someone else's triumph or disaster. On the whole I agree, though. This is important for Aristotelian virtue theory. |
| 23965 | Emotions can be analysed under fifteen headings [Solomon] |
| Full Idea: Emotions can be analysed by direction, scope/focus, object, criteria, status, evaluations, responsibility, intersubjectivity, distance, mythology, desire, power, strategy. | |
| From: Robert C. Solomon (The Passions [1976], 8) | |
| A reaction: These are the headings Solomon actually applies in his breakdown of most of the main emotions. See his book for explanations of each of them. If people say philosophy makes no progress, I'd at least point to helpful thinking of this kind. |
| 23959 | Some emotions are externally directed, others internally [Solomon] |
| Full Idea: 'Outer-directed' emotions (such as fear) are about particular situations, objects, or other people. …The 'inner-directed' emotions (such as vanity or regret) take one's Self as their focal point. | |
| From: Robert C. Solomon (The Passions [1976], 7.1) | |
| A reaction: This is Solomon's own distinction. Some of the emotions he cites, such as vanity, seem to me more like long term virtues or vices, rather than emotions. He did say, though, that you can have emotions without feeling, such as long-term hate. |
| 23946 | The passions are subjective, concerning what is important to me, rather than facts [Solomon] |
| Full Idea: The passions are uniquely subjective, although they sometimes pretend to have a certain objective status. They are not concerned with the world, but with my world. They are not concerned with 'the facts', but with what is important. | |
| From: Robert C. Solomon (The Passions [1976], Intro.5) | |
| A reaction: Values pick out what is 'important'. This idea sums up Solomon's rather solipsistic view of emotions. I accept that emotions are responses, rather than objective judgements, but there is objectivity in their social dimension. Why care about politics? |
| 23940 | Emotions are strategies for maximising our sense of dignity and self-esteem [Solomon] |
| Full Idea: Every emotion is a strategy, a purposive attempt to structure our world in such a way as to maximise our sense of personal dignity and self-esteem. | |
| From: Robert C. Solomon (The Passions [1976], Pref) | |
| A reaction: This is the main thesis of Solomon's book. There doesn't seem to be much to admire in what he takes to be our chief motivation. I would put a much more social spin on it - that our underlying urge is not self-promotion, but to fit into a community. |
| 23949 | Passions exist as emotions, moods and desires, which all generate meaning [Solomon] |
| Full Idea: There are three fundamental species passions - emotions, moods, and desires. …What all passions have in common is their ability to bestow meaning to the circumstances of our lives. | |
| From: Robert C. Solomon (The Passions [1976], 3.2) | |
| A reaction: Moods are said to be 'generalised emotions', where emotions are about something, and desires add objectives. Solomon criticises rigid divisions between mental faculties and states, but it is hard to disagree with this distinction. |
| 23956 | The Myth of the Passions says they are irrational, uncontrolled and damaging [Solomon] |
| Full Idea: The Myth of the Passions says emotions are irrational forces beyond our control, disruptive and stupid, unthinking and counterproductive, against our 'better interests', and often ridiculous. | |
| From: Robert C. Solomon (The Passions [1976], 6.4) | |
| A reaction: The Myth is very unlikely to be correct, for evolutionary reasons. How could there be a selection for a mental feature which distorts truths and leads to dangerous misjudgements? Most emotions motivate us to act successfully. So why do some run wild? |
| 23963 | Which emotions we feel depends on our sense of our own powers [Solomon] |
| Full Idea: An emotion depends on an estimation of our own power. If a lover is jealous they welcome confrontation, but if they are just envious they assume impotence from the start. | |
| From: Robert C. Solomon (The Passions [1976], 7.12) | |
| A reaction: This seems particularly true of politics, where the possibility (or not) of influencing events makes a huge difference. We can picture a huge variety of emotions when a fight breaks out in public. |
| 23936 | It is only our passions which give our lives meaning [Solomon] |
| Full Idea: It is our passions, and our passions alone, which provide our lives with meaning. | |
| From: Robert C. Solomon (The Passions [1976], Pref) | |
| A reaction: This presumably entails that the lives of plants have no meaning. It also seems to be rather egotistical, since it is not clear why anyone else's life should have meaning for me, if I don't directly experience their passions. Interesting, though. |
| 23953 | Feeling is a superficial aspect of emotion, and may be indeterminate, or even absent [Solomon] |
| Full Idea: Feeling is the ornamentation of emotion, not its essence. ...For example, what is the difference in feeling between embarrassment and shame? …We may also experience an emotion like subdued anger or envy with no feeling. | |
| From: Robert C. Solomon (The Passions [1976], 4.2) | |
| A reaction: This is very persuasive, and supports the idea that what matters in an emotion is its content, rather than its phenomenology. He adds later that we are often mistaken about our own emotions. |
| 23964 | There are no 'basic' emotions, only socially prevalent ones [Solomon] |
| Full Idea: There are no 'basic' emotions, only those emotions which are prevalent in a particular society. This reduction to a small set makes it impossible to appreciate the richness of our emotional lives. | |
| From: Robert C. Solomon (The Passions [1976], 8) | |
| A reaction: He cites Descartes as a culprit, and John Watson's famous list of fear, dependency and rage. I think Solomon is probably right. He suggests that the lists are usually individualistic and negative. Individuals may have their private basics! |
| 23937 | It is reason which needs the anchorage of passions, rather than vice versa [Solomon] |
| Full Idea: It is not the passions who require the controls and rationalisations of reason. Rather, it is reason that requires the anchorage and earthy wisdom of the passions. | |
| From: Robert C. Solomon (The Passions [1976], Pref) | |
| A reaction: I like the second half of this. We don't just follow the winds of arguments; we decide into which of the many conflicting winds we should steer the rational arguments, and that needs passions. Only a fool doesn't rationally control their passions. |
| 23947 | Dividing ourselves into confrontational reason and passion destroys our harmonious whole [Solomon] |
| Full Idea: To divide the soul into reason and passion …divides us against ourselves, forcing us each to be defensively half a person, instead of a harmonious whole. | |
| From: Robert C. Solomon (The Passions [1976], 2.3) | |
| A reaction: This is the best aspect of Solomon's book. I'm not sure, though, how this works in practice. Should I allow the winds of emotion to alter the course of my reasoning, or stunt my feelings by always insisting that reason plays a part? That's too dualist! |
| 23958 | The supposed irrationality of our emotions is often tactless or faulty expression of them [Solomon] |
| Full Idea: What is often called the 'irrationality' of our emotions is rather the faulty timing or inept choice of their expressions. | |
| From: Robert C. Solomon (The Passions [1976], 6.4) | |
| A reaction: The irrationality can be pretty obvious when having a tantrum over trivia, or resenting some tiny slight, or falling in love with a dead film star. That said, his point is well made. |
| 23944 | Emotions are our life force, and the source of most of our values [Solomon] |
| Full Idea: Emotions are the life force of the soul, the source of most of our values (not all: there is always hunger, thirst, and fatigue). | |
| From: Robert C. Solomon (The Passions [1976], Intro.4) | |
| A reaction: I am beginning to worry that Solomon's account is too individual and subjective. My personal values may derive from my emotions, but I think human and social values are based much more on objective observations and facts. We are social, not solipsists. |
| 23962 | Lovers adopt the interests of their beloved, rather than just valuing them [Solomon] |
| Full Idea: It is often said that love takes the interests of the lover as being more important than one's own; but here again we would rather say that love takes the lovers interests as its own. | |
| From: Robert C. Solomon (The Passions [1976], 7.9) | |
| A reaction: This is because he sees emotions as almost entirely self-centred, and almost never altruistic. To me the evolutionary picture suggest a more social view. Many people want the lives of their ex- to go well, without knowing their new interests. |
| 23941 | 'Absurdity' is just the result of our wrong choices in life [Solomon] |
| Full Idea: The 'absurdity of life' is nothing than our own unsatisfactory choices, typically of defensiveness and resentment, competition, and 'meaningless' routines. | |
| From: Robert C. Solomon (The Passions [1976], Pref) | |
| A reaction: He seems to have Camus particularly in mind. He sees love and co-operation as the cure. I sort of agree, but somewhere in all of our minds there lurks an abyss, with the good life looking like a distraction from it. |
| 23955 | Ideologies are mythologies which guide our actions [Solomon] |
| Full Idea: Mythologies become ideologies when we play a role in them, live in them, take action and take sides. | |
| From: Robert C. Solomon (The Passions [1976], 6.1) | |
| A reaction: This may well be a sceptical American attitude to ideology, since 'mythology' implies a fiction. But I think for most of us there exists the possibility of a good ideology, which correctly points us towards a better life. Dangerous things, though! |
| 6005 | Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley] |
| Full Idea: Hermarchus said that animal killing is justified by considerations of human safety and nourishment and by animals' inability to form contractual relations of justice with us. | |
| From: report of Hermarchus (fragments/reports [c.270 BCE]) by David A. Sedley - Hermarchus | |
| A reaction: Could the last argument be used to justify torturing animals? Or could we eat a human who was too brain-damaged to form contracts? |