22 ideas
| 7990 | Serene wisdom is freedom from ties, and indifference to fortune [Anon (Bhag)] |
| Full Idea: Who everywhere is free from all ties, who neither rejoices nor sorrows if fortune is good or is ill, his is a serene wisdom. | |
| From: Anon (Bhag) (The Bhagavad Gita [c.500 BCE], 2.57) | |
| A reaction: This is very similar to the 'apatheia' of the Stoics, though they are always more committed to rationality. This is quite a good strategy when times are hard, but as a general rule it offers a bogus state of 'wisdom' which is really half way to death. |
| 7989 | Seek salvation in the wisdom of reason [Anon (Bhag)] |
| Full Idea: Seek salvation in the wisdom of reason. | |
| From: Anon (Bhag) (The Bhagavad Gita [c.500 BCE], 2.49) | |
| A reaction: Quotations like this can usually be counterbalanced in eastern philosophy by wild irrationality, but they certainly felt to tug of reason. Only the Dhaoists seem really opposed to reason (e.g. Idea 7289). |
| 13201 | ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton] |
| Full Idea: To know if A ∈ B, we look at the set A as a single object, and check if it is among B's members. But if we want to know whether A ⊆ B then we must open up set A and check whether its various members are among the members of B. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 1:04) | |
| A reaction: This idea is one of the key ideas to grasp if you are going to get the hang of set theory. John ∈ USA ∈ UN, but John is not a member of the UN, because he isn't a country. See Idea 12337 for a special case. |
| 13204 | The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton] |
| Full Idea: The 'ordered pair' <x,y> is defined to be {{x}, {x,y}}; hence it can be proved that <u,v> = <x,y> iff u = x and v = y (given by Kuratowski in 1921). ...The definition is somewhat arbitrary, and others could be used. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 3:36) | |
| A reaction: This looks to me like one of those regular cases where the formal definitions capture all the logical behaviour of the concept that are required for inference, while failing to fully capture the concept for ordinary conversation. |
| 13206 | A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton] |
| Full Idea: A 'linear ordering' (or 'total ordering') on A is a binary relation R meeting two conditions: R is transitive (of xRy and yRz, the xRz), and R satisfies trichotomy (either xRy or x=y or yRx). | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 3:62) |
| 13200 | Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton] |
| Full Idea: Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ. A man with an empty container is better off than a man with nothing. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 1.03) |
| 13199 | The empty set may look pointless, but many sets can be constructed from it [Enderton] |
| Full Idea: It might be thought at first that the empty set would be a rather useless or even frivolous set to mention, but from the empty set by various set-theoretic operations a surprising array of sets will be constructed. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 1:02) | |
| A reaction: This nicely sums up the ontological commitments of mathematics - that we will accept absolutely anything, as long as we can have some fun with it. Sets are an abstraction from reality, and the empty set is the very idea of that abstraction. |
| 13203 | The singleton is defined using the pairing axiom (as {x,x}) [Enderton] |
| Full Idea: Given any x we have the singleton {x}, which is defined by the pairing axiom to be {x,x}. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 2:19) | |
| A reaction: An interesting contrivance which is obviously aimed at keeping the axioms to a minimum. If you can do it intuitively with a new axiom, or unintuitively with an existing axiom - prefer the latter! |
| 13202 | Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton] |
| Full Idea: It was observed by several people that for a satisfactory theory of ordinal numbers, Zermelo's axioms required strengthening. The Axiom of Replacement was proposed by Fraenkel and others, giving rise to the Zermelo-Fraenkel (ZF) axioms. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 1:15) |
| 13205 | We can only define functions if Choice tells us which items are involved [Enderton] |
| Full Idea: For functions, we know that for any y there exists an appropriate x, but we can't yet form a function H, as we have no way of defining one particular choice of x. Hence we need the axiom of choice. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 3:48) |
| 7996 | I am all the beauty and goodness of things, says Krishna [Anon (Bhag)] |
| Full Idea: I am the beauty of all things beautiful; ...I am the goodness of those who are good, says Krishna. | |
| From: Anon (Bhag) (The Bhagavad Gita [c.500 BCE], 10.36) | |
| A reaction: Another attempt to annexe everything which is admirable to the nature of God. This sounds strikingly Platonic (c.f. Idea 7992, which seems Aristotelian). One scholar dates the text to 150 BCE. I think there is influence, one way or the other. |
| 12189 | Logical necessity involves a decision about usage, and is non-realist and non-cognitive [Wright,C, by McFetridge] |
| Full Idea: Wright espouses a non-realist, indeed non-cognitive account of logical necessity. Crucial to this is the idea that acceptance of a statement as necessary always involves an element of decision (to use it in a necessary way). | |
| From: report of Crispin Wright (Inventing Logical Necessity [1986]) by Ian McFetridge - Logical Necessity: Some Issues §3 | |
| A reaction: This has little appeal to me, as I take (unfashionably) the view that that logical necessity is rooted in the behaviour of the actual physical world, with which you can't argue. We test simple logic by making up examples. |
| 7995 | In all living beings I am the light of consciousness, says Krishna [Anon (Bhag)] |
| Full Idea: In all living beings I am the light of consciousness, says Krishna. | |
| From: Anon (Bhag) (The Bhagavad Gita [c.500 BCE], 10.22) | |
| A reaction: Everything grand seems to be claimed for God at this stage of culture, but I am not sure how coherent this view is, unless this is pantheism. In what sense could we possibly be Krishna, when none of us (except Arjuna) is aware of it? |
| 7320 | Holism cannot give a coherent account of scientific methodology [Wright,C, by Miller,A] |
| Full Idea: Crispin Wright has argued that Quine's holism is implausible because it is actually incoherent: he claims that Quine's holism cannot provide us with a coherent account of scientific methodology. | |
| From: report of Crispin Wright (Inventing Logical Necessity [1986]) by Alexander Miller - Philosophy of Language 4.5 | |
| A reaction: This sounds promising, given my intuitive aversion to linguistic holism, and almost everything to do with Quine. Scientific methodology is not isolated, but spreads into our ordinary (experimental) interactions with the world (e.g. Idea 2461). |
| 7999 | All actions come from: body, lower self, perception, means of action, or Fate [Anon (Bhag)] |
| Full Idea: Whatever a man does, good or bad, in thought, word or deed, has these five sources of action: the body, the lower 'I am', the means of perception, the means of action, and Fate. | |
| From: Anon (Bhag) (The Bhagavad Gita [c.500 BCE], 18.14/15) | |
| A reaction: The 'means of action' will presumably take care of anything we haven't thought of! Nothing quite matches the idea of 'the will' here. A twitch from the first, eating from the second, a startled jump from the third, struck by lightning from the fifth. |
| 7991 | Hate and lust have their roots in man's lower nature [Anon (Bhag)] |
| Full Idea: Hate and lust for things of nature have their roots in man's lower nature. | |
| From: Anon (Bhag) (The Bhagavad Gita [c.500 BCE], 3.34) | |
| A reaction: It seems outmoded now (since Freud) to label parts of human nature as 'higher' and 'lower'. I would defend the distinction, but it is not self-evident. The basis of morality is good citizenship, and parts of our nature are detrimental to that. |
| 7988 | There is no greater good for a warrior than to fight in a just war [Anon (Bhag)] |
| Full Idea: There is no greater good for a warrior than to fight in righteous war. | |
| From: Anon (Bhag) (The Bhagavad Gita [c.500 BCE], 2.31) | |
| A reaction: What worries me now is not the urging to fight, as long as a good cause can be found, but the idea that someone should see his social role as 'warrior'. The modern 'soldier' is ready to fight, but a traditional 'warrior' is obliged to fight. |
| 7992 | The visible forms of nature are earth, water, fire, air, ether; mind, reason, and the sense of 'I' [Anon (Bhag)] |
| Full Idea: The visible forms of nature are eight: earth, water, fire, air, ether; the mind, reason, and the sense of 'I'. | |
| From: Anon (Bhag) (The Bhagavad Gita [c.500 BCE], 7.4) | |
| A reaction: Presumably there is an implication that there are also invisible forms. The Bhuddists launched an attack on 'I' as one of the categories. The first five appear to be Aristotle's, which must be of scholarly (and chronological) interest. |
| 7994 | Everything, including the gods, comes from me, says Krishna [Anon (Bhag)] |
| Full Idea: All the gods come from me, says Krishna. ...I am the one source of all | |
| From: Anon (Bhag) (The Bhagavad Gita [c.500 BCE], 10.2/8) | |
| A reaction: This seems very close to monotheism, and sounds very similar to the position that Zeus seems to occupy in later Greek religion, where he is shading off into a supreme and spiritual entity. |
| 7993 | Brahman is supreme, Atman his spirit in man, and Karma is the force of creation [Anon (Bhag)] |
| Full Idea: Brahman is supreme, the Eternal. Atman is his Spirit in man. Karma is the force of creation, wherefrom all things have their life. | |
| From: Anon (Bhag) (The Bhagavad Gita [c.500 BCE], 8.3) | |
| A reaction: I can't help wondering how they know all this stuff, but then I'm just a typical product of my culture. We seem to have a trinity here. Who's in charge? Is Atman just a servant? Is Karma totally under the control of Brahman? |
| 7997 | Only by love can men see me, know me, and come to me, says Krishna [Anon (Bhag)] |
| Full Idea: Only by love can men see me, and know me, and come unto me, says Krishna | |
| From: Anon (Bhag) (The Bhagavad Gita [c.500 BCE], 11.54) | |
| A reaction: There seems to be a paradox here, as it is unclear how you can love Krishna, if you have not already seen him in some way. This is another paradox of fideism - that faith cannot possibly be the first step in a religion, as faith needs a target. |
| 7998 | The three gates of hell are lust, anger and greed [Anon (Bhag)] |
| Full Idea: Three are the gates of this hell, the death of the soul: the gate of lust, the gate of wrath, and the gate of greed. Let a man shun the three. | |
| From: Anon (Bhag) (The Bhagavad Gita [c.500 BCE], 16.21) | |
| A reaction: Anyone who wishes to procreate, champion justice, and make a living, has to pursue all three. Wisdom consists of pursuing the three appropriately, not in shunning them. How did this bizarre puritanism ever come to grip the human race? |