18 ideas
| 7426 | Critical philosophy is what questions domination at every level [Foucault] |
| Full Idea: In its critical aspect, philosophy is that which calls into question domination at every level | |
| From: Michel Foucault (Ethics of the Concern for Self as Freedom [1984], p.300) | |
| A reaction: A very French view of the subject. It is tempting to say that they had their adolescent outburst in 1789, and it is time to grow up. With rights come responsibilities... |
| 7423 | Philosophy and politics are fundamentally linked [Foucault] |
| Full Idea: The relationship between philosophy and politics is permanent and fundamental. | |
| From: Michel Foucault (Ethics of the Concern for Self as Freedom [1984], p.293) | |
| A reaction: This idea is one of the biggest gulfs between continental and analytical philosophy. Many aspects of philosophy are turning out to be much more social than analytical philosophers might have thought - epistemology, for example. |
| 7420 | When logos controls our desires, we have actually become the logos [Foucault] |
| Full Idea: Plutarch says if you have mastered principles then logos will silence your desires like a master silencing a dog - in which case the logos functions without intervention on your part - you have become the logos, or the logos has become you. | |
| From: Michel Foucault (Ethics of the Concern for Self as Freedom [1984], p.286) | |
| A reaction: If you believe that logos is pure reason, you might be quite happy with this, but if you thought it was a cultural construct, you might feel that you had been cunningly enslaved. If I ask 'what is 7+6?', logos interrupts me to give the answer. |
| 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) |
| 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. |
| 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) |
| 7424 | Saying games of truth were merely power relations would be a horrible exaggeration [Foucault] |
| Full Idea: When I talk about power relations and games of truth, I am absolutely not saying that games of truth are just concealed power relations - that would be a horrible exaggeration. | |
| From: Michel Foucault (Ethics of the Concern for Self as Freedom [1984], p.296) | |
| A reaction: I take this to be a denial of the more absurd forms of relativism. I think there is an interesting convergence between this kind of continental thinking, and the social view of justification found in the later work of Alvin Goldman. |
| 7422 | A subject is a form which can change, in (say) political or sexual situations [Foucault] |
| Full Idea: The subject is not a substance but a form, which is not always identical to itself. You do not have the same relation to yourself when you go to vote and when you seek to fulfil your desires in a sexual relationship. | |
| From: Michel Foucault (Ethics of the Concern for Self as Freedom [1984], p.290) | |
| A reaction: I don't think I believe this. If it were true, the concept of 'sexual politics' would mean nothing to me. A brutal or sympathetic nature is likely to express itself in both situations. |
| 7419 | Ethics is the conscious practice of freedom [Foucault] |
| Full Idea: What is ethics, if not the practice of freedom, the conscious [réfléchie] practice of freedom? | |
| From: Michel Foucault (Ethics of the Concern for Self as Freedom [1984], p.284) | |
| A reaction: Makes Foucault sound very existentialist. I'm not sure I understand this kind of remark, given that serial killers seem to be exceptionally good at 'practising their freedom'. However, the idea is akin to Kant's notion of a truly good will (Idea 3710). |
| 7425 | The aim is not to eliminate power relations, but to reduce domination [Foucault] |
| Full Idea: The problem is not to dissolve power relations in a utopia of transparent communications, but to acquire the rules of law, the management techniques, the morality, the practice of the self, that allows games of power with minimum domination. | |
| From: Michel Foucault (Ethics of the Concern for Self as Freedom [1984], p.298) | |
| A reaction: If you are a democrat it is hard to disagree with this, though I am still unclear why being dominated should rank as a total disaster. A healthy personal relationship might involve domination. 'Management techniques' is interesting. |
| 7418 | The idea of liberation suggests there is a human nature which has been repressed [Foucault] |
| Full Idea: I am somewhat suspicious of the notion of liberation, because one runs the risk of falling back on the idea that there is a human nature, that has been concealed or alienated by mechanisms of repression. | |
| From: Michel Foucault (Ethics of the Concern for Self as Freedom [1984], p.282) | |
| A reaction: Personally I think there is (to some extent) a human nature, and that it fails to flourish if it gets too much 'liberation. However, the world contains a lot more repression than liberation, so we should all be fans of liberty. |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |