22 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. |
| 14239 | The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley] |
| Full Idea: The empty set is usually derived via Zermelo's axiom of separation. But the axiom of separation is conditional: it requires the existence of a set in order to generate others as subsets of it. The original set has to come from the axiom of infinity. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 1.2) | |
| A reaction: They charge that this leads to circularity, as Infinity depends on the empty set. |
| 14240 | The empty set is something, not nothing! [Oliver/Smiley] |
| Full Idea: Some authors need to be told loud and clear: if there is an empty set, it is something, not nothing. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 1.2) | |
| A reaction: I'm inclined to think of a null set as a pair of brackets, so maybe that puts it into a metalanguage. |
| 14241 | We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley] |
| Full Idea: The empty set is said to be useful to express non-existence, but saying 'there are no Us', or ¬∃xUx are no less concise, and certainly less roundabout. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 1.2) |
| 14242 | Maybe we can treat the empty set symbol as just meaning an empty term [Oliver/Smiley] |
| Full Idea: Suppose we introduce Ω not as a term standing for a supposed empty set, but as a paradigm of an empty term, not standing for anything. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 1.2) | |
| A reaction: This proposal, which they go on to explore, seems to mean that Ω (i.e. the traditional empty set symbol) is no longer part of set theory but is part of semantics. |
| 14243 | The unit set may be needed to express intersections that leave a single member [Oliver/Smiley] |
| Full Idea: Thomason says with no unit sets we couldn't call {1,2}∩{2,3} a set - but so what? Why shouldn't the intersection be the number 2? However, we then have to distinguish three different cases of intersection (common subset or member, or disjoint). | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 2.2) |
| 14234 | If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley] |
| Full Idea: A 'singularist', who refers to objects one at a time, must resort to the language of sets in order to replace plural reference to members ('Henry VIII's wives') by singular reference to a set ('the set of Henry VIII's wives'). | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], Intro) | |
| A reaction: A simple and illuminating point about the motivation for plural reference. Null sets and singletons give me the creeps, so I would personally prefer to avoid set theory when dealing with ontology. |
| 14237 | We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley] |
| Full Idea: Plurals earn their keep in set theory, to answer Skolem's remark that 'in order to treat of 'sets', we must begin with 'domains' that are constituted in a certain way'. We can speak in the plural of 'the objects', not a 'domain' of objects. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], Intro) | |
| A reaction: [Skolem 1922:291 in van Heijenoort] Zermelo has said that the domain cannot be a set, because every set belongs to it. |
| 14245 | Logical truths are true no matter what exists - but predicate calculus insists that something exists [Oliver/Smiley] |
| Full Idea: Logical truths should be true no matter what exists, so true even if nothing exists. The classical predicate calculus, however, makes it logically true that something exists. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 5.1) |
| 14246 | If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley] |
| Full Idea: If mathematics was purely concerned with mathematical objects, there would be no room for applied mathematics. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 5.1) | |
| A reaction: Love it! Of course, they are using 'objects' in the rather Fregean sense of genuine abstract entities. I don't see why fictionalism shouldn't allow maths to be wholly 'pure', although we have invented fictions which actually have application. |
| 14247 | Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley] |
| Full Idea: Identifying numbers with sets may mean one of three quite different things: 1) the sets represent the numbers, or ii) they are the numbers, or iii) they replace the numbers. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 5.2) | |
| A reaction: Option one sounds the most plausible to me. I will take numbers to be patterns embedded in nature, and sets are one way of presenting them in shorthand form, in order to bring out what is repeated. |
| 10580 | Mathematics is both necessary and a priori because it really consists of logical truths [Yablo] |
| Full Idea: Mathematics seems necessary because the real contents of mathematical statements are logical truths, which are necessary, and it seems a priori because logical truths really are a priori. | |
| From: Stephen Yablo (Abstract Objects: a Case Study [2002], 10) | |
| A reaction: Yablo says his logicism has a Kantian strain, because numbers and sets 'inscribed on our spectacles', but he takes a different view (in the present Idea) from Kant about where the necessity resides. Personally I am tempted by an a posteriori necessity. |
| 10579 | Putting numbers in quantifiable position (rather than many quantifiers) makes expression easier [Yablo] |
| Full Idea: Saying 'the number of Fs is 5', instead of using five quantifiers, puts the numeral in quantifiable position, which brings expressive advantages. 'There are more sheep in the field than cows' is an infinite disjunction, expressible in finite compass. | |
| From: Stephen Yablo (Abstract Objects: a Case Study [2002], 08) | |
| A reaction: See Hofweber with similar thoughts. This idea I take to be a key one in explaining many metaphysical confusions. The human mind just has a strong tendency to objectify properties, relations, qualities, categories etc. - for expression and for reasoning. |
| 10577 | Concrete objects have few essential properties, but properties of abstractions are mostly essential [Yablo] |
| Full Idea: Objects like me have a few essential properties, and numerous accidental ones. Abstract objects are a different story. The intrinsic properties of the empty set are mostly essential. The relations of numbers are also mostly essential. | |
| From: Stephen Yablo (Abstract Objects: a Case Study [2002], 01) |
| 10578 | We are thought to know concreta a posteriori, and many abstracta a priori [Yablo] |
| Full Idea: Our knowledge of concreta is a posteriori, but our knowledge of numbers, at least, has often been considered a priori. | |
| From: Stephen Yablo (Abstract Objects: a Case Study [2002], 02) |
| 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. |