31 ideas
| 7973 | There is no longer anything on which there is nothing to say [Baudrillard] |
| Full Idea: There is no longer anything on which there is nothing to say. | |
| From: Jean Baudrillard (The Intelligence of Evil [2004], p. 17) | |
| A reaction: Compare Ideas 2937 and 6870. I'm not sure whether Baudrillard is referring to the limits of philosophy, or merely to social taboos. I like Ansell Pearson's view: we should attempt to discuss what appears to be undiscussable. |
| 7975 | The task of philosophy is to unmask the illusion of objective reality [Baudrillard] |
| Full Idea: The task of philosophy is to unmask the illusion of objective reality - a trap that is, in a sense, laid for us by nature. | |
| From: Jean Baudrillard (The Intelligence of Evil [2004], p. 40) | |
| A reaction: There is a vast gap between this and the Lockean view (Idea 7653) that philosophers are there to help reveal reality, probably via science. I retain the Enlightenment faith that there is a reality to be found. Baudrillard must be taken seriously, though. |
| 7986 | Drunken boat pilots are less likely to collide than clearly focused ones [Baudrillard] |
| Full Idea: Two boats on Lake Constance in dense fog are in less danger of colliding if their pilots are drunk than if they are attempting to master the situation. | |
| From: Jean Baudrillard (The Intelligence of Evil [2004], p.196) | |
| A reaction: Charming, but I think empirical research would prove it false. At least rational pilots know to keep to the right (?) when a shape looms through the fog. I prefer rational pilots, but then I am one of those sad people who admires the Enlightenment. |
| 7982 | Instead of thesis and antithesis leading to synthesis, they now cancel out, and the conflict is levelled [Baudrillard] |
| Full Idea: Gone is the dialectic, the play of thesis and antithesis resolving itself in synthesis. The opposing terms now cancel each other out in a levelling of all conflict. | |
| From: Jean Baudrillard (The Intelligence of Evil [2004], p.129) | |
| A reaction: This is from someone who approved of 9/11 (p.137 of this text), and seemed to welcome conflict. His idea, which has plausibility, is that the modern media have become a great warm bath that calmly absorbs every abrasive thrown into it. |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| Full Idea: Intuitionists in mathematics deny excluded middle, because it is symptomatic of faith in the transcendent existence of mathematical objects and/or the truth of mathematical statements. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 1.2) | |
| A reaction: There are other problems with excluded middle, such as vagueness, but on the whole I, as a card-carrying 'realist', am committed to the law of excluded middle. |
| 8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
| Full Idea: It is surely wise to identify the positions in the natural numbers structure with their counterparts in the integer, rational, real and complex number structures. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.2) | |
| A reaction: The point is that this might be denied, since 3, 3/1, 3.00.., and -3*i^2 are all arrived at by different methods of construction. Natural 3 has a predecessor, but real 3 doesn't. I agree, intuitively, with Shapiro. Russell (1919) disagreed. |
| 18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
| Full Idea: A sequence a1,a2,... of rational numbers is 'Cauchy' if for each rational number ε>0 there is a natural number N such that for all natural numbers m, n, if m>N and n>N then -ε < am - an < ε. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 7.2 n4) | |
| A reaction: The sequence is 'Cauchy' if N exists. |
| 8764 | Categories are the best foundation for mathematics [Shapiro] |
| Full Idea: There is a dedicated contingent who hold that the category of 'categories' is the proper foundation for mathematics. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.3 n7) | |
| A reaction: He cites Lawvere (1966) and McLarty (1993), the latter presenting the view as a form of structuralism. I would say that the concept of a category will need further explication, and probably reduce to either sets or relations or properties. |
| 8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
| Full Idea: Zermelo said that for each number n, its successor is the singleton of n, so 3 is {{{null}}}, and 1 is not a member of 3. Von Neumann said each number n is the set of numbers less than n, so 3 is {null,{null},{null,{null}}}, and 1 is a member of 3. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.2) | |
| A reaction: See Idea 645 - Zermelo could save Plato from the criticisms of Aristotle! These two accounts are cited by opponents of the set-theoretical account of numbers, because it seems impossible to arbitrate between them. |
| 8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
| Full Idea: The structuralist vigorously rejects any sort of ontological independence among the natural numbers; the essence of a natural number is its relations to other natural numbers. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.1) | |
| A reaction: This seems to place the emphasis on ordinals (what order?) rather than on cardinality (how many?). I am strongly inclined to think that this is the correct view, though you can't really have relations if there is nothing to relate. |
| 8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
| Full Idea: A 'system' is a collection of objects with certain relations among them; a 'pattern' or 'structure' is the abstract form of a system, highlighting the interrelationships and ignoring any features they do not affect how they relate to other objects. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.1) | |
| A reaction: Note that 'ignoring' features is a psychological account of abstraction, which (thanks to Frege and Geach) is supposed to be taboo - but which I suspect is actually indispensable in any proper account of thought and concepts. |
| 8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
| Full Idea: The thesis that principles of arithmetic are derivable from the laws of logic runs against a now common view that logic itself has no ontology. There are no particular logical objects. From this perspective logicism is a non-starter. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 5.1) | |
| A reaction: This criticism strikes me as utterly devastating. There are two routes to go: prove that logic does have an ontology of objects (what would they be?), or - better - deny that arithmetic contains any 'objects'. Or give up logicism. |
| 8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
| Full Idea: Term Formalism is the view that mathematics is just about characters or symbols - the systems of numerals and other linguistic forms. ...This will cover integers and rational numbers, but what are real numbers supposed to be, if they lack names? | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 6.1.1) | |
| A reaction: Real numbers (such as pi and root-2) have infinite decimal expansions, so we can start naming those. We could also start giving names like 'Harry' to other reals, though it might take a while. OK, I give up. |
| 8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
| Full Idea: Game Formalism likens mathematics to chess, where the 'content' of mathematics is exhausted by the rules of operating with its language. ...This, however, leaves the problem of why the mathematical games are so useful to the sciences. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 6.1.2) | |
| A reaction: This thought pushes us towards structuralism. It could still be a game, but one we learned from observing nature, which plays its own games. Chess is, after all, modelled on warfare. |
| 8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
| Full Idea: The Deductivist version of formalism (sometimes called 'if-thenism') says that the practice of mathematics consists of determining logical consequences of otherwise uninterpreted axioms. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 6.2) | |
| A reaction: [Hilbert is the source] More plausible than Term or Game Formalism (qv). It still leaves the question of why it seems applicable to nature, and why those particular axioms might be chosen. In some sense, though, it is obviously right. |
| 8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
| Full Idea: Critics commonly complain that the intuitionist restrictions cripple the mathematician. On the other hand, intuitionist mathematics allows for many potentially important distinctions not available in classical mathematics, and is often more subtle. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 7.1) | |
| A reaction: The main way in which it cripples is its restriction on talk of infinity ('Cantor's heaven'), which was resented by Hilbert. Since high-level infinities are interesting, it would be odd if we were not allowed to discuss them. |
| 8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
| Full Idea: I classify conceptualists according to what they say about properties or concepts. If someone classified properties as existing independent of language I would classify her as a realist in ontology of mathematics. Or they may be idealists or nominalists. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 2.2.1) | |
| A reaction: In other words, Shapiro wants to eliminate 'conceptualist' as a useful label in philosophy of mathematics. He's probably right. All thought involves concepts, but that doesn't produce a conceptualist theory of, say, football. |
| 8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
| Full Idea: A definition of a mathematical entity is 'impredicative' if it refers to a collection that contains the defined entity. The definition of 'least upper bound' is impredicative as it refers to upper bounds and characterizes a member of this set. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 1.2) | |
| A reaction: The big question is whether mathematics can live with impredicative definitions, or whether they threaten to be viciously circular, and undermine the whole enterprise. |
| 7974 | Without God we faced reality: what do we face without reality? [Baudrillard] |
| Full Idea: The eclipse of God left us up against reality. Where will the eclipse of reality leave us? | |
| From: Jean Baudrillard (The Intelligence of Evil [2004]) | |
| A reaction: Baudrillard's distinctive view is that modern culture is thwarting all our attempts to grasp reality, which itself becomes a fiction. The answer is that you are left in the position of the ancient sceptics. Sextus Empiricus (see) is the saviour. |
| 7987 | Nothing is true, but everything is exact [Baudrillard] |
| Full Idea: Someone said: everything is true, nothing is exact. I would say the opposite: nothing is true, everything is exact. | |
| From: Jean Baudrillard (The Intelligence of Evil [2004], p.210) | |
| A reaction: In analytical terminology, this appears to say that vagueness is ontological, not epistemological, agreeing with Williamson and others. To say that 'nothing is true', though, just strikes me as silly. What does Baudrillard mean by 'true'? |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| Full Idea: Rationalism is a long-standing school that can be characterized as an attempt to extend the perceived methodology of mathematics to all of knowledge. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 1.1) | |
| A reaction: Sometimes called 'Descartes's Dream', or the 'Enlightenment Project', the dream of proving everything. Within maths, Hilbert's Programme aimed for the same certainty. Idea 22 is the motto for the opposition to this approach. |
| 7978 | There is no need to involve the idea of free will to make choices about one's life [Baudrillard] |
| Full Idea: There is no need to involve the idea of free will to make choices about one's life. | |
| From: Jean Baudrillard (The Intelligence of Evil [2004], p. 57) | |
| A reaction: Someone who believed that free will was metaphysically possible, but that they themselves lacked it, might feel paralysed, defeated or fatalistic about their decision-making. But that would be like falsely believing you were fatally ill. |
| 7980 | In modern times, being useless is the essential aesthetic ingredient for an object [Baudrillard] |
| Full Idea: Since the nineteenth century it has been art's claim that it is useless...so it is enough to elevate any object to uselessness to turn it into a work of art...and obsolete useless objects automatically acquire an aesthetic aura. | |
| From: Jean Baudrillard (The Intelligence of Evil [2004], p.111) | |
| A reaction: Art is 'purposive without purpose' (Kant). An nice summary of the situation, and this seems to explain the role of Duchamp's famous urinal, up on the wall and rendered useless. The obvious rebellion, though, is Arts and Crafts. |
| 7983 | Good versus evil has been banefully reduced to happiness versus misfortune [Baudrillard] |
| Full Idea: The ideal opposition between good and evil has been reduced to the idealogical oppositions between happiness and misfortune. The reduction of good to happiness is as baneful as that of evil to misfortune. | |
| From: Jean Baudrillard (The Intelligence of Evil [2004], p.139) | |
| A reaction: A nice example is the use in the media of the word 'tragic' for every misfortune. See the debate over the translation of the Greek 'eudaimonia'. 'Happiness' seems the wrong translation, if it leads to comments like Baudrillard's. |
| 7981 | Whole populations are terrorist threats to authorities, who unite against them [Baudrillard] |
| Full Idea: One way or another, populations themselves are a terrorist threat to the authorities...and by extension, we can hypothesize a coalition of all governments against all populations. | |
| From: Jean Baudrillard (The Intelligence of Evil [2004], p.120) | |
| A reaction: This may count as left-wing paranoia, but it is a striking thought, which plants an uneasy notion in the mind whenever we see two world leaders disappear behind closed doors for a chat. |
| 7976 | People like democracy because it means they can avoid power [Baudrillard] |
| Full Idea: If the people puts itself into the hands of the political class, it does so more to be rid of power than out of any desire for representation. | |
| From: Jean Baudrillard (The Intelligence of Evil [2004], p. 54) | |
| A reaction: Very nice. If we are all in the grips of some biological 'will to power', that needn't be power over huge numbers of other people, merely power over our immediate lives. It can be expressed by building a wall. |
| 7977 | Only in the last 200 years have people demanded the democratic privilege of being individuals [Baudrillard] |
| Full Idea: Individuality is a recent phenomenon. It is only over the last two centuries that the populations of the civilized countries have demanded the democratic privilege of being individuals. | |
| From: Jean Baudrillard (The Intelligence of Evil [2004], p. 55) | |
| A reaction: I think Aristotle's ethics and politics imply individuality, given that the only purpose of civic society seems to be to enable individuals to flourish and lead virtuous lives. Society is justified, for example, because it makes friendship possible. |
| 7979 | The arrival of the news media brought history to an end [Baudrillard] |
| Full Idea: The course of history came to an end with the entry on the scene of the news media. | |
| From: Jean Baudrillard (The Intelligence of Evil [2004], p. 83) | |
| A reaction: The sort of remark for which Baudrillard became famous. It strikes me as nonsense. The view the British people got of the Battle of Trafalgar was even more distorted than their picture of the Battle of El Alamein. We know what he means, though. |
| 7984 | Suicide is ascribed to depression, with the originality of the act of will ignored [Baudrillard] |
| Full Idea: Suicide is always ascribed to depressive motivations with no account taken of an originality of, an original will to commit, the act itself. | |
| From: Jean Baudrillard (The Intelligence of Evil [2004], p.153) | |
| A reaction: Apparently research suggests that most suicides are clinically depressed, but even within the depression there is a startling act of will that goes beyond merely feeling bad. |
| 14409 | I am a presentist, and all language and common sense supports my view [Bigelow] |
| Full Idea: I am a presentist: nothing exists which is not present. Everyone believed this until the nineteenth century; it is writing into the grammar of natural languages; it is still assumed in everyday life, even by philosophers who deny it. | |
| From: John Bigelow (Presentism and Properties [1996], p.36), quoted by Trenton Merricks - Truth and Ontology | |
| A reaction: The most likely deniers of presentism seem to be physicists and cosmologists who have overdosed on Einstein. On the whole I vote for presentism, but what justifies truths about the past and future. Traces existing in the present? |
| 7985 | Pascal says secular life is acceptable, but more fun with the hypothesis of God [Baudrillard] |
| Full Idea: What Pascal says, more or less, is that you can more or less content yourself with a secular existence and its advantages, but it's much more fun with the hypothesis of God. | |
| From: Jean Baudrillard (The Intelligence of Evil [2004], p.155) | |
| A reaction: Pascal will be a bit startled when he reads this, but it is a lovely way to present his idea. It suddenly sounds much more attractive. Life would be much more fun if we lived according to all sorts of startling beliefs. Relating your life to God is one. |