28 ideas
| 20455 | Philosophy really got started as the rival mode of discourse to tragedy [Critchley] |
| Full Idea: The pre-Socratics are interesting, but philosophy really begins in drama; it's a competitive discourse to tragedy. Which is why Plato's 'Republic' excludes the poets: they're the competition; gotta get rid of them. | |
| From: Simon Critchley (Impossible Objects: interviews [2012], 6) | |
| A reaction: That's an interesting and novel perspective. So what was the 'discourse' of tragedy saying, and why did that provoke the new rival? Was it too fatalistic? |
| 20446 | Philosophy begins in disappointment, notably in religion and politics [Critchley] |
| Full Idea: I claim that philosophy begins in disappointment, and there are two forms of disappointment that interest me: religious and political disappointment | |
| From: Simon Critchley (Impossible Objects: interviews [2012], 2) | |
| A reaction: You are only disappointed by reality if you expected something better. To be disappointed by the failures of religion strikes me as rather old-fashioned, which Critchley sort of admits. Given the size and tumult of modern states, politics isn't promising. |
| 20449 | Science gives us an excessively theoretical view of life [Critchley] |
| Full Idea: One of the problems with the scientific worldview is that it leads human beings to have an overwhelmingly theoretical relationship to the world. | |
| From: Simon Critchley (Impossible Objects: interviews [2012], 2) | |
| A reaction: Critchley is defending phenomenology, but this also supports its cousin, existentialism. I keep meeting bright elderly men who have immersed themselves in the study of science, and they seem very remote from the humanist culture I love. |
| 20448 | Phenomenology uncovers and redescribes the pre-theoretical layer of life [Critchley] |
| Full Idea: Phenomenology is a philosophical method that tries to uncover the pre-theoretical layer of human experience and redescribe it. | |
| From: Simon Critchley (Impossible Objects: interviews [2012], 2) | |
| A reaction: I would be delighted if someone could tell me what this means in practice. I have the impression of lots of talk about phenomenology, but not much doing of it. Clearly I must enquire further. |
| 19370 | 'Blind thought' is reasoning without recognition of the ingredients of the reasoning [Leibniz, by Arthur,R] |
| Full Idea: Leibniz invented the concept of 'blind thought' - reasoning by a manipulation of characters without being able to recognise what each character stands for. | |
| From: report of Gottfried Leibniz (Towards a Universal Characteristic [1677]) by Richard T.W. Arthur - Leibniz |
| 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. |
| 19391 | We can assign a characteristic number to every single object [Leibniz] |
| Full Idea: The true principle is that we can assign to every object its determined characteristic number. | |
| From: Gottfried Leibniz (Towards a Universal Characteristic [1677], p.18) | |
| A reaction: I add this as a predecessor of Gödel numbering. It is part of Leibniz's huge plan for a Universal Characteristic, to map reality numerically, and then calculate the truths about it. Gödel seems to allow metaphysics to be done mathematically. |
| 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. |
| 19390 | Everything is subsumed under number, which is a metaphysical statics of the universe, revealing powers [Leibniz] |
| Full Idea: There is nothing which is not subsumable under number; number is therefore a fundamental metaphysical form, and arithmetic a sort of statics of the universe, in which the powers of things are revealed. | |
| From: Gottfried Leibniz (Towards a Universal Characteristic [1677], p.17) | |
| A reaction: I take numbers to be a highly generalised and idealised description of an aspect of reality (seen as mainly constituted by countable substances). Seeing reality as processes doesn't lead us to number. So I like this idea. |
| 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. |
| 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. |
| 20454 | Wallace Stevens is the greatest philosophical poet of the twentieth century in English [Critchley] |
| Full Idea: Wallace Stevens is the greatest philosophical poet of the twentieth century in the English language - full stop - in my humble opinion. | |
| From: Simon Critchley (Impossible Objects: interviews [2012], 6) | |
| A reaction: I include this because I tend to agree, and love Stevens. Hear recordings of him reading. I once mentioned Stevens in a conversation with Ted Hughes, and he just shrugged and said Stevens 'wasn't much of a poet'. Wrong. |
| 20456 | Interesting art is always organised around ethical demands [Critchley] |
| Full Idea: I don't think that art can be unethical. I think that interesting art is always ethical. It is organised around ethical demands. | |
| From: Simon Critchley (Impossible Objects: interviews [2012], 8) | |
| A reaction: It is a struggle to make this fit instrumental music. Critchley likes punk rock, so he might not see the problem. How to compare Bachian, Mozart, Beethovenian and Debussyian ethics? Not impossible. |
| 20447 | The problems is not justifying ethics, but motivating it. Why should a self seek its good? [Critchley] |
| Full Idea: The issue is not so much justification as motivation, that in virtue of which the self can be motivated to act on some conception of the good. ...How does a self bind itself to whatever it determines as its good? | |
| From: Simon Critchley (Impossible Objects: interviews [2012], 2) | |
| A reaction: That is a bold and interesting idea about the starting point for ethics. It is always a problem for Aristotle, that he can offer no motivation for the quest for virtue. Contractarians start from existing motivations, but that isn't impressive. |
| 20450 | The state, law, bureaucracy and capital are limitations on life, so I prefer federalist anarchism [Critchley] |
| Full Idea: I begin with the ontological premise that the state is a limitation on human existence. I am against the state, law, bureaucracy, and capital. I see anarchism as the only desirable way of organising, politically. ...Its political form is federalist. | |
| From: Simon Critchley (Impossible Objects: interviews [2012], 3) | |
| A reaction: Hm. Some sympathy, but caution. All systems, even federalist anarchism, are limitations on our lives, so which limitations do we prefer? The law aspires to a calm egalitarian neutrality, which seems promising to me. |
| 20452 | Anarchism used to be libertarian (especially for sexuality), but now concerns responsibility [Critchley] |
| Full Idea: Anarchism in the 1960s was libertarian and organised around issues of sexual liberation. That moment has passed. People are and should be organising around responsibility. | |
| From: Simon Critchley (Impossible Objects: interviews [2012], 3) | |
| A reaction: So there are two types of anarchism, focused on freedom or on responsibility. An organisation like Greenpeace might represent the latter. |
| 20451 | Belief that humans are wicked leads to authoritarian politics [Critchley] |
| Full Idea: If you think human beings are wicked, you turn to an authoritarian conception of politics, the Hobbesian-Machiavellian-Straussian lie. | |
| From: Simon Critchley (Impossible Objects: interviews [2012], 3) | |
| A reaction: Right-wingers also tend to believe in free will, so they can blame and punish. Good people are more inspired by a great leader than bad people are? (Later, Critchley says authoritarians usually believe in original sin). |