31 ideas
| 20962 | Habermas seems to make philosophy more democratic [Habermas, by Bowie] |
| Full Idea: Habermas is concerned to avoid the traumas of modern German history by making democracy an integral part of philosophy. | |
| From: report of Jürgen Habermas (The Theory of Communicative Action [1981]) by Andrew Bowie - Introduction to German Philosophy Conc 'Habermas' | |
| A reaction: Hence Habermas's emphasis on communication as central to language, which is central to philosophy. Modern philosophy departments are amazingly hierarchical. |
| 15670 | The aim of 'post-metaphysical' philosophy is to interpret the sciences [Habermas, by Finlayson] |
| Full Idea: For Habermas, the task of what he calls 'post-metaphysical' philosophy is to be a stand-in and interpreter for the specialized sciences. | |
| From: report of Jürgen Habermas (The Theory of Communicative Action [1981]) by James Gordon Finlayson - Habermas Ch.5:65 |
| 15665 | We can do social philosophy by studying coordinated action through language use [Habermas, by Finlayson] |
| Full Idea: Habermas claims to have embarked upon a new way of doing social philosophy, one that begins from an analysis of language use and that locates the rational basis of the coordination of action in speech. | |
| From: report of Jürgen Habermas (The Theory of Communicative Action [1981]) by James Gordon Finlayson - Habermas Ch.3:28 |
| 20573 | Rather than instrumental reason, Habermas emphasises its communicative role [Habermas, by Oksala] |
| Full Idea: Instead of Enlightenment instrumental rationality (criticised by Adorno and Horkheimer), Habermas emphasizes 'communicative rationality', which makes critical discussion and mutual understanding possible. | |
| From: report of Jürgen Habermas (The Theory of Communicative Action [1981]) by Johanna Oksala - Political Philosophy: all that matters Ch.6 | |
| A reaction: There was a good reason not to smoke cigarettes, before we found out what it is. In one sense, reasons are in the world. This is interesting, but I feel analytic vertigo, as the lovely concept of 'rationality' becomes blurred and diffused. |
| 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. |
| 20961 | What is considered a priori changes as language changes [Habermas, by Bowie] |
| Full Idea: Habermas claims that what is regarded as a priori changes with history. This is because the linguistic structures on which judgements depend are themselves part of history, not prior to it. | |
| From: report of Jürgen Habermas (The Theory of Communicative Action [1981]) by Andrew Bowie - Introduction to German Philosophy Conc 'Habermas' | |
| A reaction: This is an interesting style of argument generally only found in continental philosophers, because they see the problem as historical rather than timeless. Compare Idea 20595, which sees analyticity historically. |
| 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. |
| 15667 | To understand a statement is to know what would make it acceptable [Habermas] |
| Full Idea: We understand the meaning of a speech act when we know what would make it acceptable. | |
| From: Jürgen Habermas (The Theory of Communicative Action [1981], I:297), quoted by James Gordon Finlayson - Habermas Ch.3:37 | |
| A reaction: Finlayson glosses this as requiring the reasons which would justify the speech act. |
| 15668 | Meaning is not fixed by a relation to the external world, but a relation to other speakers [Habermas, by Finlayson] |
| Full Idea: On Habermas's view, meanings are not determined by the speaker's relation to the external world, but by his relation to his interlocutors; meaning is essentially intersubjective. | |
| From: report of Jürgen Habermas (The Theory of Communicative Action [1981]) by James Gordon Finlayson - Habermas Ch.3:38 | |
| A reaction: This view is not the same as Grice's, but it is clearly much closer to Grice than to (say) the Frege/Davidson emphasis on truth-conditions. I'm not sure if I would know how to begin arbitrating between the two views! |
| 6479 | Noninterference requires justification as much as interference does [Nagel] |
| Full Idea: Noninterference requires justification as much as interference does. | |
| From: Thomas Nagel (Equality and Partiality [1991], Ch.10) | |
| A reaction: I'm not convinced by this, as a simple rule. If I spend my whole life doing just the minimum for my own survival, I don't see why I should have to justify that, and I don't see a state is obliged to justify it either. |
| 6450 | Morality must be motivating, and not because of pre-moral motives [Nagel] |
| Full Idea: My own view is that moral justification must be capable of motivating, but not in virtue of reliance on pre-moral motives. | |
| From: Thomas Nagel (Equality and Partiality [1991], Ch.5) | |
| A reaction: This may well be the core and essence of Kantian moral theory. I'm inclined to think of it as 'Kant's dream', which is of ultra-rational beings who are driven by pure rationality as a motivator. People who fit this bill tend to be academics. |
| 6447 | Game theory misses out the motivation arising from the impersonal standpoint [Nagel] |
| Full Idea: I do not favour the route taken by Hobbes's modern descendants, using game theory, since I believe the impersonal standpoint makes an essential contribution to individual motivation which must be addressed by any ethically acceptable theory. | |
| From: Thomas Nagel (Equality and Partiality [1991], Ch.4) | |
| A reaction: The assumption of self-seeking at the core of game theory seems very bizarre, and leads to moral approval of free riders. Nagel offers the best response, which is the Kantian impersonal view. Nagel may be optimistic about motivation, though. |
| 6446 | In ethics we abstract from our identity, but not from our humanity [Nagel] |
| Full Idea: In pursuit of the kind of objectivity needed in the physical sciences, we abstract even from our humanity; but nothing further than abstraction from our identity (that is, who we are) enters into ethical theory. | |
| From: Thomas Nagel (Equality and Partiality [1991], Ch.2) | |
| A reaction: The 'brief' summary of this boils down to a nice and interesting slogan. It epitomises the modern Kantian approach to ethics. But compare Idea 4122, from Bernard Williams. |
| 6477 | I can only universalise a maxim if everyone else could also universalise it [Nagel] |
| Full Idea: It is implicit in the categorical imperative that I can will that everyone should adopt as a maxim only what everyone else can also will that everyone should adopt as a maxim. | |
| From: Thomas Nagel (Equality and Partiality [1991], Ch.5) | |
| A reaction: This is a nice move, because it shifts the theory away from a highly individualistic Cartesian view of morality towards the idea that morality is a community activity. |
| 15669 | People endorse equality, universality and inclusiveness, just by their communicative practices [Habermas, by Finlayson] |
| Full Idea: The ideal of equality, universality, and inclusiveness are inscribed in the communicative practices of the lifeworld, and agents, merely by virtue of communicating, conform to them. | |
| From: report of Jürgen Habermas (The Theory of Communicative Action [1981]) by James Gordon Finlayson - Habermas Ch.4:60 | |
| A reaction: This summary of Habermas's social views strikes me as thoroughly Kantian. It is something like the ideals of the Kingdom of Ends, necessarily implemented in a liberal society. Habermas emphasises the social, where Kant starts from the liberal. |
| 6448 | A legitimate system is one accepted as both impartial and reasonably partial [Nagel] |
| Full Idea: A legitimate system is one which reconciles the two universal principles of impartiality and reasonable partiality so that no one can object that his interests are not being accorded sufficient weight or that the demands on him are excessive. | |
| From: Thomas Nagel (Equality and Partiality [1991], Ch.4) | |
| A reaction: This seems an appealing principle, and a nice attempt at stating the core of Kantian liberalism. It is obviously influenced by Scanlon's contractualist view, in the idea that 'no one can object', because everyone sees the justification. |
| 6478 | Democracy is opposed to equality, if the poor are not a majority [Nagel] |
| Full Idea: As things are, democracy is the enemy of comprehensive equality, once the poor cease to be a majority. | |
| From: Thomas Nagel (Equality and Partiality [1991], Ch.9) | |
| A reaction: This is obvious once you think about it, but it is well worth saying, because it is tempting to think that we live in an 'equal' society, merely because we are equal in things such as voting rights and equality before the law. |
| 23416 | Political involvement is needed, to challenge existing practices [Habermas, by Kymlicka] |
| Full Idea: Habermas thinks political deliberation is required precisely because in its absence people will tend to accept existing practices as given, and thereby perpetuate false needs. | |
| From: report of Jürgen Habermas (The Theory of Communicative Action [1981]) by Will Kymlicka - Community 'need' | |
| A reaction: If the dream is healthy and intelligent progress, it is not clear where that should come from. The problem with state involvement in the authority and power of the state. Locals are often prejudiced, so the intermediate level may be best. |