40 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. |
| 21812 | Being is the product of pure intellect [Plotinus] |
| Full Idea: Intellectual-Principle [Nous] by its intellective act establishes Being. | |
| From: Plotinus (The Enneads [c.245], 5.1.04) | |
| A reaction: This is a surprising view - that there is something which is prior to Being - but I take it to be Plotinus giving primacy to Plato's Form of the Good (a pure ideal), ahead of the One of Parmenides (which is Being). |
| 21817 | The One does not exist, but is the source of all existence [Plotinus] |
| Full Idea: The First is no member of existence, but can be the source of all. | |
| From: Plotinus (The Enneads [c.245], 5.1.07) | |
| A reaction: The First is the One, and this explicitly denies that it has Being. This answers the self-predication problem of Forms. Plato thought the Form of the Beautiful was beautiful, but it can't be (because of the regress). The source of existence can't exist. |
| 21824 | The One is a principle which transcends Being [Plotinus] |
| Full Idea: There exists a principle which transcends Being; this the One. | |
| From: Plotinus (The Enneads [c.245], 5.1.10) | |
| A reaction: The idea that the One transcends Being is the distinctive Plotinus doctrine. He defends the view that this was also the view of Anaxagoras, Empedocles and Plato. |
| 21813 | Number determines individual being [Plotinus] |
| Full Idea: Number is the determinant of individual being. | |
| From: Plotinus (The Enneads [c.245], 5.1.05) | |
| A reaction: You might have thought that number was the consequence of the individualities (or units) within being, but not so. You can't get more platonic than saying that the idealised numbers are the source of the particular units. |
| 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. |
| 5506 | If soul was like body, its parts would be separate, without communication [Plotinus] |
| Full Idea: If the soul had the nature of the body, it would have isolated members each unaware of the condition of the other;..there would be a particular soul as a distinct entity to each local experience, so a multiplicity of souls would administer an individual. | |
| From: Plotinus (The Enneads [c.245], 4.2.2), quoted by R Martin / J Barresi - Introduction to 'Personal Identity' p.15 | |
| A reaction: Of course, the modern 'modularity of mind' theory does suggest that we are run by a team, but a central co-ordinator is required, with a full communication network across the modules. |
| 21827 | The movement of Soul is continuous, but we are only aware of the parts of it that are sensed [Plotinus] |
| Full Idea: The Soul maintains its unfailing movement; for not all that passes in the soul is, by that fact, perceptible; we know just as much as impinges on the faculty of the sense. | |
| From: Plotinus (The Enneads [c.245], 5.1.12) | |
| A reaction: This is a straightforward argument in favour of an unconscious aspect to the mind - and a rather good argument too. No one thinks that our minds ever stop working, even in sleep. |
| 21828 | A person is the whole of their soul [Plotinus] |
| Full Idea: Man is not merely a part (the higher part) of the Soul but the total. | |
| From: Plotinus (The Enneads [c.245], 5.1.12) | |
| A reaction: The soul is psuche, which includes the vegetative soul. The higher part is normally taken to be reason. This seems pretty close to John Locke's view of the matter. |
| 21809 | Our soul has the same ideal nature as the oldest god, and is honourable above the body [Plotinus] |
| Full Idea: Our own soul is of that same ideal nature [as the oldest god of them all], so that to consider it, purified, freed from all accruement, is to recognise in ourselves which we have found soul to be, honourable above the body. For what is body but earth? | |
| From: Plotinus (The Enneads [c.245], 5.1.02) | |
| A reaction: The strongest versions of substance dualism are religious in character, because the separateness of the mind elevates us above the grubby physical character of the world. I'm with Nietzsche on this one - this view is actually harmful to us. |
| 21825 | The soul is outside of all of space, and has no connection to the bodily order [Plotinus] |
| Full Idea: We may not seek any point in space in which to seat the soul; it must be set outside of all space; its distinct quality, its separateness, its immateriality, demand that it be a thing alone, untouched by all of the bodily order. | |
| From: Plotinus (The Enneads [c.245], 5.1.10) | |
| A reaction: You can't get more dualist than that. He doesn't seem bothered about the interaction problem. He likens such influence to the radiation of the sun, rather than to physical movement. |
| 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! |
| 21826 | The Soul reasons about the Right, so there must be some permanent Right about which it reasons [Plotinus] |
| Full Idea: Since there is a Soul which reasons upon the right and good - for reasoning is an enquiry into the rightness and goodness of this rather than that - there must exist some pemanent Right, the source and foundation of this reasoning in our soul. | |
| From: Plotinus (The Enneads [c.245], 5.1.11) | |
| A reaction: This is pretty close the Kant's concept of 'the moral order within me', and Plotinus even sees it as rational. Presumably this right is 'permanent' because the revelatlons of reason about it are necessary truths. |
| 6922 | Ecstasy is for the neo-Platonist the highest psychological state of man [Plotinus, by Feuerbach] |
| Full Idea: Ecstasy or rapture is for the neo-Platonist the highest psychological state of man. | |
| From: report of Plotinus (The Enneads [c.245]) by Ludwig Feuerbach - Principles of Philosophy of the Future §29 | |
| A reaction: See Bernini's statue of St Theresa. Personally I find this very unappealing because of its utter irrationality, but what is the 'highest' human psychological state? Doing mental arithmetic? Doing what is morally right? Dignity under pressure? |
| 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. |
| 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. |
| 21816 | Soul is the logos of Nous, just as Nous is the logos of the One [Plotinus] |
| Full Idea: The soul is an utterance [logos] and act of the Intellectual-Principle [Nous], as that is an utterance and act of the One. | |
| From: Plotinus (The Enneads [c.245], 5.1.06) | |
| A reaction: Being only comes into the picture at the secondary Nous stage. Nous is the closest to the modern concept of God. |
| 21815 | Because the One is immobile, it must create by radiation, light the sun producing light [Plotinus] |
| Full Idea: Given this immobility of the Supreme ...what happened then? It must be a circumradiation, which may be compared to the brilliant light encircling the sun and ceaselessly generating from that unchanging substance, | |
| From: Plotinus (The Enneads [c.245], 5.1.06) | |
| A reaction: This is the answer given to the problem raised in Idea 21814. The sun produces energy, without apparent movement. Not an answer that will satisfy a physicist, but an interesting answer. |
| 21814 | How can multiple existence arise from the unified One? [Plotinus] |
| Full Idea: The problem endlessly debated is how, from such a unity as we have declared the One to be, does anything at all come into substantial existence, any multiplicity, dyad or number? | |
| From: Plotinus (The Enneads [c.245], 5.1.06) | |
| A reaction: This was precisely Aristotle's objection to the One of Parmenides, and especially the problem of the source of movement (which Plotinus also notices). |
| 21808 | Soul is author of all of life, and of the stars, and it gives them law and movement [Plotinus] |
| Full Idea: Soul is the author of all living things, ...it has breathed life into them all, whatever is nourished by earth and sea, the divine stars in the sky; ...it is the principle distinct from all of these to which it gives law and movement and life. | |
| From: Plotinus (The Enneads [c.245], 5.1.02) | |
| A reaction: This seems to derive from Anaxagoras, who is mentioned by Plotinus. The soul he refers to his not the same as our concept of God. Note the word 'law', which I am guessing is nomos. Not, I think, modern laws of nature, but closer to guidelines. |
| 21811 | Even the soul is secondary to the Intellectual-Principle [Nous], of which soul is an utterance [Plotinus] |
| Full Idea: Soul, for all the worth we have shown to belong to it, is yet a secondary, an image of the Intellectual-Principle [Nous]; reason uttered is an image of reason stored within the soul, and similarly soul is an utterance of the Intellectual-Principle. | |
| From: Plotinus (The Enneads [c.245], 5.1.03) | |
| A reaction: It then turns out that Nous is secondary to the One, so there is a hierarchy of Being (which only enters at the Nous stage). |