12 ideas
| 8921 | Structuralism is now common, studying relations, with no regard for what the objects might be [Hellman] |
| Full Idea: With developments in modern mathematics, structuralist ideas have become commonplace. We study 'abstract structures', having relations without regard to the objects. As Hilbert famously said, items of furniture would do. | |
| From: Geoffrey Hellman (Structuralism [2007], §1) | |
| A reaction: Hilbert is known as a Formalist, which suggests that modern Structuralism is a refined and more naturalist version of the rather austere formalist view. Presumably the sofa can't stand for six, so a structural definition of numbers is needed. |
| 8698 | Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend] |
| Full Idea: The modal structuralist thinks of mathematical structures as possibilities. The application of mathematics is just the realisation that a possible structure is actualised. As structures are possibilities, realist ontological problems are avoided. | |
| From: report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Michèle Friend - Introducing the Philosophy of Mathematics 4.3 | |
| A reaction: Friend criticises this and rejects it, but it is appealing. Mathematics should aim to be applicable to any possible world, and not just the actual one. However, does the actual world 'actualise a mathematical structure'? |
| 9557 | Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara] |
| Full Idea: Hellman represents statements of pure mathematics as elliptical for modal conditionals of a certain sort. | |
| From: report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Charles Chihara - A Structural Account of Mathematics 5.3 | |
| A reaction: It's a pity there is such difficulty in understanding conditionals (see Graham Priest on the subject). I intuit a grain of truth in this, though I take maths to reflect the structure of the actual world (with possibilities being part of that world). |
| 10263 | Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman] |
| Full Idea: The usual way to show that a sentence is possible is to show that it has a model, but for Hellman presumably a sentence is possible if it might have a model (or if, possibly, it has a model). It is not clear what this move brings us. | |
| From: comment on Geoffrey Hellman (Mathematics without Numbers [1989]) by Stewart Shapiro - Philosophy of Mathematics 7.3 | |
| A reaction: I can't assess this, but presumably the possibility of the model must be demonstrated in some way. Aren't all models merely possible, because they are based on axioms, which seem to be no more than possibilities? |
| 8922 | Maybe mathematical objects only have structural roles, and no intrinsic nature [Hellman] |
| Full Idea: There is the tantalizing possibility that perhaps mathematical objects 'have no nature' at all, beyond their 'structural role'. | |
| From: Geoffrey Hellman (Structuralism [2007], §1) | |
| A reaction: This would fit with a number being a function rather than an object. We are interested in what cars do, not the bolts that hold them together? But the ontology of mathematics is quite separate from how you do mathematics. |
| 20751 | As a young girl assumes her status as feminine, she acts in a more fragile immobile way [Young,IM] |
| Full Idea: The young girl acquires many subject habits of feminine body comportment - walking, tilting her head, standing and sitting like a girl, and so on ….The more a girl assumes her status as feminine, the more she takes herself to be fragile and immobile. | |
| From: Iris Marion Young (On Female Body Experience [2005], p.43), quoted by Kevin Aho - Existentialism: an introduction 3 'Aspects' | |
| A reaction: This strikes me as true of young women, but it largely wears off as they get older, at least among modern women. A whole book could be written about women and smiling. |
| 7602 | In the Bible God changes his mind (repenting of creating humanity, in the Flood) [Armstrong,K] |
| Full Idea: In the Bible God changes his mind, as when he repents of having made man and decides to destroy the human race in the Flood. | |
| From: Karen Armstrong (A History of God [1993], Ch.1) | |
| A reaction: It becomes apparent that the most startling feature of Christian fundamentalism is its uncritical reading of the Bible, in which passages are wilfully lifted from context, and inconvenient inconsistencies are ruthlessly ignored. |
| 7605 | Monotheism introduced intolerance into religious thinking [Armstrong,K] |
| Full Idea: We have become so used to the intolerance of monotheism that we may not appreciate that its hostility towards other gods was a new religious attitude; paganism was an essentially tolerant faith. | |
| From: Karen Armstrong (A History of God [1993], Ch.2) | |
| A reaction: The comedian Dave Allen always signed off with "may your god go with you". To me the most striking feature of monotheists is frequently their barely controlled aggression, beneath a mask of strained compassion. |
| 7599 | Around 800 BCE teachers superseded gods in India [Armstrong,K] |
| Full Idea: Around the eighth century BCE the gods ceased to be very important in India, and would be superseded by the religious teacher, who would be considered higher than the gods. | |
| From: Karen Armstrong (A History of God [1993], Ch.1) | |
| A reaction: At least there has been one culture that gave an appropriate status to teachers. It seems astonishing in that age that human beings could have higher status than gods - way before the European 'humanists'. |
| 7597 | There is virtually no sign of monotheism in the Pentateuch [Armstrong,K] |
| Full Idea: It is very difficult to find a single monotheistic statement in the whole of the Pentateuch, and even the Ten Commandments take the existence of other gods for granted ("There shall be no strange gods for you before my face"). | |
| From: Karen Armstrong (A History of God [1993], Ch.1) | |
| A reaction: The transition from polytheism to monotheism is very strange. First God is 'jealous' of other gods, then supremely above them, and eventually totally exclusive. It's like watching the rise of Stalin. |
| 7606 | The idea that Jesus was God was only settled in the fourth century [Armstrong,K] |
| Full Idea: Jesus himself certainly never claimed to be God, and the doctrine that Jesus had been God in human form was not finalised until the fourth century. | |
| From: Karen Armstrong (A History of God [1993], Ch.3) | |
| A reaction: It was this final view which seems to have provoked Muhammed into developing a religion with the slogan "there is only one God". In Christianity an initially promising set of teachings grew into a prolonged irrational hysteria. |
| 7596 | Faith is not just belief in propositions, but also putting trust in them [Armstrong,K] |
| Full Idea: There is a distinction between belief in a set of propositions and a faith which enables us to put our trust in them. | |
| From: Karen Armstrong (A History of God [1993], Intro) | |
| A reaction: This is interestingly distinct from the usual idea that faith is putting belief in propositions which are not sufficiently rationally justified. How many philosophers actually have faith in the propositions they say they believe? |