6 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. |
| 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. |
| 16634 | I can't be unaware of anything which is in me [Descartes] |
| Full Idea: Nothing can be in me of which I am entirely unaware. | |
| From: René Descartes (Reply to First Objections [1641]), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 08.4 | |
| A reaction: This I take to be a place where Descartes is utterly and catastrophically wrong. Until you grasp the utter falseness of this thought, the possibility of you (dear reader) understanding human beings is zero. Here 'I' obviously means his mind. |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
| From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
| A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |
| 3635 | Essence must be known before we discuss existence [Descartes] |
| Full Idea: According to the laws of true logic, we must never ask about the existence of anything until we first understand its essence. | |
| From: René Descartes (Reply to First Objections [1641], 108) |
| 3634 | We can't prove a first cause from our inability to grasp infinity [Descartes] |
| Full Idea: My inability to grasp an infinite chain of successive causes without a first cause does not entail that there must be a first cause, just as my inability to grasp infinite divisibility of finite things does not make that impossible. | |
| From: René Descartes (Reply to First Objections [1641], 106) |