display all the ideas for this combination of texts
6 ideas
| 13261 | Plato sees an object's structure as expressible in mathematics [Plato, by Koslicki] |
| Full Idea: The 'structure' of an object tends to be characterised by Plato as something that is mathematically expressible. | |
| From: report of Plato (works [c.375 BCE]) by Kathrin Koslicki - The Structure of Objects 5.3 | |
| A reaction: This seems to be pure Pythagoreanism (see Idea 644). Plato is pursuing Pythagoras's research programme, of trying to find mathematics buried in every aspect of reality. |
| 13265 | Plato was less concerned than Aristotle with the source of unity in a complex object [Plato, by Koslicki] |
| Full Idea: Plato was less concerned than Aristotle with the project of how to account, in completely general terms, for the source of unity within a mereologically complex object. | |
| From: report of Plato (works [c.375 BCE]) by Kathrin Koslicki - The Structure of Objects 5.5 | |
| A reaction: Plato seems to have simply asserted that some sort of harmony held things together. Aristotles puts the forms [eidos] within objects, rather than external, so he has to give a fuller account of what is going on in an object. He never managed it! |
| 14164 | The only unities are simples, or wholes composed of parts [Russell] |
| Full Idea: The only kind of unity to which I can attach any precise sense - apart from the unity of the absolutely simple - is that of a whole composed of parts. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §439) | |
| A reaction: This comes from a keen student of Leibniz, who was obsessed with unity. Russell leaves unaddressed the question of what turns some parts into a whole. |
| 14112 | A set has some sort of unity, but not enough to be a 'whole' [Russell] |
| Full Idea: In a class as many, the component terms, though they have some kind of unity, have less than is required for a whole. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §070) | |
| A reaction: This is interesting because (among many other things), sets are used to stand for numbers, but numbers are usually reqarded as wholes. |
| 593 | Plato's holds that there are three substances: Forms, mathematical entities, and perceptible bodies [Plato, by Aristotle] |
| Full Idea: Plato's doctrine was that the Forms and mathematicals are two substances and that the third substance is that of perceptible bodies. | |
| From: report of Plato (works [c.375 BCE]) by Aristotle - Metaphysics 1028b |
| 16058 | Dion and Theon coexist, but Theon lacks a foot. If Dion loses a foot, he ousts Theon? [Chrysippus, by Philo of Alexandria] |
| Full Idea: If two individuals occupied one substance …let one individual (Dion) be thought of as whole-limbed, the other (Theon) as minus one foot. Then let one of Dion's feet be amputated. Theon is the stronger candidate to have perished. | |
| From: report of Chrysippus (fragments/reports [c.240 BCE]) by Philo (Alex) - On the Eternity of the World 48 | |
| A reaction: [SVF 2.397 - from Chrysippus's lost 'On the Growing Argument'] This is the original of Tibbles the Cat. Dion must persist to change, and then ousts Theon (it seems). Philo protests at Theon ceasing to exist when nothing has happened to him. |