display all the ideas for this combination of texts
4 ideas
17785 | Real numbers as abstracted objects are now treated as complete ordered fields [Mayberry] |
Full Idea: The abstractness of the old fashioned real numbers has been replaced by generality in the modern theory of complete ordered fields. | |
From: John Mayberry (What Required for Foundation for Maths? [1994], p.408-2) | |
A reaction: In philosophy, I'm increasingly thinking that we should talk much more of 'generality', and a great deal less about 'universals'. (By which I don't mean that redness is just the set of red things). |
2084 | If a word has no parts and has a single identity, it turns out to be the same kind of thing as a letter [Plato] |
Full Idea: If a complex or a syllable has no parts and is a single identity, hasn't it turned out to be the same kind of thing as an element or letter? | |
From: Plato (Theaetetus [c.368 BCE], 205d) |
15844 | A sum is that from which nothing is lacking, which is a whole [Plato] |
Full Idea: But this sum now - isn't it just when there is nothing lacking that it is a sum? Yes, necessarily. And won't this very same thing - that from which nothing is lacking - be a whole? | |
From: Plato (Theaetetus [c.368 BCE], 205a) | |
A reaction: This seems to be right, be rather too vague and potentially circular to be of much use. What is the criterion for deciding that nothing is lacking? |
15843 | The whole can't be the parts, because it would be all of the parts, which is the whole [Plato] |
Full Idea: The whole does not consist of parts; for it did, it would be all the parts and so would be the sum. | |
From: Plato (Theaetetus [c.368 BCE], 204e) | |
A reaction: That is, 'the whole is the sum of its parts' is a tautology! The claim that 'the whole is more than the sum of its parts' gets into similar trouble. See Verity Harte on this. |