Combining Texts

Ideas for 'Theaetetus', 'The Evolution of Logic' and 'What Required for Foundation for Maths?'

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4 ideas

9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
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     Full Idea: The abstractness of the old fashioned real numbers has been replaced by generality in the modern theory of complete ordered fields.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).
9. Objects / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects
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)
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
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?
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.