Combining Texts

Ideas for 'Parmenides', 'Letters' and 'Words without Objects'

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3 ideas

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
Some non-count nouns can be used for counting, as in 'several wines' or 'fewer cheeses' [Laycock]
     Full Idea: The very words we class as non-count nouns may themselves be used for counting, of kinds or types, and phrases like 'several wines' are perfectly in order. ...Not only do we have 'less cheese', but we also have the non-generic 'fewer cheeses'.
     From: Henry Laycock (Words without Objects [2006], Intro 4 n23)
     A reaction: [compressed] Laycock generally endorses the thought that what can be counted is not simply distinguished by a precise class of applied vocabulary. He offers lots of borderline or ambiguous cases in his footnotes.
Some apparent non-count words can take plural forms, such as 'snows' or 'waters' [Laycock]
     Full Idea: Some words that seem to be semantically non-count can take syntactically plural forms: 'snows', 'sands', 'waters' and the like.
     From: Henry Laycock (Words without Objects [2006], Intro 4 n24)
     A reaction: This seems to involve parcels of the stuff. The 'snows of yesteryear' occur at different times. 'Taking the waters' probably involves occasions. The 'Arabian sands' presumably occur in different areas. Semantics won't fix what is countable.
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
One is, so numbers exist, so endless numbers exist, and each one must partake of being [Plato]
     Full Idea: If one is, there must also necessarily be number - Necessarily - But if there is number, there would be many, and an unlimited multitude of beings. ..So if all partakes of being, each part of number would also partake of it.
     From: Plato (Parmenides [c.364 BCE], 144a)
     A reaction: This seems to commit to numbers having being, then to too many numbers, and hence to too much being - but without backing down and wondering whether numbers had being after all. Aristotle disagreed.