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All the ideas for 'fragments/reports', 'Scattered Objects' and 'Concepts and Counting'

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6 ideas

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
A single object must not be counted twice, which needs knowledge of distinctness (negative identity) [Rumfitt]
     Full Idea: One requirement for a successful count is that double counting should be avoided: a single object should not be counted twice. ...but that is to make a knowledgeable judgement of distinctness - to resolve a question of identity in the negative.
     From: Ian Rumfitt (Concepts and Counting [2002], III)
     A reaction: He also notes later (p.65) that you must count all and only the right things.
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
Some 'how many?' answers are not predications of a concept, like 'how many gallons?' [Rumfitt]
     Full Idea: We hit trouble if we hear answers to some 'How many?' questions as predications about concepts. The correct answer to 'how many gallons of water are in the tank?' may be 'ten', but that doesn''t mean ten things instantiate 'gallon of water in the tank'.
     From: Ian Rumfitt (Concepts and Counting [2002], I)
     A reaction: Rumfitt makes the point that a huge number of things instantiate that concept in a ten gallon tank of water. No problem, says Rumfitt, because Frege wouldn't have counted that as a statement of number.
9. Objects / B. Unity of Objects / 3. Unity Problems / a. Scattered objects
Clearly a pipe can survive being taken apart [Cartwright,R]
     Full Idea: There is at the moment a pipe on my desk. Its stem has been removed but it remains a pipe for all that; otherwise no pipe could survive a thorough cleaning.
     From: Richard Cartwright (Scattered Objects [1974], p.175)
     A reaction: To say that the pipe survives dismantling is not to say that it is fully a pipe during its dismantled phase. He gives a further example of a book in two volumes.
Bodies don't becomes scattered by losing small or minor parts [Cartwright,R]
     Full Idea: If a branch falls from a tree, the tree does not thereby become scattered, and a human body does not become scattered upon loss of a bit of fingernail.
     From: Richard Cartwright (Scattered Objects [1974], p.184)
     A reaction: This sort of observation draws me towards essentialism. A body is scattered if you divide it in a major way, but not if you separate off a minor part. It isn't just a matter of size, or even function. We have broader idea of what is essential.
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
     Full Idea: Archelaus was the first person to say that the universe is boundless.
     From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3
27. Natural Reality / G. Biology / 3. Evolution
Archelaus said life began in a primeval slime [Archelaus, by Schofield]
     Full Idea: Archelaus wrote that life on Earth began in a primeval slime.
     From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus
     A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea.