Combining Texts

All the ideas for 'fragments/reports', 'Rechnungsmethoden (dissertation)' and 'talk'

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5 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
18256 Quantity is inconceivable without the idea of addition [Frege]
     Full Idea: There is so intimate a connection between the concepts of addition and of quantity that one cannot begin to grasp the latter without the former.
     From: Gottlob Frege (Rechnungsmethoden (dissertation) [1874], p.2), quoted by Michael Dummett - Frege philosophy of mathematics 22 'Quantit'
     A reaction: Frege offers good reasons for making cardinals prior to ordinals, though plenty of people disagree.
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
9831 Geometry appeals to intuition as the source of its axioms [Frege]
     Full Idea: The elements of all geometrical constructions are intuitions, and geometry appeals to intuition as the source of its axioms.
     From: Gottlob Frege (Rechnungsmethoden (dissertation) [1874], Ch.6), quoted by Michael Dummett - Frege philosophy of mathematics
     A reaction: Very early Frege, but he stuck to this view, while firmly rejecting intuition as a source of arithmetic. Frege would have known well that Euclid's assumption about parallels had been challenged.
14. Science / C. Induction / 5. Paradoxes of Induction / a. Grue problem
7296 'Grue' is not a colour [Milsted]
     Full Idea: 'Grue' is not a colour.
     From: Tom Milsted (talk [2006]), quoted by PG - Db (ideas)
     A reaction: This simple observation strikes me as rather crucial in assessing Goodman's paradox. Blue is a colour, but grue is some sort of behaviour. Blue is a secondary quality, but grue seems to be a primary quality.
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
1748 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
5989 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.