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

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8 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.

8. Modes of Existence / B. Properties / 8. Properties as Modes

16730	If matter is entirely atoms, anything else we notice in it can only be modes [Gassendi]
	Full Idea: Since these atoms are the whole of the corporeal matter or substance that exists in bodies, if we conceive or notice anything else to exist in these bodies, that is not a substance but only some kind of mode of the substance.
	From: Pierre Gassendi (Syntagma [1658], II.1.6.1), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 22.4
	A reaction: If the atoms have a few qualities of their own, are they just modes? If they are genuine powers, then there can be emergent powers, which are rather more than mere 'modes'.

14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction

16619	We observe qualities, and use 'induction' to refer to the substances lying under them [Gassendi]
	Full Idea: Nothing beyond qualities is perceived by the senses. …When we refer to the substance in which the qualities inhere, we do this through induction, by which we reason that some subject lies under the quality.
	From: Pierre Gassendi (Syntagma [1658], II.1.6.1), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 07.1
	A reaction: He talks of 'induction' (in an older usage), but he seems to mean abduction, since he never makes any observations of the substances being proposed.

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

26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / g. Atomism

16593	Atoms are not points, but hard indivisible things, which no force in nature can divide [Gassendi]
	Full Idea: The vulgar think atoms lack parts and are free of all magnitude, and hence nothing other than a mathematical point, but it is something solid and hard and compact, as to leave no room for division, separation and cutting. No force in nature can divide it.
	From: Pierre Gassendi (Syntagma [1658], II.1.3.5), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 03.2
	A reaction: If you gloatingly think the atom has now been split, ask whether electrons and quarks now fit his description. Pasnau notes that though atoms are indivisible, they are not incorruptible, and could go out of existence, or be squashed.

16729	How do mere atoms produce qualities like colour, flavour and odour? [Gassendi]
	Full Idea: If the only material principles of things are atoms, having only size, shape, and weight, or motion, then why are so many additional qualities created and existing within the things: color, heat, flavor, odor, and innumerable others?
	From: Pierre Gassendi (Syntagma [1658], II.1.5.7), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 22.4
	A reaction: This is pretty much the 'hard question' about the mind-body relation. Bacon said that heat was just motion of matter. I would say that this problem is gradually being solved in my lifetime.

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.