Combining Philosophers

All the ideas for Archimedes, Moses Schnfinkel and Kenelm Digby

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4 ideas

5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
17699 Variables are auxiliary notions, and not part of the 'eternal' essence of logic [Schönfinkel]
     Full Idea: A variable in a proposition of logic ....has the status of a mere auxiliary notion that is really inappropriate to the constant, 'eternal' essence of the propositions of logic.
     From: Moses Schönfinkel (Building Blocks of Mathematical Logic [1924], §1)
     A reaction: He presumably thinks that what the variables stand for (and he mentions 'argument places' and 'operators') will be included in the essence. My attention was caught by the thought that he takes logic to have an essence.
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
13007 Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz]
     Full Idea: Archimedes gave a sort of definition of 'straight line' when he said it is the shortest line between two points.
     From: report of Archimedes (fragments/reports [c.240 BCE]) by Gottfried Leibniz - New Essays on Human Understanding 4.13
     A reaction: Commentators observe that this reduces the purity of the original Euclidean axioms, because it involves distance and measurement, which are absent from the purest geometry.
9. Objects / C. Structure of Objects / 4. Quantity of an Object
16597 Quantity is the capacity to be divided [Digby]
     Full Idea: Quantity …is divisibility, or a capacity to be divided into parts.
     From: Kenelm Digby (Two treatises [1644], I.2.8), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 04.1
     A reaction: 'Quantity' is scholastic philosophy is a concept we no longer possess. Without quantity, a thing might potentially exist at a spaceless point. Quantity is what spreads things out. See Pasnau Ch. 4.
26. Natural Theory / A. Speculations on Nature / 7. Later Matter Theories / b. Corpuscles
16731 Colours arise from the rarity, density and mixture of matter [Digby]
     Full Idea: The origin of all colours in bodies is plainly deduced out of the various degrees of rarity and density, variously mixed and compounded.
     From: Kenelm Digby (Two treatises [1644], I.29.4), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 22.5
     A reaction: We are still struggling with this question, though I think the picture is gradually become clear, once you get the hang of the brain. Easy! See Idea 17396.