Combining Philosophers

All the ideas for Archimedes, Bill Brewer and Arnauld / Nicole

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8 ideas

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.

7. Existence / C. Structure of Existence / 7. Abstract/Concrete / b. Levels of abstraction

10502	We can rise by degrees through abstraction, with higher levels representing more things [Arnauld,A/Nicole,P]
	Full Idea: I can start with a triangle, and rise by degrees to all straight-lined figures and to extension itself. The lower degree will include the higher degree. Since the higher degree is less determinate, it can represent more things.
	From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], I.5)
	A reaction: [compressed] This attempts to explain the generalising ability of abstraction cited in Idea 10501. If you take a complex object and eliminate features one by one, it can only 'represent' more particulars; it could hardly represent fewer.

12. Knowledge Sources / B. Perception / 3. Representation

18258	We can only know the exterior world via our ideas [Arnauld,A/Nicole,P]
	Full Idea: We can have knowledge of what is outside us only through the mediation of ideas in us.
	From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], p.63), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 1 'Conc'

13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / c. Empirical foundations

8875	Sense experiences must have conceptual content, since they are possible reasons for judgements [Brewer,B]
	Full Idea: Given that sense experiential states do provide reasons for empirical beliefs, they must have conceptual content, ...where a mental state with conceptual content is one where the content is of a possible judgement by the subject.
	From: Bill Brewer (Perceptual experience has conceptual content [2005], I)
	A reaction: This is, I believe, wrong. Even complex observations, like a pool of blood, only become reasons when they have been interpreted. Otherwise they are just the raw ingredients of evidence. How could an uninterpreted red patch be a 'reason'?

14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence

16784	Forms make things distinct and explain the properties, by pure form, or arrangement of parts [Arnauld,A/Nicole,P]
	Full Idea: The form is what renders a thing such and distinguishes it from others, whether it is a being really distinct from the matter, according to the Schools, or whether it is only the arrangement of the parts. By this form one must explain its properties.
	From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], III.18 p240), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 27.6
	A reaction: If we ask 'what explains the properties of this thing' it is hard to avoid coming up with something that might be called the 'form'. Note that they allow either substantial or corpuscularian forms. It is hard to disagree with the idea.

15. Nature of Minds / C. Capacities of Minds / 3. Abstraction by mind

10499	We know by abstraction because we only understand composite things a part at a time [Arnauld,A/Nicole,P]
	Full Idea: The mind cannot perfectly understand things that are even slightly composite unless it considers them a part at a time. ...This is generally called knowing by abstraction. (..the human body, for example).
	From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], I.5)
	A reaction: This adds the interesting thought that the mind is forced to abstract, rather than abstraction being a luxury extra feature. Knowledge through analysis is knowledge by abstraction. Also a nice linking of abstraction to epistemology.

15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind

10501	A triangle diagram is about all triangles, if some features are ignored [Arnauld,A/Nicole,P]
	Full Idea: If I draw an equilateral triangle on a piece of paper, ..I shall have an idea of only a single triangle. But if I ignore all the particular circumstances and focus on the three equal lines, I will be able to represent all equilateral triangles.
	From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], I.5)
	A reaction: [compressed] They observed that we grasp composites through their parts, and now that we can grasp generalisations through particulars, both achieved by the psychological act of abstraction, thus showing its epistemological power.

15. Nature of Minds / C. Capacities of Minds / 6. Idealisation

10500	No one denies that a line has width, but we can just attend to its length [Arnauld,A/Nicole,P]
	Full Idea: Geometers by no means assume that there are lines without width or surfaces without depth. They only think it is possible to consider the length without paying attention to the width. We can measure the length of a path without its width.
	From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], I.5)
	A reaction: A nice example which makes the point indubitable. The modern 'rigorous' account of abstraction that starts with Frege seems to require more than one object, in order to derive abstractions like direction or number. Path widths are not comparatives.