Combining Philosophers

All the ideas for Archimedes, Paolo Mancosu and Henry of Ghent

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6 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 / E. Categories / 3. Proposed Categories

16657	Substance, Quantity and Quality are real; other categories depend on those three [Henry of Ghent]
	Full Idea: Among creatures there are only three 'res' belong to the three first categories: Substance, Quantity and Quality. All other are aspects [rationes] and intellectual concepts with respect to them, with reality only as grounded on the res of those three.
	From: Henry of Ghent (Quodlibeta [1284], VII:1-2), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 12.3
	A reaction: Pasnau connects with the 'arrangement of being', giving an 'ontologically innocent' structure to reality. That seems to be what we all want, if only we could work out the ontologically guilty bit.

8. Modes of Existence / A. Relations / 1. Nature of Relations

16658	The only reality in the category of Relation is things from another category [Henry of Ghent]
	Full Idea: There is beyond a doubt nothing real in the category of Relation, except what is a thing from another category.
	From: Henry of Ghent (Quodlibeta [1284], VII:1-2), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 12.3
	A reaction: This seems to have been the fairly orthodox scholastic view of relations.

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

16645	Accidents are diminished beings, because they are dispositions of substance (unqualified being) [Henry of Ghent]
	Full Idea: Accidents are beings only in a qualified and diminished sense, because they are not called beings, nor are they beings, except because they are dispositions of an unqualified being, a substance.
	From: Henry of Ghent (Quodlibeta [1284], XV.5), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 10.4
	A reaction: This is aimed to 'half' detach the accidents (as the Eucharist requires). Later scholastics detached them completely. Late scholastics seem to have drifted back to Henry's view. The equivocal use of 'being' here was challenged later.

9. Objects / D. Essence of Objects / 7. Essence and Necessity / b. Essence not necessities

13166	Essences are no use in mathematics, if all mathematical truths are necessary [Mancosu]
	Full Idea: Essences and essential properties do not seem to be useful in mathematical contexts, since all mathematical truths are regarded as necessary (though Kit Fine distinguishes between essential and necessary properties).
	From: Paolo Mancosu (Explanation in Mathematics [2008], §6.1)
	A reaction: I take the proviso in brackets to be crucial. This represents a distortion of notion of an essence. There is a world of difference between the central facts about the nature of a square and the peripheral inferences derivable from it.

11. Knowledge Aims / C. Knowing Reality / 3. Idealism / b. Transcendental idealism

22012	Kant says things-in-themselves cause sensations, but then makes causation transcendental! [Henry of Ghent, by Pinkard]
	Full Idea: Kant claimed that things-in-themselves caused our sensations; but causality was a transcendental condition of experience, not a property of things-in-themselves, so the great Kant had contradicted himself.
	From: report of Henry of Ghent (Quodlibeta [1284], Supplement) by Terry Pinkard - German Philosophy 1760-1860 04
	A reaction: This early objection by the conservative Jacobi (who disliked Enlightenment rational religion) is the key to the dispute over whether Kant is an idealist. Kant denied being an idealist, but how can he be, if this idea is correct?