Combining Texts

All the ideas for 'Logical Analysis of Gestalt Concepts', 'Martin Heidegger in conversation' and 'Foundations of Geometry'

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4 ideas

5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism

10053	Geometrical axioms imply the propositions, but the former may not be true [Russell]
	Full Idea: We must only assert of various geometries that the axioms imply the propositions, not that the axioms are true and therefore that the propositions are true.
	From: Bertrand Russell (Foundations of Geometry [1897], Intro vii), quoted by Alan Musgrave - Logicism Revisited §4
	A reaction: Clearly the truth of the axioms can remain a separate issue from whether they actually imply the theorems. The truth of the axioms might be as much a metaphysical as an empirical question. Musgrave sees this as the birth of if-thenism.

6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry

10052	Geometry is united by the intuitive axioms of projective geometry [Russell, by Musgrave]
	Full Idea: Russell sought what was common to Euclidean and non-Euclidean systems, found it in the axioms of projective geometry, and took a Kantian view of them.
	From: report of Bertrand Russell (Foundations of Geometry [1897]) by Alan Musgrave - Logicism Revisited §4
	A reaction: Russell's work just preceded Hilbert's famous book. Tarski later produced some logical axioms for geometry.

7. Existence / A. Nature of Existence / 3. Being / h. Dasein (being human)

15584	I say the manifestation of Being needs humans, and humans only exist as reflected in Being [Heidegger]
	Full Idea: The fundamental thought of my thinking is precisely that Being, or the manifestation of Being, needs human beings and that, vice versa, human beings are only human beings if they are standing in the manifestation of Being.
	From: Martin Heidegger (Martin Heidegger in conversation [1969], p.82), quoted by Richard Polt - Heidegger: an introduction 5 'Signs'
	A reaction: I don't think I understand the second half of this, but I sense some sort of intuition that the consciousness of humans 'enlarges' Being, or bestows an identity on it, or some such thing.

9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts

12887	A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim]
	Full Idea: A whole must possess an attribute peculiar to and characteristic of it as a whole; there must be a characteristic relation of dependence between the parts; and the whole must have some structure which gives it characteristics.
	From: Rescher,N/Oppenheim,P (Logical Analysis of Gestalt Concepts [1955], p.90), quoted by Peter Simons - Parts 9.2
	A reaction: Simons says these are basically sensible conditions, and tries to fill them out. They seem a pretty good start, and I must resist the temptation to rush to borderline cases.