Combining Texts

All the ideas for 'Leibniz: Guide for the Perplexed', 'Mathematical Thought from Ancient to Modern Times' and 'Of liberty, Fate and God's grace'

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3 ideas

5. Theory of Logic / K. Features of Logics / 1. Axiomatisation

17606	Axioms reveal the underlying assumptions, and reveal relationships between different areas [Kline]
	Full Idea: The axiomatic method ....revealed precisely what assumptions underlie each branch [of mathematics] and made possible the comparison and clarification of the relationships of various branches.
	From: Morris Kline (Mathematical Thought from Ancient to Modern Times [1972], p.1027), quoted by Penelope Maddy - Defending the Axioms 1.3
	A reaction: I take this to be the 'fruitfulness' which marks out the discovery of the essence of something.

9. Objects / B. Unity of Objects / 2. Substance / d. Substance defined

19347	Substance needs independence, unity, and stability (for individuation); also it is a subject, for predicates [Perkins]
	Full Idea: For individuation, substance needs three properties: independence, to separate it from other things; unity, to call it one thing, rather than an aggregate; and permanence or stability over time. Its other role is as subject for predicates.
	From: Franklin Perkins (Leibniz: Guide for the Perplexed [2007], 3.1)
	A reaction: Perkins is describing the Aristotelian view, which is taken up by Leibniz. 'Substance' is not a controversial idea, if we see that it only means that the world is full of 'things'. It is an unusual philosopher wholly totally denies that.

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

13082	The complete concept of an individual includes contingent properties, as well as necessary ones [Leibniz]
	Full Idea: In this complete concept of possible Peter are contained not only essential or necessary things, ..but also existential things, or contingent items included there, because the nature of an individual substance is to have a perfect or complete concept.
	From: Gottfried Leibniz (Of liberty, Fate and God's grace [1690], Grua 311), quoted by Cover,J/O'Leary-Hawthorne,J - Substance and Individuation in Leibniz 3.3.1
	A reaction: Compare Idea 13077, where he seems to say that the complete concept is only necessarily linked to properties which will predict future events - though I suppose that would have to include all of the contingent properties mentioned here.