Combining Texts

All the ideas for 'works', 'On Freedom' and 'Morals and Modals'

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7 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.
10. Modality / B. Possibility / 5. Contingency
5040 Necessary truths can be analysed into original truths; contingent truths are infinitely analysable [Leibniz]
     Full Idea: Derivative truths are of two sorts: some are analysed into original truths, others admit of an infinite process of analysis. The former are necessary, the latter are contingent.
     From: Gottfried Leibniz (On Freedom [1689], p.108)
     A reaction: An intriguing proposal. Hume would presumably see contingent truths as being analysed until you reach 'impressions'. Analysis of necessary truths soon comes to the blinding light of what is obvious, but analysis of contingency never gets there.
10. Modality / C. Sources of Modality / 1. Sources of Necessity
14629 If we are told the source of necessity, this seems to be a regress if the source is not already necessary [Blackburn]
     Full Idea: If we ask why A must be the case, and A is then proved from B, that explains it if B must be so. If the eventual source cites some truth F, then if F just is so, there is strong pressure to feel that the original necessity has not been explained.
     From: Simon Blackburn (Morals and Modals [1987], 1)
     A reaction: [compressed] Ross Cameron wrote a reply to this which I like. I'm fishing for the idea that essence is the source of necessity (as Kit Fine says), but that essence itself is not necessary (as only I say, apparently!).
14529 If something underlies a necessity, is that underlying thing necessary or contingent? [Blackburn, by Hale/Hoffmann,A]
     Full Idea: Blackburn asks of what theorists propose as underlying the necessity of a proposition, the question whether they themselves are conceived as obtaining of necessity or merely contingently.
     From: report of Simon Blackburn (Morals and Modals [1987], p.120-1) by Bob Hale/ Aviv Hoffmann - Introduction to 'Modality' 1
     A reaction: I've seen a reply to this somewhere: I think the thought was that a necessity wouldn't be any less necessary if it had a contingent source, any more than the father of a world champion boxer has to be a world champion boxer.
10. Modality / D. Knowledge of Modality / 2. A Priori Contingent
13159 Only God sees contingent truths a priori [Leibniz]
     Full Idea: Only God sees contingent truths a priori.
     From: Gottfried Leibniz (On Freedom [1689], p.95)
     A reaction: This because everything is interconnected, and the whole picture must be seen to understand a contingent truth.
10. Modality / E. Possible worlds / 3. Transworld Objects / e. Possible Objects
5039 If non-existents are possible, their existence would replace what now exists, which cannot therefore be necessary [Leibniz]
     Full Idea: If certain possibles never exist, then existing things are not always necessary; otherwise it would be impossible for other things to exist instead of them, and so all things that never exist would be impossible.
     From: Gottfried Leibniz (On Freedom [1689], p.106)
     A reaction: A neat argument, though it is not self-evident that when possibles came into existence they would have to replace what is already there. Can't something be possible, but only in another world, because this one is already booked?
28. God / A. Divine Nature / 3. Divine Perfections
5041 God does everything in a perfect way, and never acts contrary to reason [Leibniz]
     Full Idea: We can regard it as certain that everything is done by God in the most perfect way, that he does nothing which is contrary to reason.
     From: Gottfried Leibniz (On Freedom [1689], p.109)
     A reaction: The famous optimism which Voltaire laughed at in 'Candide'. I can't help thinking that there is an ideal of God being ABOVE reason. We reason, and give reasons, because we are unsure, and life is a struggle. The highest ideal is mystically self-evident.