Combining Texts

All the ideas for 'On Being (frags)', 'On Sufficient Reason' and 'Universal Arithmetick'

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3 ideas

2. Reason / B. Laws of Thought / 1. Laws of Thought
Necessities rest on contradiction, and contingencies on sufficient reason [Leibniz]
     Full Idea: The principle of contradiction is the principle of necessity, and the principle that a sufficient reason must be given is the principle of contingency.
     From: Gottfried Leibniz (On Sufficient Reason [1686], p.95)
     A reaction: [this paragraph is actually undated] Contradictions occur in concrete actuality, as well as in theories and formal systems. If so, then there are necessities in nature. Are they discoverable a posteriori? Leibniz says not.
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / b. Greek arithmetic
A number is not a multitude, but a unified ratio between quantities [Newton]
     Full Idea: By a Number we understand not so much a Multitude of Unities, as the abstracted Ratio of any Quantity to another Quantity of the same Kind, which we take for unity.
     From: Isaac Newton (Universal Arithmetick [1669]), quoted by John Mayberry - What Required for Foundation for Maths? p.407-2
     A reaction: This needs a metaphysics of 'kinds' (since lines can't have ratios with solids). Presumably Newton wants the real numbers to be more basic than the natural numbers. This is the transition from Greek to modern.
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / c. Essence and laws
Each of the infinite possible worlds has its own laws, and the individuals contain those laws [Leibniz]
     Full Idea: As there are an infinity of possible worlds, there are also an infinity of laws, some proper to one, another to another, and each possible individual of any world contains in its own notion the laws of its world.
     From: Gottfried Leibniz (On Sufficient Reason [1686], p.95)
     A reaction: Hence Leibniz is not really a scientific essentialist, in that he doesn't think the laws arise out of the nature of the matter consituting the world. I wonder if the primitive matter of bodies which attaches to the monads is the same in each world?