Ideas from 'Letters to Samuel Clarke' by Gottfried Leibniz [1716], by Theme Structure

[found in 'Philosophical Writings' by Leibniz,Gottfried (ed/tr Parkinson,G.H.R.) [Dent 1973,0-460-11905-2]].

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2. Reason / B. Laws of Thought / 2. Sufficient Reason
The principle of sufficient reason is needed if we are to proceed from maths to physics
There is always a reason why things are thus rather than otherwise
No reason could limit the quantity of matter, so there is no limit
7. Existence / C. Structure of Existence / 6. Fundamentals / c. Monads
All simply substances are in harmony, because they all represent the one universe
8. Modes of Existence / A. Relations / 1. Nature of Relations
The ratio between two lines can't be a feature of one, and cannot be in both
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / g. Atomism
Things are infinitely subdivisible and contain new worlds, which atoms would make impossible
The only simple things are monads, with no parts or extension
Atomism is irrational because it suggests that two atoms can be indistinguishable
27. Natural Reality / A. Classical Physics / 2. Thermodynamics / c. Conservation of energy
Leibniz upheld conservations of momentum and energy [Papineau]
27. Natural Reality / C. Space-Time / 1. Space / d. Substantival space
The idea that the universe could be moved forward with no other change is just a fantasy
27. Natural Reality / C. Space-Time / 2. Time / a. Time
If everything in the universe happened a year earlier, there would be no discernible difference
27. Natural Reality / C. Space-Time / 2. Time / e. Existence of time
No time exists except instants, and instants are not even a part of time, so time does not exist
27. Natural Reality / C. Space-Time / 3. Space-Time
Space and time are purely relative
28. God / B. Proving God / 3. Proofs of Evidence / a. Cosmological Proof
The existence of God, and all metaphysics, follows from the Principle of Sufficient Reason