Combining Texts

All the ideas for 'fragments/reports', 'On the Infinite' and 'Letters to Samuel Clarke'

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26 ideas

2. Reason / B. Laws of Thought / 2. Sufficient Reason
2104 No reason could limit the quantity of matter, so there is no limit [Leibniz]
2098 The principle of sufficient reason is needed if we are to proceed from maths to physics [Leibniz]
3646 There is always a reason why things are thus rather than otherwise [Leibniz]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
12456 I aim to establish certainty for mathematical methods [Hilbert]
12461 We believe all mathematical problems are solvable [Hilbert]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
12462 Only the finite can bring certainty to the infinite [Hilbert]
9633 No one shall drive us out of the paradise the Cantor has created for us [Hilbert]
12460 We extend finite statements with ideal ones, in order to preserve our logic [Hilbert]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
12455 The idea of an infinite totality is an illusion [Hilbert]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / j. Infinite divisibility
12457 There is no continuum in reality to realise the infinitely small [Hilbert]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
12459 The subject matter of mathematics is immediate and clear concrete symbols [Hilbert]
6. Mathematics / C. Sources of Mathematics / 8. Finitism
18112 Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert]
7. Existence / C. Structure of Existence / 6. Fundamentals / c. Monads
19385 All simply substances are in harmony, because they all represent the one universe [Leibniz]
8. Modes of Existence / A. Relations / 1. Nature of Relations
21346 The ratio between two lines can't be a feature of one, and cannot be in both [Leibniz]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
9636 My theory aims at the certitude of mathematical methods [Hilbert]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
468 Musical performance can reveal a range of virtues [Damon of Ath.]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / g. Atomism
2106 The only simple things are monads, with no parts or extension [Leibniz]
2102 Atomism is irrational because it suggests that two atoms can be indistinguishable [Leibniz]
2105 Things are infinitely subdivisible and contain new worlds, which atoms would make impossible [Leibniz]
27. Natural Reality / A. Classical Physics / 2. Thermodynamics / c. Conservation of energy
20965 Leibniz upheld conservations of momentum and energy [Leibniz, by Papineau]
27. Natural Reality / C. Space / 4. Substantival Space
2103 The idea that the universe could be moved forward with no other change is just a fantasy [Leibniz]
27. Natural Reality / D. Time / 1. Nature of Time / b. Relative time
2100 Space and time are purely relative [Leibniz]
27. Natural Reality / D. Time / 1. Nature of Time / i. Denying time
2107 No time exists except instants, and instants are not even a part of time, so time does not exist [Leibniz]
27. Natural Reality / D. Time / 2. Passage of Time / a. Experience of time
2101 If everything in the universe happened a year earlier, there would be no discernible difference [Leibniz]
28. God / A. Divine Nature / 5. God and Time
22894 If time were absolute that would make God's existence dependent on it [Leibniz, by Bardon]
28. God / B. Proving God / 3. Proofs of Evidence / a. Cosmological Proof
2099 The existence of God, and all metaphysics, follows from the Principle of Sufficient Reason [Leibniz]