Combining Texts

All the ideas for 'Mathematics is Megethology', 'Letters to Samuel Clarke' and 'talk'

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27 ideas

2. Reason / B. Laws of Thought / 2. Sufficient Reason
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]
2104 No reason could limit the quantity of matter, so there is no limit [Leibniz]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
10807 Mathematics reduces to set theory, which reduces, with some mereology, to the singleton function [Lewis]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
10809 We can accept the null set, but not a null class, a class lacking members [Lewis]
10811 The null set plays the role of last resort, for class abstracts and for existence [Lewis]
10812 The null set is not a little speck of sheer nothingness, a black hole in Reality [Lewis]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
10813 What on earth is the relationship between a singleton and an element? [Lewis]
10814 Are all singletons exact intrinsic duplicates? [Lewis]
4. Formal Logic / G. Formal Mereology / 1. Mereology
10806 Megethology is the result of adding plural quantification to mereology [Lewis]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
10816 We can use mereology to simulate quantification over relations [Lewis]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
10808 Mathematics is generalisations about singleton functions [Lewis]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
10815 We don't need 'abstract structures' to have structural truths about successor functions [Lewis]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
9916 Convention, yes! Arbitrary, no! [Poincaré, by Putnam]
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]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
10810 I say that absolutely any things can have a mereological fusion [Lewis]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / g. Atomism
2105 Things are infinitely subdivisible and contain new worlds, which atoms would make impossible [Leibniz]
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]
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]