Combining Texts

All the ideas for 'Exigency to Exist in Essences', 'What are Sets and What are they For?' and 'A Universe from Nothing'

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22 ideas

4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley]
The empty set is something, not nothing! [Oliver/Smiley]
We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley]
Maybe we can treat the empty set symbol as just meaning an empty term [Oliver/Smiley]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
The unit set may be needed to express intersections that leave a single member [Oliver/Smiley]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley]
We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
Logical truths are true no matter what exists - but predicate calculus insists that something exists [Oliver/Smiley]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley]
7. Existence / A. Nature of Existence / 5. Reason for Existence
Possibles demand existence, so as many of them as possible must actually exist [Leibniz]
God's sufficient reason for choosing reality is in the fitness or perfection of possibilities [Leibniz]
7. Existence / C. Structure of Existence / 2. Reduction
An understanding of the most basic physics should explain all of the subject's mysteries [Krauss]
7. Existence / C. Structure of Existence / 6. Fundamentals / c. Monads
In 1676 it was discovered that water is teeming with life [Krauss]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
The actual universe is the richest composite of what is possible [Leibniz]
27. Natural Reality / B. Modern Physics / 1. Relativity / a. Special relativity
Space itself can expand (and separate its contents) at faster than light speeds [Krauss]
27. Natural Reality / B. Modern Physics / 1. Relativity / b. General relativity
General Relativity: the density of energy and matter determines curvature and gravity [Krauss]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / d. Quantum mechanics
Uncertainty says that energy can be very high over very short time periods [Krauss]
27. Natural Reality / B. Modern Physics / 4. Standard Model / e. Protons
Most of the mass of a proton is the energy in virtual particles (rather than the quarks) [Krauss]
27. Natural Reality / C. Space / 2. Space
Empty space contains a continual flux of brief virtual particles [Krauss]
27. Natural Reality / E. Cosmology / 3. The Beginning
The universe is precisely 13.72 billion years old [Krauss]
27. Natural Reality / E. Cosmology / 10. Multiverse
It seems likely that cosmic inflation is eternal, and this would make a multiverse inevitable [Krauss]