Combining Texts

All the ideas for 'fragments/reports', 'What are Sets and What are they For?' and 'The Limits of Contingency'

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23 ideas

4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
14240 The empty set is something, not nothing! [Oliver/Smiley]
14239 The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley]
14241 We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley]
14242 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
14243 The unit set may be needed to express intersections that leave a single member [Oliver/Smiley]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
18851 Pairing (with Extensionality) guarantees an infinity of sets, just from a single element [Rosen]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
14234 If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley]
14237 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
14245 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
14246 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
14247 Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley]
9. Objects / A. Existence of Objects / 4. Impossible objects
18852 A Meinongian principle might say that there is an object for any modest class of properties [Rosen]
10. Modality / A. Necessity / 5. Metaphysical Necessity
18850 'Metaphysical' modality is the one that makes the necessity or contingency of laws of nature interesting [Rosen]
18849 Metaphysical necessity is absolute and universal; metaphysical possibility is very tolerant [Rosen]
18857 Standard Metaphysical Necessity: P holds wherever the actual form of the world holds [Rosen]
18858 Sets, universals and aggregates may be metaphysically necessary in one sense, but not another [Rosen]
18856 Non-Standard Metaphysical Necessity: when ¬P is incompatible with the nature of things [Rosen]
10. Modality / A. Necessity / 6. Logical Necessity
18848 Something may be necessary because of logic, but is that therefore a special sort of necessity? [Rosen]
10. Modality / B. Possibility / 3. Combinatorial possibility
18855 Combinatorial theories of possibility assume the principles of combination don't change across worlds [Rosen]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / a. Conceivable as possible
18853 A proposition is 'correctly' conceivable if an ominiscient being could conceive it [Rosen]
25. Social Practice / E. Policies / 5. Education / b. Education principles
13304 Learned men gain more in one day than others do in a lifetime [Posidonius]
26. Natural Theory / D. Laws of Nature / 4. Regularities / b. Best system theory
18854 The MRL view says laws are the theorems of the simplest and strongest account of the world [Rosen]
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
20820 Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]