24 ideas
10807 | Mathematics reduces to set theory, which reduces, with some mereology, to the singleton function [Lewis] |
10809 | We can accept the null set, but not a null class, a class lacking members [Lewis] |
10812 | The null set is not a little speck of sheer nothingness, a black hole in Reality [Lewis] |
10811 | The null set plays the role of last resort, for class abstracts and for existence [Lewis] |
10813 | What on earth is the relationship between a singleton and an element? [Lewis] |
10814 | Are all singletons exact intrinsic duplicates? [Lewis] |
10147 | The Axiom of Choice is consistent with the other axioms of set theory [Feferman/Feferman] |
10148 | Axiom of Choice: a set exists which chooses just one element each of any set of sets [Feferman/Feferman] |
10149 | Platonist will accept the Axiom of Choice, but others want criteria of selection or definition [Feferman/Feferman] |
10150 | The Trichotomy Principle is equivalent to the Axiom of Choice [Feferman/Feferman] |
10146 | Cantor's theories needed the Axiom of Choice, but it has led to great controversy [Feferman/Feferman] |
10806 | Megethology is the result of adding plural quantification to mereology [Lewis] |
10816 | We can use mereology to simulate quantification over relations [Lewis] |
10158 | A structure is a 'model' when the axioms are true. So which of the structures are models? [Feferman/Feferman] |
10162 | Tarski and Vaught established the equivalence relations between first-order structures [Feferman/Feferman] |
10159 | Löwenheim-Skolem Theorem, and Gödel's completeness of first-order logic, the earliest model theory [Feferman/Feferman] |
10160 | Löwenheim-Skolem says if the sentences are countable, so is the model [Feferman/Feferman] |
10161 | If a sentence holds in every model of a theory, then it is logically derivable from the theory [Feferman/Feferman] |
10156 | 'Recursion theory' concerns what can be solved by computing machines [Feferman/Feferman] |
10155 | Both Principia Mathematica and Peano Arithmetic are undecidable [Feferman/Feferman] |
10808 | Mathematics is generalisations about singleton functions [Lewis] |
10815 | We don't need 'abstract structures' to have structural truths about successor functions [Lewis] |
10810 | I say that absolutely any things can have a mereological fusion [Lewis] |
22489 | 'Good' is an attributive adjective like 'large', not predicative like 'red' [Geach, by Foot] |